'132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:48:40 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:48:20 2005 Input: 2+2/(a slkdj fz z) + asd= sdasa dfasd Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((sdasadfasd + 2)*aslkdjfzz + 2)/aslkdjfzz ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:47:18 2005 Input: 2+2/(a slkdj fz z) + asd= sdasa dfasd Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = ((sdasadfasd + 2)*aslkdjfzz + 2)/aslkdjfzz ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:47:00 2005 Input: 2+2/(a slkdj fz z) + asd= sdasa dfasd Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = ((sdasadfasd + 2)*aslkdjfzz + 2)/aslkdjfzz ? Goodbye! Errors (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:46:54 2005 Input: 2+2/(a slkdj fz z) + asd= sdasa dfasd fsadlkfg sin(I)/0 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors (if any): *** unknown function or error in formal parameters: *** ...sd=sdasadfasdfsadlkfgsin(I)/0 ^---- Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:46:38 2005 Input: 2+2/(a slkdj fz z) + asd= sdasa dfasd fsadlkfg sin(I)/0 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors (if any):...Done. *** unknown function or error in formal parameters: *** ...sd=sdasadfasdfsadlkfgsin(I)/0 ^---- Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:46:28 2005 Input: 2+2/(a slkdj fz z) + asd= sdasa dfasd fsadlkfg Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = ((sdasadfasdfsadlkfg + 2)*aslkdjfzz + 2)/aslkdjfzz ? Goodbye! Errors (if any):...Done. Timing: real 0m0.017s user 0m0.007s sys 0m0.004s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:46:14 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors (if any):...Done. Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:45:57 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors (if any) and Timing Info:...Done. Timing: real 0m0.013s user 0m0.006s sys 0m0.004s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:44:04 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors (if any) and Timing Info:Reading GPRC: /etc/gprc ...Done. Timing: real 0m0.014s user 0m0.007s sys 0m0.005s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:43:37 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors (if any) and Timing Info:Reading GPRC: /etc/gprc ...Done. Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:43:21 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors (if any) and Timing Info:Reading GPRC: /etc/gprc ...Done. Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:40:31 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors (if any) and Timing Info:Reading GPRC: /etc/gprc ...Done. Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:40:06 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors (if any) and Timing Info:Reading GPRC: /etc/gprc ...Done. Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:39:39 2005 Input: 2+2 Output: Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 1: gp-2.2.11: command not found Timing: real 0m0.002s user 0m0.000s sys 0m0.001s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:39:02 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 1024000000, primelimit = 500000 %1 = 4 Goodbye! Errors (if any) and Timing Info:Reading GPRC: /etc/gprc ...Done. Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:36:56 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 15:22:02 2004 Input: 2 Output: 2  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.008s sys 0m0.002s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 18:49:14 2004 Input: 2+21 Output: 23  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Tue Sep 7 20:27:42 2004 Input: prime(41561) Output: 500257  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Tue Sep 7 20:27:50 2004 Input: prime(42) Output: 181  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Tue Sep 7 20:28:32 2004 Input: prime(41561) Output: 500257  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Tue Sep 7 20:28:38 2004 Input: 18*19 Output: 342  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Tue Sep 7 20:28:41 2004 Input: 18*19 Output: 342  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Tue Sep 7 20:28:48 2004 Input: 2+6 Output: 8  Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.008s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Tue Sep 7 20:29:33 2004 Input: 2+3 Output: 5  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Tue Sep 7 20:43:31 2004 Input: isprime(1907) Output: 1  Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Tue Sep 7 21:00:32 2004 Input: factorint(1907^64+1) Output: Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 1: 3602 Killed /usr/bin/gp-2.1 -q Timing: real 0m21.006s user 0m20.995s sys 0m0.003s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:05:22 2004 Input: print(2+2) Output: 4  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:06:36 2004 Input: print(2+2) Output: 4  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.004s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:06:44 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:09:24 2004 Input: factor(9458094850943) Output: An error occured in the PARI system call. ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:09:33 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:10:02 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:10:03 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:10:08 2004 Input: factor(9458094850943) Output: An error occured in the PARI system call. ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:10:12 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:12:11 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:12:15 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:12:23 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:12:29 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:12:34 2004 Input: factor(12) Output:  [2 2] [3 1]   Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:12:40 2004 Input: print("'hello'") Output: 'hello'  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.008s sys 0m0.001s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:12:49 2004 Input: print("'hello'"); factor(098093860943) Output: 'hello'  [13 2] [580437047 1]   Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:12:54 2004 Input: print("'hello'"); 2+2 Output: 'hello' 4  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:14:54 2004 Input: print("'hello'"); 2+2 Output: 'hello' 4  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:15:12 2004 Input: print("'hello'"); 2+2 Output: 'hello' 4  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:15:13 2004 Input: print("'hello'"); 2+2 Output: 'hello' 4  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:15:25 2004 Input: print("'hello'"); 2+2 Output: 'hello' 4  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:16:15 2004 Input: print("'[;35m]'") Output: '[;35m]'  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:16:21 2004 Input: print("'[0;35m]'") Output: ']'  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:07:01 2004 Input: sum(j=1,10000,isprime(j)) Output: 1229  Errors (if any) and Timing Info: Timing: real 0m0.047s user 0m0.044s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:07:25 2004 Input: sum(j=1,10000,isprime(3*j+1)) Output: 1610  Errors (if any) and Timing Info: Timing: real 0m0.062s user 0m0.057s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:07:49 2004 Input: sum(j=1,15000,isprime(3*j+1)) Output: 2325  Errors (if any) and Timing Info: Timing: real 0m0.090s user 0m0.086s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:08:07 2004 Input: sum(j=1,15000,isprime(3*j+2)) Output: 2348  Errors (if any) and Timing Info: Timing: real 0m0.090s user 0m0.086s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:08:49 2004 Input: sum(j=1,20000,isprime(3*j+1)) Output: 3014  Errors (if any) and Timing Info: Timing: real 0m0.117s user 0m0.111s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:09:01 2004 Input: sum(j=1,20000,isprime(3*j+2)) Output: 3041  Errors (if any) and Timing Info: Timing: real 0m0.117s user 0m0.112s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:09:35 2004 Input: sum(j=1,25000,isprime(3*j+2)) Output: 3710  Errors (if any) and Timing Info: Timing: real 0m0.145s user 0m0.140s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:09:43 2004 Input: sum(j=1,25000,isprime(3*j+1)) Output: 3681  Errors (if any) and Timing Info: Timing: real 0m0.144s user 0m0.139s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:10:16 2004 Input: sum(j=1,30000,isprime(3*j+1)) Output: 4339  Errors (if any) and Timing Info: Timing: real 0m0.172s user 0m0.168s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:10:25 2004 Input: sum(j=1,30000,isprime(3*j+2)) Output: 4373  Errors (if any) and Timing Info: Timing: real 0m0.173s user 0m0.171s sys 0m0.001s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:11:04 2004 Input: sum(j=1,100,isprime(3*j+2)) Output: 32  Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:11:09 2004 Input: sum(j=1,100,isprime(3*j+1)) Output: 28  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:14:08 2004 Input: 2+2 Output: Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:14:18 2004 Input: 2+2 Output: 1 1  Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.004s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:14:36 2004 Input: 2+2 Output: START STOP  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:14:56 2004 Input: 9205809545 Output: START STOP  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:15:17 2004 Input: 9205809545 Output: START 9205809545 STOP  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:17:28 2004 Input: 9205809545 Output: START 9205809545 STOP  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:18:04 2004 Input: 9205809545 Output: START 9205809545 STOP  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:18:05 2004 Input: 9205809545 Output: START 9205809545 STOP  Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:18:06 2004 Input: 9205809545 Output: START 9205809545 STOP  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:18:46 2004 Input: 9205809545 Output: GP/PARI CALCULATOR Version 2.2.7 (alpha) x86_64 running linux (portable C kernel) 64-bit version compiled: Sep 3 2004, gcc-3.3.4 (Debian 1:3.3.4-9) (readline not compiled in, extended help available) Copyright (C) 2003 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. realprecision = 38 significant digits seriesprecision = 16 significant terms format = g0.38 parisize = 8000000, primelimit = 500000 START %1 = 9205809545 STOP Goodbye! Errors (if any) and Timing Info:Reading GPRC: /etc/gprc ...Done. Timing: real 0m0.009s user 0m0.002s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:19:08 2004 Input: 9205809545 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] [GP files] Options are: [-f] Faststart: do not read .gprc [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [--emacs] Run as if in Emacs shell [--help] Print this message [--test] Test mode. No history, wrap long lines (bench only) [--texmacs] Run as if using TeXmacs frontend [--version] Output version info and exit [--version-short] Output version number and exit Errors (if any) and Timing Info: Timing: real 0m0.004s user 0m0.002s sys 0m0.002s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:19:19 2004 Input: 9205809545 Output: ? START 9205809545 ? STOP ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:19:36 2004 Input: 9205809545 Output: ? 9205809545 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:19:44 2004 Input: factor(9468946849) Output: ? [101 1] [93751949 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:20:21 2004 Input: factor(9468946849) Output: GP/PARI CALCULATOR Version 2.2.7 (alpha) x86_64 running linux (portable C kernel) 64-bit version compiled: Sep 3 2004, gcc-3.3.4 (Debian 1:3.3.4-9) (readline not compiled in, extended help available) Copyright (C) 2003 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. realprecision = 38 significant digits seriesprecision = 16 significant terms format = g0.38 parisize = 8000000, primelimit = 500000 ? %1 = [101 1] [93751949 1] ? Goodbye! Errors (if any) and Timing Info:Reading GPRC: /etc/gprc ...Done. Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:20:41 2004 Input: factor(9468946849) Output: ? [101 1] [93751949 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:22:19 2004 Input: 1.0/(23*29) Output: ? 0.0014992503748125937031484257871064467766 ? Errors (if any) and Timing Info: Timing: real 0m0.041s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:40:08 2004 Input: isprime(43) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:41:47 2004 Input: isprime(1807) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:42:09 2004 Input: factor(1807) Output: ? [13 1] [139 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:43:55 2004 Input: factor(326443) Output: ? [13 1] [25111 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:44:01 2004 Input: factor(3263443) Output: ? [3263443 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:45:38 2004 Input: factor(2*3*7*43*13*139*3263443+1) Output: ? [547 1] [607 1] [1033 1] [31051 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:46:00 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:46:29 2004 Input: factor(2*3*7*43*13*139+1) Output: ? [3263443 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:46:57 2004 Input: factor(2*3*7*43*13*139*3263443+1) Output: ? [547 1] [607 1] [1033 1] [31051 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:47:21 2004 Input: factor(2*3*7*43*13*139*3263443*547+1) Output: ? [31 1] [1201073 1] [156461741 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:47:39 2004 Input: factor(2*3*7*43*13*139*3263443*547*31+1) Output: ? [11 1] [1791173 1] [9165807481 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:47:46 2004 Input: factor(2*3*7*43*13*139*3263443*547*31*11+1) Output: ? [1986523172862990763 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:48:22 2004 Input: factor(2*3*7*43*13*139*3263443*547*31*11*1986523172862990763+1) Output: ? [3946274316321643878601150356160331407 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:49:40 2004 Input: factor(2*3*7*43*13*139*3263443*547*31*11*1986523172862990763*3946274316321643878601150356160331407+1) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 4242 Killed /usr/bin/gp -q --emacs Timing: real 0m21.015s user 0m20.957s sys 0m0.044s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:50:32 2004 Input: factor(2+1) Output: ? [3 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:50:51 2004 Input: factor(2*3+1) Output: ? [7 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:51:01 2004 Input: factor(2*3*7+1) Output: ? [43 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:51:11 2004 Input: factor(2*3*7*43+1) Output: ? [13 1] [139 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:51:27 2004 Input: factor(2*3*7*43*13+1) Output: ? [53 1] [443 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:51:49 2004 Input: factor(2*3*7*43+1) Output: ? [13 1] [139 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:52:00 2004 Input: factor(2*3*7*43*13+1) Output: ? [53 1] [443 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:52:11 2004 Input: factor(2*3*7*43*13*53+1) Output: ? [5 1] [248867 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:52:22 2004 Input: factor(2*3*7*43*13*53*5+1) Output: ? [6221671 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:52:40 2004 Input: factor(2*3*7*43*13*53*5*6221671+1) Output: ? [38709183810571 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:53:06 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571+1) Output: ? [139 1] [25621 1] [420743244646304724409 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:53:20 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139+1) Output: ? [2801 1] [2897 1] [489241 1] [119812279 1] [437881957 1] ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.026s sys 0m0.009s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:53:34 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139*2801+1) Output: ? [11 1] [1009 1] [241139351 1] [217973650939627698919 1] ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.028s sys 0m0.011s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:53:58 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11+1) Output: ? [17 1] [1949 1] [193681376161759185018665262907 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:54:10 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17+1) Output: ? [5471 1] [19940260577270817092450816057441 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:54:22 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471+1) Output: ? [52662739 1] [11333415626130617914714237072849 1] ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.020s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:54:36 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17+1) Output: ? [5471 1] [19940260577270817092450816057441 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:54:42 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11+1) Output: ? [17 1] [1949 1] [193681376161759185018665262907 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:54:47 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139*2801+1) Output: ? [11 1] [1009 1] [241139351 1] [217973650939627698919 1] ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.028s sys 0m0.013s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:54:53 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139+1) Output: ? [2801 1] [2897 1] [489241 1] [119812279 1] [437881957 1] ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.030s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:55:07 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571+1) Output: ? [139 1] [25621 1] [420743244646304724409 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:55:19 2004 Input: factor(2*3*7*43*13*53*5*6221671+1) Output: ? [38709183810571 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:55:33 2004 Input: factor(2*3*7*43*13*53*5+1) Output: ? [6221671 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:55:38 2004 Input: factor(2*3*7*43*13*53+1) Output: ? [5 1] [248867 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:55:43 2004 Input: factor(2*3*7*43*13+1) Output: ? [53 1] [443 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:55:50 2004 Input: factor(2*3*7*43+1) Output: ? [13 1] [139 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:55:55 2004 Input: factor(2*3*7+1) Output: ? [43 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:12:25 2004 Input: 1.0/(3*7) Output: ? 0.047619047619047619047619047619047619048 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:12:38 2004 Input: 1.0/(13*7) Output: ? 0.010989010989010989010989010989010989011 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:12:48 2004 Input: 1.0/(19*17) Output: ? 0.0030959752321981424148606811145510835913 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:13:01 2004 Input: 1.0/19*17 Output: ? 0.89473684210526315789473684210526315789 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:13:57 2004 Input: 1.0/(19*17) Output: ? 0.0030959752321981424148606811145510835913 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:14:25 2004 Input: 1.0/(3*11) Output: ? 0.030303030303030303030303030303030303030 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:14:37 2004 Input: 1.0/(3*13) Output: ? 0.025641025641025641025641025641025641026 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:14:59 2004 Input: 1.0/(3*17) Output: ? 0.019607843137254901960784313725490196078 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:15:33 2004 Input: 1.0/(3*19) Output: ? 0.017543859649122807017543859649122807017 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:16:00 2004 Input: 1.0/(3*23) Output: ? 0.014492753623188405797101449275362318841 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:16:44 2004 Input: 1.0/(3*29) Output: ? 0.011494252873563218390804597701149425287 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 11:12:56 2004 Input: factor(x^8192+x^4096+1) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m0.267s user 0m0.165s sys 0m0.013s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 11:13:38 2004 Input: factor(x^1024+x^512+1) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m0.133s user 0m0.122s sys 0m0.010s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 11:13:51 2004 Input: factor(x^64+x^32+1) Output: ? [x^2 - x + 1 1] [x^2 + x + 1 1] [x^4 - x^2 + 1 1] [x^8 - x^4 + 1 1] [x^16 - x^8 + 1 1] [x^32 - x^16 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.008s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 11:16:22 2004 Input: factor(x^64+1) Output: ? [x^64 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.013s sys 0m0.003s ************** PARI ***************** Host 80.170.145.228 (80.170.145.228) Time: Wed Sep 8 11:40:18 2004 Input: ?ellj Output: ? ellj(x): elliptic j invariant of x. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 80.170.145.228 (80.170.145.228) Time: Wed Sep 8 11:40:32 2004 Input: ??ellj Output: ? ellj(x):  elliptic j-invariant. x must be a complex number with positive imaginary part, or convertible into a power series or a p-adic number with positive valuation.  The library syntax is jell(x,prec).  ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.022s sys 0m0.011s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 11:45:23 2004 Input: factorint(1907^2+1907+1) Output: ? [13 1] [19 1] [14731 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:00:46 2004 Input: factorint(1907^2-1907+1) Output: ? [3 1] [7 1] [73 1] [2371 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:01:52 2004 Input: factorint(1907^4-1907^2+1) Output: ? [313 1] [42253074481 1] ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:02:23 2004 Input: isprime(42253074481); factorint(1907^4-1907^2+1) Output: ? ? [313 1] [42253074481 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:02:32 2004 Input: isprime(42253074481); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:03:21 2004 Input: factorint(1907^4-1907^2+1) Output: ? [313 1] [42253074481 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:03:31 2004 Input: factorint(1907^8-1907^4+1) Output: ? [1153 1] [58834969 1] [2578343098231993 1] ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.017s sys 0m0.007s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:04:40 2004 Input: factorint(1907^16-1907^8+1) Output: ? [30011460673 1] [2824227165916129 1] [360931120130402792118884353 1] ? Errors (if any) and Timing Info: Timing: real 0m1.064s user 0m1.044s sys 0m0.021s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:06:46 2004 Input: factorint(1907^16-1907^8+1) Output: ? [30011460673 1] [2824227165916129 1] [360931120130402792118884353 1] ? Errors (if any) and Timing Info: Timing: real 0m1.064s user 0m1.044s sys 0m0.020s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:07:43 2004 Input: factorint(1907^32-1907^16+1) Output: ? [5886721 1] [52584193 1] [1672632769 1] [2723997117982753 1] [663569271483415189828884374287238562011527002801300848278885776481 1] ? Errors (if any) and Timing Info: Timing: real 0m9.437s user 0m9.411s sys 0m0.006s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:12:34 2004 Input: factorint(1907^64-1907^32+1) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 8778 Killed /usr/bin/gp -q --emacs Timing: real 0m21.041s user 0m20.995s sys 0m0.005s ************** PARI ***************** Host 128.250.6.243 (128.250.6.243) Time: Wed Sep 8 12:42:44 2004 Input: ?tate Output: ? ? Errors (if any) and Timing Info: *** tate: unknown identifier. Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 24.125.49.176 (24.125.49.176) Time: Wed Sep 8 12:50:34 2004 Input: % MathType!MTEF!2!1!+- % faaafaart1ev1aaat0uyJj1BTfMBaerbuLwBLnharmWu51MyVXgaru % WqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hh % bbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0- % yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaa % eaaakeaadaWcaaqaaiaaikdacaaIWaaabaGaaGymaiaac6cacaaIXa % aaaiabgUcaRmaalaaabaGaaGOmaiaaikdaaeaacaGGOaGaaGymaiaa % c6cacaaIXaGaaiykamaaCaaaleqabaGaaGOmaaaaaaGccqGHRaWkda % WcaaqaaiaaikdacaaI0aaabaGaaiikaiaaigdacaGGUaGaaGymaiaa % cMcadaahaaWcbeqaaiaaiodaaaaaaOGaey4kaSYaaSaaaeaacaaIYa % GaaGOnaaqaaiaacIcacaaIXaGaaiOlaiaaigdacaGGPaWaaWbaaSqa % beaacaaI0aaaaaaakiabgUcaRmaalaaabaGaaGOmaiaaiIdaaeaaca % GGOaGaaGymaiaac6cacaaIXaGaaiykamaaCaaaleqabaGaaGynaaaa % aaGccqGH9aqpaaa!4CF1! [ frac{{20}}{{1.1}} + frac{{22}}{{(1.1)^2 }} + frac{{24}}{{(1.1)^3 }} + frac{{26}}{{(1.1)^4 }} + frac{{28}}{{(1.1)^5 }} = ] Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. ************** PARI ***************** Host 128.227.95.245 (128.227.95.245) Time: Wed Sep 8 13:03:35 2004 Input: 2^445 Output: ? 90854840536950861318665475986000566794205170085914757535186274897579911014174740415773881339220445695095315200783272241691825203576832 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 128.227.95.245 (128.227.95.245) Time: Wed Sep 8 13:03:39 2004 Input: 2^4454564 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m0.010s user 0m0.003s sys 0m0.008s ************** PARI ***************** Host 194.42.0.254 (194.42.0.254) Time: Wed Sep 8 15:33:48 2004 Input: SetVerbose("Code",true); print("gf2 n151 QR"); print(MinimumDistance(QRCode(GF(2),151))); Output: ? ? gf2 n151 QR ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: SetVerbose("Code",tr ^-------------------- *** unknown function or error in formal parameters: print(MinimumDistance( *** QRCode(GF(2),151))); ^-------------------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 140.247.241.194 (140.247.241.194) Time: Wed Sep 8 17:11:49 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 140.247.241.194 (140.247.241.194) Time: Wed Sep 8 17:39:30 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:54:43 2004 Input: (1.0)/(3*29) Output: ? 0.011494252873563218390804597701149425287 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:55:01 2004 Input: (1.0)/(3*31) Output: ? 0.010752688172043010752688172043010752688 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:55:28 2004 Input: (1.0)/(3*37) Output: ? 0.0090090090090090090090090090090090090090 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:55:37 2004 Input: (1.0)/(3*41) Output: ? 0.0081300813008130081300813008130081300813 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:55:50 2004 Input: (1.0)/(3*43) Output: ? 0.0077519379844961240310077519379844961240 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:56:58 2004 Input: (1.0)/(3*7) Output: ? 0.047619047619047619047619047619047619048 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:57:18 2004 Input: (1.0)/(11*7) Output: ? 0.012987012987012987012987012987012987013 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:57:37 2004 Input: (1.0)/(13*7) Output: ? 0.010989010989010989010989010989010989011 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:57:52 2004 Input: (1.0)/(17*7) Output: ? 0.0084033613445378151260504201680672268907 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:58:12 2004 Input: (1.0)/(19*7) Output: ? 0.0075187969924812030075187969924812030075 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:58:33 2004 Input: (1.0)/(23*7) Output: ? 0.0062111801242236024844720496894409937888 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:58:52 2004 Input: (1.0)/(29*7) Output: ? 0.0049261083743842364532019704433497536946 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:59:12 2004 Input: (1.0)/(31*7) Output: ? 0.0046082949308755760368663594470046082949 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:59:59 2004 Input: (1.0)/(37*7) Output: ? 0.0038610038610038610038610038610038610038 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 22:00:19 2004 Input: (1.0)/(41*7) Output: ? 0.0034843205574912891986062717770034843205 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 22:01:05 2004 Input: (1.0)/(43*7) Output: ? 0.0033222591362126245847176079734219269103 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 22:05:23 2004 Input: (1.0)/(43*17) Output: ? 0.0013679890560875512995896032831737346101 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 22:05:32 2004 Input: (1.0)/(43*71) Output: ? 0.00032754667540124467736652472977399279397 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 22:05:40 2004 Input: (1.0)/(43*19) Output: ? 0.0012239902080783353733170134638922888617 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 22:05:49 2004 Input: (1.0)/(43*83) Output: ? 0.00028019052956010086859064163631269263099 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:19:37 2004 Input: gp Output: ? gp ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:21:44 2004 Input: M-x gpman Output: ? M - xgpman ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:27:13 2004 Input: prime(1) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:27:23 2004 Input: prime(2) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:27:32 2004 Input: prime(367) Output: ? 2477 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:28:00 2004 Input: prime(9876425) Output: ? ? Errors (if any) and Timing Info: *** not enough precomputed primes Timing: real 0m0.009s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:28:09 2004 Input: prime(987642) Output: ? ? Errors (if any) and Timing Info: *** not enough precomputed primes Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:28:14 2004 Input: prime(987) Output: ? 7793 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:44:12 2004 Input: prime(987) Output: ? 7793 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:45:18 2004 Input: listcreate(15) listput(l,x,{15}) Output: ? List([]) ? ? Errors (if any) and Timing Info: *** unexpected character: listput(l,x,{15}) ^------ Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:45:27 2004 Input: listcreate(15) Output: ? List([]) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:45:48 2004 Input: listcreate(15,9) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: listcreate(15,9) ^--- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 21:14:29 2004 Input: x^2360+1 Output: ? x^2360 + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.074s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 21:14:38 2004 Input: factor(x^2360+1) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m1.055s user 0m0.960s sys 0m0.014s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 21:15:07 2004 Input: factor(x^590+1) Output: ? [x^2 + 1 1] [x^8 - x^6 + x^4 - x^2 + 1 1] [x^116 - x^114 + x^112 - x^110 + x^108 - x^106 + x^104 - x^102 + x^100 - x^98 + x^96 - x^94 + x^92 - x^90 + x^88 - x^86 + x^84 - x^82 + x^80 - x^78 + x^76 - x^74 + x^72 - x^70 + x^68 - x^66 + x^64 - x^62 + x^60 - x^58 + x^56 - x^54 + x^52 - x^50 + x^48 - x^46 + x^44 - x^42 + x^40 - x^38 + x^36 - x^34 + x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1 1] [x^464 + x^462 - x^454 - x^452 + x^444 + x^442 - x^434 - x^432 + x^424 + x^422 - x^414 - x^412 + x^404 + x^402 - x^394 - x^392 + x^384 + x^382 - x^374 - x^372 + x^364 + x^362 - x^354 - x^352 - x^346 + x^342 + x^336 - x^332 - x^326 + x^322 + x^316 - x^312 - x^306 + x^302 + x^296 - x^292 - x^286 + x^282 + x^276 - x^272 - x^266 + x^262 + x^256 - x^252 - x^246 + x^242 + x^236 - x^232 + x^228 + x^222 - x^218 - x^212 + x^208 + x^202 - x^198 - x^192 + x^188 + x^182 - x^178 - x^172 + x^168 + x^162 - x^158 - x^152 + x^148 + x^142 - x^138 - x^132 + x^128 + x^122 - x^118 - x^112 - x^110 + x^102 + x^100 - x^92 - x^90 + x^82 + x^80 - x^72 - x^70 + x^62 + x^60 - x^52 - x^50 + x^42 + x^40 - x^32 - x^30 + x^22 + x^20 - x^12 - x^10 + x^2 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.794s user 0m0.783s sys 0m0.010s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 21:15:42 2004 Input: factor(x^295-1) Output: ? [x - 1 1] [x^4 + x^3 + x^2 + x + 1 1] [x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 1] [x^232 - x^231 + x^227 - x^226 + x^222 - x^221 + x^217 - x^216 + x^212 - x^211 + x^207 - x^206 + x^202 - x^201 + x^197 - x^196 + x^192 - x^191 + x^187 - x^186 + x^182 - x^181 + x^177 - x^176 + x^173 - x^171 + x^168 - x^166 + x^163 - x^161 + x^158 - x^156 + x^153 - x^151 + x^148 - x^146 + x^143 - x^141 + x^138 - x^136 + x^133 - x^131 + x^128 - x^126 + x^123 - x^121 + x^118 - x^116 + x^114 - x^111 + x^109 - x^106 + x^104 - x^101 + x^99 - x^96 + x^94 - x^91 + x^89 - x^86 + x^84 - x^81 + x^79 - x^76 + x^74 - x^71 + x^69 - x^66 + x^64 - x^61 + x^59 - x^56 + x^55 - x^51 + x^50 - x^46 + x^45 - x^41 + x^40 - x^36 + x^35 - x^31 + x^30 - x^26 + x^25 - x^21 + x^20 - x^16 + x^15 - x^11 + x^10 - x^6 + x^5 - x + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.274s user 0m0.264s sys 0m0.009s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 21:27:22 2004 Input: factor(x^295+1) Output: ? [x + 1 1] [x^4 - x^3 + x^2 - x + 1 1] [x^58 - x^57 + x^56 - x^55 + x^54 - x^53 + x^52 - x^51 + x^50 - x^49 + x^48 - x^47 + x^46 - x^45 + x^44 - x^43 + x^42 - x^41 + x^40 - x^39 + x^38 - x^37 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 + x^30 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1 1] [x^232 + x^231 - x^227 - x^226 + x^222 + x^221 - x^217 - x^216 + x^212 + x^211 - x^207 - x^206 + x^202 + x^201 - x^197 - x^196 + x^192 + x^191 - x^187 - x^186 + x^182 + x^181 - x^177 - x^176 - x^173 + x^171 + x^168 - x^166 - x^163 + x^161 + x^158 - x^156 - x^153 + x^151 + x^148 - x^146 - x^143 + x^141 + x^138 - x^136 - x^133 + x^131 + x^128 - x^126 - x^123 + x^121 + x^118 - x^116 + x^114 + x^111 - x^109 - x^106 + x^104 + x^101 - x^99 - x^96 + x^94 + x^91 - x^89 - x^86 + x^84 + x^81 - x^79 - x^76 + x^74 + x^71 - x^69 - x^66 + x^64 + x^61 - x^59 - x^56 - x^55 + x^51 + x^50 - x^46 - x^45 + x^41 + x^40 - x^36 - x^35 + x^31 + x^30 - x^26 - x^25 + x^21 + x^20 - x^16 - x^15 + x^11 + x^10 - x^6 - x^5 + x + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.276s user 0m0.271s sys 0m0.005s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 21:31:43 2004 Input: factorint(2232) Output: ? [2 3] [3 2] [31 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.001s sys 0m0.009s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 22:31:45 2004 Input: (2231^59+1)/2232 Output: ? 163222661996330643021625900568133161837019233177601029720608640382119886410226092659450274961762280231835890055195857302400497410073832844638125717198765425036184230570146534199935658385314011571 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 22:34:26 2004 Input: isprime(20862329904766606481) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.009s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 22:34:39 2004 Input: isprime(158491610535765167876531) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 22:34:48 2004 Input: factorint(158491610535765167876531) Output: ? [57993871231 1] [2732902756301 1] ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.018s sys 0m0.008s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 01:48:40 2004 Input: factor(x^590+1) Output: ? [x^2 + 1 1] [x^8 - x^6 + x^4 - x^2 + 1 1] [x^116 - x^114 + x^112 - x^110 + x^108 - x^106 + x^104 - x^102 + x^100 - x^98 + x^96 - x^94 + x^92 - x^90 + x^88 - x^86 + x^84 - x^82 + x^80 - x^78 + x^76 - x^74 + x^72 - x^70 + x^68 - x^66 + x^64 - x^62 + x^60 - x^58 + x^56 - x^54 + x^52 - x^50 + x^48 - x^46 + x^44 - x^42 + x^40 - x^38 + x^36 - x^34 + x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1 1] [x^464 + x^462 - x^454 - x^452 + x^444 + x^442 - x^434 - x^432 + x^424 + x^422 - x^414 - x^412 + x^404 + x^402 - x^394 - x^392 + x^384 + x^382 - x^374 - x^372 + x^364 + x^362 - x^354 - x^352 - x^346 + x^342 + x^336 - x^332 - x^326 + x^322 + x^316 - x^312 - x^306 + x^302 + x^296 - x^292 - x^286 + x^282 + x^276 - x^272 - x^266 + x^262 + x^256 - x^252 - x^246 + x^242 + x^236 - x^232 + x^228 + x^222 - x^218 - x^212 + x^208 + x^202 - x^198 - x^192 + x^188 + x^182 - x^178 - x^172 + x^168 + x^162 - x^158 - x^152 + x^148 + x^142 - x^138 - x^132 + x^128 + x^122 - x^118 - x^112 - x^110 + x^102 + x^100 - x^92 - x^90 + x^82 + x^80 - x^72 - x^70 + x^62 + x^60 - x^52 - x^50 + x^42 + x^40 - x^32 - x^30 + x^22 + x^20 - x^12 - x^10 + x^2 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.797s user 0m0.783s sys 0m0.016s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 01:53:40 2004 Input: factor((x^590+1)/(x^118+1)) Output: ? [x^8 - x^6 + x^4 - x^2 + 1 1] [x^464 + x^462 - x^454 - x^452 + x^444 + x^442 - x^434 - x^432 + x^424 + x^422 - x^414 - x^412 + x^404 + x^402 - x^394 - x^392 + x^384 + x^382 - x^374 - x^372 + x^364 + x^362 - x^354 - x^352 - x^346 + x^342 + x^336 - x^332 - x^326 + x^322 + x^316 - x^312 - x^306 + x^302 + x^296 - x^292 - x^286 + x^282 + x^276 - x^272 - x^266 + x^262 + x^256 - x^252 - x^246 + x^242 + x^236 - x^232 + x^228 + x^222 - x^218 - x^212 + x^208 + x^202 - x^198 - x^192 + x^188 + x^182 - x^178 - x^172 + x^168 + x^162 - x^158 - x^152 + x^148 + x^142 - x^138 - x^132 + x^128 + x^122 - x^118 - x^112 - x^110 + x^102 + x^100 - x^92 - x^90 + x^82 + x^80 - x^72 - x^70 + x^62 + x^60 - x^52 - x^50 + x^42 + x^40 - x^32 - x^30 + x^22 + x^20 - x^12 - x^10 + x^2 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.657s user 0m0.648s sys 0m0.009s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 01:54:50 2004 Input: factor(((x^590+1)*(x^2+1))/((x^118+1)*(x^10+1))) Output: ? [x^464 + x^462 - x^454 - x^452 + x^444 + x^442 - x^434 - x^432 + x^424 + x^422 - x^414 - x^412 + x^404 + x^402 - x^394 - x^392 + x^384 + x^382 - x^374 - x^372 + x^364 + x^362 - x^354 - x^352 - x^346 + x^342 + x^336 - x^332 - x^326 + x^322 + x^316 - x^312 - x^306 + x^302 + x^296 - x^292 - x^286 + x^282 + x^276 - x^272 - x^266 + x^262 + x^256 - x^252 - x^246 + x^242 + x^236 - x^232 + x^228 + x^222 - x^218 - x^212 + x^208 + x^202 - x^198 - x^192 + x^188 + x^182 - x^178 - x^172 + x^168 + x^162 - x^158 - x^152 + x^148 + x^142 - x^138 - x^132 + x^128 + x^122 - x^118 - x^112 - x^110 + x^102 + x^100 - x^92 - x^90 + x^82 + x^80 - x^72 - x^70 + x^62 + x^60 - x^52 - x^50 + x^42 + x^40 - x^32 - x^30 + x^22 + x^20 - x^12 - x^10 + x^2 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.612s user 0m0.589s sys 0m0.009s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 01:54:50 2004 Input: factor(((x^590+1)*(x^2+1))/((x^118+1)*(x^10+1))) Output: ? [x^464 + x^462 - x^454 - x^452 + x^444 + x^442 - x^434 - x^432 + x^424 + x^422 - x^414 - x^412 + x^404 + x^402 - x^394 - x^392 + x^384 + x^382 - x^374 - x^372 + x^364 + x^362 - x^354 - x^352 - x^346 + x^342 + x^336 - x^332 - x^326 + x^322 + x^316 - x^312 - x^306 + x^302 + x^296 - x^292 - x^286 + x^282 + x^276 - x^272 - x^266 + x^262 + x^256 - x^252 - x^246 + x^242 + x^236 - x^232 + x^228 + x^222 - x^218 - x^212 + x^208 + x^202 - x^198 - x^192 + x^188 + x^182 - x^178 - x^172 + x^168 + x^162 - x^158 - x^152 + x^148 + x^142 - x^138 - x^132 + x^128 + x^122 - x^118 - x^112 - x^110 + x^102 + x^100 - x^92 - x^90 + x^82 + x^80 - x^72 - x^70 + x^62 + x^60 - x^52 - x^50 + x^42 + x^40 - x^32 - x^30 + x^22 + x^20 - x^12 - x^10 + x^2 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.624s user 0m0.597s sys 0m0.010s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 02:07:30 2004 Input: (2231^590 + 1)*(2231^2 + 1)/((2231^118 + 1)*(2231^10 + 1)*1181*3541*794141) Output: ? 152239467487306026593551353106829467321781361064829543830227647403047242045700775476673654553868753880021057508691908000001391740442071688072434466375575485748317837485753412695904810308200594164860524353679491978402955893758988326558400376157170485876867086105812404700757868823510542752837826226111932399000172536861868978875095313074133573615526034977583290589516289267877248468764977622081393447191188331545128337997802868037204077477512825055415549948918088502025077849384166521229640479883402200098172568576327910839357127568019000412137771318377222332410557757022848604473806772575524626925232148671746603706899893433135031992515275229190171162920832157912487117182699946163659004703867744216467220315870672997512174923491664667307890509643481028129804066262238762617889866259995244445902889703365494945721247513028529261415341437924553183315606124604295262128990123637457508180599811046819758004378824542372053968483778108436617221910350620966331498151814912017861990287224325900793917807841988453035169500888178253287329499464150264836917836310283169284633792900629258484597242732991958836509460835876934624219815867976941997653420777217097385231715179326142666940272996800443770161204333271514334607377973713613556745295869467680546669147460151139063751078960945320677683451830373692686729529077085369663160067442936905894492384549891677692463979055159211220064873311427866537300959780092417153560566777594023221512396026971679430277151074559627218712102892045975723723775784123781157741049081221968422852845557960852136850695490901 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 02:09:50 2004 Input: x^20+1 Output: ? x^20 + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 02:10:14 2004 Input: factor(x^20+1) Output: ? [x^4 + 1 1] [x^16 - x^12 + x^8 - x^4 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.007s ************** PARI ***************** Host 129.199.2.17 (129.199.2.17) Time: Fri Sep 10 08:39:19 2004 Input: ellinit([1,1,1,1,1]) Output: ? [1, 1, 1, 1, 1, 5, 3, 5, 4, -47, -665, -316, 103823/316, [-1.0000000000000000000000000000000000000, -0.12500000000000000000000000000000000000 - 1.1110243021644486062614302094260909771*I, -0.12500000000000000000000000000000000000 + 1.1110243021644486062614302094260909771*I]~, 3.8328305468038347928735039871096291388, -1.9164152734019173964367519935548145694 + 1.3916292718175425841570799922317030886*I, -1.1955120413393023640413217701950360471 + 8.918031641082844838 E-39*I, 0.59775602066965118202066088509751802357 - 1.2537215372422377533513109583343891468*I, 5.3338791828486541826811913789892565008] ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.007s sys 0m0.003s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 11:13:51 2004 Input: 2230*(2231^295-1)/((2231^59-1)*(2231^5-1))/(4721*19471*46039264566131) Output: ? 167940315153702432375800550695229369802403980212020936540259277386301886139899965850294715404772422200103359497599991953309634334858953018972021070772995260207885334729065209558128776159343815628721611750691433489559906717450468487233739869084476698195634119486497201899925079549881583325141977446684624550061229847855152734492297951120716209806767305572829258556811641599326480657213226998688494649694877519120183485969243561892592052074915016200409593875204158346787559570588377248309813739653262124718520478309678094281396072053429254461125028388709076700759699551662680271551958618121975135692205436155119491493065240782926014063234138310426062848381326663489783293969970306926492857860261635568109767043121582573607424358149713141362184621437161133061 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 11:14:09 2004 Input: 2230*(2231^295-1)/((2231^59-1)*(2231^5-1)*(4721*19471*46039264566131)) Output: ? 167940315153702432375800550695229369802403980212020936540259277386301886139899965850294715404772422200103359497599991953309634334858953018972021070772995260207885334729065209558128776159343815628721611750691433489559906717450468487233739869084476698195634119486497201899925079549881583325141977446684624550061229847855152734492297951120716209806767305572829258556811641599326480657213226998688494649694877519120183485969243561892592052074915016200409593875204158346787559570588377248309813739653262124718520478309678094281396072053429254461125028388709076700759699551662680271551958618121975135692205436155119491493065240782926014063234138310426062848381326663489783293969970306926492857860261635568109767043121582573607424358149713141362184621437161133061 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 11:18:40 2004 Input: factor(x^1180+1) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m0.967s user 0m0.958s sys 0m0.009s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 11:19:03 2004 Input: factor(x^4+1) Output: ? [x^4 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 11:19:12 2004 Input: factor(x^20+1) Output: ? [x^4 + 1 1] [x^16 - x^12 + x^8 - x^4 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.006s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 11:36:30 2004 Input: factor(x^20+1) Output: ? [x^4 + 1 1] [x^16 - x^12 + x^8 - x^4 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.008s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 11:37:09 2004 Input: factor((x^236 + 1)/(x^4 + 1)) Output: ? [x^232 - x^228 + x^224 - x^220 + x^216 - x^212 + x^208 - x^204 + x^200 - x^196 + x^192 - x^188 + x^184 - x^180 + x^176 - x^172 + x^168 - x^164 + x^160 - x^156 + x^152 - x^148 + x^144 - x^140 + x^136 - x^132 + x^128 - x^124 + x^120 - x^116 + x^112 - x^108 + x^104 - x^100 + x^96 - x^92 + x^88 - x^84 + x^80 - x^76 + x^72 - x^68 + x^64 - x^60 + x^56 - x^52 + x^48 - x^44 + x^40 - x^36 + x^32 - x^28 + x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.136s user 0m0.132s sys 0m0.003s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 11:39:23 2004 Input: (2231^20+1)/(2*1153*10743331537*41*4890161) Output: ? 1878824047044678338579426144223282103202441641 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 12:07:03 2004 Input: (2231^472 + 1)/(2231^8 + 1)/(168977*33111732097*1047346707857) Output: ? 2992078726034666586133825914560578840832725607767432512727806091296194352812432948820950122145853537677146536089674328445387481433924707505110028919336070072681098595682038314384229819731756909916779655818428801034873891023857620017986040746628367888419227411882449110379063258827834365579702247126007087132865321061743713263186074942062859145316351896035257991751404963017344954273513364016272733762410030753503973839352851151365389468127929667585549632416913951528937480036163202936133494469100337615259279079785923554412883529366583611740473228592554724150961808212146209968715514284535368549959563557408087783119909185326751472413687608816658208855671874066816444126256958371451369914905874286202622279861722411797593566927423186439331899953310662921538563400159829873331290271597332229617243410194452582765111480043368685607017056538026409481910362302108082035625648328876610759104471816438432588144685735057942153072799148566464856331386321196172981062461122950774565987250645412431113621997382412520701724045149778242674991795027899200232624778429275564782087669637068205170091907826083830032463128986917474149964287738021024918104465618615092410571027799320899477528727371355921722362096710136184406894231636508536926157841359340885716225733554769373543154392472416849274814573059527989267328023060614038046394893237996942433961624251577438668584342858009303108104050914294345407458665820536131154871530318083222342255767156076096686319163194621591224011564330846501151952663238783365511995283251344928697520599625312491051764745034073279793/34679463603235908986129 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 12:08:11 2004 Input: (2231^2360 + 1)*(2231^8 + 1)/((2231^472 + 1)*(2231^40 + 1))/(33111732097*1047346707857) Output: ? 6534350810739941660477885247723695990155975625432947134500952799537260269232294238335828404157769790020633146704872673362520289815480674831035721022923679729211132381568833686610541422639460039284043499003516410502548881620114578474070459039094404975510573004150915154718575939386346806090876320654018600797133907663012135322536606615273291553411106817415340008392340646172657224255420589448366471979302643354784902187296508841135044214477571295507397028255474593596993300921498500126984761309864354118605741691780983814965451436605530019892984540966540280743485538556474934772583068298583356002861716033444201286039383093608501427940571081781364087831247445775398538484303355037506780906696148749700532351674454883819748703339905248308887330116793519841085516178986692481633064078999423054890013672240678974136960466330285563773784678413667657884262553313761105436562581374235265002362813533645741442621395574754264751022738388465437842898503168627996241189018140285138338923305429934295996316597844901382711475410781557860409717119332442668432565768246992511032669853839585440444346847155419836295875036797761196773857313527314413935268549472266739373498801664116442471269693659893446996429356851313702300446649885312347972772269593424641055838098466495969919490590414005181696674425163108862561958186678269541797784738132433346147958127240916368734489956487249773960178847449408768834375433737991106624634885057145144206661626319776850401661035402593220292891595523890728116678361115370291543668838167456726880161942870186526482160928301350945058519521777924861911253309901220911798924243678034072468446747336555151840252335207750687555721315792757742851870112351334256040614926215786273408661720675598187871943905687072524343539495475883866658102203102568645273610379340551984255150951943649839473826516237607552698438964222505652130081551715490224303502474618234611619566647957472707737515353651264184966632660955473833447794141797464011458110777081703414506791100250652756063931401175282170217909571333858386470520521764787695920858693270968084972487391845139251088349829799648827096937196170532105797465649672791044922204584521967081229641870533293650436708868126708797124707193592871934126250286010803832861908278032601693398577813701266557890222567967251942619661269107249559368161644847255727531934160320666574834831722085955216339995872175546681881663406039670619722084697047879391674642780208620167533084318267276750031609795820856151592514993119726050655815739817604474889565068159388602879529562876945635084915945759910302649205300606388695528487098380631446323877860728177316847167067832050965109497579166002695981037435243975525799650795964292777790972048912977411098366875326632516533164996422601697438886205751526869128971424331969243286950133046081047749046154140092249862911691493747108707650227794221178829891298434313516524998208821371720344678412045624992054908366425191977123232882381603821510559428000723362504504934541626881369333462903781104327155985292189976286687813827502826246199380250341776286418341180819125965266920006635264414014373046122570434141324867211929732173071149109412627120909801017608249434952907105988316382198392460152471697496062725376409560[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.015s sys 0m0.003s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 12:08:43 2004 Input: (2231^2360 + 1)*(2231^8 + 1)/((2231^472 + 1)*(2231^40 + 1)*33111732097*1047346707857) Output: ? 6534350810739941660477885247723695990155975625432947134500952799537260269232294238335828404157769790020633146704872673362520289815480674831035721022923679729211132381568833686610541422639460039284043499003516410502548881620114578474070459039094404975510573004150915154718575939386346806090876320654018600797133907663012135322536606615273291553411106817415340008392340646172657224255420589448366471979302643354784902187296508841135044214477571295507397028255474593596993300921498500126984761309864354118605741691780983814965451436605530019892984540966540280743485538556474934772583068298583356002861716033444201286039383093608501427940571081781364087831247445775398538484303355037506780906696148749700532351674454883819748703339905248308887330116793519841085516178986692481633064078999423054890013672240678974136960466330285563773784678413667657884262553313761105436562581374235265002362813533645741442621395574754264751022738388465437842898503168627996241189018140285138338923305429934295996316597844901382711475410781557860409717119332442668432565768246992511032669853839585440444346847155419836295875036797761196773857313527314413935268549472266739373498801664116442471269693659893446996429356851313702300446649885312347972772269593424641055838098466495969919490590414005181696674425163108862561958186678269541797784738132433346147958127240916368734489956487249773960178847449408768834375433737991106624634885057145144206661626319776850401661035402593220292891595523890728116678361115370291543668838167456726880161942870186526482160928301350945058519521777924861911253309901220911798924243678034072468446747336555151840252335207750687555721315792757742851870112351334256040614926215786273408661720675598187871943905687072524343539495475883866658102203102568645273610379340551984255150951943649839473826516237607552698438964222505652130081551715490224303502474618234611619566647957472707737515353651264184966632660955473833447794141797464011458110777081703414506791100250652756063931401175282170217909571333858386470520521764787695920858693270968084972487391845139251088349829799648827096937196170532105797465649672791044922204584521967081229641870533293650436708868126708797124707193592871934126250286010803832861908278032601693398577813701266557890222567967251942619661269107249559368161644847255727531934160320666574834831722085955216339995872175546681881663406039670619722084697047879391674642780208620167533084318267276750031609795820856151592514993119726050655815739817604474889565068159388602879529562876945635084915945759910302649205300606388695528487098380631446323877860728177316847167067832050965109497579166002695981037435243975525799650795964292777790972048912977411098366875326632516533164996422601697438886205751526869128971424331969243286950133046081047749046154140092249862911691493747108707650227794221178829891298434313516524998208821371720344678412045624992054908366425191977123232882381603821510559428000723362504504934541626881369333462903781104327155985292189976286687813827502826246199380250341776286418341180819125965266920006635264414014373046122570434141324867211929732173071149109412627120909801017608249434952907105988316382198392460152471697496062725376409560[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.014s sys 0m0.005s ************** PARI ***************** Host 128.107.253.39 (128.107.253.39) Time: Fri Sep 10 14:55:36 2004 Input: (2231^59-1)/(2230*709*259666907*3357332933*59353538419519*3171594949246999313) Output: ? 1404068190735005451359636488128071856652539859763273187307160085592018868940146247873543293002704545982762705521681970806906289969544542871853 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Fri Sep 10 15:23:38 2004 Input: 5.0^5 Output: ? 3125.0000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Fri Sep 10 15:24:06 2004 Input: (5.0^5)^5 Output: ? 298023223876953125.00000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Fri Sep 10 15:31:53 2004 Input: 53125.0^5 Output: ? 423150360584259033203125.00000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Fri Sep 10 15:35:08 2004 Input: 5^5 Output: ? 3125 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s ************** PARI ***************** Host 140.247.245.210 (140.247.245.210) Time: Fri Sep 10 15:49:58 2004 Input: factor(409809845) Output: ? [5 1] [89 1] [920921 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 216.51.235.246 (216.51.235.246) Time: Sat Sep 11 01:37:02 2004 Input: x/3-3x/4=1/12 Output: ? 1/3*x - 3 ? Errors (if any) and Timing Info: *** Warning: unused characters: x/4=1/12. Timing: real 0m0.272s user 0m0.004s sys 0m0.011s ************** PARI ***************** Host 216.51.235.246 (216.51.235.246) Time: Sat Sep 11 01:37:03 2004 Input: x/3-3x/4=1/12 Output: ? 1/3*x - 3 ? Errors (if any) and Timing Info: *** Warning: unused characters: x/4=1/12. Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 68.163.241.150 (68.163.241.150) Time: Sun Sep 12 00:11:11 2004 Input: -0.02y + 0.12(6000-y)= 0.11y Output: ? -0.020000000000000000000000000000000000000 ? Errors (if any) and Timing Info: *** Warning: unused characters: y+0.12(6000-y)=0.11y. Timing: real 0m0.016s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 68.163.241.150 (68.163.241.150) Time: Sun Sep 12 00:11:50 2004 Input: -0.02y+0.12(6000-y)=0.11y Output: ? -0.020000000000000000000000000000000000000 ? Errors (if any) and Timing Info: *** Warning: unused characters: y+0.12(6000-y)=0.11y. Timing: real 0m0.010s user 0m0.007s sys 0m0.004s ************** PARI ***************** Host 63.241.65.90 (63.241.65.90) Time: Sun Sep 12 00:24:44 2004 Input: y=2*x+3 x Output: ? 2*x + 3 ? x ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Sun Sep 12 05:41:33 2004 Input: e=ellinit([0,0,0,17,0]); print(e.j" "e.disc" "e.tors" "ellglobalred(e)); Output: ? ? ? Errors (if any) and Timing Info: *** unknown member function: print(e.j" "e.disc" "e.tors" "ellglobalred( ^-------------------- Timing: real 0m0.071s user 0m0.005s sys 0m0.007s ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Sun Sep 12 05:41:53 2004 Input: e=ellinit([0,0,0,17,0]); print(e.j" "e.disc" "e.tors"); Output: ? ? ? Errors (if any) and Timing Info: *** expected character: '"' instead of: ...e.j" "e.disc" "e.tors"); ^ *** Warning: run-away string. Closing it. Timing: real 0m0.010s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Sun Sep 12 05:42:15 2004 Input: e=ellinit([0,0,0,17,0]); print(e.j" "e.disc" "e.tors); Output: ? ? ? Errors (if any) and Timing Info: *** unknown member function: print(e.j" "e.disc" "e.tors); ^------ Timing: real 0m0.010s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Sun Sep 12 05:42:27 2004 Input: e=ellinit([0,0,0,17,0]); e.tors Output: ? ? ? Errors (if any) and Timing Info: *** unknown member function: e.tors ^---- Timing: real 0m0.010s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Sun Sep 12 05:42:43 2004 Input: e=ellinit([0,0,0,17,0]); elltors(e) Output: ? ? [2, [2], [[0, 0]]] ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Sun Sep 12 05:43:17 2004 Input: e=ellinit([0,0,0,17,0]); ellglobalred(e) Output: ? ? [18496, [1, 0, 0, 0], 2] ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Sun Sep 12 05:43:44 2004 Input: e=ellinit([0,0,0,17,0]); factor(ellglobalred(e)[1]) Output: ? ? [2 6] [17 2] ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Sun Sep 12 05:44:47 2004 Input: e=ellinit([0,0,0,17,0]); elllseries(e,1) Output: ? ? 3.6523718207373173530224734019481378047 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.095s user 0m0.090s sys 0m0.004s ************** PARI ***************** Host 80.104.0.185 (80.104.0.185) Time: Sun Sep 12 08:14:27 2004 Input: 123 Output: ? 123 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 80.104.0.185 (80.104.0.185) Time: Sun Sep 12 08:14:52 2004 Input: 123 Output: ? 123 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 35.9.26.234 (35.9.26.234) Time: Sun Sep 12 15:33:00 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.056s user 0m0.004s sys 0m0.009s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:08:11 2004 Input: 1.10^1/3 Output: ? 0.36666666666666666666666666666666666667 ? Errors (if any) and Timing Info: Timing: real 0m0.065s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:08:29 2004 Input: 1.10^(1/3) Output: ? 1.0322801154563671592135852250097016117 ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:09:55 2004 Input: 1.10^(3) Output: ? 1.3310000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.002s sys 0m0.008s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:10:50 2004 Input: 0.9^(3) Output: ? 0.72899999999999999999999999999999999999 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:12:12 2004 Input: 1-(0.9^(3)) Output: ? 0.27100000000000000000000000000000000001 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.006s sys 0m0.005s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:15:53 2004 Input: (1-.271)^(1/3) Output: ? 0.90000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:30:01 2004 Input: (-.99^3)+3*(-.99) Output: ? -3.9402990000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.004s sys 0m0.007s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:30:36 2004 Input: (--1.01^3)+3*(-1.01) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (--1.01^3)+3*(-1.01) ^------------------- Timing: real 0m0.019s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:30:43 2004 Input: (-1.01^3)+3*(-1.01) Output: ? -4.0603010000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 17:38:55 2004 Input: .04/.2551 Output: ? 0.15680125441003528028224225793806350451 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 18:04:07 2004 Input: .04/.2551 Output: ? 0.15680125441003528028224225793806350451 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 24.185.209.9 (24.185.209.9) Time: Sun Sep 12 20:30:20 2004 Input: 3578! Output: ? 1568147836345296343478655129144157738870498552100811568167073349024510094437388767101964723816127436799607650129576815186229608117951009415448018446658496909148985526889467538595150875712554908186778536452963456074412430243271703699624545756485663063182991850154025327315159372377794486304427408694681303207914448740594666358311506058737180004692085244327282183594315845251808961019288849800895470367494882640199759568046896384034969267618235789741414417476798217595382228643594475577638009379197216861488894939895794062484198132052553545335771930652655407597984297962604717840693900784479377353819882351629557175568714402323518530809257516922391357296800337131865134835002030205442326200401237987719255946784099255361332571189389657865444700891011514839453034603031627252617215824038289313205976764560981633044470543564880629084889498201227694074057229172636850686181179491601426961976484595368332864896850181084262438985283980635477005179405212283510513842952920136820976666534030625699069362928099884296540925358039571496091497943753150990690102879317241973060028911257070195411992467838661630426110874168995817766161418934632890075720737109370172085760406254302856724945276518396734559101537837788578627657921314821006349279330090637868051887086156420269834855684851439286766760643461083014651115417659796952763106204434406570047122763416800898182946002214609517201002936826308801844900083771708164635526982789134188997904260382299913827716357546937234398282583837875978409346800605349417960400465045320094979984226929331661607021419305672456449107829974444880965145304849901674288555489468783471983301580587691766092911297105203236074261748598115198276778058062294062170208192747018139313410218395480265457198139426707056009366628814228983915798043581761983137188223032345256122289524596049946428020020814575251582344889415206829883124778107699675350756024182829759106100652153682753872734657703650780360599230592249969450133356179723819120583906026015395321921706074209058924233195537345596354261871685324559256840698298489806517053229407795857527655976431340377029221101953943440863600798985971313578961245601305443783098331493375774975358732001725450764767991232528833356075725836251406374010861275842274276727633894743690029420721775949760837999759310289964610967770507580226378060038902144520888337249179241621965530323377220936354785168332333258442563246192018562320811267234963253611684291927056137912874680132328866684363320804830280738369674867581646918215125950445523500979693303950547131013105398381750510259495595430369855519738957971022996197272721661725136984926957012403948604099575552020557496242197981100997935383658596290878251737376138107115415993330005748642288665213070506056430167239297139424738583042725983130969987264898503644455875938347806030375389318193101183097863852290155464934349090235599560381355927694899897333501408970705937430326837211837174628108167774055925857692895871030982575826489644128189083183152400674394245555444887061992322024430513433659512622029097847229647709596078207141904014649664931829899842639783006934443508170759096629606364202518880920275555073348394521969268480676153300402636104060334677530550660285161394798716009457462214517[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.198s user 0m0.030s sys 0m0.009s ************** PARI ***************** Host 194.84.45.205 (194.84.45.205) Time: Mon Sep 13 00:57:50 2004 Input: 3490529510847650949147849619903898133417764638493387843990820577*32769132993266709549961999190834461413177642967992942539798288533 Output: ? 114381625757888867669235818371971231334378737347588181505441310531117958673000181729623470563958705058989075147599290026879543541 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 194.84.45.205 (194.84.45.205) Time: Mon Sep 13 01:14:18 2004 Input: 3490529510847650949147849619903898133417764638493387843990820577**9007 mod (32769132993266709549961999190834461413177642967992942539798288533) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...7764638493387843990820577**9007mod(3276913299 ^-------------------- Timing: real 0m0.019s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 194.84.45.205 (194.84.45.205) Time: Mon Sep 13 01:15:50 2004 Input: 3490529510847650949147849619903898133417764638493387843990820577*9007 mod (32769132993266709549961999190834461413177642967992942539798288533) Output: ? 31439199304204792098974681526474410487693806098909944310825320937039 ? Errors (if any) and Timing Info: *** Warning: unused characters: mod(32769132993266709549961999190834461413177642967992942539798288533). Timing: real 0m0.017s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 01:56:34 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 03:38:06 2004 Input: prime(12345678) Output: ? ? Errors (if any) and Timing Info: *** not enough precomputed primes Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 03:38:16 2004 Input: prime(1234568) Output: ? ? Errors (if any) and Timing Info: *** not enough precomputed primes Timing: real 0m0.009s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 03:38:26 2004 Input: prime(123458) Output: ? ? Errors (if any) and Timing Info: *** not enough precomputed primes Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 03:38:32 2004 Input: prime(23458) Output: ? 267667 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 03:38:47 2004 Input: prime(25) Output: ? 97 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 03:39:02 2004 Input: prime(5) Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 03:39:09 2004 Input: primes(5) Output: ? [2, 3, 5, 7, 11] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 03:39:22 2004 Input: primes(55) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.008s sys 0m0.001s ************** PARI ***************** Host 199.171.142.1 (199.171.142.1) Time: Mon Sep 13 10:52:26 2004 Input: factor(7751391910122739843887037070559590001412606) Output: ? [2 1] [11 1] [23269 1] [15141862388356611496151799840129845017 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.007s ************** PARI ***************** Host 128.107.253.39 (128.107.253.39) Time: Mon Sep 13 14:31:49 2004 Input: (2231^590 + 1)*(2231^2 + 1)/((2231^118 + 1)*(2231^10 + 1))/(1181*3541*794141) Output: ? 152239467487306026593551353106829467321781361064829543830227647403047242045700775476673654553868753880021057508691908000001391740442071688072434466375575485748317837485753412695904810308200594164860524353679491978402955893758988326558400376157170485876867086105812404700757868823510542752837826226111932399000172536861868978875095313074133573615526034977583290589516289267877248468764977622081393447191188331545128337997802868037204077477512825055415549948918088502025077849384166521229640479883402200098172568576327910839357127568019000412137771318377222332410557757022848604473806772575524626925232148671746603706899893433135031992515275229190171162920832157912487117182699946163659004703867744216467220315870672997512174923491664667307890509643481028129804066262238762617889866259995244445902889703365494945721247513028529261415341437924553183315606124604295262128990123637457508180599811046819758004378824542372053968483778108436617221910350620966331498151814912017861990287224325900793917807841988453035169500888178253287329499464150264836917836310283169284633792900629258484597242732991958836509460835876934624219815867976941997653420777217097385231715179326142666940272996800443770161204333271514334607377973713613556745295869467680546669147460151139063751078960945320677683451830373692686729529077085369663160067442936905894492384549891677692463979055159211220064873311427866537300959780092417153560566777594023221512396026971679430277151074559627218712102892045975723723775784123781157741049081221968422852845557960852136850695490901 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 128.107.253.39 (128.107.253.39) Time: Mon Sep 13 14:51:10 2004 Input: (2231^2360 + 1)*(2231^8 + 1)/((2231^472 + 1)*(2231^40 + 1)) Output: ? 6534350810739941660477885247723695990155975625432947134500952799537260269232294238335828404157769790020633146704872673362520289815480674831035721022923679729211132381568833686610541422639460039284043499003516410502548881620114578474070459039094404975510573004150915154718575939386346806090876320654018600797133907663012135322536606615273291553411106817415340008392340646172657224255420589448366471979302643354784902187296508841135044214477571295507397028255474593596993300921498500126984761309864354118605741691780983814965451436605530019892984540966540280743485538556474934772583068298583356002861716033444201286039383093608501427940571081781364087831247445775398538484303355037506780906696148749700532351674454883819748703339905248308887330116793519841085516178986692481633064078999423054890013672240678974136960466330285563773784678413667657884262553313761105436562581374235265002362813533645741442621395574754264751022738388465437842898503168627996241189018140285138338923305429934295996316597844901382711475410781557860409717119332442668432565768246992511032669853839585440444346847155419836295875036797761196773857313527314413935268549472266739373498801664116442471269693659893446996429356851313702300446649885312347972772269593424641055838098466495969919490590414005181696674425163108862561958186678269541797784738132433346147958127240916368734489956487249773960178847449408768834375433737991106624634885057145144206661626319776850401661035402593220292891595523890728116678361115370291543668838167456726880161942870186526482160928301350945058519521777924861911253309901220911798924243678034072468446747336555151840252335207750687555721315792757742851870112351334256040614926215786273408661720675598187871943905687072524343539495475883866658102203102568645273610379340551984255150951943649839473826516237607552698438964222505652130081551715490224303502474618234611619566647957472707737515353651264184966632660955473833447794141797464011458110777081703414506791100250652756063931401175282170217909571333858386470520521764787695920858693270968084972487391845139251088349829799648827096937196170532105797465649672791044922204584521967081229641870533293650436708868126708797124707193592871934126250286010803832861908278032601693398577813701266557890222567967251942619661269107249559368161644847255727531934160320666574834831722085955216339995872175546681881663406039670619722084697047879391674642780208620167533084318267276750031609795820856151592514993119726050655815739817604474889565068159388602879529562876945635084915945759910302649205300606388695528487098380631446323877860728177316847167067832050965109497579166002695981037435243975525799650795964292777790972048912977411098366875326632516533164996422601697438886205751526869128971424331969243286950133046081047749046154140092249862911691493747108707650227794221178829891298434313516524998208821371720344678412045624992054908366425191977123232882381603821510559428000723362504504934541626881369333462903781104327155985292189976286687813827502826246199380250341776286418341180819125965266920006635264414014373046122570434141324867211929732173071149109412627120909801017608249434952907105988316382198392460152471697496062725376409560[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.012s sys 0m0.005s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:51:25 2004 Input: (r1+b)*sin w3 = x2-x3+(r1+a)*(x1-x2+r1*sin w1)/(r1+a) Output: ? sinw1*r1^2 + (sinw1*b + (-x3 + x1))*r1 + (-x3 + x1)*b ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:51:48 2004 Input: (r1+b)*sin(w3) = x2-x3+(r1+a)*(x1-x2+r1*sin(w1))/(r1+a) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (r1+b)*sin(w3)=x2-x3+(r1+a)*(x1-x ^-------------------- Timing: real 0m0.009s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:52:18 2004 Input: (r1+b)*sin(w3) = x2-x3+(r1+a)*(x1 - x2 + r1*sin(w1))/(r1+a) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (r1+b)*sin(w3)=x2-x3+(r1+a)*(x1-x ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 128.107.253.39 (128.107.253.39) Time: Mon Sep 13 14:52:33 2004 Input: (2231^1180 + 1)*(2231^4 + 1)/((2231^236 + 1)*(2231^20 + 1)*198241) Output: ? 1289459611275041988195210056585206806410614084401135640479222664045769803591479690589717250628933460238307683337743645320339109228658943102343982115804448039233769992702578660444097102749918320340496288615167272422272379035481129224408741120123060633692817472406046988439452102203287959094815737110537691461874612805826793594075312453312968242778332100458437125673193379975931037064432110582767389977175612492393277539339744992094632099663885400758083900295190968549713896692958238574068888519018229346775417031722016125463201059730056703802804593518003521063911362932655632842008839899080544855503991771638642004164198129115480948843643820523789774352780610631114486522017869777461789993174649739094191335437704484177831242563949137031177943172811683858038790678569607858584220926893871795219838949150359526494044964470909496367876787866746320183625778761692644288518243530397384396547182256665167216304974969831373883366950933890318902922727340003762162113057889466370396883353544593047853142065591064803810488301183812747116340049386741364251144723947724119744045366782599827038640833816813508545524699558279735717481168569356350676805263349555599713747952874214769431466210013977287072133383364932859198544023793310419123285068298336070004787238695911938909700570537098346340491665553063998784474454161236911031840755337060581977681559962122670603754590598825568152740584854970612183933837874292716173072442936834101358188825490484369762849853108302033020223818808366127539168245624264464650554132670608278496939617008439302281320194114542205403777512385100038930034556715403151466036429661746992286310824650498732301746810128719185087093394926835604196015481609742101938982272000709437795472290874168456500316722612336016886476849700907316525206912306597386194441886873751591175573840163309814383160746362518400215087927991511089076291223297660110284881250544994303953041087974253934597024738438478477055360710506018704493335097484819208348847552668908442669888461558339812986365601959317027821972696038310903998111633164357379655640624289630886984712380123230308926635948294510536082796236853126251730091089211452890931680803323760411906469252262765014919017599368945227117703011625303913839499607952380984480817987350416403596260580581048766268751267980180944101655545053910056681340620023358494552404889493936818897398638536529861238810491507564596427454099716918690555584398852276288317134008602972664360303771682100411165070906789601758922723215836150877013163996628861999711660397392091971276225766687797899017718051709732552633122078712780353937390733719786158223050833770894698981549222005547082262483271803898663216500668723882082424201229010112432910392928477008055582517060405503932038412451480399585926077262102319937797345470755500358109056901019453751194562475815349091214534321493144904989115254862258310372856766455307486129497558829470061525458150084364948511232833683350699737351774282400205295937445856524938565236610331007570210527187394906814667251416126174766596677311815215382560438544236362437425990226574062165431012050930752880377419881319502057443979190101560674711643681 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:52:33 2004 Input: (r1 + b) * sin(w3) = x2 - x3 + (r1 + a) * (x1 - x2 + r1*sin(w1))/(r1+a) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (r1+b)*sin(w3)=x2-x3+(r1+a)*(x1-x ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:52:41 2004 Input: (r1 + b) * sin(w3) = x2 - x3 + (r1 + a) * (x1 - x2 + r1 * sin(w1))/(r1 + a) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (r1+b)*sin(w3)=x2-x3+(r1+a)*(x1-x ^-------------------- Timing: real 0m0.009s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:53:17 2004 Input: (r1 + b) * sin(w3) = x2 - x3 + (r1 + a) * (x1 - y + r1 * sin(w1))/(r1 + a) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (r1+b)*sin(w3)=x2-x3+(r1+a)*(x1-y ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:53:53 2004 Input: (a + b) * sin(c) = d - e + (a + f) * (g - y + h * sin(c))/(a + f) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (a+b)*sin(c)=d-e+(a+f)*(g-y+h*s ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:54:11 2004 Input: (a + b) * sin(c) = d - e + (a + f) * (g - y + h * s(c))/(a + f) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (a+b)*sin(c)=d-e+(a+f)*(g-y+h*s ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:54:22 2004 Input: (a + b) * sin(c) = d - e + (a + f) * (g - y + h * SIN(c))/(a + f) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (a+b)*sin(c)=d-e+(a+f)*(g-y+h*S ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:54:28 2004 Input: SIN(1) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: SIN(1) ^------ Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:54:34 2004 Input: sin(1) Output: ? 0.84147098480789650665250232163029899962 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:54:57 2004 Input: sin(a) Output: ? a - 1/6*a^3 + 1/120*a^5 - 1/5040*a^7 + 1/362880*a^9 - 1/39916800*a^11 + 1/6227020800*a^13 - 1/1307674368000*a^15 + O(a^17) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:55:08 2004 Input: b*sin(a) Output: ? (a - 1/6*a^3 + 1/120*a^5 - 1/5040*a^7 + 1/362880*a^9 - 1/39916800*a^11 + 1/6227020800*a^13 - 1/1307674368000*a^15 + O(a^17))*b ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:55:32 2004 Input: b1*sin(a) Output: ? (a - 1/6*a^3 + 1/120*a^5 - 1/5040*a^7 + 1/362880*a^9 - 1/39916800*a^11 + 1/6227020800*a^13 - 1/1307674368000*a^15 + O(a^17))*b1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:55:37 2004 Input: b1*sin(a1) Output: ? (a1 - 1/6*a1^3 + 1/120*a1^5 - 1/5040*a1^7 + 1/362880*a1^9 - 1/39916800*a1^11 + 1/6227020800*a1^13 - 1/1307674368000*a1^15 + O(a1^17))*b1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:55:42 2004 Input: b1*sin(a1)=c Output: ? ? Errors (if any) and Timing Info: *** unexpected character: b1*sin(a1)=c ^--- Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:56:03 2004 Input: b1*sin(a1) == c Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:56:34 2004 Input: (y2-y1+a*cos(w2))/(cos (w1) - cos (w2)) Output: ? ((-2*w1^-2 - 1/6 - 1/120*w1^2 - 1/3024*w1^4 - 1/86400*w1^6 - 1/2661120*w1^8 - 691/59439744000*w1^10 - 1/2874009600*w1^12 + O(w1^14)) + (-2*w1^-4 - 1/3*w1^-2 - 11/360 - 31/15120*w1^2 - 41/362880*w1^4 - 31/5702400*w1^6 - 10331/43589145600*w1^8 - 3421/356638464000*w1^10 + O(w1^12))*w2^2 + (-2*w1^-6 - 1/3*w1^-4 - 7/180*w1^-2 - 19/5040 - 557/1814400*w1^2 - 73/3421440*w1^4 - 40409/31135104000*w1^6 - 18521/261534873600*w1^8 + O(w1^10))*w2^4 + (-2*w1^-8 - 1/3*w1^-6 - 7/180*w1^-4 - 31/7560*w1^-2 - 247/604800 - 637/17107200*w1^2 - 396073/130767436800*w1^4 - 8191/37362124800*w1^6 + O(w1^8))*w2^6 + (-2*w1^-10 - 1/3*w1^-8 - 7/180*w1^-6 - 31/7560*w1^-4 - 127/302400*w1^-2 - 1013/23950080 - 2673989/653837184000*w1^2 - 32051/87178291200*w1^4 + O(w1^6))*w2^8 + (-2*w1^-12 - 1/3*w1^-10 - 7/180*w1^-8 - 31/7560*w1^-6 - 127/302400*w1^-4 - 73/1710720*w1^-2 - 940451/217945728000 - 1682479/3923023104000*w1^2 + O(w1^4))*w2^10 + (-2*w1^-14 - 1/3*w1^-12 - 7/180*w1^-10 - 31/7560*w1^-8 - 127/302400*w1^-6 - 73/1710720*w1^-4 - 1414477/326918592000*w1^-2 - 16369/37362124800 + O(w1^2))*w2^12 + (-2*w1^-16 - 1/3*w1^-14 - 7/180*w1^-12 - 31/7560*w1^-10 - 127/302400*w1^-8 - 73/1710720*w1^-6 - 1414477/326918592000*w1^-4 - 8191/18681062400*w1^-2 + O(1))*w2^14 + (-2*w1^-18 - 1/3*w1^-16 - 7/180*w1^-14 - 31/7560*w1^-12 - 127/302400*w1^-10 - 73/1710720*w1^-8 - 1414477/326918592000*w1^-6 - 8191/18681062400*w1^-4 + O(w1^-2))*w2^16 + O(w2^18))*y2 + (((2*w1^-2 + 1/6 + 1/120*w1^2 + 1/3024*w1^4 + 1/86400*w1^6 + 1/2661120*w1^8 + 691/59439744000*w1^10 + 1/2874009600*w1^12 + O(w1^14)) + (2*w1^-4 + 1/3*w1^-2 + 11/360 + 31/15120*w1^2 + 41/362880*w1^4 + 31/5702400*w1^6 + 10331/43589145600*w1^8 + 3421/356638464000*w1^10 + O(w1^12))*w2^2 + (2*w1^-6 + 1/3*w1^-4 + 7/180*w1^-2 + 19/5040 + 557/1814400*w1^2 + 73/3421440*w1^4 + 40409/31135104000*w1^6 + 18521/261534873600*w1^8 + O(w1^10))*w2^4 + (2*w1^-8 + 1/3*w1^-6 + 7/180*w1^-4 + 31/7560*w1^-2 + 247/604800 + 637/17107200*w1^2 + 396073/130767436800*w1^4 + 8191/37362124800*w1^6 + O(w1^8))*w2^6 + (2*w1^-10 + 1/3*w1^-8 + 7/180*w1^-6 + 31/7560*w1^-4 + 127/302400*w1^-2 + 1013/23950080 + 2673989/653837184000*w1^2 + 32051/87178291200*w1^4 + O(w1^6))*w2^8 + (2*w1^-12 + 1/3*w1^-10 + 7/180*w1^-8 + 31/7560*w1^-6 + 127/302400*w1^-4 + 73/1710720*w1^-2 + 940451/217945728000 + 1682479/3923023104000*w1^2 + O(w1^4))*w2^10 + (2*w1^-14 + 1/3*w1^-12 + 7/180*w1^-10 + 31/7560*w1^-8 + 127/302400*w1^-6 + 73/1710720*w1^-4 + 1414477/326918592000*w1^-2 + 16369/37362124800 + O(w1^2))*w2^12 + (2*w1^-16 + 1/3*w1^-14 + 7/180*w1^-12 + 31/7560*w1^-10 + 127/302400*w1^-8 + 73/1710720*w1^-6 + 1414477/326918592000*w1^-4 + 8191/18681062400*w1^-2 + O(1))*w2^14 + (2*w1^-18 + 1/3*w1^-16 + 7/180*w1^-14 + 31/7560*w1^-12 + 127/302400*w1^-10 + 73/1710720*w1^-8 + 1414477/326918592000*w1^-6 + 8191/18681062400*w1^-4 + O(w1^-2))*w2^16 + O(w2^18))*y1 + ((-2*w1^-2 - 1/6 - 1/120*w1^2 - 1/3024*w1^4 - 1/86400*w1^6 - 1/2661120*w1^8 - 691/59439744000*w1^10 - 1/2874009600*w1^12 + O(w1^14)) + (-2*w1^-4 + 2/3*w1^-2 + 19/360 + 2/945*w1^2 + 19/362880*w1^4 + 1/2851200*w1^6 - 2141/43589145600*w1^8 - 337/89159616000*w1^10 + O(w1^12))*w2^2 + (-2*w1^-6 + 2/3*w1^-4 + 2/45*w1^-2 + 23/5040 + 673/1814400*w1^2 + 2/93[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.006s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:56:48 2004 Input: Simplify((y2-y1+a*cos(w2))/(cos (w1) - cos (w2))) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Simplify((y2-y1+a*co ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:56:57 2004 Input: Simplify((y2-y1+a*cos(w2))/(cos(w1) - cos(w2))) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Simplify((y2-y1+a*co ^-------------------- Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:57:57 2004 Input: Simplify((y2-y1+a*cos(w2))/(cos(w1) - cos(w2))) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Simplify((y2-y1+a*co ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:01:37 2004 Input: simplify((y2-y1+a*cos(w2))/(cos(w1) - cos(w2))) Output: ? ((-2*w1^-2 - 1/6 - 1/120*w1^2 - 1/3024*w1^4 - 1/86400*w1^6 - 1/2661120*w1^8 - 691/59439744000*w1^10 - 1/2874009600*w1^12 + O(w1^14)) + (-2*w1^-4 - 1/3*w1^-2 - 11/360 - 31/15120*w1^2 - 41/362880*w1^4 - 31/5702400*w1^6 - 10331/43589145600*w1^8 - 3421/356638464000*w1^10 + O(w1^12))*w2^2 + (-2*w1^-6 - 1/3*w1^-4 - 7/180*w1^-2 - 19/5040 - 557/1814400*w1^2 - 73/3421440*w1^4 - 40409/31135104000*w1^6 - 18521/261534873600*w1^8 + O(w1^10))*w2^4 + (-2*w1^-8 - 1/3*w1^-6 - 7/180*w1^-4 - 31/7560*w1^-2 - 247/604800 - 637/17107200*w1^2 - 396073/130767436800*w1^4 - 8191/37362124800*w1^6 + O(w1^8))*w2^6 + (-2*w1^-10 - 1/3*w1^-8 - 7/180*w1^-6 - 31/7560*w1^-4 - 127/302400*w1^-2 - 1013/23950080 - 2673989/653837184000*w1^2 - 32051/87178291200*w1^4 + O(w1^6))*w2^8 + (-2*w1^-12 - 1/3*w1^-10 - 7/180*w1^-8 - 31/7560*w1^-6 - 127/302400*w1^-4 - 73/1710720*w1^-2 - 940451/217945728000 - 1682479/3923023104000*w1^2 + O(w1^4))*w2^10 + (-2*w1^-14 - 1/3*w1^-12 - 7/180*w1^-10 - 31/7560*w1^-8 - 127/302400*w1^-6 - 73/1710720*w1^-4 - 1414477/326918592000*w1^-2 - 16369/37362124800 + O(w1^2))*w2^12 + (-2*w1^-16 - 1/3*w1^-14 - 7/180*w1^-12 - 31/7560*w1^-10 - 127/302400*w1^-8 - 73/1710720*w1^-6 - 1414477/326918592000*w1^-4 - 8191/18681062400*w1^-2 + O(1))*w2^14 + (-2*w1^-18 - 1/3*w1^-16 - 7/180*w1^-14 - 31/7560*w1^-12 - 127/302400*w1^-10 - 73/1710720*w1^-8 - 1414477/326918592000*w1^-6 - 8191/18681062400*w1^-4 + O(w1^-2))*w2^16 + O(w2^18))*y2 + (((2*w1^-2 + 1/6 + 1/120*w1^2 + 1/3024*w1^4 + 1/86400*w1^6 + 1/2661120*w1^8 + 691/59439744000*w1^10 + 1/2874009600*w1^12 + O(w1^14)) + (2*w1^-4 + 1/3*w1^-2 + 11/360 + 31/15120*w1^2 + 41/362880*w1^4 + 31/5702400*w1^6 + 10331/43589145600*w1^8 + 3421/356638464000*w1^10 + O(w1^12))*w2^2 + (2*w1^-6 + 1/3*w1^-4 + 7/180*w1^-2 + 19/5040 + 557/1814400*w1^2 + 73/3421440*w1^4 + 40409/31135104000*w1^6 + 18521/261534873600*w1^8 + O(w1^10))*w2^4 + (2*w1^-8 + 1/3*w1^-6 + 7/180*w1^-4 + 31/7560*w1^-2 + 247/604800 + 637/17107200*w1^2 + 396073/130767436800*w1^4 + 8191/37362124800*w1^6 + O(w1^8))*w2^6 + (2*w1^-10 + 1/3*w1^-8 + 7/180*w1^-6 + 31/7560*w1^-4 + 127/302400*w1^-2 + 1013/23950080 + 2673989/653837184000*w1^2 + 32051/87178291200*w1^4 + O(w1^6))*w2^8 + (2*w1^-12 + 1/3*w1^-10 + 7/180*w1^-8 + 31/7560*w1^-6 + 127/302400*w1^-4 + 73/1710720*w1^-2 + 940451/217945728000 + 1682479/3923023104000*w1^2 + O(w1^4))*w2^10 + (2*w1^-14 + 1/3*w1^-12 + 7/180*w1^-10 + 31/7560*w1^-8 + 127/302400*w1^-6 + 73/1710720*w1^-4 + 1414477/326918592000*w1^-2 + 16369/37362124800 + O(w1^2))*w2^12 + (2*w1^-16 + 1/3*w1^-14 + 7/180*w1^-12 + 31/7560*w1^-10 + 127/302400*w1^-8 + 73/1710720*w1^-6 + 1414477/326918592000*w1^-4 + 8191/18681062400*w1^-2 + O(1))*w2^14 + (2*w1^-18 + 1/3*w1^-16 + 7/180*w1^-14 + 31/7560*w1^-12 + 127/302400*w1^-10 + 73/1710720*w1^-8 + 1414477/326918592000*w1^-6 + 8191/18681062400*w1^-4 + O(w1^-2))*w2^16 + O(w2^18))*y1 + ((-2*w1^-2 - 1/6 - 1/120*w1^2 - 1/3024*w1^4 - 1/86400*w1^6 - 1/2661120*w1^8 - 691/59439744000*w1^10 - 1/2874009600*w1^12 + O(w1^14)) + (-2*w1^-4 + 2/3*w1^-2 + 19/360 + 2/945*w1^2 + 19/362880*w1^4 + 1/2851200*w1^6 - 2141/43589145600*w1^8 - 337/89159616000*w1^10 + O(w1^12))*w2^2 + (-2*w1^-6 + 2/3*w1^-4 + 2/45*w1^-2 + 23/5040 + 673/1814400*w1^2 + 2/93[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.008s sys 0m0.005s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:04:32 2004 Input: r1:=(y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: r1:=(y2-y1+a*cos(w2))/ ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:04:42 2004 Input: (y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) Output: ? ((-2*w1^-2 - 1/6 - 1/120*w1^2 - 1/3024*w1^4 - 1/86400*w1^6 - 1/2661120*w1^8 - 691/59439744000*w1^10 - 1/2874009600*w1^12 + O(w1^14)) + (-2*w1^-4 - 1/3*w1^-2 - 11/360 - 31/15120*w1^2 - 41/362880*w1^4 - 31/5702400*w1^6 - 10331/43589145600*w1^8 - 3421/356638464000*w1^10 + O(w1^12))*w2^2 + (-2*w1^-6 - 1/3*w1^-4 - 7/180*w1^-2 - 19/5040 - 557/1814400*w1^2 - 73/3421440*w1^4 - 40409/31135104000*w1^6 - 18521/261534873600*w1^8 + O(w1^10))*w2^4 + (-2*w1^-8 - 1/3*w1^-6 - 7/180*w1^-4 - 31/7560*w1^-2 - 247/604800 - 637/17107200*w1^2 - 396073/130767436800*w1^4 - 8191/37362124800*w1^6 + O(w1^8))*w2^6 + (-2*w1^-10 - 1/3*w1^-8 - 7/180*w1^-6 - 31/7560*w1^-4 - 127/302400*w1^-2 - 1013/23950080 - 2673989/653837184000*w1^2 - 32051/87178291200*w1^4 + O(w1^6))*w2^8 + (-2*w1^-12 - 1/3*w1^-10 - 7/180*w1^-8 - 31/7560*w1^-6 - 127/302400*w1^-4 - 73/1710720*w1^-2 - 940451/217945728000 - 1682479/3923023104000*w1^2 + O(w1^4))*w2^10 + (-2*w1^-14 - 1/3*w1^-12 - 7/180*w1^-10 - 31/7560*w1^-8 - 127/302400*w1^-6 - 73/1710720*w1^-4 - 1414477/326918592000*w1^-2 - 16369/37362124800 + O(w1^2))*w2^12 + (-2*w1^-16 - 1/3*w1^-14 - 7/180*w1^-12 - 31/7560*w1^-10 - 127/302400*w1^-8 - 73/1710720*w1^-6 - 1414477/326918592000*w1^-4 - 8191/18681062400*w1^-2 + O(1))*w2^14 + (-2*w1^-18 - 1/3*w1^-16 - 7/180*w1^-14 - 31/7560*w1^-12 - 127/302400*w1^-10 - 73/1710720*w1^-8 - 1414477/326918592000*w1^-6 - 8191/18681062400*w1^-4 + O(w1^-2))*w2^16 + O(w2^18))*y2 + (((2*w1^-2 + 1/6 + 1/120*w1^2 + 1/3024*w1^4 + 1/86400*w1^6 + 1/2661120*w1^8 + 691/59439744000*w1^10 + 1/2874009600*w1^12 + O(w1^14)) + (2*w1^-4 + 1/3*w1^-2 + 11/360 + 31/15120*w1^2 + 41/362880*w1^4 + 31/5702400*w1^6 + 10331/43589145600*w1^8 + 3421/356638464000*w1^10 + O(w1^12))*w2^2 + (2*w1^-6 + 1/3*w1^-4 + 7/180*w1^-2 + 19/5040 + 557/1814400*w1^2 + 73/3421440*w1^4 + 40409/31135104000*w1^6 + 18521/261534873600*w1^8 + O(w1^10))*w2^4 + (2*w1^-8 + 1/3*w1^-6 + 7/180*w1^-4 + 31/7560*w1^-2 + 247/604800 + 637/17107200*w1^2 + 396073/130767436800*w1^4 + 8191/37362124800*w1^6 + O(w1^8))*w2^6 + (2*w1^-10 + 1/3*w1^-8 + 7/180*w1^-6 + 31/7560*w1^-4 + 127/302400*w1^-2 + 1013/23950080 + 2673989/653837184000*w1^2 + 32051/87178291200*w1^4 + O(w1^6))*w2^8 + (2*w1^-12 + 1/3*w1^-10 + 7/180*w1^-8 + 31/7560*w1^-6 + 127/302400*w1^-4 + 73/1710720*w1^-2 + 940451/217945728000 + 1682479/3923023104000*w1^2 + O(w1^4))*w2^10 + (2*w1^-14 + 1/3*w1^-12 + 7/180*w1^-10 + 31/7560*w1^-8 + 127/302400*w1^-6 + 73/1710720*w1^-4 + 1414477/326918592000*w1^-2 + 16369/37362124800 + O(w1^2))*w2^12 + (2*w1^-16 + 1/3*w1^-14 + 7/180*w1^-12 + 31/7560*w1^-10 + 127/302400*w1^-8 + 73/1710720*w1^-6 + 1414477/326918592000*w1^-4 + 8191/18681062400*w1^-2 + O(1))*w2^14 + (2*w1^-18 + 1/3*w1^-16 + 7/180*w1^-14 + 31/7560*w1^-12 + 127/302400*w1^-10 + 73/1710720*w1^-8 + 1414477/326918592000*w1^-6 + 8191/18681062400*w1^-4 + O(w1^-2))*w2^16 + O(w2^18))*y1 + ((-2*w1^-2 - 1/6 - 1/120*w1^2 - 1/3024*w1^4 - 1/86400*w1^6 - 1/2661120*w1^8 - 691/59439744000*w1^10 - 1/2874009600*w1^12 + O(w1^14)) + (-2*w1^-4 + 2/3*w1^-2 + 19/360 + 2/945*w1^2 + 19/362880*w1^4 + 1/2851200*w1^6 - 2141/43589145600*w1^8 - 337/89159616000*w1^10 + O(w1^12))*w2^2 + (-2*w1^-6 + 2/3*w1^-4 + 2/45*w1^-2 + 23/5040 + 673/1814400*w1^2 + 2/93[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:04:53 2004 Input: r1 := (y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: r1:=(y2-y1+a*cos(w2))/ ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:08:10 2004 Input: r1(y2,y1,a,w2,w1) = (y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:08:38 2004 Input: r1(y2,y1,a,w2,w1) = (y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) r1(a,b,c,d,e) Output: ? ? ? ((-2*e^-2 - 1/6 - 1/120*e^2 - 1/3024*e^4 - 1/86400*e^6 - 1/2661120*e^8 - 691/59439744000*e^10 - 1/2874009600*e^12 + O(e^14)) + (-2*e^-4 - 1/3*e^-2 - 11/360 - 31/15120*e^2 - 41/362880*e^4 - 31/5702400*e^6 - 10331/43589145600*e^8 - 3421/356638464000*e^10 + O(e^12))*d^2 + (-2*e^-6 - 1/3*e^-4 - 7/180*e^-2 - 19/5040 - 557/1814400*e^2 - 73/3421440*e^4 - 40409/31135104000*e^6 - 18521/261534873600*e^8 + O(e^10))*d^4 + (-2*e^-8 - 1/3*e^-6 - 7/180*e^-4 - 31/7560*e^-2 - 247/604800 - 637/17107200*e^2 - 396073/130767436800*e^4 - 8191/37362124800*e^6 + O(e^8))*d^6 + (-2*e^-10 - 1/3*e^-8 - 7/180*e^-6 - 31/7560*e^-4 - 127/302400*e^-2 - 1013/23950080 - 2673989/653837184000*e^2 - 32051/87178291200*e^4 + O(e^6))*d^8 + (-2*e^-12 - 1/3*e^-10 - 7/180*e^-8 - 31/7560*e^-6 - 127/302400*e^-4 - 73/1710720*e^-2 - 940451/217945728000 - 1682479/3923023104000*e^2 + O(e^4))*d^10 + (-2*e^-14 - 1/3*e^-12 - 7/180*e^-10 - 31/7560*e^-8 - 127/302400*e^-6 - 73/1710720*e^-4 - 1414477/326918592000*e^-2 - 16369/37362124800 + O(e^2))*d^12 + (-2*e^-16 - 1/3*e^-14 - 7/180*e^-12 - 31/7560*e^-10 - 127/302400*e^-8 - 73/1710720*e^-6 - 1414477/326918592000*e^-4 - 8191/18681062400*e^-2 + O(1))*d^14 + (-2*e^-18 - 1/3*e^-16 - 7/180*e^-14 - 31/7560*e^-12 - 127/302400*e^-10 - 73/1710720*e^-8 - 1414477/326918592000*e^-6 - 8191/18681062400*e^-4 + O(e^-2))*d^16 + O(d^18))*a + (((2*e^-2 + 1/6 + 1/120*e^2 + 1/3024*e^4 + 1/86400*e^6 + 1/2661120*e^8 + 691/59439744000*e^10 + 1/2874009600*e^12 + O(e^14)) + (2*e^-4 + 1/3*e^-2 + 11/360 + 31/15120*e^2 + 41/362880*e^4 + 31/5702400*e^6 + 10331/43589145600*e^8 + 3421/356638464000*e^10 + O(e^12))*d^2 + (2*e^-6 + 1/3*e^-4 + 7/180*e^-2 + 19/5040 + 557/1814400*e^2 + 73/3421440*e^4 + 40409/31135104000*e^6 + 18521/261534873600*e^8 + O(e^10))*d^4 + (2*e^-8 + 1/3*e^-6 + 7/180*e^-4 + 31/7560*e^-2 + 247/604800 + 637/17107200*e^2 + 396073/130767436800*e^4 + 8191/37362124800*e^6 + O(e^8))*d^6 + (2*e^-10 + 1/3*e^-8 + 7/180*e^-6 + 31/7560*e^-4 + 127/302400*e^-2 + 1013/23950080 + 2673989/653837184000*e^2 + 32051/87178291200*e^4 + O(e^6))*d^8 + (2*e^-12 + 1/3*e^-10 + 7/180*e^-8 + 31/7560*e^-6 + 127/302400*e^-4 + 73/1710720*e^-2 + 940451/217945728000 + 1682479/3923023104000*e^2 + O(e^4))*d^10 + (2*e^-14 + 1/3*e^-12 + 7/180*e^-10 + 31/7560*e^-8 + 127/302400*e^-6 + 73/1710720*e^-4 + 1414477/326918592000*e^-2 + 16369/37362124800 + O(e^2))*d^12 + (2*e^-16 + 1/3*e^-14 + 7/180*e^-12 + 31/7560*e^-10 + 127/302400*e^-8 + 73/1710720*e^-6 + 1414477/326918592000*e^-4 + 8191/18681062400*e^-2 + O(1))*d^14 + (2*e^-18 + 1/3*e^-16 + 7/180*e^-14 + 31/7560*e^-12 + 127/302400*e^-10 + 73/1710720*e^-8 + 1414477/326918592000*e^-6 + 8191/18681062400*e^-4 + O(e^-2))*d^16 + O(d^18))*b + ((-2*e^-2 - 1/6 - 1/120*e^2 - 1/3024*e^4 - 1/86400*e^6 - 1/2661120*e^8 - 691/59439744000*e^10 - 1/2874009600*e^12 + O(e^14)) + (-2*e^-4 + 2/3*e^-2 + 19/360 + 2/945*e^2 + 19/362880*e^4 + 1/2851200*e^6 - 2141/43589145600*e^8 - 337/89159616000*e^10 + O(e^12))*d^2 + (-2*e^-6 + 2/3*e^-4 + 2/45*e^-2 + 23/5040 + 673/1814400*e^2 + 2/93555*e^4 + 14603/15567552000*e^6 + 8377/261534873600*e^8 + O(e^10))*d^4 + (-2*e^-8 + 2/3*e^-6 + 2/45*e^-4 + 4/945*e^-2 + 263/604800 + 2539/59875200*e^2 + 221701/65383718400*e^4 + 4/1824322[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:09:49 2004 Input: r1(y2,y1,a,w2,w1) = (y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) (r1(y2,y1,a,w2,w1)+b)*sin w3 = x2-x3+(r1(y2,y1,a,w2,w1)+a)*(x1-x2+r1*sin w1)/(r1(y2,y1,a,w2,w1)+a) Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.014s user 0m0.008s sys 0m0.005s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:10:08 2004 Input: r1(y2,y1,a,w2,w1) = (y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) eval((r1(y2,y1,a,w2,w1)+b)*sin w3 = x2-x3+(r1(y2,y1,a,w2,w1)+a)*(x1-x2+r1*sin w1)/(r1(y2,y1,a,w2,w1)+a)) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:10:18 2004 Input: r1(y2,y1,a,w2,w1) = (y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) (r1(y2,y1,a,w2,w1)+b)*sin w3 = x2-x3+(r1(y2,y1,a,w2,w1)+a)*(x1-x2+r1*sin w1)/(r1(y2,y1,a,w2,w1)+a) Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.013s user 0m0.007s sys 0m0.007s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:10:52 2004 Input: r1(y2,y1,a,w2,w1) = (y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) (r1(y2,y1,a,w2,w1)+b)*sin w3 = x2-x3+(r1(y2,y1,a,w2,w1)+a)*(x1-x2+r1*sin w1)/(r1(y2,y1,a,w2,w1)+a) Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.013s user 0m0.009s sys 0m0.004s ************** PARI ***************** Host 128.107.253.39 (128.107.253.39) Time: Mon Sep 13 17:14:48 2004 Input: 325313081408936690707937788121346326696346318407751610198083376450388028308079503167465854169242019593646411323750697612266136676131257298464029314111563154373521679078211167496773278289469507571923731919001892792914221553449227182957429438776166026709285933999810647898320217868796698979278618746587154562910827711187655097004006972308335688789576074964131835599898955697005480507583106089134529566926420807971531201031016704211189890531318056269521511979177076114131422338958943833978750550978117932216405193385573662189454415408715189174660163738716326135995592315960060707868657009648863651544009725759647919142454130239393853487875203374883415815706698400328309201178704336183423764127771318306927730196170885845518823351857307078641958018955754407322040205640586952171876261278620244616443229362185583008017815708570427181463511179814453872281076051629125155761396797007479763563179139019708264877402238052580650116995513528190177043215959831673321266282037953976421135501126750855402044046243493902328929017200426032527598348753631131987263625641952627207188158441633692891642272836415001239905309936386434311548836198096504386710841047896184706008478140316065139414896512020348441181503023011522376267877865185790296839968373198872144783317199208834066353452043399939858444211695007112806550701834021848030994544332888949600163606787134127417390253142106975034099834152256449683670956145172630782129708034193270228447783759231817643856915734318454936463390537487293000908776998796343165893282316885152865675750419751312340367916855842390082573709800757101956358053300615366322453623877620567408798800135412694435709304694370763401782712817281764976546924789048940120632012044546225200399890538792777401890111917243072500813725963571173353068036442126358098872919724267290688335774418380774067768626215678175217914308241559258813771671568034447876718295090631345343848457071986450638795543532664654556204228674085922336682194991640092400533681151579151775989970024243891758646855305979543840848832966580897015919454958717312422765554320699488520382171703021034929279093328120215658028423429078841079158705117763645890316526156192385508035403082741886673383528495826008807547974210581957109253766840456798757773552234056859007683707894347686295322255874935239274365114733363148682363081581845713233364149858078547650239045092858460164075155760406711144201363740474719421519242480014360205958320813962179760466909049841731085830759141880403236266584738623506059064423753363797456651060658398480861297121667835031722385992711544954217466420521926253719209040582096855880004296846624392485154780584653016786695198938230820438356661242744161656303174744468863929184672335988327827257425090542873576328955502827566850362206495321451204767556737283761857884032476455871018073070472909826826452713206900763370405932883484426669826883983454244686868309152734631853869495061614175536511518491302440754320907915586224210860795627969648616261770105475388332947066542883395431268346200752186954537222222724972161217509854421051371659112415449461991317140799832759242323056731629565898934957645706875698457392344418421827252120029707194181465135082488002832371009514021615065575808570319073092449984703972879233463899184530319400159457158648185265823208702071598006296037507632281016114771821888547019938469048843519961019299523706516579688912995078387959370413718437887349111623425474573014991992689864236408458231649526094532393144090296107060168720483683747788139641827935620272959132821534132213429723958943472179258791811884422984681572908171490428799099428995233203500337549798787648390962748616930106949412345197109156032279471611915943154461609935373192428467523024241077154018726437559770330296414794593693097462598115989909991587146180028551965232696580791915046399543359917101930569244566340554556705602208423478911930675294241811103880760462949178664644866630941699775087961262445835482337693075145475746673543845591054370050199401815482299546322134244005040571037406575510714756973291502473578854680741999596073299938637044389797214859553164962554130043864257211129788921511975450361920753659982444359367717876226660999482263872008860639385529365252726941284546578543984629362657737474286474387753465051174717436643806782457689590881103501915561217547863704206208061344963418122790629658621167561069062783361472707964846595010426033942589834913271683214757016904260153230295235892044353061732663684372927251064607473611563311458716076973871279015354808480921502011293891218184524945836283918840665303340617882262208710513477032352182125513101626250584942222487220778791496464628016216722210119810961384513005554699974497980850597465005827501884544226842875533871361261325777513712615225320490021275452382904907766095409313831380893086140563828235391827164372946835103378732264821434520478407134916816524129878083863795975169631960679167975600314392540362966547838191365516780619111548996745113262409003659069610268095224396286811859236850899092419890096585096917552354681326828328529973546420177328471735543041036594203258903948920308131621641493969989599979860361282283126667786724203694769144487851426816071235994027051365139183894635691042004882384315086847761309718856090766212121102848723625040021405566566478216762884495896082571118625380594618831144189230855630912040873368061578211006823676321092957490425307291019674505806942428128458843790803147333568531900063044834472090838496745769988044055004798414192297102766130187456706645327014136387425045847725833772284092163687518403096572375036113932225182670447004292141952055327638527268266290150778657257117358988501748236772511525799834680981951927080607118430234587524879061856852597252020731777090064981167959043756094212787191284967069129506268780772230725311403951951483896823176764434032435707140452947082335139667461788105366002668241279680078669643596370471393541754729479635325153680340424719685541943806234990181969556878550811966605312606381855248793748729323840697344962117730138767391747059124015711490148990761367097918895428967599101616486655573024611506883599002049604596241171991755145907194041809672069641870092191320634150526335631244978439823366957592368021636982975510249524102678950234701917757281374965809602099409184267988514120275848433089037584367677904415121428162156088353683002745344484447535746920180546492731507362537294763003672907271167069569563202458475236503321390083316618597868325130900362522928602393397896512856246985064170368355871431548912339910221911189780355425362600174818500805197330312265426990830753027594750268079379682352203631251772788404859152768581227622369844038384510597042652949014520176442164611601405564811146795903941341322636285143774325162203127217611689887767799080906452127898638911245441151988692640956897478310775822118797409298388116183615615178357133203484060725243103678150349618501702364131302389505915456950039261999655988232055501539709318761335748537076000836033403412603034736654622987725515963158604308917325578007402393815818253295053837141478732717680512365945089705002091751726774360099752169221037825971247815024097207425658225223570962717437436969414054755676232533205035043191133361313024217247639773440326414070415175068266880670203235241977603174092952986870615094170178782255986847484523748283731577176776538132007511070979595829011328022552751831906809314654108944034536873669221763961197999730436339298822887268810855798008996980167089904256124597813881361314388891406121641174171382384404814569779986784657884890281049426991826103174131113561925562903392836841624990542037656479841084570864404750540171084150264769509997157596708806265973533619067445688066124868085533172663214007642007619763197315959348033311462332588416520508105476310487235126599170073710016266493315369982721517769627010445811630871842628294110250225191167071370304883170358317557237320946341537570302126082762543352998298419984859117084481460248514887685283131134757071637819282499300248733004333735349942530798290300772000316901737307224628640765069939174245201916701512209226289364648942782834142745490657188705563464304932873526169822468238445668028578148413047966767042721822354191188784826603662826375230123402171456825294922887268535098339296090938420538313400512387150495188478573102251319092430765147666871037835182575546502431979682785947378347479881712787800131378679859431079648826997220918587695145985573512323208197202266669624421204393665810419776263821709004461512675647543840788316205572335227256747892149238802511309604107864391306748947391806292353587602144623383379879722920358447024506997574018411200844889243706507821670062894834916517644112590794236018913407697685523493717373736338779187399272139097066705480424428502188752687993234400317214173275326328909225334139111537250934278953469978088011879992647319740027338288946889835752260094689609066375763409350621255988935511328401742769901540367841111820372739710147855618853962301388794865695959605256843502846464528001608590413439902204778857705376180747225665462327211035459730536969229670581212476647344593090367287911789015682456528100118896769542204597656369128234005973468814997478059010351454836376867682972122060687312317067514102727580590733500429107950091156199045497760844859912560971090552722832357772237940114198119849050024965806640709365226239630974949094524516899969417684801712659124131024678440604531409904168030329418867612975414351521381173549613332283176136129857979663144856917178220410001/1575071 Output: ? 2065386775637013764509268395655474113207254266047382055780871950854202942648804423213085976246416952592273055143232893071271940605415611730925331709564604734475599379826123187442174214936783850200554336401355194736708513796833458193042913232331533160786313340794228627778177732107293569491652241369355124708097779155273985090221373971765943813260329692846429371119771462346811543781728608355652091663972105435066299874932728138675589167290351077948368752768459809837978239323553946672745232125904914332219977343151982749917015902195616509825018451477529115423975124397313268467698643487492713989045634931756396499855905735293163631911673844384687520852753294298024084001157435672318414624659912590016118195282440511224692876396412016211599083590236595095218185120801455630710464869701875309852338271494971229919272310318521686841186912715772519919934250910778784929450144133232595632598017099036857798012929182573869051725258820257564116431678062967785714207689926066675223754999785729376022058981744276304553439287501490615518908980951532546705917546840444825707464352030058917290980996008529147193398328941275880970120306945505976471605667604166318254913449236993539589103580168896185893724810011812307992896052718803090761241673379796035510674231188364423358397507435537444714836421310576556907915273876681419637556302750091580634546676226875660953634808475979654467003926503989024518075414664942918650205025895297864213408689254210239689873762733987578569241580458831970120132851146369548838708111043153945858159730067732263119363615074129293743416708203992721320867778662773718279706907673498955975945212218450434524597968563771178580411377120661639866056354215454034266595042665036847230378126057763601779793494497981821142118202694171712596245099059828782949295109390416626858952862559089552583779564322358644263746258051600586981613346750936610963685415391632157177984084984019454607414799286283948826460703511688821244770521402781794601854018971710810344358889372249833554467419601907113018072410491850189711571446358401065239380029984041916335086937052494998189155240164539983645362167350416845203541333170146906966838486367867769186502723259725349989832385307240173982937748270280876920810343409641843178964962430626041668494359266012048316058487997907645270372667221751582515093488368751080004419799857140075909206918880853372096084276584399758132816639633862342850063536691453021520669994012728186605346102174706607421702000366208274016006800573583705490510737315103874407255677098990971589833865697705257238473647927902641960053994530571978781966276962097936410512902888977020624179993058427313985815235873372187275092114849071322221685084319810750938749252166971062429931254467531137176222249681617951510517344902683442237001104948816668314533328824261706412428839543803592513941995039593538135143957850055182717648182103881315108133596217152317920077857198908338332122923292362317345192108264238400750574390792349351973731787998606972847237150216614968031716323903825205051310209017402848260284837029067587249458039767410243673568625159327796920412201936481377023225985658467940165601375077176976956925243558590020268706204878941983138353823503966583510050077554085327534123[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.025s sys 0m0.008s ************** PARI ***************** Host 64.102.254.33 (64.102.254.33) Time: Mon Sep 13 23:44:52 2004 Input: (2231^1180 + 1)*(2231^4 + 1)/((2231^236 + 1)*(2231^20 + 1)*198241*5952200129551518881) Output: ? 216635795707393167284097542738660076485566469026640083396720239219810006187867841253558311437092699785174312585509398965512294974149220947080033883055800648568674824953102457979045408143225702247411137338328547455750391173100671203810590428057248688800156549914329571663816011952183277134743832568851262612149714731901422248140915130965312742331748026981132126355390827205039913019807022720782258490870075018080069170500528792750473435900472119217957546892893531467117144939344075354628760871332203988230802128136781767476888639473029534622192962037621181751573301118607315197616818092521603699312698702955228195490027563493433690016068480374582985403046776769421825703449822536791606260192458949540177924173569079081064206988286246398797108129167345582140524963079105491917216809614892879175004498154852421041925990069095947939715499101861629064960921794124762096334083521645647350263789416937977930388183514529974402984448477067947864097776301941647382649334705810768027779822415336220507020038072087454801436705989760294539407859060603291657136934507812030921806155844439668279911066460558816736600468951911104892395313005045778802411243331814428427389146949881818624940059760498248969570267130844326894383843060348422772960510901611516022186181146571835153777299181764563174109406371713307492986827419205531324274530755127814459750229732120219233038949710681888327160787919435887724925023085526772218522552003952059321576765846644927672173911374581528722237867859870835139600262896929326159478978831064167088090263293097471024720597372753152971665673234110633870094156723736081687975595914286856545369892016879932386007707891676730611707053918873446588521407823555307014709821366348286401139922575668532142017527908705499914127857482481823398976150246099099747696913630740322683594748834305319348006187011619275876898683317415995019662180097525825600390079952109421738556796114650266634024945379676665548063818433672712222443613088343132854491357088736932417773691911412651681716420522354049264555324111163547653242959995683748344223954532449977165003466994265112427109122168995557803641100307380355954250529410279335007498360037584816525110719493794366419680450223157993690680677490844939710095375904145228104592423371570045422660220152759589714878629209245120371751324460846511668832804394270793460544407490233305901596163759760378327180855921859269675911808016054457758956043709664568531881216402043749739875346975672954346250111575607240614744989129180029374694679789820497851295497195854211215556662657882288190876171780846552910483600209418151030896069758500111312797041898872186502278327299130239852846723670200544346212363630098661799643282312555408979966654119515660372246825562848328641637335997450886848186842968859845149913838038658226188745287964492105064158037199798968206188959128513367393195529982493507765372046592821254993112298567112427128605104210736227808384431614313658369870392816429610701147469523762456266952165435304145273157257327023199755255159690232412723843752485465347862266700142247412131658752734465374601493681967105656767871067443087938815420801 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.005s ************** PARI ***************** Host 217.255.22.3 (217.255.22.3) Time: Tue Sep 14 19:42:44 2004 Input: vector(x^2,x,1,10) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: vector(x^2,x,1,10) ^---- Timing: real 0m0.182s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 217.255.22.3 (217.255.22.3) Time: Tue Sep 14 19:54:50 2004 Input: a(n)=if(n<=0,n==0,2*(issquare(n)-issquare(2*n)+2*sum(i=1,sqrtint(n2),issquare(n-2*i^2)))) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.001s sys 0m0.008s ************** PARI ***************** Host 203.160.1.69 (203.160.1.69) Time: Tue Sep 14 23:25:22 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 203.160.1.69 (203.160.1.69) Time: Tue Sep 14 23:25:23 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 203.160.1.69 (203.160.1.69) Time: Tue Sep 14 23:25:34 2004 Input: 12 Output: ? 12 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 202.154.65.186 (202.154.65.186) Time: Wed Sep 15 00:26:15 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 193.13.42.18 (193.13.42.18) Time: Wed Sep 15 04:50:58 2004 Input: 5*34 Output: ? 170 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.005s ************** PARI ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 06:57:53 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" AutomorphismGroup(ExtraSpecialGroup(2,3)); Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: AutomorphismGroup( *** ExtraSpecialGroup(2, ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:02:49 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: E:=ExtraSpecialGroup( ^-------------------- *** unexpected character: A:=AutomorphismGroup( ^-------------------- Timing: real 0m0.018s user 0m0.005s sys 0m0.006s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:45:41 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:46:25 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:46:42 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" ?l Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? Errors (if any) and Timing Info: *** l: unknown identifier. Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:46:57 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" ?igcd Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? Errors (if any) and Timing Info: *** igcd: unknown identifier. Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:47:11 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" ?gcd Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? gcd(x,{y},{flag=0}): greatest common divisor of x and y. flag is optional, and can be 0: default, 1: use the modular gcd algorithm (x and y must be polynomials), 2 use the subresultant algorithm (x and y must be polynomials) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:51:31 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" ?gcd a=x-1; b=x^3+2*x+x+1; g=a*b; h=subs(g,x=x^3); Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? gcd(x,{y},{flag=0}): greatest common divisor of x and y. flag is optional, and can be 0: default, 1: use the modular gcd algorithm (x and y must be polynomials), 2 use the subresultant algorithm (x and y must be polynomials) ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: h=subs(g,x=x^3); ^- Timing: real 0m0.028s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:52:49 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" ?subs Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? Errors (if any) and Timing Info: *** subs: unknown identifier. Timing: real 0m0.009s user 0m0.007s sys 0m0.001s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:53:05 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" ?subst Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? subst(x,y,z): in expression x, replace the variable y by the expression z. ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:57:47 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" a=x-1; b=x^3+2*x+x+1; g=a*b; h=subst(g,x,x^3); Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:58:00 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" a=x-1; b=x^3+2*x+x+1; g=a*b; h=subst(g,x,x^3); Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 134.157.158.46 (134.157.158.46) Time: Wed Sep 15 10:03:07 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 12.47.104.34 (12.47.104.34) Time: Wed Sep 15 13:49:17 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.169s user 0m0.006s sys 0m0.007s ************** PARI ***************** Host 12.47.104.34 (12.47.104.34) Time: Wed Sep 15 13:49:31 2004 Input: isprime (1, 2) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 134.129.67.107 (134.129.67.107) Time: Wed Sep 15 14:30:08 2004 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 15:47:30 2004 Input: mod(2,5) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(2,5) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file) New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.023s user 0m0.002s sys 0m0.008s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 15:49:10 2004 Input: Mod(2,5) Output: ? Mod(2, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 15:52:35 2004 Input: Mod(2,1) Output: ? Mod(0, 1) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 15:53:10 2004 Input: Mod(2,1) Output: ? Mod(0, 1) ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 15:53:16 2004 Input: Mod(2,7) Output: ? Mod(2, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 15:53:17 2004 Input: Mod(2,7) Output: ? Mod(2, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 16:44:43 2004 Input: Mod(5,2927)^709 Output: ? Mod(236, 2927) ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 16:47:28 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(n,4)==Mod(1,4),n,0),0)) Output: ? [0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 109, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 173, 0, 0, 0, 0, 0, 0, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 16:50:30 2004 Input: vector(200,n,if(isprime(n)==3,if(Mod(n,4)==Mod(3,4),n,0),0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.004s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 16:50:45 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(n,4)==Mod(3,4),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 7, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 67, 0, 0, 0, 71, 0, 0, 0, 0, 0, 0, 0, 79, 0, 0, 0, 83, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 103, 0, 0, 0, 107, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127, 0, 0, 0, 131, 0, 0, 0, 0, 0, 0, 0, 139, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 163, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 179, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 0, 0, 0, 0, 0, 0, 199, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 17:17:21 2004 Input: isprime(1,100) Output: ? ? Errors (if any) and Timing Info: *** invalid flag in gisprime. Timing: real 0m0.010s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 17:18:23 2004 Input: vector(n=1,100,isprime(n)*n) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: vector(n=1,100,isprime(n)*n) ^----------------- Timing: real 0m0.017s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 17:19:26 2004 Input: vector(n=1,100,(isprime(n))*n) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: vector(n=1,100,(isprime(n))*n) ^------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 17:20:10 2004 Input: vector(n=100,n,(isprime(n))*n) Output: ? [0, 2, 3, 0, 5, 0, 7, 0, 0, 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 0, 0, 23, 0, 0, 0, 0, 0, 29, 0, 31, 0, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 43, 0, 0, 0, 47, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 59, 0, 61, 0, 0, 0, 0, 0, 67, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 79, 0, 0, 0, 83, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:27:02 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(n,8)==Mod(1,8),n,0),0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:28:55 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(n,8)==Mod(3,8),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 67, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 107, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0, 0, 0, 0, 0, 0, 139, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 163, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 179, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:31:15 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(n,8)==Mod(5,8),n,0),0)) Output: ? [0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 109, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 173, 0, 0, 0, 0, 0, 0, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:33:22 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(n,8)==Mod(7,8),n,0),0)) Output: ? [0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71, 0, 0, 0, 0, 0, 0, 0, 79, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 103, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 0, 0, 0, 0, 0, 0, 199, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.009s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:39:43 2004 Input: issquare(Mod(-1,p)) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in issquare. Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:40:34 2004 Input: vector(200,n,if(isprime(n)==1,if(issquare(Mod(-1,n))==1,n,0),0)) Output: ? [0, 2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 109, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 173, 0, 0, 0, 0, 0, 0, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:40:50 2004 Input: vecsort(vector(200,n,if(isprime(n)==1,if(issquare(Mod(-1,n))==1,n,0),0))) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.008s sys 0m0.004s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:43:29 2004 Input: vecsort(vector(200,n,if(isprime(n)==1,if(issquare(Mod(-2,n))==1,n,0),0))) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 11, 17, 19, 41, 43, 59, 67, 73, 83, 89, 97, 107, 113, 131, 137, 139, 163, 179, 193] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:47:19 2004 Input: vecsort(vector(200,n,if(isprime(n)==1,if(issquare(Mod(2,n))==1,n,0),0))) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 7, 17, 23, 31, 41, 47, 71, 73, 79, 89, 97, 103, 113, 127, 137, 151, 167, 191, 193, 199] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:50:41 2004 Input: vecsort(vector(200,n,if(isprime(n)==1,if(issquare(Mod(3,n))==1,n,0),0))) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 11, 13, 23, 37, 47, 59, 61, 71, 73, 83, 97, 107, 109, 131, 157, 167, 179, 181, 191, 193] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:54:05 2004 Input: vecsort(vector(700,n,if(isprime(n)==1,if(issquare(Mod(3,n))==1,n,0),0))) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 11, 13, 23, 37, 47, 59, 61, 71, 73, 83, 97, 107, 109, 131, 157, 167, 179, 181, 191, 193, 227, 229, 239, 241, 251, 263, 277, 311, 313, 337, 347, 349, 359, 373, 383, 397, 409, 419, 421, 431, 433, 443, 457, 467, 479, 491, 503, 541, 563, 577, 587, 599, 601, 613, 647, 659, 661, 673, 683] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:54:42 2004 Input: vecsort(vector(500000,n,if(isprime(n)==1,if(issquare(Mod(3,n))==1,n,0),0))) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m3.815s user 0m3.803s sys 0m0.011s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:25:07 2004 Input: isprime(17) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:25:22 2004 Input: isprime(37) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:25:25 2004 Input: isprime(37) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:25:29 2004 Input: isprime(36) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:25:44 2004 Input: isprime(29) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:25:52 2004 Input: isprime(53) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:26:11 2004 Input: isprime(41) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:26:19 2004 Input: isprime(97) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:26:33 2004 Input: isprime(61) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:26:41 2004 Input: isprime(89) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:26:58 2004 Input: isprime(117) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:27:16 2004 Input: isprime(113) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 202.154.65.186 (202.154.65.186) Time: Wed Sep 15 22:02:17 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 202.154.65.186 (202.154.65.186) Time: Wed Sep 15 22:03:31 2004 Input: /p 70 exp(Pi*sqrt(-1)) Output: ? ? -1.0000000000000000000000000000000000000 + 0.E-38*I ? Errors (if any) and Timing Info: *** unexpected character: ^- Timing: real 0m0.028s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 62.2.79.21 (62.2.79.21) Time: Thu Sep 16 10:27:38 2004 Input: 100001100001100001100001100001100001 / 7 Output: ? 100001100001100001100001100001100001/7 ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Thu Sep 16 10:52:40 2004 Input: Mod(2,5)^2 Output: ? Mod(4, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Thu Sep 16 10:52:47 2004 Input: mod(2,5)^2 Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(2,5)^2 ^---------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file) New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.009s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Thu Sep 16 10:52:56 2004 Input: 3+88 Output: ? 91 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Thu Sep 16 10:53:05 2004 Input: Mod(5,2927)^3 Output: ? Mod(125, 2927) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 128.196.226.99 (128.196.226.99) Time: Thu Sep 16 11:35:14 2004 Input: {v=[]; print(hello);v } Output: ? hello [] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 217.255.64.110 (217.255.64.110) Time: Thu Sep 16 16:12:08 2004 Input: lim 3^n Output: ? ? Errors (if any) and Timing Info: *** gpow: need integer exponent if series valuation != 0. Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:02:17 2004 Input: Mod(3,4) Output: ? Mod(3, 4) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:02:39 2004 Input: Mod(3,4) Output: ? Mod(3, 4) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:02:52 2004 Input: (Mod(3,4)) Output: ? Mod(3, 4) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:03:04 2004 Input: Mod(3,1,4) Output: ? ? Errors (if any) and Timing Info: *** invalid flag in Mod. Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:03:09 2004 Input: Mod(3,1) Output: ? Mod(0, 1) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:03:26 2004 Input: Mod(3,3) Output: ? Mod(0, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:03:41 2004 Input: Mod(28,3) Output: ? Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:04:04 2004 Input: (Mod(5,2927))^709 Output: ? Mod(236, 2927) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:04:31 2004 Input: (Mod(5,2927))^709 Output: ? Mod(236, 2927) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:05:54 2004 Input: (Mod(5^709,2927)) Output: ? Mod(236, 2927) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:05:58 2004 Input: (Mod(5^709,2927)) Output: ? Mod(236, 2927) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:05:59 2004 Input: (Mod(5^709,2927)) Output: ? Mod(236, 2927) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:06:08 2004 Input: (Mod((5^709),2927)) Output: ? Mod(236, 2927) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 202.246.252.129 (202.246.252.129) Time: Thu Sep 16 23:48:05 2004 Input: 10000! Output: ? 2846259680917054518906413212119868890148051401702799230794179994274411340003764443772990786757784775815884062142317528830042339940153518739052421161382716174819824199827592418289259787898124253120594659962598670656016157203603239792632873671705574197596209947972034615369811989709261127750048419884541047554464244213657330307670362882580354896746111709736957860367019107151273058728104115864056128116538532596842582599558468814643042558983664931705925171720427659740744613340005419405246230343686915405940406622782824837151203832217864462718382292389963899282722187970245938769380309462733229257055545969002787528224254434802112755901916942542902891690721909708369053987374745248337289952180236328274121704026808676921045155584056717255537201585213282903427998981844931361064038148930449962159999935967089298019033699848440466541923625842494716317896119204123310826865107135451684554093603300960721034694437798234943078062606942230268188522759205702923084312618849760656074258627944882715595683153344053442544664841689458042570946167361318760523498228632645292152942347987060334429073715868849917893258069148316885425195600617237263632397442078692464295601230628872012265295296409150830133663098273380635397290150658182257429547589439976511386554120812578868370423920876448476156900126488927159070630640966162803878404448519164379080718611237062213341541506599184387596102392671327654698616365770662643863802984805195276953619525924093090861447190739076858575593478698172073437209310482547562856777769408156407496227525499338411280928963751699021987049240561753178634693979802461973707904186832993101655415074230839317687836692369484902599960772968429397742753626311982541668153189176323483919082100014717893218422780513518173492190114624687576983537344145601312261522139117875968836736408720793700299203827919803870237207803914031236899760815284030605111670948472222487038919999344207139583698306396223207911562404425080891991431983712044559834404755675948921210149815245454359428541439084356441998422485547853216362403009844285533182925315420655123707970581639346029624769701038874220644153662673371542870078912274934068433644288984710084064160009362393526124803797529334392876439831639031277645072247926785170082666959838952615075900734921519759265919270887320259406638211880198885474826604834225645770574397312225970067193606176351357952982179429079770532728326750148802444352868164502616566283754651900617187344226043891929850607151539003110668472736013581670643786175675743918437647965813610059963868955233464878174614324357322486432679848198145843270303589550842053478849336458248259203328808902578238823326577020524897093704721021424841334246526820680673231421448385407418213962184687010835958294696523563276487047571835161687923506836627174371191572336114307012112076760869785155972184648598591864364171685089962551682091079357023111851817477501080462258552131476489749066075287708289766751495100968232968973200062239288805665803614031128546592908407803397490066495320587316494809388381619865885082738246803489786475711667989042356801830350413387573197263089790943571068779730163391808786847494363353389337358690640584841782806519627582643442925805842221294764940294862267076183298[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.282s user 0m0.274s sys 0m0.007s ************** PARI ***************** Host 202.246.252.129 (202.246.252.129) Time: Thu Sep 16 23:48:39 2004 Input: 100000! Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 8015 Killed /usr/bin/gp -q --emacs Timing: real 0m21.042s user 0m20.989s sys 0m0.012s ************** PARI ***************** Host 62.2.79.21 (62.2.79.21) Time: Fri Sep 17 02:22:51 2004 Input: 111112111112111112111112111112111112 / 7 Output: ? 111112111112111112111112111112111112/7 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 144.51.64.179 (144.51.64.179) Time: Fri Sep 17 10:06:48 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 208.59.175.120 (208.59.175.120) Time: Fri Sep 17 11:30:22 2004 Input: 2+2; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 65.96.160.100 (65.96.160.100) Time: Fri Sep 17 22:09:06 2004 Input: print("test") Output: ? test ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '65.96.1' ************** PARI ***************** Host 65.96.160.100 (65.96.160.100) Time: Fri Sep 17 22:09:58 2004 Input: print("test") Output: ? test ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '211.30.' ************** PARI ***************** Host 211.30.187.85 (211.30.187.85) Time: Sat Sep 18 02:05:47 2004 Input: 234*321^45 Output: ? 14519187563252854243456798984676802268540497489860429586839182546659153102649370371736217164580823311320389518633834 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '129.94.' ************** PARI ***************** Host 129.94.6.30 (129.94.6.30) Time: Sat Sep 18 03:59:21 2004 Input: 37249588852282552285743302297396100822355179407163315972232664422849771058311 Output: ? 37249588852282552285743302297396100822355179407163315972232664422849771058311 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '66.185.' ************** PARI ***************** Host 66.185.84.202 (66.185.84.202) Time: Sat Sep 18 04:19:31 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '211.28.' ************** PARI ***************** Host 211.28.121.5 (211.28.121.5) Time: Sat Sep 18 08:06:59 2004 Input: 13724958885228255228574330229739610082235517940716331597223266442284977105831 Output: ? 13724958885228255228574330229739610082235517940716331597223266442284977105831 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '211.28.' ************** PARI ***************** Host 211.28.121.5 (211.28.121.5) Time: Sat Sep 18 08:07:07 2004 Input: 13724958885228255228574330229739610082235517940716331597223266442284977105831 Output: ? 13724958885228255228574330229739610082235517940716331597223266442284977105831 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '144.137' ************** PARI ***************** Host 144.137.23.49 (144.137.23.49) Time: Sat Sep 18 08:07:37 2004 Input: 37249588852282552285743302297396100822355179407163315972232664422849771058311 Output: ? 37249588852282552285743302297396100822355179407163315972232664422849771058311 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 08:48:28 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 08:50:12 2004 Input: prime(3152546242366210213560206523355521600144252221600021436516044530245051102652416651041420302) Output: ? ? Errors (if any) and Timing Info: *** impossible assignment I-->S Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 08:50:34 2004 Input: prime(12) Output: ? 37 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.004s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 08:55:04 2004 Input: isprime(12) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 08:55:10 2004 Input: isprime(3152546242366210213560206523355521600144252221600021436516044530245051102652416651041420302) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 08:57:11 2004 Input: factor(127) Output: ? [127 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 08:57:18 2004 Input: factor(128) Output: ? [2 7] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.003s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 08:58:52 2004 Input: factor(3152546242366210213560206523355521600144252221600021436516044530245051102652416651041420302) Output: ? [2 1] [138937 1] [656311 1] [9208136731 1] [689051894591149 1] [2724458387055134565470788141331979134670860991565018247 1] ? Errors (if any) and Timing Info: Timing: real 0m2.245s user 0m2.239s sys 0m0.006s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 09:00:08 2004 Input: isprime(37249588852282552285743302297396100822355179407163315972232664422849771058311) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 09:00:21 2004 Input: factor(37249588852282552285743302297396100822355179407163315972232664422849771058311) Output: ? [89954413 1] [5299151939 1] [5302144343 1] [5963856163 1] [4281936962959 1] [4710694442959 1] [122514848197837 1] ? Errors (if any) and Timing Info: Timing: real 0m0.841s user 0m0.819s sys 0m0.022s '80.164.' ************** PARI ***************** Host 80.164.88.73 (80.164.88.73) Time: Sat Sep 18 23:56:35 2004 Input: (2x-4)+(5x-19) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (2x-4)+(5x-19) ^------------ Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '80.164.' ************** PARI ***************** Host 80.164.88.73 (80.164.88.73) Time: Sat Sep 18 23:56:55 2004 Input: (2*x-4)+(5*x-19) Output: ? 7*x - 23 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '66.159.' ************** PARI ***************** Host 66.159.153.176 (66.159.153.176) Time: Sun Sep 19 21:34:52 2004 Input: vector(49,n,isprime(4*n+1)*(4*n+1)) Output: ? [5, 0, 13, 17, 0, 0, 29, 0, 37, 41, 0, 0, 53, 0, 61, 0, 0, 73, 0, 0, 0, 89, 0, 97, 101, 0, 109, 113, 0, 0, 0, 0, 0, 137, 0, 0, 149, 0, 157, 0, 0, 0, 173, 0, 181, 0, 0, 193, 197] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.001s sys 0m0.008s '24.225.' ************** PARI ***************** Host 24.225.143.141 (24.225.143.141) Time: Tue Sep 21 09:42:29 2004 Input: 16486*6; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.001s sys 0m0.007s '24.225.' ************** PARI ***************** Host 24.225.143.141 (24.225.143.141) Time: Tue Sep 21 09:42:57 2004 Input: 16486*6-102400; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.005s sys 0m0.005s '132.205' ************** PARI ***************** Host 132.205.154.57 (132.205.154.57) Time: Tue Sep 21 13:41:19 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '131.215' ************** PARI ***************** Host 131.215.103.145 (131.215.103.145) Time: Tue Sep 21 14:38:44 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '194.126' ************** PARI ***************** Host 194.126.125.249 (194.126.125.249) Time: Tue Sep 21 17:34:40 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:32:53 2004 Input: Mod(2,7) Output: ? Mod(2, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:33:39 2004 Input: Mod(2, 7) Output: ? Mod(2, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:33:42 2004 Input: Mod(2, 7) Output: ? Mod(2, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:34:05 2004 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:34:23 2004 Input: isprime(7) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:34:37 2004 Input: Mod(4,8) Output: ? Mod(4, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:34:48 2004 Input: Mod(18,8) Output: ? Mod(2, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:39:05 2004 Input: if(Mod(n,9)==Mod(5,9),n,0) Output: ? ? Errors (if any) and Timing Info: *** forbidden division t_POL % t_INT. Timing: real 0m0.016s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:42:05 2004 Input: vector(200,n,if isprime(n)== 1, if(Mod(n,9) == Mod(5,9),n,0),0)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...tor(200,n,ifisprime(n)==1 *** ,if(Mod(n,9)==Mod(5, ^-------------------- Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:44:20 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,9) == Mod(5,9),n,0),0)) Output: ? [0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:45:00 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,9) == Mod(5,9),n,0),99)) Output: ? [99, 0, 0, 99, 5, 99, 0, 99, 99, 99, 0, 99, 0, 99, 99, 99, 0, 99, 0, 99, 99, 99, 23, 99, 99, 99, 99, 99, 0, 99, 0, 99, 99, 99, 99, 99, 0, 99, 99, 99, 41, 99, 0, 99, 99, 99, 0, 99, 99, 99, 99, 99, 0, 99, 99, 99, 99, 99, 59, 99, 0, 99, 99, 99, 99, 99, 0, 99, 99, 99, 0, 99, 0, 99, 99, 99, 99, 99, 0, 99, 99, 99, 0, 99, 99, 99, 99, 99, 0, 99, 99, 99, 99, 99, 99, 99, 0, 99, 99, 99, 0, 99, 0, 99, 99, 99, 0, 99, 0, 99, 99, 99, 113, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 0, 99, 99, 99, 131, 99, 99, 99, 99, 99, 0, 99, 0, 99, 99, 99, 99, 99, 99, 99, 99, 99, 149, 99, 0, 99, 99, 99, 99, 99, 0, 99, 99, 99, 99, 99, 0, 99, 99, 99, 167, 99, 99, 99, 99, 99, 0, 99, 99, 99, 99, 99, 0, 99, 0, 99, 99, 99, 99, 99, 99, 99, 99, 99, 0, 99, 0, 99, 99, 99, 0, 99, 0, 99] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:51:11 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,9) == Mod(1,4),n,0),0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:51:25 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,4) == Mod(1,4),n,0),0)) Output: ? [0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 109, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 173, 0, 0, 0, 0, 0, 0, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 20:08:57 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,4) == Mod(3,4),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 7, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 67, 0, 0, 0, 71, 0, 0, 0, 0, 0, 0, 0, 79, 0, 0, 0, 83, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 103, 0, 0, 0, 107, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127, 0, 0, 0, 131, 0, 0, 0, 0, 0, 0, 0, 139, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 163, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 179, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 0, 0, 0, 0, 0, 0, 199, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 20:15:23 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,8) == Mod(1,8),n,0),0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 20:24:04 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,8) == Mod(3,8),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 67, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 107, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0, 0, 0, 0, 0, 0, 139, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 163, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 179, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 20:30:39 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,8) == Mod(5,8),n,0),0)) Output: ? [0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 109, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 173, 0, 0, 0, 0, 0, 0, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 20:33:46 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,8) == Mod(7,8),n,0),0)) Output: ? [0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71, 0, 0, 0, 0, 0, 0, 0, 79, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 103, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 0, 0, 0, 0, 0, 0, 199, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 20:49:15 2004 Input: issquare(4) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 20:55:46 2004 Input: vector(200,n,if (isprime(n)== 1, if(issquare(Mod(-1,n) == 1,n,0),0)) Output: ? ? Errors (if any) and Timing Info: *** expected character: '&' instead of: ...if(issquare(Mod(-1,n)==1, *** n,0),0)) ^-------- Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 20:56:01 2004 Input: vector(200,n,if (isprime(n)== 1, if(issquare(Mod(-1,n)) == 1,n,0),0)) Output: ? [0, 2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 109, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 173, 0, 0, 0, 0, 0, 0, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 21:07:47 2004 Input: vector(200,n,if (isprime(n)== 1, if(issquare(Mod(2,n)) == 1,n,0),0)) Output: ? [0, 2, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 79, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 103, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 193, 0, 0, 0, 0, 0, 199, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 21:08:03 2004 Input: vector(200,n,if (isprime(n)== 1, if(issquare(Mod(-2,n)) == 1,n,0),0)) Output: ? [0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 17, 0, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 67, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 0, 0, 0, 0, 107, 0, 0, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0, 0, 0, 0, 137, 0, 139, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 163, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 179, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 21:14:06 2004 Input: vector(200,n,if (isprime(n)== 1, if(issquare(Mod(3,n)) == 1,n,0),0)) Output: ? [0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 11, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 0, 0, 0, 0, 107, 0, 109, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 179, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 193, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '69.199.' ************** PARI ***************** Host 69.199.8.11 (69.199.8.11) Time: Tue Sep 21 23:43:27 2004 Input: test Output: ? test ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '130.113' ************** PARI ***************** Host 130.113.128.11 (130.113.128.11) Time: Wed Sep 22 11:32:27 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '198.24.' ************** PARI ***************** Host 198.24.6.134 (198.24.6.134) Time: Wed Sep 22 17:26:56 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:40:16 2004 Input: 43137-2*21063 Output: ? 1011 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:40:22 2004 Input: 2*21063 Output: ? 42126 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:41:11 2004 Input: 21063/1011 Output: ? 7021/337 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:41:21 2004 Input: 21063/1011*1.0 Output: ? 20.833827893175074183976261127596439169 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:41:39 2004 Input: 1011*20 Output: ? 20220 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:41:50 2004 Input: 21063-1011*20 Output: ? 843 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:42:20 2004 Input: 1011-843 Output: ? 168 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:43:02 2004 Input: 168+5*3 Output: ? 183 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:43:12 2004 Input: 168*5+3 Output: ? 843 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:43:44 2004 Input: 163 / 3 Output: ? 163/3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:43:52 2004 Input: 163 / 3 *1.60 Output: ? 86.933333333333333333333333333333333333 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:43:57 2004 Input: 163 / 3 *1.0 Output: ? 54.333333333333333333333333333333333333 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:44:31 2004 Input: 163 - 3 *54 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:45:24 2004 Input: 43137 - 21063*2 - 1011 Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:45:39 2004 Input: 21063*2 - 1011*20 + 843 Output: ? 22749 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:45:47 2004 Input: 21063 - 1011*20 - 843 Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:46:02 2004 Input: 1011 - 843 -168 Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:46:13 2004 Input: 843 -168*5-3 Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.001s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:46:26 2004 Input: 168-3*54 Output: ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:46:54 2004 Input: 163/3 Output: ? 163/3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:47:05 2004 Input: 163/3*1.0 Output: ? 54.333333333333333333333333333333333333 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:47:16 2004 Input: 163-3*54 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:57:16 2004 Input: 843 - 168 * 5 Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:57:35 2004 Input: 168/3 Output: ? 56 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 18:07:46 2004 Input: 21063 * 256 - 43137 *256 Output: ? -5650944 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 18:07:55 2004 Input: 21063 * 256 - 43137 *125 Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 18:10:51 2004 Input: 6*256 Output: ? 1536 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 18:11:20 2004 Input: 6*125 Output: ? 750 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 18:25:11 2004 Input: gcd(x^2,x) Output: ? x ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 18:26:05 2004 Input: gcd(x^4+x, x^3+x+1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 18:52:26 2004 Input: x^4+x+ x^3+x+1 Output: ? x^4 + x^3 + 2*x + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 18:53:23 2004 Input: (x^4+x)(x)+ (x^3+x+1)(-x^2-x+1) Output: ? x^4 + x ? Errors (if any) and Timing Info: *** Warning: unused characters: (x)+(x^3+x+1)(-x^2-x+1). Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:04:29 2004 Input: vector(49,n,isprime(4*n+1)*(4*n+1)) Output: ? [5, 0, 13, 17, 0, 0, 29, 0, 37, 41, 0, 0, 53, 0, 61, 0, 0, 73, 0, 0, 0, 89, 0, 97, 101, 0, 109, 113, 0, 0, 0, 0, 0, 137, 0, 0, 149, 0, 157, 0, 0, 0, 173, 0, 181, 0, 0, 193, 197] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:06:09 2004 Input: vector(49,n,isprime(4*n+3)*(4*n+3)) Output: ? [7, 11, 0, 19, 23, 0, 31, 0, 0, 43, 47, 0, 0, 59, 0, 67, 71, 0, 79, 83, 0, 0, 0, 0, 103, 107, 0, 0, 0, 0, 127, 131, 0, 139, 0, 0, 151, 0, 0, 163, 167, 0, 0, 179, 0, 0, 191, 0, 199] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:07:46 2004 Input: vector(49,n,isprime(8*n+1)*(8*n+1)) Output: ? [0, 17, 0, 0, 41, 0, 0, 0, 73, 0, 89, 97, 0, 113, 0, 0, 137, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 0, 233, 241, 0, 257, 0, 0, 281, 0, 0, 0, 313, 0, 0, 337, 0, 353, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:07:58 2004 Input: vector(25,n,isprime(8*n+1)*(8*n+1)) Output: ? [0, 17, 0, 0, 41, 0, 0, 0, 73, 0, 89, 97, 0, 113, 0, 0, 137, 0, 0, 0, 0, 0, 0, 193, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:08:11 2004 Input: vector(24,n,isprime(8*n+1)*(8*n+1)) Output: ? [0, 17, 0, 0, 41, 0, 0, 0, 73, 0, 89, 97, 0, 113, 0, 0, 137, 0, 0, 0, 0, 0, 0, 193] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:11:17 2004 Input: vector(24,n,isprime(8*n+3)*(8*n+3)) Output: ? [11, 19, 0, 0, 43, 0, 59, 67, 0, 83, 0, 0, 107, 0, 0, 131, 139, 0, 0, 163, 0, 179, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:11:49 2004 Input: vector(24,n,isprime(8*n+5)*(8*n+5)) Output: ? [13, 0, 29, 37, 0, 53, 61, 0, 0, 0, 0, 101, 109, 0, 0, 0, 0, 149, 157, 0, 173, 181, 0, 197] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:12:55 2004 Input: vector(24,n,isprime(8*n+7)*(8*n+7)) Output: ? [0, 23, 31, 0, 47, 0, 0, 71, 79, 0, 0, 103, 0, 0, 127, 0, 0, 151, 0, 167, 0, 0, 191, 199] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:13:06 2004 Input: vector(24,n,isprime(8*n+5)*(8*n+5)) Output: ? [13, 0, 29, 37, 0, 53, 61, 0, 0, 0, 0, 101, 109, 0, 0, 0, 0, 149, 157, 0, 173, 181, 0, 197] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:13:53 2004 Input: vector(24,n,isprime(8*n+7)*(8*n+7)) Output: ? [0, 23, 31, 0, 47, 0, 0, 71, 79, 0, 0, 103, 0, 0, 127, 0, 0, 151, 0, 167, 0, 0, 191, 199] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:19:35 2004 Input: vector(200,p,isprime(p)*lift(Mod(-1,p))) Output: ? [0, 1, 2, 0, 4, 0, 6, 0, 0, 0, 10, 0, 12, 0, 0, 0, 16, 0, 18, 0, 0, 0, 22, 0, 0, 0, 0, 0, 28, 0, 30, 0, 0, 0, 0, 0, 36, 0, 0, 0, 40, 0, 42, 0, 0, 0, 46, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 58, 0, 60, 0, 0, 0, 0, 0, 66, 0, 0, 0, 70, 0, 72, 0, 0, 0, 0, 0, 78, 0, 0, 0, 82, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 100, 0, 102, 0, 0, 0, 106, 0, 108, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 126, 0, 0, 0, 130, 0, 0, 0, 0, 0, 136, 0, 138, 0, 0, 0, 0, 0, 0, 0, 0, 0, 148, 0, 150, 0, 0, 0, 0, 0, 156, 0, 0, 0, 0, 0, 162, 0, 0, 0, 166, 0, 0, 0, 0, 0, 172, 0, 0, 0, 0, 0, 178, 0, 180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 190, 0, 192, 0, 0, 0, 196, 0, 198, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:20:13 2004 Input: vector(200,p,isprime(p)*p) Output: ? [0, 2, 3, 0, 5, 0, 7, 0, 0, 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 0, 0, 23, 0, 0, 0, 0, 0, 29, 0, 31, 0, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 43, 0, 0, 0, 47, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 59, 0, 61, 0, 0, 0, 0, 0, 67, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 79, 0, 0, 0, 83, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 101, 0, 103, 0, 0, 0, 107, 0, 109, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127, 0, 0, 0, 131, 0, 0, 0, 0, 0, 137, 0, 139, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 151, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 163, 0, 0, 0, 167, 0, 0, 0, 0, 0, 173, 0, 0, 0, 0, 0, 179, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 193, 0, 0, 0, 197, 0, 199, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:21:47 2004 Input: vector(200,p,isprime(p)*issquare(p)*p) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:21:58 2004 Input: Mod(-1,5) Output: ? Mod(4, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:22:08 2004 Input: lift(Mod(-1,5)) Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:22:34 2004 Input: vector(200,n,issquare(lift(Mod(-1,n)))*lift(Mod(-1,))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...t(Mod(-1,n)))*lift(Mod(-1,))) ^---- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:22:41 2004 Input: vector(200,n,issquare(lift(Mod(-1,n)))*lift(Mod(-1,n))) Output: ? [0, 1, 0, 0, 4, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 121, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 169, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:23:46 2004 Input: vector(200,n,issquare(lift(Mod(-1,n)))*n) Output: ? [1, 2, 0, 0, 5, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 145, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 170, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:24:00 2004 Input: vector(200,n,isprime(n)*issquare(lift(Mod(-1,n)))*n) Output: ? [0, 2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:25:58 2004 Input: vector(200,n,isprime(n)*issquare(lift(Mod(2,n)))*n) Output: ? [0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:26:24 2004 Input: vector(200,n,isprime(n)*issquare(lift(Mod(-2,n)))*n) Output: ? [0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:28:26 2004 Input: vector(200,n,isprime(n)*issquare(lift(Mod(3,n)))*n) Output: ? [0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:32:41 2004 Input: vector(200,n,isprime(n)*issquare(lift(Mod(3,n)))*n) Output: ? [0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:33:44 2004 Input: Mod(19,3) Output: ? Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:33:53 2004 Input: lift(Mod(19,3)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:34:03 2004 Input: lift(Mod(3,19)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.002s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:34:09 2004 Input: lift(Mod(3,17)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.001s sys 0m0.009s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:34:16 2004 Input: lift(Mod(3,13)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:37:25 2004 Input: lift(Mod(-1,5)) Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:37:48 2004 Input: lift(Mod(3,5)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:38:13 2004 Input: vector(200,p,lift(Mod(3,p)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...ctor(200,p,lift(Mod(3,p)) ^ Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:38:21 2004 Input: vector(200,p,lift(Mod(3,p))) Output: ? [0, 1, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:38:43 2004 Input: vector(200,p,lift(Mod(-1,p))) Output: ? [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.008s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:38:53 2004 Input: vector(200,p,lift(Mod(-2,p))) Output: ? [0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:39:03 2004 Input: vector(200,p,lift(Mod(-3,p))) Output: ? [0, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:39:10 2004 Input: vector(200,p,lift(Mod(3,p))) Output: ? [0, 1, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:50:17 2004 Input: 16-3 Output: ? 13 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:50:28 2004 Input: Mod(16,3) Output: ? Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:50:41 2004 Input: Mod(3,16) Output: ? Mod(3, 16) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:53:19 2004 Input: output(1) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: output(1) ^--------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:53:25 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:55:30 2004 Input: a=1 p=3 lift(Mod(10^a,p)) Output: ? 1 ? 3 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:06:48 2004 Input: lift(Mod(10^1,3)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:07:37 2004 Input: lift(Mod(10^1,7)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:07:41 2004 Input: lift(Mod(10^2,7)) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:07:46 2004 Input: lift(Mod(10^3,7)) Output: ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:07:50 2004 Input: lift(Mod(10^4,7)) Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:07:53 2004 Input: lift(Mod(10^5,7)) Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:07:56 2004 Input: lift(Mod(10^6,7)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:08:05 2004 Input: lift(Mod(10^1,7)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:08:09 2004 Input: lift(Mod(10^2,7)) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:08:15 2004 Input: lift(Mod(10^1,11)) Output: ? 10 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:08:19 2004 Input: lift(Mod(10^2,11)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:10:19 2004 Input: for(x=1,100) lift(Mod(10^x,11)) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: for(x=1,100) ^- *** forbidden division t_SER % t_INT. Timing: real 0m0.019s user 0m0.004s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:10:29 2004 Input: for(x=1,100), lift(Mod(10^x,11)) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: for(x=1,100), ^-- *** forbidden division t_SER % t_INT. Timing: real 0m0.017s user 0m0.004s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:10:40 2004 Input: for(x=1,100,1) lift(Mod(10^x,11)) Output: ? ? ? Errors (if any) and Timing Info: *** forbidden division t_SER % t_INT. Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:10:50 2004 Input: for(x=1,100,1) lift(Mod(10^x,11)) end Output: ? ? ? end ? Errors (if any) and Timing Info: *** forbidden division t_SER % t_INT. Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:11:00 2004 Input: for(x=1,100,1) lift(Mod(10^x,11)) Output: ? ? ? Errors (if any) and Timing Info: *** forbidden division t_SER % t_INT. Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:11:09 2004 Input: for(x=1,100,1) 10^x Output: ? ? 1 + 2.3025850929940456840179914546843642076*x + 2.6509490552391990052808331942970088458*x^2 + 2.0346785922934761968309911917138105302*x^3 + 1.1712551489122669631782576160326523407*x^4 + 0.53938292919558141019969155571017253478*x^5 + 0.20699584869686809669966601589738494188*x^6 + 0.068089365074437062365404040265376061225*x^7 + 0.019597694626478523696827890871476903106*x^8 + 0.0050139288337754400980709098716421545357*x^9 + 0.0011544997789984348762744932557410281187*x^10 + 0.00024166672554424694181414834840877523750*x^11 + 0.000046371516642572196673822381767030756722*x^12 + 0.0000082134125354393875826732889780792315594*x^13 + 0.0000013508629476223687713847303012234340105*x^14 + 0.00000020736512572488417743337826110640379206*x^15 + 0.000000029842240456309650539215555966289087226*x^16 + O(x^17) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:11:19 2004 Input: for(x=1,100,1) x Output: ? ? x ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:11:26 2004 Input: for(x=1,100,1) x^10 Output: ? ? x^10 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:11:45 2004 Input: for(x=1,100,x^10) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:11:52 2004 Input: for(x=1,100,x) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:12:55 2004 Input: for(x=1,100,print(x)) Output: ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:13:16 2004 Input: for(x=1,100,print(lift(Mod(10^x,11)))) Output: ? 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:13:29 2004 Input: for(x=1,100,print(lift(Mod(10^x,7)))) Output: ? 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:13:38 2004 Input: for(x=1,100,print(xlift(Mod(10^x,7)))) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: print(xlift( *** Mod(10^x,7)))) ^-------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:14:09 2004 Input: for(x=1,100,print(x,lift(Mod(10^x,7))))) Output: ? 13 22 36 44 55 61 73 82 96 104 115 121 133 142 156 164 175 181 193 202 216 224 235 241 253 262 276 284 295 301 313 322 336 344 355 361 373 382 396 404 415 421 433 442 456 464 475 481 493 502 516 524 535 541 553 562 576 584 595 601 613 622 636 644 655 661 673 682 696 704 715 721 733 742 756 764 775 781 793 802 816 824 835 841 853 862 876 884 895 901 913 922 936 944 955 961 973 982 996 1004 ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:14:20 2004 Input: for(x=1,100,print(lift(Mod(10^x,7)))) Output: ? 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:14:22 2004 Input: for(x=1,100,print(lift(Mod(10^x,7))) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...,print(lift(Mod(10^x,7))) ^ Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:14:27 2004 Input: for(x=1,100,print(lift(Mod(10^x,7)))) Output: ? 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:14:31 2004 Input: for(x=1,100,print(x,lift(Mod(10^x,7)))) Output: ? 13 22 36 44 55 61 73 82 96 104 115 121 133 142 156 164 175 181 193 202 216 224 235 241 253 262 276 284 295 301 313 322 336 344 355 361 373 382 396 404 415 421 433 442 456 464 475 481 493 502 516 524 535 541 553 562 576 584 595 601 613 622 636 644 655 661 673 682 696 704 715 721 733 742 756 764 775 781 793 802 816 824 835 841 853 862 876 884 895 901 913 922 936 944 955 961 973 982 996 1004 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:14:43 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,7)))) Output: ? 1: 3 2: 2 3: 6 4: 4 5: 5 6: 1 7: 3 8: 2 9: 6 10: 4 11: 5 12: 1 13: 3 14: 2 15: 6 16: 4 17: 5 18: 1 19: 3 20: 2 21: 6 22: 4 23: 5 24: 1 25: 3 26: 2 27: 6 28: 4 29: 5 30: 1 31: 3 32: 2 33: 6 34: 4 35: 5 36: 1 37: 3 38: 2 39: 6 40: 4 41: 5 42: 1 43: 3 44: 2 45: 6 46: 4 47: 5 48: 1 49: 3 50: 2 51: 6 52: 4 53: 5 54: 1 55: 3 56: 2 57: 6 58: 4 59: 5 60: 1 61: 3 62: 2 63: 6 64: 4 65: 5 66: 1 67: 3 68: 2 69: 6 70: 4 71: 5 72: 1 73: 3 74: 2 75: 6 76: 4 77: 5 78: 1 79: 3 80: 2 81: 6 82: 4 83: 5 84: 1 85: 3 86: 2 87: 6 88: 4 89: 5 90: 1 91: 3 92: 2 93: 6 94: 4 95: 5 96: 1 97: 3 98: 2 99: 6 100: 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:14:48 2004 Input: for(x=1,100,print1(x,": ",lift(Mod(10^x,7)))) Output: ? 1: 32: 23: 64: 45: 56: 17: 38: 29: 610: 411: 512: 113: 314: 215: 616: 417: 518: 119: 320: 221: 622: 423: 524: 125: 326: 227: 628: 429: 530: 131: 332: 233: 634: 435: 536: 137: 338: 239: 640: 441: 542: 143: 344: 245: 646: 447: 548: 149: 350: 251: 652: 453: 554: 155: 356: 257: 658: 459: 560: 161: 362: 263: 664: 465: 566: 167: 368: 269: 670: 471: 572: 173: 374: 275: 676: 477: 578: 179: 380: 281: 682: 483: 584: 185: 386: 287: 688: 489: 590: 191: 392: 293: 694: 495: 596: 197: 398: 299: 6100: 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:14:56 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,7)))) Output: ? 1: 3 2: 2 3: 6 4: 4 5: 5 6: 1 7: 3 8: 2 9: 6 10: 4 11: 5 12: 1 13: 3 14: 2 15: 6 16: 4 17: 5 18: 1 19: 3 20: 2 21: 6 22: 4 23: 5 24: 1 25: 3 26: 2 27: 6 28: 4 29: 5 30: 1 31: 3 32: 2 33: 6 34: 4 35: 5 36: 1 37: 3 38: 2 39: 6 40: 4 41: 5 42: 1 43: 3 44: 2 45: 6 46: 4 47: 5 48: 1 49: 3 50: 2 51: 6 52: 4 53: 5 54: 1 55: 3 56: 2 57: 6 58: 4 59: 5 60: 1 61: 3 62: 2 63: 6 64: 4 65: 5 66: 1 67: 3 68: 2 69: 6 70: 4 71: 5 72: 1 73: 3 74: 2 75: 6 76: 4 77: 5 78: 1 79: 3 80: 2 81: 6 82: 4 83: 5 84: 1 85: 3 86: 2 87: 6 88: 4 89: 5 90: 1 91: 3 92: 2 93: 6 94: 4 95: 5 96: 1 97: 3 98: 2 99: 6 100: 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:15:10 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,13)))) Output: ? 1: 10 2: 9 3: 12 4: 3 5: 4 6: 1 7: 10 8: 9 9: 12 10: 3 11: 4 12: 1 13: 10 14: 9 15: 12 16: 3 17: 4 18: 1 19: 10 20: 9 21: 12 22: 3 23: 4 24: 1 25: 10 26: 9 27: 12 28: 3 29: 4 30: 1 31: 10 32: 9 33: 12 34: 3 35: 4 36: 1 37: 10 38: 9 39: 12 40: 3 41: 4 42: 1 43: 10 44: 9 45: 12 46: 3 47: 4 48: 1 49: 10 50: 9 51: 12 52: 3 53: 4 54: 1 55: 10 56: 9 57: 12 58: 3 59: 4 60: 1 61: 10 62: 9 63: 12 64: 3 65: 4 66: 1 67: 10 68: 9 69: 12 70: 3 71: 4 72: 1 73: 10 74: 9 75: 12 76: 3 77: 4 78: 1 79: 10 80: 9 81: 12 82: 3 83: 4 84: 1 85: 10 86: 9 87: 12 88: 3 89: 4 90: 1 91: 10 92: 9 93: 12 94: 3 95: 4 96: 1 97: 10 98: 9 99: 12 100: 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:16:04 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,17)))) Output: ? 1: 10 2: 15 3: 14 4: 4 5: 6 6: 9 7: 5 8: 16 9: 7 10: 2 11: 3 12: 13 13: 11 14: 8 15: 12 16: 1 17: 10 18: 15 19: 14 20: 4 21: 6 22: 9 23: 5 24: 16 25: 7 26: 2 27: 3 28: 13 29: 11 30: 8 31: 12 32: 1 33: 10 34: 15 35: 14 36: 4 37: 6 38: 9 39: 5 40: 16 41: 7 42: 2 43: 3 44: 13 45: 11 46: 8 47: 12 48: 1 49: 10 50: 15 51: 14 52: 4 53: 6 54: 9 55: 5 56: 16 57: 7 58: 2 59: 3 60: 13 61: 11 62: 8 63: 12 64: 1 65: 10 66: 15 67: 14 68: 4 69: 6 70: 9 71: 5 72: 16 73: 7 74: 2 75: 3 76: 13 77: 11 78: 8 79: 12 80: 1 81: 10 82: 15 83: 14 84: 4 85: 6 86: 9 87: 5 88: 16 89: 7 90: 2 91: 3 92: 13 93: 11 94: 8 95: 12 96: 1 97: 10 98: 15 99: 14 100: 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:16:36 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,19)))) Output: ? 1: 10 2: 5 3: 12 4: 6 5: 3 6: 11 7: 15 8: 17 9: 18 10: 9 11: 14 12: 7 13: 13 14: 16 15: 8 16: 4 17: 2 18: 1 19: 10 20: 5 21: 12 22: 6 23: 3 24: 11 25: 15 26: 17 27: 18 28: 9 29: 14 30: 7 31: 13 32: 16 33: 8 34: 4 35: 2 36: 1 37: 10 38: 5 39: 12 40: 6 41: 3 42: 11 43: 15 44: 17 45: 18 46: 9 47: 14 48: 7 49: 13 50: 16 51: 8 52: 4 53: 2 54: 1 55: 10 56: 5 57: 12 58: 6 59: 3 60: 11 61: 15 62: 17 63: 18 64: 9 65: 14 66: 7 67: 13 68: 16 69: 8 70: 4 71: 2 72: 1 73: 10 74: 5 75: 12 76: 6 77: 3 78: 11 79: 15 80: 17 81: 18 82: 9 83: 14 84: 7 85: 13 86: 16 87: 8 88: 4 89: 2 90: 1 91: 10 92: 5 93: 12 94: 6 95: 3 96: 11 97: 15 98: 17 99: 18 100: 9 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:16:46 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,23)))) Output: ? 1: 10 2: 8 3: 11 4: 18 5: 19 6: 6 7: 14 8: 2 9: 20 10: 16 11: 22 12: 13 13: 15 14: 12 15: 5 16: 4 17: 17 18: 9 19: 21 20: 3 21: 7 22: 1 23: 10 24: 8 25: 11 26: 18 27: 19 28: 6 29: 14 30: 2 31: 20 32: 16 33: 22 34: 13 35: 15 36: 12 37: 5 38: 4 39: 17 40: 9 41: 21 42: 3 43: 7 44: 1 45: 10 46: 8 47: 11 48: 18 49: 19 50: 6 51: 14 52: 2 53: 20 54: 16 55: 22 56: 13 57: 15 58: 12 59: 5 60: 4 61: 17 62: 9 63: 21 64: 3 65: 7 66: 1 67: 10 68: 8 69: 11 70: 18 71: 19 72: 6 73: 14 74: 2 75: 20 76: 16 77: 22 78: 13 79: 15 80: 12 81: 5 82: 4 83: 17 84: 9 85: 21 86: 3 87: 7 88: 1 89: 10 90: 8 91: 11 92: 18 93: 19 94: 6 95: 14 96: 2 97: 20 98: 16 99: 22 100: 13 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:17:06 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,29)))) Output: ? 1: 10 2: 13 3: 14 4: 24 5: 8 6: 22 7: 17 8: 25 9: 18 10: 6 11: 2 12: 20 13: 26 14: 28 15: 19 16: 16 17: 15 18: 5 19: 21 20: 7 21: 12 22: 4 23: 11 24: 23 25: 27 26: 9 27: 3 28: 1 29: 10 30: 13 31: 14 32: 24 33: 8 34: 22 35: 17 36: 25 37: 18 38: 6 39: 2 40: 20 41: 26 42: 28 43: 19 44: 16 45: 15 46: 5 47: 21 48: 7 49: 12 50: 4 51: 11 52: 23 53: 27 54: 9 55: 3 56: 1 57: 10 58: 13 59: 14 60: 24 61: 8 62: 22 63: 17 64: 25 65: 18 66: 6 67: 2 68: 20 69: 26 70: 28 71: 19 72: 16 73: 15 74: 5 75: 21 76: 7 77: 12 78: 4 79: 11 80: 23 81: 27 82: 9 83: 3 84: 1 85: 10 86: 13 87: 14 88: 24 89: 8 90: 22 91: 17 92: 25 93: 18 94: 6 95: 2 96: 20 97: 26 98: 28 99: 19 100: 16 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:17:20 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,31)))) Output: ? 1: 10 2: 7 3: 8 4: 18 5: 25 6: 2 7: 20 8: 14 9: 16 10: 5 11: 19 12: 4 13: 9 14: 28 15: 1 16: 10 17: 7 18: 8 19: 18 20: 25 21: 2 22: 20 23: 14 24: 16 25: 5 26: 19 27: 4 28: 9 29: 28 30: 1 31: 10 32: 7 33: 8 34: 18 35: 25 36: 2 37: 20 38: 14 39: 16 40: 5 41: 19 42: 4 43: 9 44: 28 45: 1 46: 10 47: 7 48: 8 49: 18 50: 25 51: 2 52: 20 53: 14 54: 16 55: 5 56: 19 57: 4 58: 9 59: 28 60: 1 61: 10 62: 7 63: 8 64: 18 65: 25 66: 2 67: 20 68: 14 69: 16 70: 5 71: 19 72: 4 73: 9 74: 28 75: 1 76: 10 77: 7 78: 8 79: 18 80: 25 81: 2 82: 20 83: 14 84: 16 85: 5 86: 19 87: 4 88: 9 89: 28 90: 1 91: 10 92: 7 93: 8 94: 18 95: 25 96: 2 97: 20 98: 14 99: 16 100: 5 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:26:04 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,37)))) Output: ? 1: 10 2: 26 3: 1 4: 10 5: 26 6: 1 7: 10 8: 26 9: 1 10: 10 11: 26 12: 1 13: 10 14: 26 15: 1 16: 10 17: 26 18: 1 19: 10 20: 26 21: 1 22: 10 23: 26 24: 1 25: 10 26: 26 27: 1 28: 10 29: 26 30: 1 31: 10 32: 26 33: 1 34: 10 35: 26 36: 1 37: 10 38: 26 39: 1 40: 10 41: 26 42: 1 43: 10 44: 26 45: 1 46: 10 47: 26 48: 1 49: 10 50: 26 51: 1 52: 10 53: 26 54: 1 55: 10 56: 26 57: 1 58: 10 59: 26 60: 1 61: 10 62: 26 63: 1 64: 10 65: 26 66: 1 67: 10 68: 26 69: 1 70: 10 71: 26 72: 1 73: 10 74: 26 75: 1 76: 10 77: 26 78: 1 79: 10 80: 26 81: 1 82: 10 83: 26 84: 1 85: 10 86: 26 87: 1 88: 10 89: 26 90: 1 91: 10 92: 26 93: 1 94: 10 95: 26 96: 1 97: 10 98: 26 99: 1 100: 10 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:26:14 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,41)))) Output: ? 1: 10 2: 18 3: 16 4: 37 5: 1 6: 10 7: 18 8: 16 9: 37 10: 1 11: 10 12: 18 13: 16 14: 37 15: 1 16: 10 17: 18 18: 16 19: 37 20: 1 21: 10 22: 18 23: 16 24: 37 25: 1 26: 10 27: 18 28: 16 29: 37 30: 1 31: 10 32: 18 33: 16 34: 37 35: 1 36: 10 37: 18 38: 16 39: 37 40: 1 41: 10 42: 18 43: 16 44: 37 45: 1 46: 10 47: 18 48: 16 49: 37 50: 1 51: 10 52: 18 53: 16 54: 37 55: 1 56: 10 57: 18 58: 16 59: 37 60: 1 61: 10 62: 18 63: 16 64: 37 65: 1 66: 10 67: 18 68: 16 69: 37 70: 1 71: 10 72: 18 73: 16 74: 37 75: 1 76: 10 77: 18 78: 16 79: 37 80: 1 81: 10 82: 18 83: 16 84: 37 85: 1 86: 10 87: 18 88: 16 89: 37 90: 1 91: 10 92: 18 93: 16 94: 37 95: 1 96: 10 97: 18 98: 16 99: 37 100: 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:26:21 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,43)))) Output: ? 1: 10 2: 14 3: 11 4: 24 5: 25 6: 35 7: 6 8: 17 9: 41 10: 23 11: 15 12: 21 13: 38 14: 36 15: 16 16: 31 17: 9 18: 4 19: 40 20: 13 21: 1 22: 10 23: 14 24: 11 25: 24 26: 25 27: 35 28: 6 29: 17 30: 41 31: 23 32: 15 33: 21 34: 38 35: 36 36: 16 37: 31 38: 9 39: 4 40: 40 41: 13 42: 1 43: 10 44: 14 45: 11 46: 24 47: 25 48: 35 49: 6 50: 17 51: 41 52: 23 53: 15 54: 21 55: 38 56: 36 57: 16 58: 31 59: 9 60: 4 61: 40 62: 13 63: 1 64: 10 65: 14 66: 11 67: 24 68: 25 69: 35 70: 6 71: 17 72: 41 73: 23 74: 15 75: 21 76: 38 77: 36 78: 16 79: 31 80: 9 81: 4 82: 40 83: 13 84: 1 85: 10 86: 14 87: 11 88: 24 89: 25 90: 35 91: 6 92: 17 93: 41 94: 23 95: 15 96: 21 97: 38 98: 36 99: 16 100: 31 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:26:35 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,47)))) Output: ? 1: 10 2: 6 3: 13 4: 36 5: 31 6: 28 7: 45 8: 27 9: 35 10: 21 11: 22 12: 32 13: 38 14: 4 15: 40 16: 24 17: 5 18: 3 19: 30 20: 18 21: 39 22: 14 23: 46 24: 37 25: 41 26: 34 27: 11 28: 16 29: 19 30: 2 31: 20 32: 12 33: 26 34: 25 35: 15 36: 9 37: 43 38: 7 39: 23 40: 42 41: 44 42: 17 43: 29 44: 8 45: 33 46: 1 47: 10 48: 6 49: 13 50: 36 51: 31 52: 28 53: 45 54: 27 55: 35 56: 21 57: 22 58: 32 59: 38 60: 4 61: 40 62: 24 63: 5 64: 3 65: 30 66: 18 67: 39 68: 14 69: 46 70: 37 71: 41 72: 34 73: 11 74: 16 75: 19 76: 2 77: 20 78: 12 79: 26 80: 25 81: 15 82: 9 83: 43 84: 7 85: 23 86: 42 87: 44 88: 17 89: 29 90: 8 91: 33 92: 1 93: 10 94: 6 95: 13 96: 36 97: 31 98: 28 99: 45 100: 27 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:30:07 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,53)))) Output: ? 1: 10 2: 47 3: 46 4: 36 5: 42 6: 49 7: 13 8: 24 9: 28 10: 15 11: 44 12: 16 13: 1 14: 10 15: 47 16: 46 17: 36 18: 42 19: 49 20: 13 21: 24 22: 28 23: 15 24: 44 25: 16 26: 1 27: 10 28: 47 29: 46 30: 36 31: 42 32: 49 33: 13 34: 24 35: 28 36: 15 37: 44 38: 16 39: 1 40: 10 41: 47 42: 46 43: 36 44: 42 45: 49 46: 13 47: 24 48: 28 49: 15 50: 44 51: 16 52: 1 53: 10 54: 47 55: 46 56: 36 57: 42 58: 49 59: 13 60: 24 61: 28 62: 15 63: 44 64: 16 65: 1 66: 10 67: 47 68: 46 69: 36 70: 42 71: 49 72: 13 73: 24 74: 28 75: 15 76: 44 77: 16 78: 1 79: 10 80: 47 81: 46 82: 36 83: 42 84: 49 85: 13 86: 24 87: 28 88: 15 89: 44 90: 16 91: 1 92: 10 93: 47 94: 46 95: 36 96: 42 97: 49 98: 13 99: 24 100: 28 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:30:24 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,59)))) Output: ? 1: 10 2: 41 3: 56 4: 29 5: 54 6: 9 7: 31 8: 15 9: 32 10: 25 11: 14 12: 22 13: 43 14: 17 15: 52 16: 48 17: 8 18: 21 19: 33 20: 35 21: 55 22: 19 23: 13 24: 12 25: 2 26: 20 27: 23 28: 53 29: 58 30: 49 31: 18 32: 3 33: 30 34: 5 35: 50 36: 28 37: 44 38: 27 39: 34 40: 45 41: 37 42: 16 43: 42 44: 7 45: 11 46: 51 47: 38 48: 26 49: 24 50: 4 51: 40 52: 46 53: 47 54: 57 55: 39 56: 36 57: 6 58: 1 59: 10 60: 41 61: 56 62: 29 63: 54 64: 9 65: 31 66: 15 67: 32 68: 25 69: 14 70: 22 71: 43 72: 17 73: 52 74: 48 75: 8 76: 21 77: 33 78: 35 79: 55 80: 19 81: 13 82: 12 83: 2 84: 20 85: 23 86: 53 87: 58 88: 49 89: 18 90: 3 91: 30 92: 5 93: 50 94: 28 95: 44 96: 27 97: 34 98: 45 99: 37 100: 16 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:30:40 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,61)))) Output: ? 1: 10 2: 39 3: 24 4: 57 5: 21 6: 27 7: 26 8: 16 9: 38 10: 14 11: 18 12: 58 13: 31 14: 5 15: 50 16: 12 17: 59 18: 41 19: 44 20: 13 21: 8 22: 19 23: 7 24: 9 25: 29 26: 46 27: 33 28: 25 29: 6 30: 60 31: 51 32: 22 33: 37 34: 4 35: 40 36: 34 37: 35 38: 45 39: 23 40: 47 41: 43 42: 3 43: 30 44: 56 45: 11 46: 49 47: 2 48: 20 49: 17 50: 48 51: 53 52: 42 53: 54 54: 52 55: 32 56: 15 57: 28 58: 36 59: 55 60: 1 61: 10 62: 39 63: 24 64: 57 65: 21 66: 27 67: 26 68: 16 69: 38 70: 14 71: 18 72: 58 73: 31 74: 5 75: 50 76: 12 77: 59 78: 41 79: 44 80: 13 81: 8 82: 19 83: 7 84: 9 85: 29 86: 46 87: 33 88: 25 89: 6 90: 60 91: 51 92: 22 93: 37 94: 4 95: 40 96: 34 97: 35 98: 45 99: 23 100: 47 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:30:58 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,67)))) Output: ? 1: 10 2: 33 3: 62 4: 17 5: 36 6: 25 7: 49 8: 21 9: 9 10: 23 11: 29 12: 22 13: 19 14: 56 15: 24 16: 39 17: 55 18: 14 19: 6 20: 60 21: 64 22: 37 23: 35 24: 15 25: 16 26: 26 27: 59 28: 54 29: 4 30: 40 31: 65 32: 47 33: 1 34: 10 35: 33 36: 62 37: 17 38: 36 39: 25 40: 49 41: 21 42: 9 43: 23 44: 29 45: 22 46: 19 47: 56 48: 24 49: 39 50: 55 51: 14 52: 6 53: 60 54: 64 55: 37 56: 35 57: 15 58: 16 59: 26 60: 59 61: 54 62: 4 63: 40 64: 65 65: 47 66: 1 67: 10 68: 33 69: 62 70: 17 71: 36 72: 25 73: 49 74: 21 75: 9 76: 23 77: 29 78: 22 79: 19 80: 56 81: 24 82: 39 83: 55 84: 14 85: 6 86: 60 87: 64 88: 37 89: 35 90: 15 91: 16 92: 26 93: 59 94: 54 95: 4 96: 40 97: 65 98: 47 99: 1 100: 10 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:31:21 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,71)))) Output: ? 1: 10 2: 29 3: 6 4: 60 5: 32 6: 36 7: 5 8: 50 9: 3 10: 30 11: 16 12: 18 13: 38 14: 25 15: 37 16: 15 17: 8 18: 9 19: 19 20: 48 21: 54 22: 43 23: 4 24: 40 25: 45 26: 24 27: 27 28: 57 29: 2 30: 20 31: 58 32: 12 33: 49 34: 64 35: 1 36: 10 37: 29 38: 6 39: 60 40: 32 41: 36 42: 5 43: 50 44: 3 45: 30 46: 16 47: 18 48: 38 49: 25 50: 37 51: 15 52: 8 53: 9 54: 19 55: 48 56: 54 57: 43 58: 4 59: 40 60: 45 61: 24 62: 27 63: 57 64: 2 65: 20 66: 58 67: 12 68: 49 69: 64 70: 1 71: 10 72: 29 73: 6 74: 60 75: 32 76: 36 77: 5 78: 50 79: 3 80: 30 81: 16 82: 18 83: 38 84: 25 85: 37 86: 15 87: 8 88: 9 89: 19 90: 48 91: 54 92: 43 93: 4 94: 40 95: 45 96: 24 97: 27 98: 57 99: 2 100: 20 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:31:33 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,73)))) Output: ? 1: 10 2: 27 3: 51 4: 72 5: 63 6: 46 7: 22 8: 1 9: 10 10: 27 11: 51 12: 72 13: 63 14: 46 15: 22 16: 1 17: 10 18: 27 19: 51 20: 72 21: 63 22: 46 23: 22 24: 1 25: 10 26: 27 27: 51 28: 72 29: 63 30: 46 31: 22 32: 1 33: 10 34: 27 35: 51 36: 72 37: 63 38: 46 39: 22 40: 1 41: 10 42: 27 43: 51 44: 72 45: 63 46: 46 47: 22 48: 1 49: 10 50: 27 51: 51 52: 72 53: 63 54: 46 55: 22 56: 1 57: 10 58: 27 59: 51 60: 72 61: 63 62: 46 63: 22 64: 1 65: 10 66: 27 67: 51 68: 72 69: 63 70: 46 71: 22 72: 1 73: 10 74: 27 75: 51 76: 72 77: 63 78: 46 79: 22 80: 1 81: 10 82: 27 83: 51 84: 72 85: 63 86: 46 87: 22 88: 1 89: 10 90: 27 91: 51 92: 72 93: 63 94: 46 95: 22 96: 1 97: 10 98: 27 99: 51 100: 72 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:31:51 2004 Input: for(x=1,100,print1(x,": ",lift(Mod(10^x,73)," "))) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: ...x,": ",lift(Mod(10^x,73)," "))) ^----------- Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:32:27 2004 Input: for(x=1,100,print1(x,": ",lift(Mod(10^x,73))," ")) Output: ? 1: 10 2: 27 3: 51 4: 72 5: 63 6: 46 7: 22 8: 1 9: 10 10: 27 11: 51 12: 72 13: 63 14: 46 15: 22 16: 1 17: 10 18: 27 19: 51 20: 72 21: 63 22: 46 23: 22 24: 1 25: 10 26: 27 27: 51 28: 72 29: 63 30: 46 31: 22 32: 1 33: 10 34: 27 35: 51 36: 72 37: 63 38: 46 39: 22 40: 1 41: 10 42: 27 43: 51 44: 72 45: 63 46: 46 47: 22 48: 1 49: 10 50: 27 51: 51 52: 72 53: 63 54: 46 55: 22 56: 1 57: 10 58: 27 59: 51 60: 72 61: 63 62: 46 63: 22 64: 1 65: 10 66: 27 67: 51 68: 72 69: 63 70: 46 71: 22 72: 1 73: 10 74: 27 75: 51 76: 72 77: 63 78: 46 79: 22 80: 1 81: 10 82: 27 83: 51 84: 72 85: 63 86: 46 87: 22 88: 1 89: 10 90: 27 91: 51 92: 72 93: 63 94: 46 95: 22 96: 1 97: 10 98: 27 99: 51 100: 72 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:32:42 2004 Input: for(x=1,100,print1(x,": ",lift(Mod(10^x,79))," ")) Output: ? 1: 10 2: 21 3: 52 4: 46 5: 65 6: 18 7: 22 8: 62 9: 67 10: 38 11: 64 12: 8 13: 1 14: 10 15: 21 16: 52 17: 46 18: 65 19: 18 20: 22 21: 62 22: 67 23: 38 24: 64 25: 8 26: 1 27: 10 28: 21 29: 52 30: 46 31: 65 32: 18 33: 22 34: 62 35: 67 36: 38 37: 64 38: 8 39: 1 40: 10 41: 21 42: 52 43: 46 44: 65 45: 18 46: 22 47: 62 48: 67 49: 38 50: 64 51: 8 52: 1 53: 10 54: 21 55: 52 56: 46 57: 65 58: 18 59: 22 60: 62 61: 67 62: 38 63: 64 64: 8 65: 1 66: 10 67: 21 68: 52 69: 46 70: 65 71: 18 72: 22 73: 62 74: 67 75: 38 76: 64 77: 8 78: 1 79: 10 80: 21 81: 52 82: 46 83: 65 84: 18 85: 22 86: 62 87: 67 88: 38 89: 64 90: 8 91: 1 92: 10 93: 21 94: 52 95: 46 96: 65 97: 18 98: 22 99: 62 100: 67 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:33:15 2004 Input: for(x=1,100,print1(x,": ",lift(Mod(10^x,83))," ")) Output: ? 1: 10 2: 17 3: 4 4: 40 5: 68 6: 16 7: 77 8: 23 9: 64 10: 59 11: 9 12: 7 13: 70 14: 36 15: 28 16: 31 17: 61 18: 29 19: 41 20: 78 21: 33 22: 81 23: 63 24: 49 25: 75 26: 3 27: 30 28: 51 29: 12 30: 37 31: 38 32: 48 33: 65 34: 69 35: 26 36: 11 37: 27 38: 21 39: 44 40: 25 41: 1 42: 10 43: 17 44: 4 45: 40 46: 68 47: 16 48: 77 49: 23 50: 64 51: 59 52: 9 53: 7 54: 70 55: 36 56: 28 57: 31 58: 61 59: 29 60: 41 61: 78 62: 33 63: 81 64: 63 65: 49 66: 75 67: 3 68: 30 69: 51 70: 12 71: 37 72: 38 73: 48 74: 65 75: 69 76: 26 77: 11 78: 27 79: 21 80: 44 81: 25 82: 1 83: 10 84: 17 85: 4 86: 40 87: 68 88: 16 89: 77 90: 23 91: 64 92: 59 93: 9 94: 7 95: 70 96: 36 97: 28 98: 31 99: 61 100: 29 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:33:27 2004 Input: for(x=1,100,print1(x,": ",lift(Mod(10^x,89))," ")) Output: ? 1: 10 2: 11 3: 21 4: 32 5: 53 6: 85 7: 49 8: 45 9: 5 10: 50 11: 55 12: 16 13: 71 14: 87 15: 69 16: 67 17: 47 18: 25 19: 72 20: 8 21: 80 22: 88 23: 79 24: 78 25: 68 26: 57 27: 36 28: 4 29: 40 30: 44 31: 84 32: 39 33: 34 34: 73 35: 18 36: 2 37: 20 38: 22 39: 42 40: 64 41: 17 42: 81 43: 9 44: 1 45: 10 46: 11 47: 21 48: 32 49: 53 50: 85 51: 49 52: 45 53: 5 54: 50 55: 55 56: 16 57: 71 58: 87 59: 69 60: 67 61: 47 62: 25 63: 72 64: 8 65: 80 66: 88 67: 79 68: 78 69: 68 70: 57 71: 36 72: 4 73: 40 74: 44 75: 84 76: 39 77: 34 78: 73 79: 18 80: 2 81: 20 82: 22 83: 42 84: 64 85: 17 86: 81 87: 9 88: 1 89: 10 90: 11 91: 21 92: 32 93: 53 94: 85 95: 49 96: 45 97: 5 98: 50 99: 55 100: 16 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:33:41 2004 Input: for(x=1,100,print1(x,": ",lift(Mod(10^x,97))," ")) Output: ? 1: 10 2: 3 3: 30 4: 9 5: 90 6: 27 7: 76 8: 81 9: 34 10: 49 11: 5 12: 50 13: 15 14: 53 15: 45 16: 62 17: 38 18: 89 19: 17 20: 73 21: 51 22: 25 23: 56 24: 75 25: 71 26: 31 27: 19 28: 93 29: 57 30: 85 31: 74 32: 61 33: 28 34: 86 35: 84 36: 64 37: 58 38: 95 39: 77 40: 91 41: 37 42: 79 43: 14 44: 43 45: 42 46: 32 47: 29 48: 96 49: 87 50: 94 51: 67 52: 88 53: 7 54: 70 55: 21 56: 16 57: 63 58: 48 59: 92 60: 47 61: 82 62: 44 63: 52 64: 35 65: 59 66: 8 67: 80 68: 24 69: 46 70: 72 71: 41 72: 22 73: 26 74: 66 75: 78 76: 4 77: 40 78: 12 79: 23 80: 36 81: 69 82: 11 83: 13 84: 33 85: 39 86: 2 87: 20 88: 6 89: 60 90: 18 91: 83 92: 54 93: 55 94: 65 95: 68 96: 1 97: 10 98: 3 99: 30 100: 9 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:34:59 2004 Input: lift(Mod(3,1)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:35:07 2004 Input: lift(Mod(1,3)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:35:18 2004 Input: lift(Mod(1,7)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:35:27 2004 Input: lift(Mod(1,11)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:35:42 2004 Input: lift(Mod(11,2)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:35:50 2004 Input: lift(Mod(41,5)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:36:43 2004 Input: for(x=1,100,print1(x,": ",lift(Mod(10^x,73))," ")) Output: ? 1: 10 2: 27 3: 51 4: 72 5: 63 6: 46 7: 22 8: 1 9: 10 10: 27 11: 51 12: 72 13: 63 14: 46 15: 22 16: 1 17: 10 18: 27 19: 51 20: 72 21: 63 22: 46 23: 22 24: 1 25: 10 26: 27 27: 51 28: 72 29: 63 30: 46 31: 22 32: 1 33: 10 34: 27 35: 51 36: 72 37: 63 38: 46 39: 22 40: 1 41: 10 42: 27 43: 51 44: 72 45: 63 46: 46 47: 22 48: 1 49: 10 50: 27 51: 51 52: 72 53: 63 54: 46 55: 22 56: 1 57: 10 58: 27 59: 51 60: 72 61: 63 62: 46 63: 22 64: 1 65: 10 66: 27 67: 51 68: 72 69: 63 70: 46 71: 22 72: 1 73: 10 74: 27 75: 51 76: 72 77: 63 78: 46 79: 22 80: 1 81: 10 82: 27 83: 51 84: 72 85: 63 86: 46 87: 22 88: 1 89: 10 90: 27 91: 51 92: 72 93: 63 94: 46 95: 22 96: 1 97: 10 98: 27 99: 51 100: 72 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.008s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 21:19:50 2004 Input: (x^4+x)*(x)+ (x^3+x+1)*(-x^2-x+1) Output: ? -x^4 - x^2 + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 21:20:28 2004 Input: ((x^4+x)*(x))+ (((x^3+x+1)*(-x^2-x+1)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...)+(((x^3+x+1)*(-x^2-x+1)) ^ Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 21:20:40 2004 Input: ((x^4+x)*(x))+ ((x^3+x+1)*(-x^2-x+1)) Output: ? -x^4 - x^2 + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 21:22:40 2004 Input: bezout((x^3+x+1),(x^4+x)) Output: ? [x^3 - x^2 + 1, -x^2 + x - 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 21:40:26 2004 Input: (x^3+x+1)*(-x^2-x+1)+(x^4+x)(-x^2+x+1) Output: ? -x^5 - 2*x^2 + x + 1 ? Errors (if any) and Timing Info: *** Warning: unused characters: (-x^2+x+1). Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 21:40:53 2004 Input: bezout((x^3+x+1),(x^4+x)) Output: ? [x^3 - x^2 + 1, -x^2 + x - 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:35:48 2004 Input: primes(100) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:35:57 2004 Input: primes(30) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:36:06 2004 Input: primes(25) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:40:09 2004 Input: vector(100,n,if(isprime(n)==1,if(100,m,Mod(10^m,n)==1),0) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...(100,m,Mod(10^m,n)==1),0) ^ Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:40:29 2004 Input: vector(100,n,if(isprime(n)==1,if(100,m,Mod(10^m,n)==1),m),0) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...(100,m,Mod(10^m,n)==1),m),0) ^--- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:41:07 2004 Input: vector(100,n,if(isprime(n)==1,if(100,m,Mod(10^m,n)==1),m)),0) Output: ? [m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m] ? Errors (if any) and Timing Info: *** Warning: unused characters: ,0). Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:41:42 2004 Input: Mod(10,2) Output: ? Mod(0, 2) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '128.250' ************** PARI ***************** Host 128.250.87.84 (128.250.87.84) Time: Wed Sep 22 22:41:54 2004 Input: factor(37249588852282552285743302297396100822355179407163315972232664422849771058311) Output: ? [89954413 1] [5299151939 1] [5302144343 1] [5963856163 1] [4281936962959 1] [4710694442959 1] [122514848197837 1] ? Errors (if any) and Timing Info: Timing: real 0m0.850s user 0m0.818s sys 0m0.024s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:42:02 2004 Input: Mod(10,5) Output: ? Mod(0, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:42:07 2004 Input: Mod(10,3) Output: ? Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:42:40 2004 Input: vector(200,n,Mod(10,n)) Output: ? [Mod(0, 1), Mod(0, 2), Mod(1, 3), Mod(2, 4), Mod(0, 5), Mod(4, 6), Mod(3, 7), Mod(2, 8), Mod(1, 9), Mod(0, 10), Mod(10, 11), Mod(10, 12), Mod(10, 13), Mod(10, 14), Mod(10, 15), Mod(10, 16), Mod(10, 17), Mod(10, 18), Mod(10, 19), Mod(10, 20), Mod(10, 21), Mod(10, 22), Mod(10, 23), Mod(10, 24), Mod(10, 25), Mod(10, 26), Mod(10, 27), Mod(10, 28), Mod(10, 29), Mod(10, 30), Mod(10, 31), Mod(10, 32), Mod(10, 33), Mod(10, 34), Mod(10, 35), Mod(10, 36), Mod(10, 37), Mod(10, 38), Mod(10, 39), Mod(10, 40), Mod(10, 41), Mod(10, 42), Mod(10, 43), Mod(10, 44), Mod(10, 45), Mod(10, 46), Mod(10, 47), Mod(10, 48), Mod(10, 49), Mod(10, 50), Mod(10, 51), Mod(10, 52), Mod(10, 53), Mod(10, 54), Mod(10, 55), Mod(10, 56), Mod(10, 57), Mod(10, 58), Mod(10, 59), Mod(10, 60), Mod(10, 61), Mod(10, 62), Mod(10, 63), Mod(10, 64), Mod(10, 65), Mod(10, 66), Mod(10, 67), Mod(10, 68), Mod(10, 69), Mod(10, 70), Mod(10, 71), Mod(10, 72), Mod(10, 73), Mod(10, 74), Mod(10, 75), Mod(10, 76), Mod(10, 77), Mod(10, 78), Mod(10, 79), Mod(10, 80), Mod(10, 81), Mod(10, 82), Mod(10, 83), Mod(10, 84), Mod(10, 85), Mod(10, 86), Mod(10, 87), Mod(10, 88), Mod(10, 89), Mod(10, 90), Mod(10, 91), Mod(10, 92), Mod(10, 93), Mod(10, 94), Mod(10, 95), Mod(10, 96), Mod(10, 97), Mod(10, 98), Mod(10, 99), Mod(10, 100), Mod(10, 101), Mod(10, 102), Mod(10, 103), Mod(10, 104), Mod(10, 105), Mod(10, 106), Mod(10, 107), Mod(10, 108), Mod(10, 109), Mod(10, 110), Mod(10, 111), Mod(10, 112), Mod(10, 113), Mod(10, 114), Mod(10, 115), Mod(10, 116), Mod(10, 117), Mod(10, 118), Mod(10, 119), Mod(10, 120), Mod(10, 121), Mod(10, 122), Mod(10, 123), Mod(10, 124), Mod(10, 125), Mod(10, 126), Mod(10, 127), Mod(10, 128), Mod(10, 129), Mod(10, 130), Mod(10, 131), Mod(10, 132), Mod(10, 133), Mod(10, 134), Mod(10, 135), Mod(10, 136), Mod(10, 137), Mod(10, 138), Mod(10, 139), Mod(10, 140), Mod(10, 141), Mod(10, 142), Mod(10, 143), Mod(10, 144), Mod(10, 145), Mod(10, 146), Mod(10, 147), Mod(10, 148), Mod(10, 149), Mod(10, 150), Mod(10, 151), Mod(10, 152), Mod(10, 153), Mod(10, 154), Mod(10, 155), Mod(10, 156), Mod(10, 157), Mod(10, 158), Mod(10, 159), Mod(10, 160), Mod(10, 161), Mod(10, 162), Mod(10, 163), Mod(10, 164), Mod(10, 165), Mod(10, 166), Mod(10, 167), Mod(10, 168), Mod(10, 169), Mod(10, 170), Mod(10, 171), Mod(10, 172), Mod(10, 173), Mod(10, 174), Mod(10, 175), Mod(10, 176), Mod(10, 177), Mod(10, 178), Mod(10, 179), Mod(10, 180), Mod(10, 181), Mod(10, 182), Mod(10, 183), Mod(10, 184), Mod(10, 185), Mod(10, 186), Mod(10, 187), Mod(10, 188), Mod(10, 189), Mod(10, 190), Mod(10, 191), Mod(10, 192), Mod(10, 193), Mod(10, 194), Mod(10, 195), Mod(10, 196), Mod(10, 197), Mod(10, 198), Mod(10, 199), Mod(10, 200)] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:43:10 2004 Input: vector(200,n,if(isprime(n)==1, Mod(10,n)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...(isprime(n)==1,Mod(10,n)) ^ Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:43:19 2004 Input: vector(200,n,if(isprime(n)==1, Mod(10,n))) Output: ? [0, Mod(0, 2), Mod(1, 3), 0, Mod(0, 5), 0, Mod(3, 7), 0, 0, 0, Mod(10, 11), 0, Mod(10, 13), 0, 0, 0, Mod(10, 17), 0, Mod(10, 19), 0, 0, 0, Mod(10, 23), 0, 0, 0, 0, 0, Mod(10, 29), 0, Mod(10, 31), 0, 0, 0, 0, 0, Mod(10, 37), 0, 0, 0, Mod(10, 41), 0, Mod(10, 43), 0, 0, 0, Mod(10, 47), 0, 0, 0, 0, 0, Mod(10, 53), 0, 0, 0, 0, 0, Mod(10, 59), 0, Mod(10, 61), 0, 0, 0, 0, 0, Mod(10, 67), 0, 0, 0, Mod(10, 71), 0, Mod(10, 73), 0, 0, 0, 0, 0, Mod(10, 79), 0, 0, 0, Mod(10, 83), 0, 0, 0, 0, 0, Mod(10, 89), 0, 0, 0, 0, 0, 0, 0, Mod(10, 97), 0, 0, 0, Mod(10, 101), 0, Mod(10, 103), 0, 0, 0, Mod(10, 107), 0, Mod(10, 109), 0, 0, 0, Mod(10, 113), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, Mod(10, 127), 0, 0, 0, Mod(10, 131), 0, 0, 0, 0, 0, Mod(10, 137), 0, Mod(10, 139), 0, 0, 0, 0, 0, 0, 0, 0, 0, Mod(10, 149), 0, Mod(10, 151), 0, 0, 0, 0, 0, Mod(10, 157), 0, 0, 0, 0, 0, Mod(10, 163), 0, 0, 0, Mod(10, 167), 0, 0, 0, 0, 0, Mod(10, 173), 0, 0, 0, 0, 0, Mod(10, 179), 0, Mod(10, 181), 0, 0, 0, 0, 0, 0, 0, 0, 0, Mod(10, 191), 0, Mod(10, 193), 0, 0, 0, Mod(10, 197), 0, Mod(10, 199), 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:43:32 2004 Input: vector(200,n,if(isprime(n)==1, Mod(10,n)),2) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...(isprime(n)==1,Mod(10,n)),2) ^--- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:43:40 2004 Input: vector(200,n,if(isprime(n)==1, Mod(10,n),2)) Output: ? [2, Mod(0, 2), Mod(1, 3), 2, Mod(0, 5), 2, Mod(3, 7), 2, 2, 2, Mod(10, 11), 2, Mod(10, 13), 2, 2, 2, Mod(10, 17), 2, Mod(10, 19), 2, 2, 2, Mod(10, 23), 2, 2, 2, 2, 2, Mod(10, 29), 2, Mod(10, 31), 2, 2, 2, 2, 2, Mod(10, 37), 2, 2, 2, Mod(10, 41), 2, Mod(10, 43), 2, 2, 2, Mod(10, 47), 2, 2, 2, 2, 2, Mod(10, 53), 2, 2, 2, 2, 2, Mod(10, 59), 2, Mod(10, 61), 2, 2, 2, 2, 2, Mod(10, 67), 2, 2, 2, Mod(10, 71), 2, Mod(10, 73), 2, 2, 2, 2, 2, Mod(10, 79), 2, 2, 2, Mod(10, 83), 2, 2, 2, 2, 2, Mod(10, 89), 2, 2, 2, 2, 2, 2, 2, Mod(10, 97), 2, 2, 2, Mod(10, 101), 2, Mod(10, 103), 2, 2, 2, Mod(10, 107), 2, Mod(10, 109), 2, 2, 2, Mod(10, 113), 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, Mod(10, 127), 2, 2, 2, Mod(10, 131), 2, 2, 2, 2, 2, Mod(10, 137), 2, Mod(10, 139), 2, 2, 2, 2, 2, 2, 2, 2, 2, Mod(10, 149), 2, Mod(10, 151), 2, 2, 2, 2, 2, Mod(10, 157), 2, 2, 2, 2, 2, Mod(10, 163), 2, 2, 2, Mod(10, 167), 2, 2, 2, 2, 2, Mod(10, 173), 2, 2, 2, 2, 2, Mod(10, 179), 2, Mod(10, 181), 2, 2, 2, 2, 2, 2, 2, 2, 2, Mod(10, 191), 2, Mod(10, 193), 2, 2, 2, Mod(10, 197), 2, Mod(10, 199), 2] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:45:51 2004 Input: vector(200,n,if(isprime(n)==1,ifMod(n,9)==Mod(5,9), n,0),0)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...=1,ifMod(n,9)==Mod(5,9),n,0),0)) ^------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:46:11 2004 Input: vector(200,n,if(isprime(n)==1,ifMod(n,9)==Mod(5,9),n,0),0)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...=1,ifMod(n,9)==Mod(5,9),n,0),0)) ^------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:46:16 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(n,9)==Mod(5,9),n,0),0)) Output: ? [0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:46:38 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(n,9)==Mod(1,n),n,0),0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:47:15 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(10,n)==Mod(1,n),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:47:29 2004 Input: vector(100,n,if(isprime(n)==1,if(Mod(10,n)==Mod(1,n),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:47:37 2004 Input: vector(100,n,if(isprime(n)==1,if(Mod(10^2,n)==Mod(1,n),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:47:44 2004 Input: vector(100,n,if(isprime(n)==1,if(Mod(10^3,n)==Mod(1,n),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:47:54 2004 Input: vector(100,n,if(isprime(n)==1,if(Mod(10^4,n)==Mod(1,n),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:48:00 2004 Input: vector(100,n,if(isprime(n)==1,if(Mod(10^5,n)==Mod(1,n),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:49:05 2004 Input: vector(100,n,if(Mod(10^n,3)==Mod(1,3),n,0)) Output: ? [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:49:37 2004 Input: vector(100,n,if(Mod(10^n,7)==Mod(1,7),n,0)) Output: ? [0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 78, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:49:50 2004 Input: vector(100,n,if(Mod(10^n,11)==Mod(1,11),n,0)) Output: ? [0, 2, 0, 4, 0, 6, 0, 8, 0, 10, 0, 12, 0, 14, 0, 16, 0, 18, 0, 20, 0, 22, 0, 24, 0, 26, 0, 28, 0, 30, 0, 32, 0, 34, 0, 36, 0, 38, 0, 40, 0, 42, 0, 44, 0, 46, 0, 48, 0, 50, 0, 52, 0, 54, 0, 56, 0, 58, 0, 60, 0, 62, 0, 64, 0, 66, 0, 68, 0, 70, 0, 72, 0, 74, 0, 76, 0, 78, 0, 80, 0, 82, 0, 84, 0, 86, 0, 88, 0, 90, 0, 92, 0, 94, 0, 96, 0, 98, 0, 100] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:00:35 2004 Input: vector(100,n,if(Mod(10^n,3)==Mod(1,3),n,0)) Output: ? [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:00:55 2004 Input: vector(100,n,if(Mod(10^n,7)==Mod(1,7),n,0)) Output: ? [0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 78, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:01:25 2004 Input: Mod(10^6,7) Output: ? Mod(1, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:01:50 2004 Input: vector(100,n,if(Mod(10^n,11)==Mod(1,11),n,0)) Output: ? [0, 2, 0, 4, 0, 6, 0, 8, 0, 10, 0, 12, 0, 14, 0, 16, 0, 18, 0, 20, 0, 22, 0, 24, 0, 26, 0, 28, 0, 30, 0, 32, 0, 34, 0, 36, 0, 38, 0, 40, 0, 42, 0, 44, 0, 46, 0, 48, 0, 50, 0, 52, 0, 54, 0, 56, 0, 58, 0, 60, 0, 62, 0, 64, 0, 66, 0, 68, 0, 70, 0, 72, 0, 74, 0, 76, 0, 78, 0, 80, 0, 82, 0, 84, 0, 86, 0, 88, 0, 90, 0, 92, 0, 94, 0, 96, 0, 98, 0, 100] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:02:08 2004 Input: vector(100,n,if(Mod(10^n,13)==Mod(1,13),n,0)) Output: ? [0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 78, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:02:35 2004 Input: vector(100,n,if(Mod(10^n,17)==Mod(1,17),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:02:54 2004 Input: vector(100,n,if(Mod(10^n,19)==Mod(1,19),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:03:11 2004 Input: vector(100,n,if(Mod(10^n,23)==Mod(1,23),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:03:41 2004 Input: Mod(10^22,23) Output: ? Mod(1, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:04:00 2004 Input: vector(100,n,if(Mod(10^n,29)==Mod(1,29),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:04:32 2004 Input: vector(100,n,if(Mod(10^n,31)==Mod(1,31),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 75, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:04:46 2004 Input: vector(100,n,if(Mod(10^n,37)==Mod(1,37),n,0)) Output: ? [0, 0, 3, 0, 0, 6, 0, 0, 9, 0, 0, 12, 0, 0, 15, 0, 0, 18, 0, 0, 21, 0, 0, 24, 0, 0, 27, 0, 0, 30, 0, 0, 33, 0, 0, 36, 0, 0, 39, 0, 0, 42, 0, 0, 45, 0, 0, 48, 0, 0, 51, 0, 0, 54, 0, 0, 57, 0, 0, 60, 0, 0, 63, 0, 0, 66, 0, 0, 69, 0, 0, 72, 0, 0, 75, 0, 0, 78, 0, 0, 81, 0, 0, 84, 0, 0, 87, 0, 0, 90, 0, 0, 93, 0, 0, 96, 0, 0, 99, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:05:02 2004 Input: vector(100,n,if(Mod(10^n,41)==Mod(1,41),n,0)) Output: ? [0, 0, 0, 0, 5, 0, 0, 0, 0, 10, 0, 0, 0, 0, 15, 0, 0, 0, 0, 20, 0, 0, 0, 0, 25, 0, 0, 0, 0, 30, 0, 0, 0, 0, 35, 0, 0, 0, 0, 40, 0, 0, 0, 0, 45, 0, 0, 0, 0, 50, 0, 0, 0, 0, 55, 0, 0, 0, 0, 60, 0, 0, 0, 0, 65, 0, 0, 0, 0, 70, 0, 0, 0, 0, 75, 0, 0, 0, 0, 80, 0, 0, 0, 0, 85, 0, 0, 0, 0, 90, 0, 0, 0, 0, 95, 0, 0, 0, 0, 100] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:05:14 2004 Input: vector(100,n,if(Mod(10^n,43)==Mod(1,43),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 63, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:05:53 2004 Input: Mod(10^5,41) Output: ? Mod(1, 41) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:06:05 2004 Input: Mod(10^21,43) Output: ? Mod(1, 43) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:06:32 2004 Input: vector(100,n,if(Mod(10^n,47)==Mod(1,47),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:06:56 2004 Input: vector(100,n,if(Mod(10^n,53)==Mod(1,53),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 91, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.009s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:07:29 2004 Input: vector(100,n,if(Mod(10^n,59)==Mod(1,59),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:07:40 2004 Input: primes(25) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:08:16 2004 Input: vector(100,n,if(Mod(10^n,61)==Mod(1,61),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:08:42 2004 Input: vector(100,n,if(Mod(10^n,67)==Mod(1,67),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 99, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:09:06 2004 Input: vector(100,n,if(Mod(10^n,71)==Mod(1,71),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:09:30 2004 Input: vector(100,n,if(Mod(10^n,73)==Mod(1,73),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:09:49 2004 Input: vector(100,n,if(Mod(10^n,79)==Mod(1,79),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 91, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:10:04 2004 Input: vector(100,n,if(Mod(10^n,83)==Mod(1,83),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:10:29 2004 Input: vector(100,n,if(Mod(10^n,89)==Mod(1,89),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:10:46 2004 Input: vector(100,n,if(Mod(10^n,89)==Mod(1,97),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:11:05 2004 Input: vector(100,n,if(Mod(10^n,97)==Mod(1,97),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.188.198 (68.118.188.198) Time: Thu Sep 23 02:33:13 2004 Input: vector(200,n,isprime(n)*n*issquare(Mod(-1,n))) Output: ? [0, 2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 109, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 173, 0, 0, 0, 0, 0, 0, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.188.198 (68.118.188.198) Time: Thu Sep 23 02:33:45 2004 Input: vector(200,n,isprime(n)*n*issquare(Mod(2,n))) Output: ? [0, 2, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 79, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 103, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 193, 0, 0, 0, 0, 0, 199, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:54:05 2004 Input: Mod(3,419) Output: ? Mod(3, 419) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:54:13 2004 Input: lift(Mod(3,419)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:54:20 2004 Input: lift(Mod(3,557)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:54:26 2004 Input: lift(Mod(3,661)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:54:44 2004 Input: lift(Mod(3,1)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:54:47 2004 Input: lift(Mod(3,3)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:54:51 2004 Input: lift(Mod(3,5)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:54:57 2004 Input: lift(Mod(3,2)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:55:11 2004 Input: lift(Mod(3,1)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.248.' ************** PARI ***************** Host 68.248.251.86 (68.248.251.86) Time: Thu Sep 23 13:36:22 2004 Input: 7+3 x=7+3 Output: ? 10 ? 10 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.248.' ************** PARI ***************** Host 68.248.251.86 (68.248.251.86) Time: Thu Sep 23 13:36:42 2004 Input: 7+3 x=7+3 x=3 x^3 Output: ? 10 ? 10 ? 3 ? 27 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.248.' ************** PARI ***************** Host 68.248.251.86 (68.248.251.86) Time: Thu Sep 23 13:37:00 2004 Input: 7+3 x=7+3 x=3 x^3 (x+5)^5 Output: ? 10 ? 10 ? 3 ? 27 ? 32768 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '68.248.' ************** PARI ***************** Host 68.248.251.86 (68.248.251.86) Time: Thu Sep 23 13:37:17 2004 Input: 7+3 x=7+3 x=3 x^3 (x+5)^5 (y+5)^5 Output: ? 10 ? 10 ? 3 ? 27 ? 32768 ? y^5 + 25*y^4 + 250*y^3 + 1250*y^2 + 3125*y + 3125 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '129.93.' ************** PARI ***************** Host 129.93.181.78 (129.93.181.78) Time: Thu Sep 23 16:55:01 2004 Input: 2 +3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '82.253.' ************** PARI ***************** Host 82.253.190.110 (82.253.190.110) Time: Fri Sep 24 09:05:49 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '82.253.' ************** PARI ***************** Host 82.253.190.110 (82.253.190.110) Time: Fri Sep 24 09:06:05 2004 Input: 2^160 Output: ? 1461501637330902918203684832716283019655932542976 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '82.253.' ************** PARI ***************** Host 82.253.190.110 (82.253.190.110) Time: Fri Sep 24 09:06:20 2004 Input: 2^768 Output: ? 1552518092300708935148979488462502555256886017116696611139052038026050952686376886330878408828646477950487730697131073206171580044114814391444287275041181139204454976020849905550265285631598444825262999193716468750892846853816057856 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '82.253.' ************** PARI ***************** Host 82.253.190.110 (82.253.190.110) Time: Fri Sep 24 09:06:49 2004 Input: 2^1024 Output: ? 179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '82.253.' ************** PARI ***************** Host 82.253.190.110 (82.253.190.110) Time: Fri Sep 24 09:07:03 2004 Input: 2^2048 Output: ? 32317006071311007300714876688669951960444102669715484032130345427524655138867890893197201411522913463688717960921898019494119559150490921095088152386448283120630877367300996091750197750389652106796057638384067568276792218642619756161838094338476170470581645852036305042887575891541065808607552399123930385521914333389668342420684974786564569494856176035326322058077805659331026192708460314150258592864177116725943603718461857357598351152301645904403697613233287231227125684710820209725157101726931323469678542580656697935045997268352998638215525166389437335543602135433229604645318478604952148193555853611059596230656 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Fri Sep 24 19:34:49 2004 Input: factor(4323110550526375709294437681284209923347881) Output: ? [471463684608646013689 1] [9169551529965486638129 1] ? Errors (if any) and Timing Info: Timing: real 0m0.753s user 0m0.703s sys 0m0.029s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Fri Sep 24 19:35:13 2004 Input: factor(4323110550526375709294437681284209923347881-1) Output: ? [2 3] [5 1] [97 1] [15910439 1] [70029730174991641814638753601159 1] ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.022s sys 0m0.004s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Fri Sep 24 19:35:38 2004 Input: factor(4323110550526375709294437681284209923347881) Output: ? [471463684608646013689 1] [9169551529965486638129 1] ? Errors (if any) and Timing Info: Timing: real 0m0.727s user 0m0.708s sys 0m0.019s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Fri Sep 24 19:36:06 2004 Input: factor(4323110550526375709294437681284209923347881) Output: ? [471463684608646013689 1] [9169551529965486638129 1] ? Errors (if any) and Timing Info: Timing: real 0m0.733s user 0m0.711s sys 0m0.022s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Fri Sep 24 19:36:15 2004 Input: factor(4323110550526375709294437681284209923347881-1) Output: ? [2 3] [5 1] [97 1] [15910439 1] [70029730174991641814638753601159 1] ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.022s sys 0m0.005s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Sun Sep 26 00:47:10 2004 Input: SetVerbose("Factorization",true) f := Factorization(35); Output: ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: SetVerbose("Factoriz ^-------------------- *** unexpected character: f:=Factorization(35); ^-------------------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Sun Sep 26 00:47:24 2004 Input: SetVerbose("Factorization",true) Factorization(35); Output: ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: SetVerbose("Factoriz ^-------------------- *** unknown function or error in formal parameters: Factorization(35); ^------------------ Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '219.167' ************** PARI ***************** Host 219.167.136.209 (219.167.136.209) Time: Sun Sep 26 11:44:42 2004 Input: 1-365!/365^23*(365-23)! Output: ? -21279115957131455770888363190937546639565804346409980201181533910272215619457419076391037401530210411162516050923706022317037842995049009898940972876530778268329906077799129156407000448076415875526298200295939743790272789687450310994840749315496098408315338198781100420675349981897342078450746710412052607469020723280197652681072126856314506865659925237059778099364310995965400859606052262285593568638785520251747374964246303505021192532263934313673463777907416383851853229478400531095525942124090780356828031533597134773245184764619916121460139973001524443343297351486508976341403318289892184037560893609416113349605339650037390000350448173187881215091218954620267423226023112396503197856446234006644723775458275894412740658910793349662123185323639776306318565577600157297290751623083542516802063863713353699119773456839393988931045804591998629446003495383668290224129829841098205939194885162167357098048113628782890101575205036400852954878268986171459816507036831657257635054059590464156402359509175450620302815962947123217270091644123717952742468313981681054570977196954544356151736485627426058394764425929582917574925286634824457765782061715755996297710531668091984746333873415693834533868394867617916871506563574518165254670015588297473897244407961393792181569265064984970558553522497739404734835410580880438067199999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999877954985960253411326304591/122045014039746588673695409 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s '219.167' ************** PARI ***************** Host 219.167.136.209 (219.167.136.209) Time: Sun Sep 26 11:45:10 2004 Input: 1-365!/(365^23)*(365-23)! Output: ? -21279115957131455770888363190937546639565804346409980201181533910272215619457419076391037401530210411162516050923706022317037842995049009898940972876530778268329906077799129156407000448076415875526298200295939743790272789687450310994840749315496098408315338198781100420675349981897342078450746710412052607469020723280197652681072126856314506865659925237059778099364310995965400859606052262285593568638785520251747374964246303505021192532263934313673463777907416383851853229478400531095525942124090780356828031533597134773245184764619916121460139973001524443343297351486508976341403318289892184037560893609416113349605339650037390000350448173187881215091218954620267423226023112396503197856446234006644723775458275894412740658910793349662123185323639776306318565577600157297290751623083542516802063863713353699119773456839393988931045804591998629446003495383668290224129829841098205939194885162167357098048113628782890101575205036400852954878268986171459816507036831657257635054059590464156402359509175450620302815962947123217270091644123717952742468313981681054570977196954544356151736485627426058394764425929582917574925286634824457765782061715755996297710531668091984746333873415693834533868394867617916871506563574518165254670015588297473897244407961393792181569265064984970558553522497739404734835410580880438067199999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999877954985960253411326304591/122045014039746588673695409 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '219.167' ************** PARI ***************** Host 219.167.136.209 (219.167.136.209) Time: Sun Sep 26 11:45:23 2004 Input: 1-(365!/((365^23)*(365-23)!)) Output: ? 38093904702297390785243708291056390518886454060947061/75091883268515350125426207425223147563269805908203125 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '219.167' ************** PARI ***************** Host 219.167.136.209 (219.167.136.209) Time: Sun Sep 26 11:46:12 2004 Input: 1-(365!/((365^36)*(365-36)!)) Output: ? 1020254677714162459167299678915417850742696997256154883555348053744834851444570835157/1225999297380266462740712388357774027978304889870366990534898156352341175079345703125 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 13:41:31 2004 Input: a1(b1,c,wA1)=sqrt((a1(b1,c,wA1)+b1)^2+c^2+2*c*(a1+b1)*cos(wA1)) Output: ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: ...,c,wA1)+b1)^2+c^2+2*c*(a1 *** +b1)*cos(wA1)) ^-------------- Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 13:42:03 2004 Input: a1(b1,c,wA1)=sqrt((a1(b1,c,wA1)+b1)^2+c^2+2*c*(a1(b1,c,wA1)+b1)*cos(wA1)) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '128.196' ************** PARI ***************** Host 128.196.224.39 (128.196.224.39) Time: Sun Sep 26 14:32:17 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:42:15 2004 Input: simplify(x+x+1+1-x=a) Output: ? 2*x + (-a + 2) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:42:44 2004 Input: simplify(x+1+1-x=a) Output: ? x + (-a + 2) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:42:55 2004 Input: simplify(x+1+1-x-a) Output: ? -a + 2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:43:02 2004 Input: simplify(x+x+1+1-x-a) Output: ? x + (-a + 2) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:43:09 2004 Input: simplify(x+x+x+1+1-x-a) Output: ? 2*x + (-a + 2) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:43:36 2004 Input: simplify((b2^2-b1^2+2a2b2)^2/(4b1^2)-(b2^2+2a2b2-c^2)^2/(4c^2) - a2^2+(2a2b2+b2^2-c^2)^2/(4c^2) - y^2)^2 - 4y^2(a2^2-(2a2b2+b2^2-c^2)^2/(4c^2)) = 0 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: simplify((b2^2-b1^2+2 *** a2b2)^2/(4b1^2)-(b2^ ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:44:23 2004 Input: simplify((b2^2-b1^2+2*a2*b2)^2/(4*b1^2)-(b2^2+2*a2*b2-c^2)^2/(4c^2) - a2^2+(2*a2*b2+b2^2-c^2)^2/(4*c^2) - y^2)^2 - 4*y^2*(a2^2-(2*a2*b2+b2^2-c^2)^2/(4*c^2)) = 0 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...)-(b2^2+2*a2*b2-c^2)^2/(4 *** c^2)-a2^2+(2*a2*b2+b ^-------------------- Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:44:53 2004 Input: simplify((b2^2-b1^2+2*a2*b2)^2/(4*b1^2)-(b2^2+2*a2*b2-c^2)^2/(4*c^2) - a2^2+(2*a2*b2+b2^2-c^2)^2/(4*c^2) - y^2)^2 - 4*y^2*(a2^2-(2*a2*b2+b2^2-c^2)^2/(4*c^2)) = 0 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...a2*b2+b2^2-c^2)^2/(4*c^2))=0 ^--- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:45:05 2004 Input: simplify((b2^2-b1^2+2*a2*b2)^2/(4*b1^2)-(b2^2+2*a2*b2-c^2)^2/(4*c^2) - a2^2+(2*a2*b2+b2^2-c^2)^2/(4*c^2) - y^2)^2 - 4*y^2*(a2^2-(2*a2*b2+b2^2-c^2)^2/(4*c^2))=0) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...a2*b2+b2^2-c^2)^2/(4*c^2))=0) ^---- Timing: real 0m0.009s user 0m0.005s sys 0m0.002s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:45:33 2004 Input: simplify((b2^2-b1^2+2*a2*b2)^2/(4*b1^2)-(b2^2+2*a2*b2-c^2)^2/(4*c^2) - a2^2+(2*a2*b2+b2^2-c^2)^2/(4*c^2) - y^2)^2 - 4*y^2*(a2^2-(2*a2*b2+b2^2-c^2)^2/(4*c^2))) Output: ? 1/(16*b1^4)*b2^8 + a2/(2*b1^4)*b2^7 + ((-b1^2 + 6*a2^2)/(4*b1^4))*b2^6 + ((-3*a2*b1^2 + 4*a2^3)/(2*b1^4))*b2^5 + ((((3*c^2 + 8*y^2)/c^2)*b1^4 + (-28*a2^2 - 4*y^2)*b1^2 + 8*a2^4)/(8*b1^4))*b2^4 + ((((3*c^2 + 8*y^2)/c^2)*a2*b1^2 + (-8*a2^3 - 4*y^2*a2))/(2*b1^2))*b2^3 + ((-b1^4 + (((10*c^2 + 16*y^2)/c^2)*a2^2 - 4*y^2)*b1^2 + (-8*a2^4 - 8*y^2*a2^2))/(4*b1^2))*b2^2 + (-1/2*a2*b1^2 + (2*a2^3 - 2*y^2*a2))*b2 + (1/16*b1^4 + (-1/2*a2^2 - 1/2*y^2)*b1^2 + (a2^4 - 2*y^2*a2^2 + (y^2*c^2 + y^4))) ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '194.84.' ************** PARI ***************** Host 194.84.45.205 (194.84.45.205) Time: Mon Sep 27 03:42:24 2004 Input: 12345678901234567890123456789012345678901234567890123456789012345678901234567890*11111111112222222221111111111222222222111111111122222222211111111112222222221111111111222222222 Output: ? 137174210027434841989026063200274348418655692742002743484063100138420027434828283950742099999997256652973935651579972578875418256515799727023322072565157997393690009725651580 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '80.141.' ************** PARI ***************** Host 80.141.98.24 (80.141.98.24) Time: Mon Sep 27 16:24:40 2004 Input: 36 = x+y+z Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 36=x+y+z ^------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '80.141.' ************** PARI ***************** Host 80.141.98.24 (80.141.98.24) Time: Mon Sep 27 16:25:03 2004 Input: x+y+z=36 Output: ? x + (y + 36) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '134.71.' ************** PARI ***************** Host 134.71.86.83 (134.71.86.83) Time: Mon Sep 27 17:14:47 2004 Input: 932123/11 Output: ? 932123/11 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '134.71.' ************** PARI ***************** Host 134.71.86.83 (134.71.86.83) Time: Mon Sep 27 17:15:03 2004 Input: 932123/11 Output: ? 932123/11 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '134.71.' ************** PARI ***************** Host 134.71.86.83 (134.71.86.83) Time: Mon Sep 27 17:15:05 2004 Input: 932123/11 Output: ? 932123/11 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '134.71.' ************** PARI ***************** Host 134.71.86.83 (134.71.86.83) Time: Mon Sep 27 17:15:11 2004 Input: 932123/11. Output: ? 84738.454545454545454545454545454545455 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '134.71.' ************** PARI ***************** Host 134.71.86.83 (134.71.86.83) Time: Mon Sep 27 17:29:05 2004 Input: precprime(11) Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Mon Sep 27 22:48:49 2004 Input: NextPrime(Random(2^93))*NextPrime(Random(2^93)) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: NextPrime( *** Random(2^93))*NextPr ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Mon Sep 27 22:54:38 2004 Input: NextPrime(Random(2^93))*NextPrime(Random(2^93)); Factorization(4878143993485443754165069625209697799685333596237977) Output: ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: NextPrime( *** Random(2^93))*NextPr ^-------------------- *** unknown function or error in formal parameters: Factorization(487814 ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:00:50 2004 Input: binomial(-3,7) Output: ? -36 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.003s sys 0m0.006s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:01:00 2004 Input: binomial(-3,8) Output: ? 45 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:01:10 2004 Input: binomial(9,-5) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.006s sys 0m0.003s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:05:11 2004 Input: 392+O(6^5) Output: ? 2 + 5*6 + 4*6^2 + 6^3 + O(6^5) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.006s sys 0m0.003s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:05:23 2004 Input: 2 + 5*6 + 4*6^2 + 6^3 Output: ? 392 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.003s sys 0m0.007s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:05:44 2004 Input: 392+O(6^25) Output: ? 2 + 5*6 + 4*6^2 + 6^3 + O(6^25) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:06:46 2004 Input: Mod(1,5) Output: ? Mod(1, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:07:12 2004 Input: Mod(1,5)*(x^2+1) Output: ? Mod(1, 5)*x^2 + Mod(1, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:07:53 2004 Input: factor(Mod(1,5)*(x^2+1)) Output: ? [Mod(1, 5)*x + Mod(2, 5) 1] [Mod(1, 5)*x + Mod(3, 5) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.004s sys 0m0.007s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:08:12 2004 Input: lift(factor(Mod(1,5)*(x^2+1))) Output: ? [x + 2 1] [x + 3 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:23:09 2004 Input: 4^7 Output: ? 16384 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:23:23 2004 Input: 4^7*3 Output: ? 49152 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:23:28 2004 Input: 4^9*3 Output: ? 786432 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:31:29 2004 Input: vector(999,x,if(x=lift(Mod(x^2,10^3)),x,0)) Output: ? [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:33:38 2004 Input: lift(Mod(100^2,10^3)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.001s sys 0m0.009s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:33:45 2004 Input: lift(Mod(101^2,10^3)) Output: ? 201 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:33:54 2004 Input: lift(Mod(101^2,10^3)) 101^2 Output: ? 201 ? 10201 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:34:02 2004 Input: lift(Mod(102^2,10^3)) 102^2 Output: ? 404 ? 10404 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:35:05 2004 Input: for(x=100,999,if(lift(Mod(x^2,10^3))=x,x,0)) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...999,if(lift(Mod(x^2,10^3))=x,x,0)) ^--------- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:35:24 2004 Input: for(x=100,999,if(lift(Mod(x^2,10^3))=x,print(x),print(0))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...999,if(lift(Mod(x^2,10^3))=x,print(x),print(0 ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:36:52 2004 Input: for(x=100,999,if(lift(Mod(x^2,10^3))=x,print(x),print(0)))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...999,if(lift(Mod(x^2,10^3))=x,print(x),print(0 ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:36:58 2004 Input: for(x=100,999,if(lift(Mod(x^2,10^3))=x,print(x),print(0)))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...999,if(lift(Mod(x^2,10^3))=x,print(x),print(0 ^-------------------- Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:37:09 2004 Input: for(x=100,999,if(lift(Mod(x^2,10^3))=x,print(x),print(0 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...999,if(lift(Mod(x^2,10^3))=x,print(x),print(0 ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:37:23 2004 Input: for(x=100,999,if(lift(Mod(x^2,10^3))=x,print(x),print(0))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...999,if(lift(Mod(x^2,10^3))=x,print(x),print(0 ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:37:33 2004 Input: for(x=100,999,if(lift(Mod(x^2,10^3))=x,print(x),print("0"))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...999,if(lift(Mod(x^2,10^3))=x,print(x),print(" ^-------------------- Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:41:06 2004 Input: bezout(21,65) Output: ? [31, -10, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:41:29 2004 Input: 21*31+65*-10 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:47:15 2004 Input: 16*31 Output: ? 496 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:47:41 2004 Input: lift(Mod(496,65)) Output: ? 41 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:48:22 2004 Input: Mod(496,65) Output: ? Mod(41, 65) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:48:34 2004 Input: 21*41 Output: ? 861 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:48:41 2004 Input: Mod(21*41,65) Output: ? Mod(16, 65) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '216.58.' ************** PARI ***************** Host 216.58.64.34 (216.58.64.34) Time: Tue Sep 28 20:40:37 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:11:27 2004 Input: factorint(32) Output: ? [2 5] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:11:47 2004 Input: factorint(random(2^9)) Output: ? [7 1] [53 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.005s sys 0m0.004s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:12:07 2004 Input: factorint(nextprime(random(2^9))) Output: ? [373 1] ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.007s sys 0m0.003s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:12:22 2004 Input: factorint(nextprime(random(2^9))*nextprime(random(2^9)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...))*nextprime(random(2^9)) ^ Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:12:28 2004 Input: factorint(nextprime(random(2^9))*nextprime(random(2^9))) Output: ? [373 1] [503 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:12:54 2004 Input: factorint(nextprime(random(2^93))*nextprime(random(2^93))) Output: ? [3751220971129886190247702609 1] [7193692355178276170440144247 1] ? Errors (if any) and Timing Info: Timing: real 0m15.398s user 0m15.277s sys 0m0.074s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:15:31 2004 Input: //Factorization(NextPrime(Random(2^93))*NextPrime(Random(2^93))) factorint(nextprime(random(2^93))*nextprime(random(2^93))) Output: ? ? [3751220971129886190247702609 1] [7193692355178276170440144247 1] ? Errors (if any) and Timing Info: *** unexpected character: ^- Timing: real 0m15.700s user 0m15.607s sys 0m0.091s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:16:45 2004 Input: //Factorization(NextPrime(Random(2^93))*NextPrime(Random(2^93))) factorint(nextprime(random(2^93))*nextprime(random(2^93))) 3751220971129886190247702609*3751220971129886190247702609 Output: ? ? [3751220971129886190247702609 1] [7193692355178276170440144247 1] ? 14071658774244646442417825845321489074333496002505406881 ? Errors (if any) and Timing Info: *** unexpected character: ^- Timing: real 0m15.704s user 0m15.616s sys 0m0.087s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:30:09 2004 Input: n := NextPrime(Random(2^90))*NextPrime(Random(2^90)); n; Factorization(n); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: n:=NextPrime(Random(2 ^-------------------- *** expected character: '=' instead of: Factorization(n); ^- Timing: real 0m0.016s user 0m0.005s sys 0m0.004s '134.157' ************** PARI ***************** Host 134.157.86.77 (134.157.86.77) Time: Wed Sep 29 06:38:29 2004 Input: (a+b)^2; Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.005s sys 0m0.003s '134.157' ************** PARI ***************** Host 134.157.86.77 (134.157.86.77) Time: Wed Sep 29 06:38:37 2004 Input: (a+b)^2 Output: ? a^2 + 2*b*a + b^2 ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '134.157' ************** PARI ***************** Host 134.157.86.77 (134.157.86.77) Time: Wed Sep 29 06:39:13 2004 Input: nf=nfini(x^3+x+1) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: nf=nfini(x^3+x+1) ^------- Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '134.157' ************** PARI ***************** Host 134.157.86.77 (134.157.86.77) Time: Wed Sep 29 06:39:31 2004 Input: nf=nfinit(x^3+x+1) Output: ? [x^3 + x + 1, [1, 1], -31, 1, [[1, 1.4655712318767680266567312252199391080, -0.68232780382801932736948373971104825689; 1, -0.23278561593838401332836561260996955402 + 0.79255199251544784832589830065336124352*I, 0.34116390191400966368474186985552412844 + 1.1615413999972519360879176872471740748*I], [1, 1.4655712318767680266567312252199391080, -0.68232780382801932736948373971104825689; 1, 0.55976637657706383499753268804339168950, 1.5027053019112615997726595571026982033; 1, -1.0253376084538318616542639132633307975, -0.82037749808324227240317581739164994640], 0, [3, 1, 0; 1, 1, -3; 0, -3, -2], [31, 20, 17; 0, 1, 0; 0, 0, 1], [-11, 2, -3; 2, -6, 9; -3, 9, 2], [31, [14, -1, 10; -11, 3, 1; 1, 11, 14]]], [-0.68232780382801932736948373971104825689, 0.34116390191400966368474186985552412844 + 1.1615413999972519360879176872471740748*I], [1, x^2 + 1, x], [1, 0, -1; 0, 0, 1; 0, 1, 0], [1, 0, 0, 0, 0, -1, 0, -1, -1; 0, 1, 0, 1, 1, 0, 0, 0, 1; 0, 0, 1, 0, -1, 0, 1, 0, 0]] ? ? Errors (if any) and Timing Info: Timing: real 0m0.123s user 0m0.006s sys 0m0.005s '141.84.' ************** PARI ***************** Host 141.84.69.18 (141.84.69.18) Time: Wed Sep 29 15:48:37 2004 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) Boole's rule. The h conveniently cancel for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( Trapezoidal rule. Could be improved sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each evaluated at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, redundancy could be avoided by counting how often each gcd(i,S) value occurs n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and evaluating nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '141.84.' ************** PARI ***************** Host 141.84.69.18 (141.84.69.18) Time: Wed Sep 29 15:49:52 2004 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) Boole's rule. The h conveniently cancel for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( Trapezoidal rule. Could be improved sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each e.valuated at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, redundancy could be avoided by counting how often each gcd(i,S) value occurs n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and e.valuating nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '141.84.' ************** PARI ***************** Host 141.84.69.18 (141.84.69.18) Time: Wed Sep 29 15:50:51 2004 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) Boole's rule. The h conveniently cancel for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( Trapezoidal rule. Could be improved sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each e valuated at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, redundancy could be avoided by counting how often each gcd(i,S) value occurs n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and e valuating nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '141.84.' ************** PARI ***************** Host 141.84.69.18 (141.84.69.18) Time: Wed Sep 29 15:51:41 2004 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) Boole's rule. The h conveniently cancel for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( Trapezoidal rule. Could be improved sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, redundancy could be avoided by counting how often each gcd(i,S) value occurs n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? TheprobabilityofECMfindingafactornearNwithstage1parameterB1 ? stage2parameterB2 ? ? ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: srule.Thehconvenientlycancel. *** Warning: unused characters: ,butalpha-1= tablemax, but alpha - 1 < tablemax which would give negative result if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( Trapezoidal rule. Could be improved sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, redundancy could be avoided by counting how often each gcd(i,S) value occurs n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: ? ? ? ? ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? TheprobabilityofECMfindingafactornearNwithstage1parameterB1 ? stage2parameterB2 ? ? ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: srule.Thehconvenientlycancel. *** Warning: unused characters: ,butalpha-1= tablemax, but alpha - 1 < tablemax which would give negative result if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( Trapezoidal rule. Could be improved sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each e valuated at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, redundancy could be avoided by counting how often each gcd(i,S) value occurs n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } /* The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and e valuating nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function */ ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '141.84.' ************** PARI ***************** Host 141.84.69.18 (141.84.69.18) Time: Wed Sep 29 15:54:37 2004 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) Boole's rule. The h conveniently cancel for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( Trapezoidal rule. Could be improved sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each e-valuated at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, redundancy could be avoided by counting how often each gcd(i,S) value occurs n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } /* The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and e-valuating nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function */ ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '141.84.' ************** PARI ***************** Host 141.84.69.18 (141.84.69.18) Time: Wed Sep 29 15:54:54 2004 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) Boole's rule. The h conveniently cancel for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( Trapezoidal rule. Could be improved sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each valuated at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, redundancy could be avoided by counting how often each gcd(i,S) value occurs n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } /* The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and valuating nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function */ ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: srule.Thehconvenientlycancel. *** Warning: unused characters: ,butalpha-1= tablemax, but alpha - 1 < tablemax which would give negative result */ if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, /* dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified */ return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( /* Trapezoidal rule. Could be improved */ sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) /* Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 */ + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each e-valuated at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, /* redundancy could be avoided by counting how often each gcd(i,S) value occurs */ n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } /* The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and e-valuating nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function */ ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '141.84.' ************** PARI ***************** Host 141.84.69.18 (141.84.69.18) Time: Wed Sep 29 15:57:14 2004 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) /* Boole's rule. The h conveniently cancel */ for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); /* Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result */ if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, /* dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified */ return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( /* Trapezoidal rule. Could be improved */ sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) /* Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 */ + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, /* redundancy could be avoided by counting how often each gcd(i,S) value occurs */ n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } /* The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function */ ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1901.8734260571884364237051189878883491 ? Errors (if any) and Timing Info: Timing: real 0m0.105s user 0m0.087s sys 0m0.005s '141.84.' ************** PARI ***************** Host 141.84.69.18 (141.84.69.18) Time: Wed Sep 29 16:10:06 2004 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) /* Boole's rule. The h conveniently cancel */ for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); /* Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result */ if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, /* dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified */ return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( /* Trapezoidal rule. Could be improved */ sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) /* Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 */ + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, /* redundancy could be avoided by counting how often each gcd(i,S) value occurs */ n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } /* The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function */ ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1./ecmprob(1000000,100000000,sqrt(10)*10^34,5*4320^2,-6) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1200.8796622338720043522991602435422102 ? Errors (if any) and Timing Info: Timing: real 0m0.222s user 0m0.217s sys 0m0.005s '68.85.1' ************** PARI ***************** Host 68.85.131.94 (68.85.131.94) Time: Wed Sep 29 17:06:45 2004 Input: yhjhjhj Output: ? yhjhjhj ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '68.85.1' ************** PARI ***************** Host 68.85.131.94 (68.85.131.94) Time: Wed Sep 29 17:07:21 2004 Input: calc Output: ? calc ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Thu Sep 30 00:20:25 2004 Input: 596501*9634321 Output: ? 5746882110821 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '212.19.' ************** PARI ***************** Host 212.19.143.148 (212.19.143.148) Time: Thu Sep 30 02:31:46 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 06:04:31 2004 Input: x=4 x^2= Output: ? 4 ? ? Errors (if any) and Timing Info: *** unexpected character: x^2= ^-- Timing: real 0m0.009s user 0m0.002s sys 0m0.009s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 06:05:10 2004 Input: x=4 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 06:05:38 2004 Input: gp Output: ? gp ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 09:56:57 2004 Input: gcd(6,4) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.003s sys 0m0.009s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 09:57:23 2004 Input: gcd(173,168) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 09:58:12 2004 Input: 173 is prime Output: ? 173 ? Errors (if any) and Timing Info: *** Warning: unused characters: isprime. Timing: real 0m0.021s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 09:58:34 2004 Input: ? isprime 173 Output: ? ? Errors (if any) and Timing Info: *** isprime173: unknown identifier. Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 09:59:27 2004 Input: ?isprime Output: ? isprime(x,{flag=0}): if flag is omitted or 0, true(1) if x is a (proven) prime number, false(0) if not. If flag is 1, the primality is certified by the Pocklington-Lehmer Test. If flag is 2, the primality is certified using the APRCL test. ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:00:13 2004 Input: 173 isprime Output: ? 173 ? Errors (if any) and Timing Info: *** Warning: unused characters: isprime. Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:00:51 2004 Input: ?173 Output: ? ? Errors (if any) and Timing Info: *** no such section in help: ?: 173 ^--- Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:01:56 2004 Input: isprime(173) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:10:51 2004 Input: ?addprimes Output: ? addprimes({x=[]}): add primes in the vector x (with at most 100 components) to the prime table. x may also be a single integer. The "primes" may in fact be composite, obtained for example by the function factor(x,0), and in that case the message "impossible inverse modulo" will give you some factors. List the current extra primes if x is omitted. If some primes are added which divide non trivially the existing table, suitable updating is done. ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.005s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:11:57 2004 Input: addprime({x=[]}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: addprime({x=[]}) ^-------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:12:12 2004 Input: addprime({x=[1]}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: addprime({x=[1]}) ^--------- Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:12:28 2004 Input: ?addprime Output: ? ? Errors (if any) and Timing Info: *** addprime: unknown identifier. Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:12:57 2004 Input: addprimes({v=[]}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: addprimes({v=[]}) ^-------- Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:13:10 2004 Input: ?addprimes Output: ? addprimes({x=[]}): add primes in the vector x (with at most 100 components) to the prime table. x may also be a single integer. The "primes" may in fact be composite, obtained for example by the function factor(x,0), and in that case the message "impossible inverse modulo" will give you some factors. List the current extra primes if x is omitted. If some primes are added which divide non trivially the existing table, suitable updating is done. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:13:41 2004 Input: addprimes({x=[]}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: addprimes({x=[]}) ^-------- Timing: real 0m0.009s user 0m0.001s sys 0m0.008s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:13:49 2004 Input: addprimes({x=[1]}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: addprimes({x=[1]}) ^--------- Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:13:52 2004 Input: addprimes({x=[1]}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: addprimes({x=[1]}) ^--------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:14:53 2004 Input: ?prime Output: ? prime(n): returns the n-th prime (n C-integer) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:15:15 2004 Input: prime(31) Output: ? 127 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:15:24 2004 Input: prime(35) Output: ? 149 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:15:33 2004 Input: prime(42) Output: ? 181 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:15:38 2004 Input: prime(41) Output: ? 179 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:15:44 2004 Input: prime(40) Output: ? 173 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:16:31 2004 Input: ?divisors Output: ? divisors(x): gives a vector formed by the divisors of x in increasing order. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:16:48 2004 Input: divisors(143) Output: ? [1, 11, 13, 143] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:17:15 2004 Input: ?eulerphi Output: ? eulerphi(x): Euler's totient function of x. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:17:34 2004 Input: eulerphi(17) Output: ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:17:45 2004 Input: eulerphi(12) Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:18:16 2004 Input: ?factor Output: ? factor(x,{lim}): factorization of x. lim is optional and can be set whenever x is of (possibly recursive) rational type. If lim is set return partial factorization, using primes up to lim (up to primelimit if lim=0) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:18:55 2004 Input: factor(143) Output: ? [11 1] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:19:31 2004 Input: ?factormod Output: ? factormod(x,p,{flag=0}): factorization mod p of the polynomial x using Berlekamp. flag is optional, and can be 0: default or 1: simple factormod, same except that only the degrees of the irreducible factors are given. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:20:24 2004 Input: ?primes Output: ? primes(n): returns the vector of the first n primes (n C-integer) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:21:49 2004 Input: 2^3+123 Output: ? 131 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:24:26 2004 Input: ?card Output: ? ? Errors (if any) and Timing Info: *** card: unknown identifier. Timing: real 0m0.009s user 0m0.008s sys 0m0.001s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:25:24 2004 Input: ?Mod Output: ? Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:26:06 2004 Input: ?4 Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numbpart numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfbsolve quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:26:18 2004 Input: ?3 Output: ? Euler I Pi abs acos acosh agm arg asin asinh atan atanh bernfrac bernreal bernvec besselh1 besselh2 besseli besselj besseljh besselk besseln cos cosh cotan dilog eint1 erfc eta exp gamma gammah hyperu incgam incgamc lngamma log polylog psi sin sinh sqr sqrt sqrtn tan tanh teichmuller theta thetanullk weber zeta ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:26:41 2004 Input: ?5 Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:26:49 2004 Input: ?1 Output: ? divrem lex max min shift shiftmul sign vecmax vecmin ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:26:58 2004 Input: ?2 Output: ? List Mat Mod Pol Polrev Qfb Ser Set Str Strchr Strexpand Strtex Vec Vecsmall binary bitand bitneg bitnegimply bitor bittest bitxor ceil centerlift changevar component conj conjvec denominator floor frac imag length lift norm norml2 numerator numtoperm padicprec permtonum precision random real round simplify sizebyte sizedigit truncate valuation variable ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:27:21 2004 Input: ?Pol Output: ? Pol(x,{v=x}): convert x (usually a vector or a power series) into a polynomial with variable v, starting with the leading coefficient. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.002s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:39:38 2004 Input: 2^4*3^3 Output: ? 432 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '83.29.2' ************** PARI ***************** Host 83.29.28.90 (83.29.28.90) Time: Thu Sep 30 10:43:47 2004 Input: 3(3^2+1)/2 Output: ? 3 ? Errors (if any) and Timing Info: *** Warning: unused characters: (3^2+1)/2. Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '83.29.2' ************** PARI ***************** Host 83.29.28.90 (83.29.28.90) Time: Thu Sep 30 10:44:56 2004 Input: 3(3^2+1)/2=15 Output: ? 3 ? Errors (if any) and Timing Info: *** Warning: unused characters: (3^2+1)/2=15. Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '83.29.2' ************** PARI ***************** Host 83.29.28.90 (83.29.28.90) Time: Thu Sep 30 10:45:18 2004 Input: 15=45 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 15=45 ^---- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 11:01:40 2004 Input: ?1 Output: ? divrem lex max min shift shiftmul sign vecmax vecmin ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 11:01:49 2004 Input: ?0 Output: ? x ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 11:02:00 2004 Input: ?2 Output: ? List Mat Mod Pol Polrev Qfb Ser Set Str Strchr Strexpand Strtex Vec Vecsmall binary bitand bitneg bitnegimply bitor bittest bitxor ceil centerlift changevar component conj conjvec denominator floor frac imag length lift norm norml2 numerator numtoperm padicprec permtonum precision random real round simplify sizebyte sizedigit truncate valuation variable ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 11:02:30 2004 Input: ?3 Output: ? Euler I Pi abs acos acosh agm arg asin asinh atan atanh bernfrac bernreal bernvec besselh1 besselh2 besseli besselj besseljh besselk besseln cos cosh cotan dilog eint1 erfc eta exp gamma gammah hyperu incgam incgamc lngamma log polylog psi sin sinh sqr sqrt sqrtn tan tanh teichmuller theta thetanullk weber zeta ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 11:03:17 2004 Input: sqrt(2491) Output: ? 49.909918853871121075615758305504873551 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 11:04:19 2004 Input: x=2491 49^2-x Output: ? 2491 ? -90 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 11:04:51 2004 Input: x=2491 50^2-x Output: ? 2491 ? 9 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '213.35.' ************** PARI ***************** Host 213.35.248.103 (213.35.248.103) Time: Thu Sep 30 16:07:01 2004 Input: f(x) = x+2 f(25) Output: ? ? 27 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '213.35.' ************** PARI ***************** Host 213.35.248.103 (213.35.248.103) Time: Thu Sep 30 16:07:13 2004 Input: f(x) = x+2 f(25) Output: ? ? 27 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '213.35.' ************** PARI ***************** Host 213.35.248.103 (213.35.248.103) Time: Thu Sep 30 16:07:18 2004 Input: f(x) = x+2; f(25) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '148.205' ************** PARI ***************** Host 148.205.196.207 (148.205.196.207) Time: Thu Sep 30 17:23:59 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '148.205' ************** PARI ***************** Host 148.205.196.207 (148.205.196.207) Time: Thu Sep 30 17:24:34 2004 Input: ifactor(42344); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: ifactor(42344); ^--------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '148.205' ************** PARI ***************** Host 148.205.196.207 (148.205.196.207) Time: Thu Sep 30 17:24:50 2004 Input: factor(42344); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '141.99.' ************** PARI ***************** Host 141.99.112.99 (141.99.112.99) Time: Fri Oct 1 09:02:22 2004 Input: primes(2^300) Output: ? ? Errors (if any) and Timing Info: *** impossible assignment I-->S Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '141.99.' ************** PARI ***************** Host 141.99.112.99 (141.99.112.99) Time: Fri Oct 1 09:03:21 2004 Input: primes(2^15) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 40[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.010s sys 0m0.010s '130.235' ************** PARI ***************** Host 130.235.5.15 (130.235.5.15) Time: Fri Oct 1 18:43:53 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^48*y + b^239; Fa := ext< Fb | Pa>; Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: F2:=FiniteField(2); ^----------------- *** unexpected character: Rb:=PolynomialRing(F2 ^-------------------- *** unexpected character: Pb:=z^8+z^7+z^5+z^3+1; ^-------------------- *** unexpected character: Fb:=ext; ^-------------- *** unexpected character: Ra:=PolynomialRing(Fb ^-------------------- *** unexpected character: Pa:=y^4+b^23*y^2+b^48* ^-------------------- *** unexpected character: Fa:=ext; ^-------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Fri Oct 1 21:16:21 2004 Input: polroots(t^7-10*t^5+15*t+5,t) Output: ? ? Errors (if any) and Timing Info: *** this should be an integer: ...lroots(t^7-10*t^5+15*t+5,t) ^-- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Fri Oct 1 21:16:35 2004 Input: polroots(t^7-10*t^5+15*t+5) Output: ? [-3.1404055499933226795309181312088379193 + 0.E-38*I, -1.0326291777230510661764404208905927807 + 0.E-38*I, -0.33616291367665955187567025555163601513 + 0.E-38*I, 1.2240391489606568351016059767239666043 + 0.E-38*I, 3.1349957859561454402143908930036408448 + 0.E-38*I, 0.075081353238115511133515968961729633009 - 1.0906925270223230614181269769106148080*I, 0.075081353238115511133515968961729633009 + 1.0906925270223230614181269769106148080*I]~ ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.009s sys 0m0.009s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Fri Oct 1 21:18:03 2004 Input: polroots(7*t^6-50*t^4+15) Output: ? [-2.6646487187671384468288849167903923728 + 0.E-38*I, -0.75566037524740221237709057333202109750 + 0.E-38*I, 0.75566037524740221237709057333202109750 + 0.E-38*I, 2.6646487187671384468288849167903923728 + 0.E-38*I, 0.E-38 + 0.72699260951487969538996615411691019901*I, 0.E-38 - 0.72699260951487969538996615411691019901*I]~ ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '217.128' ************** PARI ***************** Host 217.128.165.34 (217.128.165.34) Time: Sat Oct 2 15:11:29 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '217.128' ************** PARI ***************** Host 217.128.165.34 (217.128.165.34) Time: Sat Oct 2 15:11:59 2004 Input: mathilbert(4) Output: ? [1 1/2 1/3 1/4] [1/2 1/3 1/4 1/5] [1/3 1/4 1/5 1/6] [1/4 1/5 1/6 1/7] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '24.163.' ************** PARI ***************** Host 24.163.67.137 (24.163.67.137) Time: Sat Oct 2 20:38:44 2004 Input: isprime(93765148492242264567029972255389350259464798239451657084614346917544207303437017955778498518892186487775118891243248166551193560238678154222030471135346171589706161232448266715976868851392806655819280199034662286366335385787715566578868562458753495442936870044120123060287256617835002677172150130389096817830440707819595743475905812319746873814938471290537042994565688636675227598251281361269910873320686397937702756298056910147418903972497581686633504786552830388193255547719196203688678295088373840072848219875279138255237582427777746396717849638757745880930385332714682685210249834687435279645620019567449545258236711196234206995621852473973037600952366485124085377638006543147877639254951338300587939502432425544557152465872240259812120295419623677181821041108312706298086584081806164223357592908717748875674823222242283587529410026360045380548699090922495157883134815716379269137533273835179641823093105863823759516081813095147630344718580367225923653064123453445882459206401831073108402162148861789366899914173308862186733844461466576176748932119573982709258772054289548086065532491022520617817438570083902593621001522373) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m3.802s user 0m3.400s sys 0m0.015s '24.163.' ************** PARI ***************** Host 24.163.67.137 (24.163.67.137) Time: Sat Oct 2 20:39:30 2004 Input: isprime(10882457724216911840228791111154926772453526692453533870975446245163515796795194175191855421148397726142656128323901533563140522112118769137427951738880932930340528218075961574811420850470784095714535204248610413359024722989094205169388503860139) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m13.822s user 0m12.540s sys 0m0.047s '63.241.' ************** PARI ***************** Host 63.241.65.90 (63.241.65.90) Time: Sun Oct 3 00:53:20 2004 Input: F(x)=2*x^2 F(10) Output: ? ? 200 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '80.170.' ************** PARI ***************** Host 80.170.31.206 (80.170.31.206) Time: Sun Oct 3 03:03:16 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.084s user 0m0.004s sys 0m0.009s '66.169.' ************** PARI ***************** Host 66.169.137.157 (66.169.137.157) Time: Sun Oct 3 15:13:28 2004 Input: mathilbert(3) Output: ? [1 1/2 1/3] [1/2 1/3 1/4] [1/3 1/4 1/5] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.005s sys 0m0.005s '66.169.' ************** PARI ***************** Host 66.169.137.157 (66.169.137.157) Time: Sun Oct 3 15:13:58 2004 Input: o3 mathilbert(3) Output: ? o3 ? [1 1/2 1/3] [1/2 1/3 1/4] [1/3 1/4 1/5] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '83.129.' ************** PARI ***************** Host 83.129.243.192 (83.129.243.192) Time: Sun Oct 3 15:31:38 2004 Input: a+Sqrt(a^2+b); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: a+Sqrt(a^2+b); ^------ Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '83.129.' ************** PARI ***************** Host 83.129.243.192 (83.129.243.192) Time: Sun Oct 3 15:31:49 2004 Input: a+Sqrt(a^2+b) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: a+Sqrt(a^2+b) ^----- Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '83.129.' ************** PARI ***************** Host 83.129.243.192 (83.129.243.192) Time: Sun Oct 3 15:32:03 2004 Input: a+sqrt(a^2+b) Output: ? ? Errors (if any) and Timing Info: *** 2 should divide valuation (= 1) in sqrtn. Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '83.129.' ************** PARI ***************** Host 83.129.243.192 (83.129.243.192) Time: Sun Oct 3 15:32:17 2004 Input: a+sqrt(a^2+b)=0 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: a+sqrt(a^2+b)=0 ^--- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '83.129.' ************** PARI ***************** Host 83.129.243.192 (83.129.243.192) Time: Sun Oct 3 15:32:46 2004 Input: sqrt(a^2+b)=-a Output: ? ? Errors (if any) and Timing Info: *** unexpected character: sqrt(a^2+b)=-a ^---- Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '134.82.' ************** PARI ***************** Host 134.82.104.102 (134.82.104.102) Time: Sun Oct 3 22:12:52 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m3.394s user 0m0.005s sys 0m0.009s '80.58.3' ************** PARI ***************** Host 80.58.3.235 (80.58.3.235) Time: Mon Oct 4 18:46:43 2004 Input: 123456789^12345 Output: ? 5654486280073803310290180594951405950850756477699818775556017861442082882683751453688537977423471844951416047026558934644990166000933155967967928464383198582942849347537979532022676988293878450451007849562469818382431052947092429668386990500711362538468456239004924300455953003962732800885306294109406111828615683010389028238065540377192905035352592097228157740682318633268815966716635430982674394658388984952419989176798733112564021428729778158755197379363828379245013509331118049131705623492027163432765353181559439096591214528906958479766117332571355174718480826163425102431231697153436335264147999803123080957216238309318741217052093409303597960086034966266525676184806636605409620712815872277046006828633135559276122977252403982859529084791171743709142328193989158472680885085951996868638160443922137747867323379350407430890287782144424668143820094093292303548349588889191204701652555050550560290425143017440605178441266483835184244033215736485915452568183081870901013326627529887994705995397915642236980304081882699455851996656414791589060902341162158827324107038566151513832337131425506384835540832367609743309854345740423091391083628849307320834996477477356312574126057771379655426227166099856703411175555112233204520210449082785877874593757246898664441228840871574828048744634364340624989183616163331436964493208107211498120938457489905736960342523511703849014308984674531161318041241246185798473649498398788418772691183709970885464354357394830159050899042537716276194614421029962425223675953796209430822320899112944474407071682144552260371754257973975287684547244805798523764951758073274849789484766080458753980937860446041062791025490167244514642985907398660443252060314671342702009122115686657125470896649899598484981619384744758872993600089106664996402104076036333675514467257900903939778895626327629577557637573104099973443144869296945181301613150129222652299698535448901785770543734041895255171145565162939494718284905449813770305549705046801659167339538006775761169644687713088959393718146620649994000674336267192280538844561432274884113662663764295066151261299014680308346483514183878891652916991741550037642463088071342360113024436703468370546931985476894629335042697204141858803859152708124294850696944410046663367143977448080678318297418759879509157339811544295840249743853717830349232395757414462211215404283186607622239530796200642308349016836089709365038767630367259618504023972269531878319565085010582876030546559335969309103702359363833203566500324424125884952024962619954011456356464510021053351320123377815436356639164125060287998752461135377064387644586966747003157400412741632695309173801802579270412224907314768672413671497225659525033539286868380525931023816512284007663134113007747945143200159687534687468350306066660223573897797343376593678966005523630129301783809147907664972271994996159631147389051675544340814016302491680233675765193835240309828429528175842618338844567293966191560796007803341521061801199812139192156892504905510192802482443116649573541974231084022373585668123475663905193891869032298475305973430582872042381032800888409036436687641942277578793791202824497190838609184471388046861361915986507130377685476310365017104551897843943575306252[+++] ? Errors (if any) and Timing Info: Timing: real 0m5.070s user 0m2.084s sys 0m0.032s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 00:27:43 2004 Input: 23^2 Output: ? 529 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 00:28:08 2004 Input: isprime(23^2) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 00:28:20 2004 Input: isprime(17) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 00:29:21 2004 Input: isprime(149) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 00:30:37 2004 Input: isprime(7837) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 00:31:24 2004 Input: isprime(25261) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.005s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:52:12 2004 Input: binomial(1,k) Output: ? ? Errors (if any) and Timing Info: *** this should be an integer: binomial(1,k) ^-- Timing: real 0m0.180s user 0m0.004s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:54:40 2004 Input: vector(10,k,binomial(1,k)) Output: ? [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:54:51 2004 Input: vector(10,k,binomial(2,k)) Output: ? [2, 1, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:55:26 2004 Input: vector(10,k,binomial(3,k)) Output: ? [3, 3, 1, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:55:39 2004 Input: vector(10,k,binomial(4,k)) Output: ? [4, 6, 4, 1, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.006s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:55:54 2004 Input: vector(10,k=1,binomial(4,k)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: vector(10,k=1,binomial(4,k)) ^----------------- Timing: real 0m0.010s user 0m0.002s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:56:05 2004 Input: vector(10,k,binomial(4,k)) Output: ? [4, 6, 4, 1, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:56:16 2004 Input: vector(10,k,binomial(5,k)) Output: ? [5, 10, 10, 5, 1, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:56:25 2004 Input: vector(10,k,binomial(6,k)) Output: ? [6, 15, 20, 15, 6, 1, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:56:36 2004 Input: vector(10,k,binomial(7,k)) Output: ? [7, 21, 35, 35, 21, 7, 1, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.003s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:56:44 2004 Input: vector(10,k,binomial(6,k)) Output: ? [6, 15, 20, 15, 6, 1, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:56:51 2004 Input: vector(10,k,binomial(7,k)) Output: ? [7, 21, 35, 35, 21, 7, 1, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:56:58 2004 Input: vector(10,k,binomial(8,k)) Output: ? [8, 28, 56, 70, 56, 28, 8, 1, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:57:08 2004 Input: vector(10,k,binomial(9,k)) Output: ? [9, 36, 84, 126, 126, 84, 36, 9, 1, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:57:16 2004 Input: vector(10,k,binomial(10,k)) Output: ? [10, 45, 120, 210, 252, 210, 120, 45, 10, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:57:34 2004 Input: vector(20,k,binomial(11,k)) Output: ? [11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:58:22 2004 Input: vector(20,k,binomial(13,k)) Output: ? [13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:58:36 2004 Input: vector(20,k,binomial(13,k)) Output: ? [13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:59:00 2004 Input: vector(20,k,binomial(11,k)) Output: ? [11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:59:18 2004 Input: vector(20,k,binomial(1,k)) Output: ? [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:04:27 2004 Input: vector(20,k,binomial(2,k)) Output: ? [2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:04:58 2004 Input: vector(20,k,binomial(3,k)) Output: ? [3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:05:18 2004 Input: vector(20,k,binomial(4,k)) Output: ? [4, 6, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:05:58 2004 Input: vector(20,k,binomial(5,k)) Output: ? [5, 10, 10, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:06:31 2004 Input: vector(20,k,binomial(7,k)) Output: ? [7, 21, 35, 35, 21, 7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:07:12 2004 Input: vector(20,k,binomial(9,k)) Output: ? [9, 36, 84, 126, 126, 84, 36, 9, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:07:32 2004 Input: vector(20,k,binomial(11,k)) Output: ? [11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:10:05 2004 Input: vector(20,k,binomial(13,k)) Output: ? [13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:10:44 2004 Input: vector(20,k,binomial(15,k)) Output: ? [15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:11:26 2004 Input: vector(20,k,binomial(31,k)) Output: ? [31, 465, 4495, 31465, 169911, 736281, 2629575, 7888725, 20160075, 44352165, 84672315, 141120525, 206253075, 265182525, 300540195, 300540195, 265182525, 206253075, 141120525, 84672315] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:11:42 2004 Input: vector(40,k,binomial(31,k)) Output: ? [31, 465, 4495, 31465, 169911, 736281, 2629575, 7888725, 20160075, 44352165, 84672315, 141120525, 206253075, 265182525, 300540195, 300540195, 265182525, 206253075, 141120525, 84672315, 44352165, 20160075, 7888725, 2629575, 736281, 169911, 31465, 4495, 465, 31, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:12:20 2004 Input: vector(40,k,binomial(63,k)) Output: ? [63, 1953, 39711, 595665, 7028847, 67945521, 553270671, 3872894697, 23667689815, 127805525001, 615790256823, 2668424446233, 10468434365991, 37387265592825, 122131734269895, 366395202809685, 1012974972473835, 2588713818544245, 6131164307078475, 13488561475572645, 27619435402363035, 52728013040874885, 93993414551124795, 156655690918541325, 244382877832924467, 357174975294274221, 489462003181042451, 629308289804197437, 759510004936100355, 860778005594247069, 916312070471295267, 916312070471295267, 860778005594247069, 759510004936100355, 629308289804197437, 489462003181042451, 357174975294274221, 244382877832924467, 156655690918541325, 93993414551124795] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:12:31 2004 Input: vector(70,k,binomial(63,k)) Output: ? [63, 1953, 39711, 595665, 7028847, 67945521, 553270671, 3872894697, 23667689815, 127805525001, 615790256823, 2668424446233, 10468434365991, 37387265592825, 122131734269895, 366395202809685, 1012974972473835, 2588713818544245, 6131164307078475, 13488561475572645, 27619435402363035, 52728013040874885, 93993414551124795, 156655690918541325, 244382877832924467, 357174975294274221, 489462003181042451, 629308289804197437, 759510004936100355, 860778005594247069, 916312070471295267, 916312070471295267, 860778005594247069, 759510004936100355, 629308289804197437, 489462003181042451, 357174975294274221, 244382877832924467, 156655690918541325, 93993414551124795, 52728013040874885, 27619435402363035, 13488561475572645, 6131164307078475, 2588713818544245, 1012974972473835, 366395202809685, 122131734269895, 37387265592825, 10468434365991, 2668424446233, 615790256823, 127805525001, 23667689815, 3872894697, 553270671, 67945521, 7028847, 595665, 39711, 1953, 63, 1, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:28:22 2004 Input: vector(10,x,if(Mod(x^2,10^2)==x,x,0)) Output: ? [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.008s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:28:49 2004 Input: Mod(36,100) Output: ? Mod(36, 100) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:29:00 2004 Input: Mod(36,10) Output: ? Mod(6, 10) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:29:18 2004 Input: vector(10,x,if(Mod(x^2,10)==x,x,0)) Output: ? [1, 0, 0, 0, 5, 6, 0, 0, 0, 10] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:31:45 2004 Input: vector(9,x,if(Mod(x^2,10)==x,x,0)) Output: ? [1, 0, 0, 0, 5, 6, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:33:03 2004 Input: vector(99,x,if(Mod(x^2,10^2)==x,x,0)) Output: ? [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:37:36 2004 Input: vector(999,x,if(Mod(x^2,10^2)==x,x,0)) Output: ? [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 101, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200, 201, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 225, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 276, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 300, 301, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 325, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 400, 401, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 425, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 476, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 500, 501, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 525, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600, 601, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 625, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 676, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 700, 701, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 725, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 776, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 800, 801, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 825, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 876, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 900, 901, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 925, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 976, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:38:48 2004 Input: vector(999,x,if(Mod(x^2,10^3)==x,x,0)) Output: ? [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 625, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.006s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:39:40 2004 Input: vector(9999,x,if(Mod(x^2,10^4)==x,x,0)) Output: ? 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Errors (if any) and Timing Info: Timing: real 0m0.041s user 0m0.030s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:42:00 2004 Input: vector(9999,x,if( x>999 ,if(Mod(x^2,10^4)==x,x,0),0,0) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...f(Mod(x^2,10^4)==x,x,0),0,0) ^--- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:42:23 2004 Input: vector(9999,x,if( x>999 ,if(Mod(x^2,10^4)==x,x,0),0)) Output: ? 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Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.035s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:42:39 2004 Input: vector(9999,x,if( x>999 ,if(Mod(x^2,10^4)==x,x,0)-)) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...,if(Mod(x^2,10^4)==x,x,0)-)) ^--- Timing: real 0m0.128s user 0m0.005s sys 0m0.011s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:42:48 2004 Input: vector(9999,x,if( x>999 ,if(Mod(x^2,10^4)==x,x,0))) Output: ? 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Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.031s sys 0m0.009s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:43:59 2004 Input: vector(9999,x,if( x>999 ,if(Mod(x^2,10^5)==x,x,0)0)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...,if(Mod(x^2,10^5)==x,x,0)0)) ^--- Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:44:07 2004 Input: vector(9999,x,if( x>999 ,if(Mod(x^2,10^5)==x,x,0),0)) Output: ? 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Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.031s sys 0m0.010s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:46:37 2004 Input: vector(4444,x,if( x>999 ,if(Mod(x^2,10^5)==x,x,0),0)) Output: ? 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Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.018s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:47:27 2004 Input: vector(9999,1000999 ,if(Mod(x^2,10^5)==x,x,0),0)) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: vector(9999,1000999 ^-------------------- Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '81.131.' ************** PARI ***************** Host 81.131.209.115 (81.131.209.115) Time: Tue Oct 5 13:42:09 2004 Input: 8988499897*89879798879 Output: ? 807884562966272215463 ? Errors (if any) and Timing Info: Timing: real 0m0.164s user 0m0.005s sys 0m0.004s '192.16.' ************** PARI ***************** Host 192.16.204.78 (192.16.204.78) Time: Tue Oct 5 17:24:40 2004 Input: Sin(2*3) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Sin(2*3) ^-------- Timing: real 0m0.019s user 0m0.003s sys 0m0.007s '80.201.' ************** PARI ***************** Host 80.201.155.32 (80.201.155.32) Time: Tue Oct 5 17:42:37 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '80.201.' ************** PARI ***************** Host 80.201.155.32 (80.201.155.32) Time: Tue Oct 5 17:43:38 2004 Input: (1+7*p)^45 Output: ? 107006904423598033356356300384937784807*p^45 + 687901528437415928719433359617457188045*p^44 + 2161976232231878633118219130226294019570*p^43 + 4426903713617656248765877266653840135310*p^42 + 6640355570426484373148815899980760202965*p^41 + 7778702239642453122831470054263176237759*p^40 + 7408287847278526783649019099298263083580*p^39 + 5896392368242092746169627446380250209380*p^38 + 4001123392735705792043675767186598356365*p^37 + 2349866119543192290565333387077843479135*p^36 + 1208502575765070320862171456211462360698*p^35 + 549319352620486509482805207368846527590*p^34 + 222343547489244539552564012506437880215*p^33 + 80630077660934833024556180359477473045*p^32 + 26328188623978720987610181341870195280*p^31 + 7773084260412765243961101158075962416*p^30 + 2082076141181990690346723524484632790*p^29 + 507396706674602773277772959748355890*p^28 + 112754823705467282950616213277412420*p^27 + 22890076992839222854636374123985980*p^26 + 4251014298670141387289612337311682*p^25 + 722961615420092072668301417910150*p^24 + 112669342662871491844410610583400*p^23 + 16095620380410213120630087226200*p^22 + 2107759811720385051511082851050*p^21 + 252931177406446206181329942126*p^20 + 27794634879829253426519773860*p^19 + 2794169644003999021713628060*p^18 + 256607416286081542810435230*p^17 + 21489291019031459250134970*p^16 + 1637279315735730228581712*p^15 + 113175989566985960501040*p^14 + 7073499347936622531315*p^13 + 398075720879550185745*p^12 + 20071044750229421130*p^11 + 901148947969484214*p^10 + 35759878887677945*p^9 + 1242621274089195*p^8 + 37372068393660*p^7 + 958258163940*p^6 + 20534103513*p^5 + 357736995*p^4 + 4867170*p^3 + 48510*p^2 + 315*p + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.004s sys 0m0.005s '70.112.' ************** PARI ***************** Host 70.112.34.157 (70.112.34.157) Time: Tue Oct 5 21:10:18 2004 Input: k=bnfinit(y^6-2*y+2); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.191s user 0m0.028s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.161.171 (140.247.161.171) Time: Wed Oct 6 00:02:17 2004 Input: 91^3+4*91^2+2*91-2 Output: ? 786875 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '140.247' ************** PARI ***************** Host 140.247.161.171 (140.247.161.171) Time: Wed Oct 6 00:02:55 2004 Input: 3*91^2+8*91+2 Output: ? 25573 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.161.171 (140.247.161.171) Time: Wed Oct 6 00:03:20 2004 Input: 25573/625 Output: ? 25573/625 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.161.171 (140.247.161.171) Time: Wed Oct 6 00:03:54 2004 Input: 625*120 Output: ? 75000 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.161.171 (140.247.161.171) Time: Wed Oct 6 00:04:41 2004 Input: 30*625 Output: ? 18750 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.161.171 (140.247.161.171) Time: Wed Oct 6 00:05:27 2004 Input: 18750*2 Output: ? 37500 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.161.171 (140.247.161.171) Time: Wed Oct 6 00:05:37 2004 Input: 18750*2-625 Output: ? 36875 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.161.171 (140.247.161.171) Time: Wed Oct 6 00:06:33 2004 Input: 16^3+4*16^2+2*16-2 Output: ? 5150 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.161.171 (140.247.161.171) Time: Wed Oct 6 00:06:46 2004 Input: 5150/625 Output: ? 206/25 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.161.171 (140.247.161.171) Time: Wed Oct 6 00:07:42 2004 Input: 91^3+4*91^2+2*91-2 Output: ? 786875 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.161.171 (140.247.161.171) Time: Wed Oct 6 00:07:55 2004 Input: 786875/625 Output: ? 1259 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '24.201.' ************** PARI ***************** Host 24.201.42.177 (24.201.42.177) Time: Wed Oct 6 08:42:40 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.149s user 0m0.004s sys 0m0.006s '128.131' ************** PARI ***************** Host 128.131.48.175 (128.131.48.175) Time: Wed Oct 6 10:30:59 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '192.16.' ************** PARI ***************** Host 192.16.204.78 (192.16.204.78) Time: Wed Oct 6 11:18:04 2004 Input: A:=FreeAbelianGroup(1); B:=FreeAbelianGroup(2); C:=FreeAbelianGroup(1); D:=FreeAbelianGroup(0); D; f:=homB|x:->Id(B)>; g:=homC| y:->w,z:->2*w>; C:=Complex([*f,g*],3); Output: ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: A:=FreeAbelianGroup( ^-------------------- *** Warning: unused characters: ,z>:=FreeAbelianGroup(2);. *** incorrect type in comparison. *** unexpected character: C:=FreeAbelianGroup( ^-------------------- *** unexpected character: D:=FreeAbelianGroup(0 ^-------------------- *** unexpected character: f:=homB|x:->Id(B) ^-------------------- *** unexpected character: g:=homC|y:->w,z:- ^-------------------- *** unexpected character: C:=Complex([*f,g*],3) ^-------------------- Timing: real 0m0.029s user 0m0.002s sys 0m0.008s '157.252' ************** PARI ***************** Host 157.252.169.17 (157.252.169.17) Time: Wed Oct 6 12:43:28 2004 Input: 0 = 3^x-5 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 0=3^x-5 ^------- Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.161.171 (140.247.161.171) Time: Wed Oct 6 15:46:09 2004 Input: factorpadic(x^3+5x+25, 5) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: factorpadic(x^3+5x+25,5) ^------- Timing: real 0m0.166s user 0m0.003s sys 0m0.012s '140.247' ************** PARI ***************** Host 140.247.161.171 (140.247.161.171) Time: Wed Oct 6 15:46:25 2004 Input: factorpadic(x^3+5x+25, 5, 4) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: factorpadic(x^3+5x+25,5,4) ^--------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.161.171 (140.247.161.171) Time: Wed Oct 6 15:47:40 2004 Input: factorpadic(x^3+5x+25, 5, 4) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: factorpadic(x^3+5x+25,5,4) ^--------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '81.51.5' ************** PARI ***************** Host 81.51.56.182 (81.51.56.182) Time: Thu Oct 7 04:06:15 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '81.51.5' ************** PARI ***************** Host 81.51.56.182 (81.51.56.182) Time: Thu Oct 7 04:06:42 2004 Input: mathhnf Output: ? mathhnf ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Oct 7 06:12:11 2004 Input: a=1 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.005s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Oct 7 06:12:25 2004 Input: a:=1; Output: ? ? Errors (if any) and Timing Info: *** unexpected character: a:=1; ^---- Timing: real 0m0.017s user 0m0.006s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Oct 7 06:16:21 2004 Input: a:=1; for x := 1 to 54 do b:= mod(x,55); print( b); end for; Output: ? ? ? ? b ? ? Errors (if any) and Timing Info: *** unexpected character: a:=1; ^---- *** unexpected character: forx:=1to54do ^--------- *** unexpected character: b:=mod(x,55); ^------------ Timing: real 0m0.027s user 0m0.003s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Oct 7 06:20:56 2004 Input: a:=1; for x := 1 to 54 do c:=x^2; c mod 55; print(x); print(c); end for; Output: ? ? ? ? ? x ? c ? ? Errors (if any) and Timing Info: *** unexpected character: a:=1; ^---- *** unexpected character: forx:=1to54do ^--------- *** unexpected character: c:=x^2; ^------ Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Thu Oct 7 08:49:15 2004 Input: ellap(ellinit([0,0,0,1,0]),5) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.271s user 0m0.005s sys 0m0.006s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Thu Oct 7 08:49:31 2004 Input: ellap(ellinit([0,0,0,1,0]),13) Output: ? -6 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.002s '151.36.' ************** PARI ***************** Host 151.36.177.27 (151.36.177.27) Time: Thu Oct 7 10:37:21 2004 Input: eulerphi(100) Output: ? 40 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '151.36.' ************** PARI ***************** Host 151.36.177.27 (151.36.177.27) Time: Thu Oct 7 10:37:57 2004 Input: eulerphi(100); eulerphi(200) Output: ? 80 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '137.222' ************** PARI ***************** Host 137.222.103.215 (137.222.103.215) Time: Thu Oct 7 14:15:21 2004 Input: factor(12) Output: ? [2 2] [3 1] ? Errors (if any) and Timing Info: Timing: real 0m0.078s user 0m0.006s sys 0m0.003s '137.222' ************** PARI ***************** Host 137.222.103.215 (137.222.103.215) Time: Thu Oct 7 14:15:50 2004 Input: factor(2^(2^7)+1) Output: ? [59649589127497217 1] [5704689200685129054721 1] ? Errors (if any) and Timing Info: Timing: real 0m0.369s user 0m0.262s sys 0m0.021s '137.222' ************** PARI ***************** Host 137.222.103.215 (137.222.103.215) Time: Thu Oct 7 14:16:08 2004 Input: factor(2^(2^8)+1) Output: ? [1238926361552897 1] [93461639715357977769163558199606896584051237541638188580280321 1] ? Errors (if any) and Timing Info: Timing: real 0m6.605s user 0m6.022s sys 0m0.007s '137.222' ************** PARI ***************** Host 137.222.103.215 (137.222.103.215) Time: Thu Oct 7 14:16:16 2004 Input: factor(12) Output: ? [2 2] [3 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '200.69.' ************** PARI ***************** Host 200.69.53.234 (200.69.53.234) Time: Thu Oct 7 17:01:27 2004 Input: I ws wsbknk fk zobnsnk ox vk zkbon csx xywlbo i oc exk vsxok swkqsxkbsk de psqebk Output: ? Iwswsbknkfkzobnsnkoxvkzkboncsxxywlbo ? iocexkvsxokswkqsxkbskdepsqebk ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.005s sys 0m0.005s '67.85.1' ************** PARI ***************** Host 67.85.182.59 (67.85.182.59) Time: Thu Oct 7 19:50:54 2004 Input: factor(12345678987654321) Output: ? [3 4] [37 2] [333667 2] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.008s sys 0m0.002s '67.85.1' ************** PARI ***************** Host 67.85.182.59 (67.85.182.59) Time: Thu Oct 7 19:51:13 2004 Input: factor(4) Output: ? [2 2] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '67.85.1' ************** PARI ***************** Host 67.85.182.59 (67.85.182.59) Time: Thu Oct 7 19:51:20 2004 Input: factor(37) Output: ? [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.070s user 0m0.004s sys 0m0.007s '67.85.1' ************** PARI ***************** Host 67.85.182.59 (67.85.182.59) Time: Thu Oct 7 19:51:30 2004 Input: 2 + 2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '67.11.2' ************** PARI ***************** Host 67.11.249.215 (67.11.249.215) Time: Thu Oct 7 23:49:38 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '67.11.2' ************** PARI ***************** Host 67.11.249.215 (67.11.249.215) Time: Thu Oct 7 23:51:18 2004 Input: 3227785^9640370 mod 31779547 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** Warning: unused characters: mod31779547. *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m4.673s user 0m4.261s sys 0m0.019s '67.11.2' ************** PARI ***************** Host 67.11.249.215 (67.11.249.215) Time: Thu Oct 7 23:52:05 2004 Input: 3227785^9640370 mod 31779547 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** Warning: unused characters: mod31779547. *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m4.693s user 0m4.274s sys 0m0.005s '66.190.' ************** PARI ***************** Host 66.190.53.65 (66.190.53.65) Time: Fri Oct 8 00:52:31 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '193.190' ************** PARI ***************** Host 193.190.148.199 (193.190.148.199) Time: Fri Oct 8 04:00:29 2004 Input: a=5 a^b Output: ? 5 ? ? 1 + 1.6094379124341003746007593332261876395*b + 1.2951451969901174725900855024963274477*b^2 + 0.69481859404760878829862955905644443859*b^3 + 0.27956684688109503219695907351715128656*b^4 + 0.089989096486018674769936612712314957070*b^5 + 0.024138643931714788934883074071207055487*b^6 + 0.0055499498140641592651415220955242805490*b^7 + 0.0011165374553576805018781864815814938655*b^8 + 0.00019966641236726087197027647067819097611*b^9 + 0.000032135069390357057934695871967032070832*b^10 + 0.0000047017635450492019924595772942507957056*b^11 + 0.00000063059970872522857568336954920840106393*b^12 + 0.000000078070082984021817719332900683721903621*b^13 + 0.0000000089749250986686468529374274145592197734*b^14 + 0.00000000096297231433691195454685338424699746040*b^15 + 9.6865259457389617689846266491425208585 E-11*b^16 + O(b^17) ? Errors (if any) and Timing Info: Timing: real 0m0.317s user 0m0.007s sys 0m0.006s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:40:25 2004 Input: ellinit([0,0,0,Mod(1,5),0]) Output: ? [0, 0, 0, Mod(1, 5), 0, 0, Mod(2, 5), 0, Mod(4, 5), Mod(2, 5), Mod(0, 5), Mod(1, 5), Mod(3, 5), 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.183s user 0m0.004s sys 0m0.011s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:41:55 2004 Input: E=ellinit([0,0,0,Mod(1,5),0]); P=[Mod(2,5),Mod(0,5)] ellisptoncurve(E,P) Output: ? ? [Mod(2, 5), Mod(0, 5)] ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: ellisptoncurve(E,P) ^ Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:42:15 2004 Input: E=ellinit([0,0,0,Mod(1,5),0]); P=[Mod(2,5),Mod(0,5)]; ellisptoncurve(E,P) Output: ? ? ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: ellisptoncurve(E,P) ^ Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:42:30 2004 Input: E=ellinit([0,0,0,Mod(1,5),0]); P=[Mod(2,5),Mod(0,5)]; ellispointoncurve(E,P) Output: ? ? ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: ellispointoncurve(E,P) ^ Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:43:09 2004 Input: E=ellinit([0,0,0,Mod(1,5),0]); P=[Mod(2,5),Mod(0,5)]; elladd(E,P,P) Output: ? ? ? [0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:44:59 2004 Input: E=ellinit([0,0,0,Mod(1,7),0]); P=[Mod(1,7),Mod(3,7)]; elladd(E,P,P) Output: ? ? ? [Mod(0, 7), Mod(0, 7)] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:45:16 2004 Input: E=ellinit([0,0,0,Mod(1,7),0]); P=[Mod(1,7),Mod(3,7)]; ellpow(E,P,2) Output: ? ? ? [Mod(0, 7), Mod(0, 7)] ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.003s sys 0m0.008s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:45:23 2004 Input: E=ellinit([0,0,0,Mod(1,7),0]); P=[Mod(1,7),Mod(3,7)]; ellpow(E,P,3) Output: ? ? ? [Mod(1, 7), Mod(4, 7)] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:45:29 2004 Input: E=ellinit([0,0,0,Mod(1,7),0]); P=[Mod(1,7),Mod(3,7)]; ellpow(E,P,-3) Output: ? ? ? [Mod(1, 7), Mod(3, 7)] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:45:37 2004 Input: E=ellinit([0,0,0,Mod(1,7),0]); P=[Mod(1,7),Mod(3,7)]; ellpow(E,P,-1) Output: ? ? ? [Mod(1, 7), Mod(4, 7)] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.004s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:45:48 2004 Input: E=ellinit([0,0,0,Mod(1,7),0]); P=[Mod(1,7),Mod(3,7)]; ellpow(E,P,7) Output: ? ? ? [Mod(1, 7), Mod(4, 7)] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:45:52 2004 Input: E=ellinit([0,0,0,Mod(1,7),0]); P=[Mod(1,7),Mod(3,7)]; ellpow(E,P,7) Output: ? ? ? [Mod(1, 7), Mod(4, 7)] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:45:58 2004 Input: E=ellinit([0,0,0,Mod(1,7),0]); P=[Mod(1,7),Mod(3,7)]; ellpow(E,P,-7) Output: ? ? ? [Mod(1, 7), Mod(3, 7)] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:46:39 2004 Input: E=ellinit([0,0,0,Mod(1,7),0]); P=[Mod(1,7),Mod(3,7)]; ellpow(E,P,7) Output: ? ? ? [Mod(1, 7), Mod(4, 7)] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:46:48 2004 Input: E=ellinit([0,0,0,Mod(1,7),0]); P=[Mod(1,7),Mod(3,7)]; ellpow(E,P,-7) Output: ? ? ? [Mod(1, 7), Mod(3, 7)] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:50:00 2004 Input: E=ellinit([0,0,0,Mod(1,11),0]); P=[Mod(5,11),Mod(3,11)]; ellpow(E,P,-11) Output: ? ? ? [Mod(5, 11), Mod(3, 11)] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.009s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:50:30 2004 Input: E=ellinit([0,0,0,Mod(1,11),0]); P=[Mod(5,11),Mod(3,11)]; ellpow(E,P,11) Output: ? ? ? [Mod(5, 11), Mod(8, 11)] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:50:37 2004 Input: E=ellinit([0,0,0,Mod(1,11),0]); P=[Mod(5,11),Mod(3,11)]; ellpow(E,P,3) Output: ? ? ? [0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:50:44 2004 Input: E=ellinit([0,0,0,Mod(1,11),0]); P=[Mod(5,11),Mod(3,11)]; ellpow(E,P,4) Output: ? ? ? [Mod(5, 11), Mod(3, 11)] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:52:21 2004 Input: E=ellinit([0,0,0,Mod(1,11),0]); P=[Mod(7,11),Mod(3,11)]; ellpow(E,P,4) Output: ? ? ? [Mod(5, 11), Mod(8, 11)] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.002s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:52:29 2004 Input: E=ellinit([0,0,0,Mod(1,11),0]); P=[Mod(7,11),Mod(3,11)]; ellpow(E,P,8) Output: ? ? ? [Mod(5, 11), Mod(3, 11)] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.008s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:52:37 2004 Input: E=ellinit([0,0,0,Mod(1,11),0]); P=[Mod(7,11),Mod(3,11)]; ellpow(E,P,11) Output: ? ? ? [Mod(7, 11), Mod(8, 11)] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:52:46 2004 Input: E=ellinit([0,0,0,Mod(1,11),0]); P=[Mod(7,11),Mod(3,11)]; ellpow(E,P,-11) Output: ? ? ? [Mod(7, 11), Mod(3, 11)] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:53:38 2004 Input: E=ellinit([0,0,0,Mod(1,11),0]); P=[Mod(0,11),Mod(0,11)]; ellpow(E,P,-11) Output: ? ? ? [Mod(0, 11), Mod(0, 11)] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:53:44 2004 Input: E=ellinit([0,0,0,Mod(1,11),0]); P=[Mod(0,11),Mod(0,11)]; ellpow(E,P,11) Output: ? ? ? [Mod(0, 11), Mod(0, 11)] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Fri Oct 8 09:53:50 2004 Input: E=ellinit([0,0,0,Mod(1,11),0]); P=[Mod(0,11),Mod(0,11)]; ellpow(E,P,-11) Output: ? ? ? [Mod(0, 11), Mod(0, 11)] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Fri Oct 8 14:49:05 2004 Input: factor(40) Output: ? [2 3] [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '80.13.4' ************** PARI ***************** Host 80.13.48.250 (80.13.48.250) Time: Sat Oct 9 00:20:56 2004 Input: v=vector(10,j,1) Output: ? [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.003s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.113.254 (209.184.113.254) Time: Sat Oct 9 12:47:55 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.113.254 (209.184.113.254) Time: Sat Oct 9 12:49:10 2004 Input: m=14808811; k=4789985; Mod(5941389,m)^k Output: ? ? ? Mod(70, 14808811) ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.004s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.113.254 (209.184.113.254) Time: Sat Oct 9 12:49:52 2004 Input: m=14808811; k=4789985; Mod(5941389,m)^k; Mod(4855204,m)^k Output: ? ? ? ? Mod(111, 14808811) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.113.254 (209.184.113.254) Time: Sat Oct 9 12:50:30 2004 Input: m=14808811; k=4789985; Mod(5941389,m)^k; Mod(4855204,m)^k Mod(9306403,m)^k Output: ? ? ? ? Mod(111, 14808811) ? Mod(103, 14808811) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.113.254 (209.184.113.254) Time: Sat Oct 9 12:51:01 2004 Input: m=14808811; k=4789985; Mod(5941389,m)^k; Mod(4855204,m)^k Mod(9306403,m)^k Mod(3658770,m)^k Output: ? ? ? ? Mod(111, 14808811) ? Mod(103, 14808811) ? Mod(104, 14808811) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.113.254 (209.184.113.254) Time: Sat Oct 9 12:51:30 2004 Input: m=14808811; k=4789985; Mod(5941389,m)^k; Mod(4855204,m)^k Mod(9306403,m)^k Mod(3658770,m)^k Mod(4855204,m)^k Output: ? ? ? ? Mod(111, 14808811) ? Mod(103, 14808811) ? Mod(104, 14808811) ? Mod(111, 14808811) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.113.254 (209.184.113.254) Time: Sat Oct 9 12:51:51 2004 Input: m=14808811; k=4789985; Mod(5941389,m)^k; Mod(4855204,m)^k Mod(9306403,m)^k Mod(3658770,m)^k Mod(4855204,m)^k Mod(13721432,m)^k Output: ? ? ? ? Mod(111, 14808811) ? Mod(103, 14808811) ? Mod(104, 14808811) ? Mod(111, 14808811) ? Mod(114, 14808811) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.113.254 (209.184.113.254) Time: Sat Oct 9 12:52:20 2004 Input: m=14808811; k=4789985; Mod(5941389,m)^k; Mod(4855204,m)^k Mod(9306403,m)^k Mod(3658770,m)^k Mod(4855204,m)^k Mod(13721432,m)^k Mod(1322621,m)^k Output: ? ? ? ? Mod(111, 14808811) ? Mod(103, 14808811) ? Mod(104, 14808811) ? Mod(111, 14808811) ? Mod(114, 14808811) ? Mod(110, 14808811) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.008s '24.250.' ************** PARI ***************** Host 24.250.172.227 (24.250.172.227) Time: Sun Oct 10 00:13:20 2004 Input: 22! Output: ? 1124000727777607680000 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.004s sys 0m0.005s '218.47.' ************** PARI ***************** Host 218.47.138.40 (218.47.138.40) Time: Sun Oct 10 12:21:34 2004 Input: factor(754838685673403250817815467686560425964416958861401194449084381071630229722100857179323372193549672196641809541) Output: ? [754838685673403250817815467686560425964416958861401194449084381071630229722100857179323372193549672196641809541 1] ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.020s sys 0m0.005s '218.47.' ************** PARI ***************** Host 218.47.138.40 (218.47.138.40) Time: Sun Oct 10 12:21:47 2004 Input: factor(13051070336175283765241555981) Output: ? [13051070336175283765241555981 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.004s '218.47.' ************** PARI ***************** Host 218.47.138.40 (218.47.138.40) Time: Sun Oct 10 12:22:01 2004 Input: factor(44150768863179970138761108743) Output: ? [44150768863179970138761108743 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '218.47.' ************** PARI ***************** Host 218.47.138.40 (218.47.138.40) Time: Sun Oct 10 12:22:14 2004 Input: factor(2250730917458155049758192191801593358179895870713183709236603472205265143969889245038426722302018046269879964204429407/44150768863179970138761108743) Output: ? [50978294951850258538993701135036765568108019089176244471733547982180755616368273282307049 1] ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.017s sys 0m0.003s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 06:01:11 2004 Input: factor(x^30-1) Output: ? [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] [x^4 - x^3 + x^2 - x + 1 1] [x^4 + x^3 + x^2 + x + 1 1] [x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1] [x^8 + x^7 - x^5 - x^4 - x^3 + x + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.097s user 0m0.009s sys 0m0.006s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 06:01:49 2004 Input: factor(x^2 + 222222*x + 111111) Output: ? [x^2 + 222222*x + 111111 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 06:02:12 2004 Input: factor(x^11 + x + 1) Output: ? [x^2 + x + 1 1] [x^9 - x^8 + x^6 - x^5 + x^3 - x^2 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 06:02:21 2004 Input: factor(x^12 + x + 1) Output: ? [x^12 + x + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 06:02:26 2004 Input: factor(x^13 + x + 1) Output: ? [x^13 + x + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.005s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 06:02:31 2004 Input: factor(x^14 + x + 1) Output: ? [x^2 + x + 1 1] [x^12 - x^11 + x^9 - x^8 + x^6 - x^5 + x^3 - x^2 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 06:02:43 2004 Input: factor(x^15 + x + 1) Output: ? [x^15 + x + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 06:02:49 2004 Input: factor(x^2005 + x + 1) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m0.022s user 0m0.013s sys 0m0.010s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 06:03:21 2004 Input: factor(x^200 + x + 1) Output: ? [x^2 + x + 1 1] [x^198 - x^197 + x^195 - x^194 + x^192 - x^191 + x^189 - x^188 + x^186 - x^185 + x^183 - x^182 + x^180 - x^179 + x^177 - x^176 + x^174 - x^173 + x^171 - x^170 + x^168 - x^167 + x^165 - x^164 + x^162 - x^161 + x^159 - x^158 + x^156 - x^155 + x^153 - x^152 + x^150 - x^149 + x^147 - x^146 + x^144 - x^143 + x^141 - x^140 + x^138 - x^137 + x^135 - x^134 + x^132 - x^131 + x^129 - x^128 + x^126 - x^125 + x^123 - x^122 + x^120 - x^119 + x^117 - x^116 + x^114 - x^113 + x^111 - x^110 + x^108 - x^107 + x^105 - x^104 + x^102 - x^101 + x^99 - x^98 + x^96 - x^95 + x^93 - x^92 + x^90 - x^89 + x^87 - x^86 + x^84 - x^83 + x^81 - x^80 + x^78 - x^77 + x^75 - x^74 + x^72 - x^71 + x^69 - x^68 + x^66 - x^65 + x^63 - x^62 + x^60 - x^59 + x^57 - x^56 + x^54 - x^53 + x^51 - x^50 + x^48 - x^47 + x^45 - x^44 + x^42 - x^41 + x^39 - x^38 + x^36 - x^35 + x^33 - x^32 + x^30 - x^29 + x^27 - x^26 + x^24 - x^23 + x^21 - x^20 + x^18 - x^17 + x^15 - x^14 + x^12 - x^11 + x^9 - x^8 + x^6 - x^5 + x^3 - x^2 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.226s user 0m0.180s sys 0m0.008s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 06:03:34 2004 Input: factor(x^1000 + x + 1) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m0.023s user 0m0.009s sys 0m0.015s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 06:04:01 2004 Input: factor(x^200 + 5*x + 1) Output: ? [x^200 + 5*x + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.515s user 0m0.446s sys 0m0.004s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 07:19:25 2004 Input: solve(x^11+x^10+x^9+x^8-10000) Output: ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: solve(x^11+x^10+x^9+x^8-100 ^-------------------- Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 07:19:38 2004 Input: solve(x^11+x^10+x^9+x^8-10000=0) Output: ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: solve(x^11+x^10+x^9+x^8-100 ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 07:20:00 2004 Input: solve(x^11 + x^10 + x^9 + x^8 - 10000 = 0) Output: ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: solve(x^11+x^10+x^9+x^8-100 ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.004s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 07:20:06 2004 Input: solve(x^11 + x^10 + x^9 + x^8 - 100= 0) Output: ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: solve(x^11+x^10+x^9+x^8-100 ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 07:21:50 2004 Input: solve(x== 0) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: solve(x==0) ^---- Timing: real 0m0.020s user 0m0.005s sys 0m0.004s '218.217' ************** PARI ***************** Host 218.217.241.246 (218.217.241.246) Time: Mon Oct 11 07:21:59 2004 Input: zero(x== 0) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: zero(x==0) ^---- Timing: real 0m0.018s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 11 11:08:42 2004 Input: i^2 Output: ? i^2 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 11 11:08:49 2004 Input: I^2 Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 11 11:09:13 2004 Input: sprt(2) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: sprt(2) ^------- Timing: real 0m0.019s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 11 11:09:22 2004 Input: sqrt(2) Output: ? 1.4142135623730950488016887242096980786 ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 11 11:09:53 2004 Input: -1 + sqrt(3 * I)/2 Output: ? -0.38762756430420547545067898132352715201 + 0.61237243569579452454932101867647284799*I ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 11 11:10:07 2004 Input: (-1 + sqrt(3 * I))/2 Output: ? 0.11237243569579452454932101867647284799 + 0.61237243569579452454932101867647284799*I ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 11 11:10:23 2004 Input: ((-1 + sqrt(3 * I))/2)^3 Output: ? -0.12500000000000000000000000000000000000 - 0.20644134645630821317601847198529072801*I ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 11 11:10:50 2004 Input: ((-1 + sqrt(3 )*I)/2)^3 Output: ? 1.0000000000000000000000000000000000000 + 0.E-38*I ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 11 11:11:04 2004 Input: ((-1 + sqrt(3 )*I)/2)^6 Output: ? 1.0000000000000000000000000000000000000 + 0.E-38*I ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 11 11:16:41 2004 Input: I^4 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 11 11:16:45 2004 Input: I^3 Output: ? -I ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.008s sys 0m0.001s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 11 11:16:58 2004 Input: I^0 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 11 11:17:21 2004 Input: I^1 Output: ? I ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 11 11:17:30 2004 Input: I^2 Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '151.100' ************** PARI ***************** Host 151.100.50.6 (151.100.50.6) Time: Mon Oct 11 12:29:44 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.239.' ************** PARI ***************** Host 68.239.107.214 (68.239.107.214) Time: Tue Oct 12 08:18:22 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(x^2+6); OK := MaximalOrder(K); [K!b : b in Basis(OK)]; Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: R:=PolynomialRing(Ra ^-------------------- *** unexpected character: K:=NumberField(x^2+6) ^-------------------- *** unexpected character: OK:=MaximalOrder(K); ^------------------ *** ; or ] expected: [K!b:binBasis(OK)]; ^---------------- Timing: real 0m0.015s user 0m0.004s sys 0m0.006s '68.239.' ************** PARI ***************** Host 68.239.107.214 (68.239.107.214) Time: Tue Oct 12 08:18:54 2004 Input: R := PolynomialRing(RationalField()); Output: ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: R:=PolynomialRing(Ra ^-------------------- Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '68.239.' ************** PARI ***************** Host 68.239.107.214 (68.239.107.214) Time: Tue Oct 12 08:20:05 2004 Input: > A := Matrix(2,2,[1,2,3,4]); Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: ^- Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '68.239.' ************** PARI ***************** Host 68.239.107.214 (68.239.107.214) Time: Tue Oct 12 08:21:06 2004 Input: > A := Matrix(2,2,[1,2,3,4]); > A; [1 2] [3 4] > SmithForm(A); Output: ? ? ? ? [12] ? [34] ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: ^- *** unexpected character: ^- *** unexpected character: ^- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:18:41 2004 Input: EulerPhi(100) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: EulerPhi(100) ^------------- Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:18:50 2004 Input: Phi(100) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Phi(100) ^-------- Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:18:55 2004 Input: phi(100) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: phi(100) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file) New syntax: phi(x) ===> eulerphi(x) eulerphi(x): Euler's totient function of x. Timing: real 0m0.014s user 0m0.005s sys 0m0.005s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:19:01 2004 Input: eulerphi(100) Output: ? 40 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.004s sys 0m0.008s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:19:14 2004 Input: eulerphi(100) Output: ? 40 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:19:39 2004 Input: EulerPhi(100) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: EulerPhi(100) ^------------- Timing: real 0m0.022s user 0m0.003s sys 0m0.006s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:19:48 2004 Input: eulerphi(10) Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:19:59 2004 Input: eulerphi(100000) Output: ? 40000 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:20:09 2004 Input: eulerphi(100001) Output: ? 90900 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.005s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:20:14 2004 Input: eulerphi(100000) Output: ? 40000 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:20:42 2004 Input: eulerphi(1000000000) Output: ? 400000000 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:22:45 2004 Input: eulerphi(10000000000000000000000000000000) Output: ? 4000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:22:54 2004 Input: eulerphi(10000000000000000000000000000001) Output: ? 9090909090909090909090909090900 ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.006s sys 0m0.007s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:22:59 2004 Input: eulerphi(10000000000000000000000000000002) Output: ? 3283582089552238805970149253600 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:23:11 2004 Input: eulerphi(1052345342553245234523452000000000000000000000000000002) Output: ? 502607615045299715592807380256022539161011067493457920 ? Errors (if any) and Timing Info: Timing: real 0m0.646s user 0m0.539s sys 0m0.035s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:23:15 2004 Input: eulerphi(1052345342553245234523452000000000000000000000000000002) Output: ? 502607615045299715592807380256022539161011067493457920 ? Errors (if any) and Timing Info: Timing: real 0m0.616s user 0m0.545s sys 0m0.029s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Tue Oct 12 10:23:57 2004 Input: eulerphi(1052345342553245234523452000000000000000000000000000002) Output: ? 502607615045299715592807380256022539161011067493457920 ? Errors (if any) and Timing Info: Timing: real 0m0.633s user 0m0.547s sys 0m0.025s '130.113' ************** PARI ***************** Host 130.113.226.6 (130.113.226.6) Time: Tue Oct 12 15:53:10 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '203.218' ************** PARI ***************** Host 203.218.225.29 (203.218.225.29) Time: Wed Oct 13 08:43:41 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.008s sys 0m0.002s '146.6.1' ************** PARI ***************** Host 146.6.101.9 (146.6.101.9) Time: Wed Oct 13 12:46:15 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '146.6.1' ************** PARI ***************** Host 146.6.101.9 (146.6.101.9) Time: Wed Oct 13 12:46:17 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 14 08:31:21 2004 Input: ?Mod Output: ? Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 14 08:32:18 2004 Input: Mod(13^9,17) Output: ? Mod(13, 17) ? Errors (if any) and Timing Info: Timing: real 0m0.068s user 0m0.005s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 14 08:32:35 2004 Input: x=13^9 Output: ? 10604499373 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 14 08:33:04 2004 Input: x=13^9 Mod( 10604499373, 17) Output: ? 10604499373 ? Mod(13, 17) ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.002s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 14 08:34:02 2004 Input: Mod(6,4) Output: ? Mod(2, 4) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 14 08:34:25 2004 Input: 13^9 Output: ? 10604499373 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 14 08:34:49 2004 Input: Mod(10604499373, 17) Output: ? Mod(13, 17) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 14 08:38:39 2004 Input: ?1 Output: ? divrem lex max min shift shiftmul sign vecmax vecmin ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 14 08:38:51 2004 Input: ?2 Output: ? List Mat Mod Pol Polrev Qfb Ser Set Str Strchr Strexpand Strtex Vec Vecsmall binary bitand bitneg bitnegimply bitor bittest bitxor ceil centerlift changevar component conj conjvec denominator floor frac imag length lift norm norml2 numerator numtoperm padicprec permtonum precision random real round simplify sizebyte sizedigit truncate valuation variable ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.001s sys 0m0.009s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 14 08:39:00 2004 Input: ?3 Output: ? Euler I Pi abs acos acosh agm arg asin asinh atan atanh bernfrac bernreal bernvec besselh1 besselh2 besseli besselj besseljh besselk besseln cos cosh cotan dilog eint1 erfc eta exp gamma gammah hyperu incgam incgamc lngamma log polylog psi sin sinh sqr sqrt sqrtn tan tanh teichmuller theta thetanullk weber zeta ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.008s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 14 08:39:07 2004 Input: ?4 Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numbpart numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfbsolve quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 14 08:39:17 2004 Input: ?5 Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 14 08:39:26 2004 Input: ?6 Output: ? bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark dirzetak factornf galoisexport galoisfixedfield galoisidentify galoisinit galoisisabelian galoispermtopol galoissubcyclo galoissubfields galoissubgroups idealadd idealaddtoone idealappr idealchinese idealcoprime idealdiv idealfactor idealhnf idealintersect idealinv ideallist ideallistarch ideallog idealmin idealmul idealnorm idealpow idealprimedec idealprincipal idealred idealstar idealtwoelt idealval ideleprincipal matalgtobasis matbasistoalg modreverse newtonpoly nfalgtobasis nfbasis nfbasistoalg nfdetint nfdisc nfeltdiv nfeltdiveuc nfeltdivmodpr nfeltdivrem nfeltmod nfeltmul nfeltmulmodpr nfeltpow nfeltpowmodpr nfeltreduce nfeltreducemodpr nfeltval nffactor nffactormod nfgaloisapply nfgaloisconj nfhilbert nfhnf nfhnfmod nfinit nfisideal nfisincl nfisisom nfkermodpr nfmodprinit nfnewprec nfroots nfrootsof1 nfsnf nfsolvemodpr nfsubfields polcompositum polgalois polred polredabs polredord poltschirnhaus rnfalgtobasis rnfbasis rnfbasistoalg rnfcharpoly rnfconductor rnfdedekind rnfdet rnfdisc rnfeltabstorel rnfeltdown rnfeltreltoabs rnfeltup rnfequation rnfhnfbasis rnfidealabstorel rnfidealdown rnfidealhnf rnfidealmul rnfidealnormabs rnfidealnormrel rnfidealreltoabs rnfidealtwoelt rnfidealup rnfinit rnfisfree rnfisnorm rnfisnorminit rnfkummer rnflllgram rnfnormgroup rnfpolred rnfpolredabs rnfpseudobasis rnfsteinitz subgrouplist zetak zetakinit ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 14 08:39:37 2004 Input: ?7 Output: ? O deriv eval factorpadic intformal padicappr polcoeff polcyclo poldegree poldisc poldiscreduced polhensellift polinterpolate polisirreducible pollead pollegendre polrecip polresultant polroots polrootsmod polrootspadic polsturm polsubcyclo polsylvestermatrix polsym poltchebi polzagier serconvol serlaplace serreverse subst taylor thue thueinit ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 14 08:39:45 2004 Input: ?8 Output: ? algdep charpoly concat lindep listcreate listinsert listkill listput listsort matadjoint matcompanion matdet matdetint matdiagonal mateigen mathess mathilbert mathnf mathnfmod mathnfmodid matid matimage matimagecompl matindexrank matintersect matinverseimage matisdiagonal matker matkerint matmuldiagonal matmultodiagonal matpascal matrank matrix matrixqz matsize matsnf matsolve matsolvemod matsupplement mattranspose qfgaussred qfjacobi qflll qflllgram qfminim qfperfection qfrep qfsign setintersect setisset setminus setsearch setunion trace vecextract vecsort vector vectorsmall vectorv ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 14 08:40:01 2004 Input: ?matrix Output: ? matrix(m,n,{X},{Y},{expr=0}): mXn matrix of expression expr, the row variable X going from 1 to m and the column variable Y going from 1 to n. By default, fill with 0s. ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.002s sys 0m0.008s '192.219' ************** PARI ***************** Host 192.219.240.44 (192.219.240.44) Time: Thu Oct 14 14:48:17 2004 Input: Factorization(43764674364367346743674374437843734674436743764376); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorization(437646 ^-------------------- Timing: real 0m0.021s user 0m0.004s sys 0m0.006s '192.219' ************** PARI ***************** Host 192.219.240.44 (192.219.240.44) Time: Thu Oct 14 14:48:24 2004 Input: Factor(43764674364367346743674374437843734674436743764376); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(4376467436436 ^-------------------- Timing: real 0m0.018s user 0m0.004s sys 0m0.007s '192.219' ************** PARI ***************** Host 192.219.240.44 (192.219.240.44) Time: Thu Oct 14 14:48:29 2004 Input: factor(43764674364367346743674374437843734674436743764376); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.142s user 0m0.100s sys 0m0.016s '192.219' ************** PARI ***************** Host 192.219.240.44 (192.219.240.44) Time: Thu Oct 14 14:48:30 2004 Input: factor(43764674364367346743674374437843734674436743764376); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.114s user 0m0.101s sys 0m0.014s '84.80.2' ************** PARI ***************** Host 84.80.201.203 (84.80.201.203) Time: Fri Oct 15 16:09:48 2004 Input: Modexp(2,3,5) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Modexp(2,3,5) ^------------- Timing: real 0m0.016s user 0m0.006s sys 0m0.005s '68.60.2' ************** PARI ***************** Host 68.60.227.249 (68.60.227.249) Time: Sat Oct 16 14:58:55 2004 Input: sin x=1/2 Output: ? 1/2 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.008s '68.60.2' ************** PARI ***************** Host 68.60.227.249 (68.60.227.249) Time: Sat Oct 16 14:59:34 2004 Input: sin 64=1/2xy Output: ? 1/2 ? Errors (if any) and Timing Info: *** Warning: unused characters: xy. Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '68.60.2' ************** PARI ***************** Host 68.60.227.249 (68.60.227.249) Time: Sat Oct 16 14:59:53 2004 Input: 64=1/2xy Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: 64=1/2xy ^------- Timing: real 0m0.019s user 0m0.003s sys 0m0.006s '68.60.2' ************** PARI ***************** Host 68.60.227.249 (68.60.227.249) Time: Sat Oct 16 15:00:15 2004 Input: 64=1/2 x Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: 64=1/2x ^------ Timing: real 0m0.010s user 0m0.002s sys 0m0.008s '68.60.2' ************** PARI ***************** Host 68.60.227.249 (68.60.227.249) Time: Sat Oct 16 15:00:35 2004 Input: 64=1/n Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: 64=1/n ^----- Timing: real 0m0.044s user 0m0.008s sys 0m0.001s '80.182.' ************** PARI ***************** Host 80.182.43.172 (80.182.43.172) Time: Sat Oct 16 16:07:48 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '80.182.' ************** PARI ***************** Host 80.182.43.172 (80.182.43.172) Time: Sat Oct 16 16:07:57 2004 Input: 3*5 Output: ? 15 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '80.182.' ************** PARI ***************** Host 80.182.43.172 (80.182.43.172) Time: Sat Oct 16 16:08:04 2004 Input: 12314 Output: ? 12314 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '80.182.' ************** PARI ***************** Host 80.182.43.172 (80.182.43.172) Time: Sat Oct 16 16:08:10 2004 Input: a=3 Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '80.182.' ************** PARI ***************** Host 80.182.43.172 (80.182.43.172) Time: Sat Oct 16 16:08:13 2004 Input: a Output: ? a ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '80.182.' ************** PARI ***************** Host 80.182.43.172 (80.182.43.172) Time: Sat Oct 16 16:08:18 2004 Input: a= Output: ? ? Errors (if any) and Timing Info: *** unexpected character: a= ^- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '80.182.' ************** PARI ***************** Host 80.182.43.172 (80.182.43.172) Time: Sat Oct 16 16:08:25 2004 Input: a:=4+4 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: a:=4+4 ^----- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '80.182.' ************** PARI ***************** Host 80.182.43.172 (80.182.43.172) Time: Sat Oct 16 16:08:29 2004 Input: a=4+4 Output: ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.003s sys 0m0.009s '80.182.' ************** PARI ***************** Host 80.182.43.172 (80.182.43.172) Time: Sat Oct 16 16:08:33 2004 Input: a=4+4 a Output: ? 8 ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '80.182.' ************** PARI ***************** Host 80.182.43.172 (80.182.43.172) Time: Sat Oct 16 16:08:38 2004 Input: a Output: ? ? a ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.006s '80.182.' ************** PARI ***************** Host 80.182.43.172 (80.182.43.172) Time: Sat Oct 16 16:15:51 2004 Input: a Output: ? ? a ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '64.252.' ************** PARI ***************** Host 64.252.251.95 (64.252.251.95) Time: Sat Oct 16 23:42:51 2004 Input: factor(140739635773439) Output: ? [65537 1] [2147483647 1] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.006s sys 0m0.005s '64.252.' ************** PARI ***************** Host 64.252.251.95 (64.252.251.95) Time: Sat Oct 16 23:43:14 2004 Input: factor(140739635773439) (65537-1)(2147483647-1) Output: ? [65537 1] [2147483647 1] ? 65536 ? Errors (if any) and Timing Info: *** Warning: unused characters: (2147483647-1). Timing: real 0m0.010s user 0m0.008s sys 0m0.003s '64.252.' ************** PARI ***************** Host 64.252.251.95 (64.252.251.95) Time: Sat Oct 16 23:43:30 2004 Input: factor(140739635773439) (65537-1)*(2147483647-1) Output: ? [65537 1] [2147483647 1] ? 140737488224256 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '64.252.' ************** PARI ***************** Host 64.252.251.95 (64.252.251.95) Time: Sat Oct 16 23:48:53 2004 Input: factor(140739635773439) (65537-1)*(2147483647-1) Mod(1/5,140737488224256) Output: ? [65537 1] [2147483647 1] ? 140737488224256 ? Mod(112589990579405, 140737488224256) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '64.252.' ************** PARI ***************** Host 64.252.251.95 (64.252.251.95) Time: Sat Oct 16 23:52:30 2004 Input: factor(140739635773439) (65537-1)*(2147483647-1) Mod(1/5,140737488224256) Mod(120501770072722,140739635773439)^112589990579405 Output: ? [65537 1] [2147483647 1] ? 140737488224256 ? Mod(112589990579405, 140737488224256) ? ? Mod(12012713011807, 140739635773439) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.006s '64.252.' ************** PARI ***************** Host 64.252.251.95 (64.252.251.95) Time: Sat Oct 16 23:56:24 2004 Input: n=17 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/(2^n-1) Output: ? 17 ? ? 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/131071 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '64.252.' ************** PARI ***************** Host 64.252.251.95 (64.252.251.95) Time: Sat Oct 16 23:56:28 2004 Input: n=19 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/(2^n-1) Output: ? 19 ? ? 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/524287 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '64.252.' ************** PARI ***************** Host 64.252.251.95 (64.252.251.95) Time: Sat Oct 16 23:56:55 2004 Input: vector(100,n,1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/(2^prime(n)-1)) Output: ? [1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/3, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/7, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/31, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/127, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2047, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/8191, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/131071, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/524287, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/8388607, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/536870911, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2147483647, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/137438953471, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2199023255551, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/8796093022207, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/140737488355327, 11679847981112819759721399310592745791658017001955007325132913837831330495881519756453703742878526[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.007s sys 0m0.005s '64.252.' ************** PARI ***************** Host 64.252.251.95 (64.252.251.95) Time: Sat Oct 16 23:57:11 2004 Input: vector(100,n,1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/(2^prime(n+10)-1)) Output: ? [1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2147483647, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/137438953471, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2199023255551, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/8796093022207, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/140737488355327, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/9007199254740991, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/576460752303423487, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2305843009213693951, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/147573952589676412927, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2361183241434822606847, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/9444732965739290427391, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/604462909807314587353087, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/9671406556917033397649407, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/618970019642690137449562111, 11679847981112819759721399310592745791658017001955007325132913837831330495881519756453703742878526148841468880674425122194137487680106575725753849[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '64.252.' ************** PARI ***************** Host 64.252.251.95 (64.252.251.95) Time: Sat Oct 16 23:57:19 2004 Input: vector(100,n,1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/(2^prime(n+20)-1)) Output: ? [1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/9444732965739290427391, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/604462909807314587353087, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/9671406556917033397649407, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/618970019642690137449562111, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/158456325028528675187087900671, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2535301200456458802993406410751, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/10141204801825835211973625643007, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/162259276829213363391578010288127, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/649037107316853453566312041152511, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/10384593717069655257060992658440191, 6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2722258935367507707706996859454145691647, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/174224571863520493293247799005065324265471, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/696898287454081973172991196020261297061887, 116798479811128197597213993[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '64.252.' ************** PARI ***************** Host 64.252.251.95 (64.252.251.95) Time: Sat Oct 16 23:57:41 2004 Input: vector(100,n,1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/(2^prime(n+20)-1)) isprime(6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151) Output: ? [1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/9444732965739290427391, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/604462909807314587353087, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/9671406556917033397649407, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/618970019642690137449562111, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/158456325028528675187087900671, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2535301200456458802993406410751, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/10141204801825835211973625643007, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/162259276829213363391578010288127, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/649037107316853453566312041152511, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/10384593717069655257060992658440191, 6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2722258935367507707706996859454145691647, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/174224571863520493293247799005065324265471, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/696898287454081973172991196020261297061887, 116798479811128197597213993[+++] ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m2.438s user 0m1.300s sys 0m0.009s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:10:24 2004 Input: isprime(1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:11:01 2004 Input: 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/65537 Output: ? 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/65537 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:11:37 2004 Input: 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2147483647 Output: ? 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2147483647 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:15:52 2004 Input: 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2147483647 Output: ? 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2147483647 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:16:13 2004 Input: 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/65537 Output: ? 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/65537 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:17:10 2004 Input: 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2147483647 Output: ? 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/2147483647 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:31:57 2004 Input: Mod(12,91)^(-1) Output: ? Mod(38, 91) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:32:49 2004 Input: 38*13 Output: ? 494 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:33:18 2004 Input: Mod(494,91) Output: ? Mod(39, 91) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:34:35 2004 Input: 12*39 Output: ? 468 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:34:44 2004 Input: 12*39 Output: ? 468 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:34:54 2004 Input: 91*12 Output: ? 1092 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:36:27 2004 Input: 473+1092 Output: ? 1565 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:36:45 2004 Input: Mod(1565,12) Output: ? Mod(5, 12) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:36:54 2004 Input: Mod(1565,91) Output: ? Mod(18, 91) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:38:02 2004 Input: 23*28 Output: ? 644 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:38:19 2004 Input: 23*38 Output: ? 874 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:38:47 2004 Input: Mod(874,91) Output: ? Mod(55, 91) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:39:23 2004 Input: 12*55 Output: ? 660 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:39:38 2004 Input: 12*91 Output: ? 1092 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:40:04 2004 Input: 665+1092 Output: ? 1757 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:40:20 2004 Input: Mod(1757,12) Output: ? Mod(5, 12) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:40:29 2004 Input: Mod(1757,28) Output: ? Mod(21, 28) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 02:40:37 2004 Input: Mod(1757,91) Output: ? Mod(28, 91) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 03:07:15 2004 Input: 12*38 Output: ? 456 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 03:09:19 2004 Input: (456*28)-(455*5) Output: ? 10493 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 17 03:09:38 2004 Input: Mod((456*28)-(455*5),1092) Output: ? Mod(665, 1092) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '82.84.1' ************** PARI ***************** Host 82.84.156.82 (82.84.156.82) Time: Sun Oct 17 11:59:11 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.175s user 0m0.008s sys 0m0.004s '62.123.' ************** PARI ***************** Host 62.123.114.34 (62.123.114.34) Time: Sun Oct 17 15:20:39 2004 Input: 12323 Output: ? 12323 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:31:19 2004 Input: issquare(Mod(-19,29)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.043s user 0m0.006s sys 0m0.002s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:31:41 2004 Input: issquare(Mod(-23,29)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:31:46 2004 Input: issquare(Mod(-17,29)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:31:54 2004 Input: issquare(Mod(-13,29)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:32:03 2004 Input: issquare(Mod(-11,29)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:32:13 2004 Input: issquare(Mod(-7,29)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:32:21 2004 Input: issquare(Mod(-5,29)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:32:29 2004 Input: issquare(Mod(-3,29)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:32:38 2004 Input: issquare(Mod(3,29)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:32:45 2004 Input: issquare(Mod(5,29)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.008s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:32:55 2004 Input: issquare(Mod(7,29)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:33:03 2004 Input: issquare(Mod(11,29)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.002s sys 0m0.007s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:33:09 2004 Input: issquare(Mod(13,29)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:33:18 2004 Input: issquare(Mod(17,29)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.049s user 0m0.006s sys 0m0.003s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:33:27 2004 Input: issquare(Mod(19,29)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:33:35 2004 Input: issquare(Mod(23,29)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:33:40 2004 Input: issquare(Mod(23,29)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:34:22 2004 Input: issquare(Mod(-23,31)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.003s sys 0m0.006s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:34:33 2004 Input: issquare(Mod(-19,31)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:34:41 2004 Input: issquare(Mod(-17,31)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:34:48 2004 Input: issquare(Mod(-13,31)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:34:55 2004 Input: issquare(Mod(-11,31)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:35:04 2004 Input: issquare(Mod(-7,31)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:35:12 2004 Input: issquare(Mod(-5,31)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.005s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:35:19 2004 Input: issquare(Mod(-3,31)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:35:27 2004 Input: issquare(Mod(3,31)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:35:33 2004 Input: issquare(Mod(5,31)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:35:41 2004 Input: issquare(Mod(7,31)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.007s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:35:49 2004 Input: issquare(Mod(11,31)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:35:55 2004 Input: issquare(Mod(13,31)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.008s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:36:04 2004 Input: issquare(Mod(17,31)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:36:12 2004 Input: issquare(Mod(19,31)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:36:20 2004 Input: issquare(Mod(23,31)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.002s sys 0m0.007s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:36:45 2004 Input: issquare(Mod(-23,107)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.008s sys 0m0.002s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:36:53 2004 Input: issquare(Mod(-19,107)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:37:01 2004 Input: issquare(Mod(-17,107)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:37:09 2004 Input: issquare(Mod(-13,107)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:37:17 2004 Input: issquare(Mod(-11,107)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.009s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:37:22 2004 Input: issquare(Mod(-11,107)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:37:27 2004 Input: issquare(Mod(-7,107)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:37:34 2004 Input: issquare(Mod(-5,107)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:37:42 2004 Input: issquare(Mod(-3,107)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:37:49 2004 Input: issquare(Mod(3,107)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:37:55 2004 Input: issquare(Mod(5,107)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:38:04 2004 Input: issquare(Mod(7,107)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.005s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:38:13 2004 Input: issquare(Mod(11,107)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:38:23 2004 Input: issquare(Mod(13,107)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.003s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:38:31 2004 Input: issquare(Mod(17,107)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:38:38 2004 Input: issquare(Mod(19,107)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:38:45 2004 Input: issquare(Mod(23,107)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:39:43 2004 Input: issquare(Mod(-23,109)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.084s user 0m0.003s sys 0m0.008s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:39:53 2004 Input: issquare(Mod(-19,109)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.008s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:40:01 2004 Input: issquare(Mod(-17,109)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:40:08 2004 Input: issquare(Mod(-13,109)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:40:15 2004 Input: issquare(Mod(-11,109)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:40:22 2004 Input: issquare(Mod(-7,109)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:40:30 2004 Input: issquare(Mod(-5,109)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:40:38 2004 Input: issquare(Mod(-3,109)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.008s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:40:45 2004 Input: issquare(Mod(3,109)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:40:50 2004 Input: issquare(Mod(5,109)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.002s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:40:57 2004 Input: issquare(Mod(7,109)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:41:06 2004 Input: issquare(Mod(11,109)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:41:13 2004 Input: issquare(Mod(13,109)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:41:20 2004 Input: issquare(Mod(17,109)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:41:27 2004 Input: issquare(Mod(19,109)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.195 (152.163.100.195) Time: Sun Oct 17 16:41:36 2004 Input: issquare(Mod(23,109)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 00:24:33 2004 Input: (2^31)-1 Output: ? 2147483647 ? Errors (if any) and Timing Info: Timing: real 0m0.145s user 0m0.007s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 00:26:09 2004 Input: 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/31 Output: ? 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/31 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 00:26:54 2004 Input: (1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777) Output: ? 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 00:27:05 2004 Input: isprime (1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 00:32:43 2004 Input: (1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/((2^607)-1)) Output: ? 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.008s sys 0m0.001s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 00:32:57 2004 Input: (1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/((2^521)-1)) Output: ? 170141183460469231731687303715884105727 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 00:39:03 2004 Input: ((2^521)-1)) Output: ? 6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151 ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 00:39:44 2004 Input: isprime(170141183460469231731687303715884105727) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.273s user 0m0.018s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 00:46:05 2004 Input: isprime(6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m1.288s user 0m1.281s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 00:50:00 2004 Input: (6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151-1)*(170141183460469231731687303715884105727-1) Output: ? 1167984798111281975972139931059274579158936902535370122798309482984051656370882540345227068878458151424961344884044856167291189127349203017598088675065925115777984293715856076132693129201132240900 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 00:53:25 2004 Input: Mod(13,1167984798111281975972139931059274579158936902535370122798309482984051656370882540345227068878458151424961344884044856167291189127349203017598088675065925115777984293715856076132693129201132240900)^(-1) Output: ? Mod(808604860230887521826866106117959324033110163293717777321906565142804992872149451008234124608163335601896315688954131192740054011241755935260215236584102003230912203341746514245710627908476166777, 1167984798111281975972139931059274579158936902535370122798309482984051656370882540345227068878458151424961344884044856167291189127349203017598088675065925115777984293715856076132693129201132240900) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 01:00:14 2004 Input: Mod(345154507061192622106247700216781134665062333599881715949805910472011109627250 535887572574536169242342944939400290427370728152540591009657462420993512634062 686954128751428017686266514962825793972,116798479811128197597213993105927457916580170019550073251329138378313304958815197564537037428785261488414688806744251221941374876801065757257538498645740597 3985247465176041951676954461208131403777)^808604860230887521826866106117959324033110163293717777321906565142804992872149451008234124608163335601896315688954131192740054011241755935260215236584102003230912203341746514245710627908476166777 Output: ? Mod(6051813012027051920272114270904091520, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 02:33:29 2004 Input: I^2 Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 02:34:45 2004 Input: (259+1513*I)-(789+566*I)*(1+i) Output: ? (-789 - 566*I)*i + (-530 + 947*I) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 02:34:53 2004 Input: (259+1513*I)-(789+566*I)*(1+I) Output: ? 36 + 158*I ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 03:09:41 2004 Input: (789+566*I)-(36+158*I)*(10-3*I) Output: ? -45 - 906*I ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 03:24:30 2004 Input: (789+566*I)-(36+158*I)*(2-4*I) Output: ? 85 + 394*I ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 03:29:25 2004 Input: (789+566*I)-(36+158*I)*(4-4*I) Output: ? 13 + 78*I ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 03:45:46 2004 Input: (36+158*I)-(13+78*I)*(2) Output: ? 10 + 2*I ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 03:54:14 2004 Input: (13+78*I)-(10+2*I)*(3-7i) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (13+78*I)-(10+2*I)*(3-7i) ^-- Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 03:54:22 2004 Input: (13+78*I)-(10+2*I)*(3-7*I) Output: ? -31 + 142*I ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 03:56:03 2004 Input: (13+78*I)-(10+2*I)*(3+7*I) Output: ? -3 + 2*I ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 04:08:28 2004 Input: (10+2*I)-(-3+2*I)*(-2+(-2)*I) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 04:17:13 2004 Input: (259+1513*I)/(-3+2*I) Output: ? 173 - 389*I ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Mon Oct 18 04:17:37 2004 Input: (789+566*I)/(-3+2*I) Output: ? -95 - 252*I ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.004s '220.99.' ************** PARI ***************** Host 220.99.172.57 (220.99.172.57) Time: Mon Oct 18 12:25:59 2004 Input: factor(228959385605609456144661299952264449837379302624349774657942512573374696311606008641) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 20136 Killed /usr/bin/gp -q --emacs Timing: real 0m21.010s user 0m20.976s sys 0m0.024s '129.64.' ************** PARI ***************** Host 129.64.53.39 (129.64.53.39) Time: Mon Oct 18 15:47:16 2004 Input: T = x^4 - x^3 + 6 x^2 - 6x + 1 nf = nfinit(T) nf.disc polgalois(T) Output: ? x^4 - x^3 + 6 ? [x^4 - x^3 + 6, [0, 2], 54324, 1, [[1, 1.3977691303734727828968759965804199757 + 1.0500701151949852002274028244673476669*I, 0.85111129499940486550617935409370475362 + 2.9355111834945337036868938486756823674*I, -2.7439467669453188162167827495037529962 + 2.0613822662440026603207154184328381126*I; 1, -0.89776913037347278289687599658041997570 + 1.0756861561119704381475456959284608021*I, -0.35111129499940486550617935409370475362 - 1.9314356498548547701764438147526926417*I, 2.7439467669453188162167827495037529962 + 3.2877333943119650830079539087846813283*I], [1, 2.4478392455684579831242788210477676426, 3.7866224784939385691930732027693871211, -0.68256450070131615589606733107091488357; 1, 0.34769901517848758266947317211307230875, -2.0843998884951288381807144945819776138, -4.8053290331893214765374981679365911089; 1, 0.17791702573849765525066969934804082637, -2.2825469448542596356826231688463973953, 6.0316801612572838992247366582884343246; 1, -1.9734552864854432210444216925088807778, 1.5803243548554499046702644606589878881, -0.54378662736664626679117115928092833214], 0, [4, 1, 1, 0; 1, 1, 1, -24; 1, 1, -23, -6; 0, -24, -6, 0], [3018, 750, 2922, 2994; 0, 6, 0, 0; 0, 0, 3, 1; 0, 0, 0, 1], [750, -6, 24, 32; -6, -8, 32, -125; 24, 32, -128, -3; 32, -125, -3, -4], [3018, [-982, 18, -8286, 2826; -471, -982, 18, -8304; 1381, 910, -72, 18; -3, 1381, 910, -982]]], [1.3977691303734727828968759965804199757 + 1.0500701151949852002274028244673476669*I, -0.89776913037347278289687599658041997570 + 1.0756861561119704381475456959284608021*I], [1, x, x^2, x^3 - x^2], [1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 1; 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, -6, 0, 0, -6, 0, 0, -6, 0, 0; 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -6, 0, 0, -6, 6; 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, -6; 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0]] ? 54324 ? [24, -1, 1] ? Errors (if any) and Timing Info: *** Warning: unused characters: x^2-6x+1. Timing: real 0m0.065s user 0m0.007s sys 0m0.007s '129.64.' ************** PARI ***************** Host 129.64.53.39 (129.64.53.39) Time: Mon Oct 18 15:47:49 2004 Input: T = x^4 - x^3 + 6*x^2 - 6*x + 1 nf = nfinit(T) nf.disc polgalois(T) Output: ? x^4 - x^3 + 6*x^2 - 6*x + 1 ? [x^4 - x^3 + 6*x^2 - 6*x + 1, [2, 1], -12875, 1, [[1, 0.20924118844764902036288377065773353743, -3.7791737727115540105884196433300197563, -0.73539189776856944073249801534148281402; 1, 0.81621118745887736421554406594350229465, -0.22517311127934318791489136547261924600, 3.4410275912536874575632781617458904014; 1, -0.012726187953263192289213918300617916039 + 2.4197423921975308875828706043189126043*I, 1.0021734419954485992516555044013195011 + 0.41325570176109459182242054289051507742*I, -1.8528178467425590084153900732022037937 + 0.35166750879792563918759463039298639851*I], [1, 0.20924118844764902036288377065773353743, -3.7791737727115540105884196433300197563, -0.73539189776856944073249801534148281402; 1, 0.81621118745887736421554406594350229465, -0.22517311127934318791489136547261924600, 3.4410275912536874575632781617458904014; 1, 2.4070162042442676952936566860182946883, 1.4154291437565431910740760472918345786, -1.5011503379446333692277954428092173952; 1, -2.4324685801507940798720845226195305204, 0.58891774023435400742923496151080442373, -2.2044853555404846476029847035951901922], 0, [4, 1, -2, -1; 1, -11, -3, 1; -2, -3, 16, -2; -1, 1, -2, 19], [515, 105, 240, 326; 0, 5, 0, 3; 0, 0, 5, 3; 0, 0, 0, 1], [-139, -8, -20, -9; -8, 44, 7, -2; -20, 7, -34, -5; -9, -2, -5, -28], [515, [4, -290, 14, 39; 81, 50, 129, -163; 48, -81, -141, -47; 1, 82, -48, 87]]], [0.20924118844764902036288377065773353743, 0.81621118745887736421554406594350229465, -0.012726187953263192289213918300617916039 + 2.4197423921975308875828706043189126043*I], [1, x, x^3 - x^2 + 6*x - 5, x^3 + 6*x - 2], [1, 0, -3, 2; 0, 1, 0, -6; 0, 0, -1, 0; 0, 0, 1, 1], [1, 0, 0, 0, 0, -3, -1, 1, 0, -1, 2, -1, 0, 1, -1, 6; 0, 1, 0, 0, 1, 0, 1, -2, 0, 1, 1, 0, 0, -2, 0, -1; 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, -3, -1, 0, 0, -1, 1; 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, -1, 0, 1, 1, 0, 2]] ? -12875 ? [24, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.008s sys 0m0.005s '129.64.' ************** PARI ***************** Host 129.64.53.39 (129.64.53.39) Time: Mon Oct 18 15:48:40 2004 Input: T = x^4 - x^3 + 6*x^2 - 6*x + 1 poldisc(T) Output: ? x^4 - x^3 + 6*x^2 - 6*x + 1 ? -12875 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '129.64.' ************** PARI ***************** Host 129.64.53.39 (129.64.53.39) Time: Mon Oct 18 15:49:07 2004 Input: factor(12875) Output: ? [5 3] [103 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '129.64.' ************** PARI ***************** Host 129.64.53.39 (129.64.53.39) Time: Mon Oct 18 15:49:54 2004 Input: polgalois(x^4 - x^3 + 6* x^2 - 6*x +1) Output: ? [24, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.008s sys 0m0.002s '82.48.2' ************** PARI ***************** Host 82.48.226.96 (82.48.226.96) Time: Mon Oct 18 17:18:14 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '82.48.2' ************** PARI ***************** Host 82.48.226.96 (82.48.226.96) Time: Mon Oct 18 17:18:30 2004 Input: 2 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.003s '201.129' ************** PARI ***************** Host 201.129.12.101 (201.129.12.101) Time: Mon Oct 18 23:30:38 2004 Input: 2^1000 Output: ? 10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '24.2.25' ************** PARI ***************** Host 24.2.250.189 (24.2.250.189) Time: Tue Oct 19 00:41:17 2004 Input: 140739635773439^(1/5) Output: ? 675.59011197132951834158328040724976565 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '24.2.25' ************** PARI ***************** Host 24.2.250.189 (24.2.250.189) Time: Tue Oct 19 00:42:20 2004 Input: 120501770072722^(1/5) Output: ? 654.93573192993512093844665958706282673 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '24.2.25' ************** PARI ***************** Host 24.2.250.189 (24.2.250.189) Time: Tue Oct 19 00:43:58 2004 Input: Factor(140739635773439) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(1407396357734 ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '24.2.25' ************** PARI ***************** Host 24.2.250.189 (24.2.250.189) Time: Tue Oct 19 00:44:04 2004 Input: factor(140739635773439) Output: ? [65537 1] [2147483647 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '24.2.25' ************** PARI ***************** Host 24.2.250.189 (24.2.250.189) Time: Tue Oct 19 00:45:46 2004 Input: 65536*2147483646 Output: ? 140737488224256 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '24.2.25' ************** PARI ***************** Host 24.2.250.189 (24.2.250.189) Time: Tue Oct 19 00:46:40 2004 Input: mod(5, 140737488224256) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(5,14073748822425 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file) New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '24.2.25' ************** PARI ***************** Host 24.2.250.189 (24.2.250.189) Time: Tue Oct 19 00:47:03 2004 Input: Mod(5, 140737488224256) Output: ? Mod(5, 140737488224256) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '24.2.25' ************** PARI ***************** Host 24.2.250.189 (24.2.250.189) Time: Tue Oct 19 00:47:12 2004 Input: Mod(5, 140737488224256) Output: ? Mod(5, 140737488224256) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.004s '24.2.25' ************** PARI ***************** Host 24.2.250.189 (24.2.250.189) Time: Tue Oct 19 00:47:26 2004 Input: Mod(5, 140737488224256) Output: ? Mod(5, 140737488224256) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '24.2.25' ************** PARI ***************** Host 24.2.250.189 (24.2.250.189) Time: Tue Oct 19 00:47:37 2004 Input: Mod{5, 140737488224256} Output: ? ? Errors (if any) and Timing Info: *** Warning: unused characters: {5,140737488224256}. *** unexpected character: Mod{5,140737488224256} ^-------------------- Timing: real 0m0.020s user 0m0.005s sys 0m0.004s '24.2.25' ************** PARI ***************** Host 24.2.250.189 (24.2.250.189) Time: Tue Oct 19 00:47:58 2004 Input: Mod(5, 140737488224256)^-1 Output: ? Mod(112589990579405, 140737488224256) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '24.2.25' ************** PARI ***************** Host 24.2.250.189 (24.2.250.189) Time: Tue Oct 19 00:51:39 2004 Input: 120501770072722^112589990579405 Mod 140737488224256 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** Warning: unused characters: Mod140737488224256. *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m8.360s user 0m8.342s sys 0m0.016s '24.2.25' ************** PARI ***************** Host 24.2.250.189 (24.2.250.189) Time: Tue Oct 19 00:52:16 2004 Input: (120501770072722^112589990579405) Mod 140737488224256 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** Warning: unused characters: Mod140737488224256. *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m8.359s user 0m8.334s sys 0m0.022s '149.156' ************** PARI ***************** Host 149.156.24.18 (149.156.24.18) Time: Tue Oct 19 07:02:27 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '80.11.1' ************** PARI ***************** Host 80.11.182.12 (80.11.182.12) Time: Tue Oct 19 07:33:20 2004 Input: sd qsd dsdqsd Output: ? sdqsddsdqsd ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '66.168.' ************** PARI ***************** Host 66.168.42.37 (66.168.42.37) Time: Wed Oct 20 01:16:13 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '193.140' ************** PARI ***************** Host 193.140.92.250 (193.140.92.250) Time: Wed Oct 20 03:58:23 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '134.58.' ************** PARI ***************** Host 134.58.253.114 (134.58.253.114) Time: Wed Oct 20 10:36:13 2004 Input: factor(2^385+1) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 29591 Killed /usr/bin/gp -q --emacs Timing: real 0m21.019s user 0m20.994s sys 0m0.006s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Oct 20 12:06:43 2004 Input: factorint(1562) Output: ? [2 1] [11 1] [71 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Oct 20 12:09:22 2004 Input: 9742924*278755104499778487295242384357847+186986377650663848995328905001288 Output: ? 2715889984739777469216361107706197125916 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Oct 20 12:11:55 2004 Input: factorint(2715889984739777469216361107706197125916) Output: ? [2 2] [3 1] [1787 1] [68737 1] [144340087 1] [12765235716600005145281 1] ? Errors (if any) and Timing Info: Timing: real 0m0.074s user 0m0.056s sys 0m0.016s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Oct 20 12:13:30 2004 Input: factorint(12765235716600005145281) Output: ? [12765235716600005145281 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Oct 20 12:13:37 2004 Input: isprime(12765235716600005145281) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Oct 20 12:13:59 2004 Input: isprime(144340087) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 21:15:13 2004 Input: Mod(120501770072722,140739635773439)^112589990579405 Output: ? Mod(12012713011807, 140739635773439) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 21:17:19 2004 Input: Mod(91605033826542,140739635773439)^112589990579405 Output: ? Mod(5270519202716, 140739635773439) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 21:18:25 2004 Input: Mod(62956878901959,140739635773439)^112589990579405 Output: ? Mod(5200920050000, 140739635773439) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 21:33:48 2004 Input: Mod(116506357477892,140739635773439)^112589990579405 Output: ? Mod(12012703123027, 140739635773439) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 21:34:47 2004 Input: Mod(24986135501133,140739635773439)^112589990579405 Output: ? Mod(16152118180109, 140739635773439) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 22:01:27 2004 Input: Mod(85851910580958,140739635773439)^112589990579405 Output: ? Mod(20270430160514, 140739635773439) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.008s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 22:02:36 2004 Input: Mod(27534122132210,140739635773439)^112589990579405 Output: ? Mod(4180527040527, 140739635773439) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 22:03:58 2004 Input: Mod(139930233613466,140739635773439)^112589990579405 Output: ? Mod(22151927161805, 140739635773439) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 22:04:50 2004 Input: Mod(37977045465311,140739635773439)^112589990579405 Output: ? Mod(13090518190000, 140739635773439) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 22:56:18 2004 Input: 116798479811128197597213993105927457916580170019550073251329138378313304958815 197564537037428785261488414688806744251221941374876801065757257538498645740597 3985247465176041951676954461208131403777.0/112589990579405.0 Output: ? 1.0373788931863807785271056345544556645 E181 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 22:56:56 2004 Input: 116798479811128197597213993105927457916580170019550073251329138378313304958815 197564537037428785261488414688806744251221941374876801065757257538498645740597 3985247465176041951676954461208131403777.0/140739635773439 Output: ? 8.2989045103931495229341241164269649888 E180 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 22:58:31 2004 Input: Mod(140739635773439,1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777) Output: ? Mod(140739635773439, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 22:59:01 2004 Input: Mod(1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777,140739635773439) Output: ? Mod(126414007245319, 140739635773439) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.001s sys 0m0.008s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 23:00:15 2004 Input: Mod(1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777,140737488224256) Output: ? Mod(138401026277377, 140737488224256) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 23:14:45 2004 Input: Mod(1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777,65537) Output: ? Mod(32513, 65537) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 23:15:08 2004 Input: Mod(1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777,2147483647) Output: ? Mod(234881017, 2147483647) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 23:15:32 2004 Input: Mod(1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777,65536) Output: ? Mod(1, 65536) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.003s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 23:16:37 2004 Input: Mod(1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777,2147483646) Output: ? Mod(259969, 2147483646) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Wed Oct 20 23:16:47 2004 Input: Mod(1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777,65536) Output: ? Mod(1, 65536) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:19:14 2004 Input: 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777/65537.0 Output: ? 1.7821761724083830141326882998295231383 E190 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:20:28 2004 Input: Mod(1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777,65537) Output: ? Mod(32513, 65537) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.002s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:21:40 2004 Input: Mod(1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777,2147483647) Output: ? Mod(234881017, 2147483647) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:39:11 2004 Input: Factor(65536) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(65536) ^------------- Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:39:46 2004 Input: factor(65536) Output: ? [2 16] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:40:15 2004 Input: 65536.0/2 Output: ? 32768.000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:40:29 2004 Input: 65536.0/16 Output: ? 4096.0000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:40:50 2004 Input: mod(65536,16) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(65536,16) ^------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file) New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:41:04 2004 Input: mod(65537,16) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(65537,16) ^------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file) New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:41:13 2004 Input: Mod(65536,16) Output: ? Mod(0, 16) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:41:20 2004 Input: Mod(65536,2) Output: ? Mod(0, 2) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:41:34 2004 Input: Mod(65536,4) Output: ? Mod(0, 4) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:41:38 2004 Input: Mod(65536,8) Output: ? Mod(0, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:41:42 2004 Input: Mod(65536,32) Output: ? Mod(0, 32) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:43:18 2004 Input: 65537/13.0 Output: ? 5041.3076923076923076923076923076923077 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:43:52 2004 Input: Mod(13,65536)^-1 Output: ? Mod(20165, 65536) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:46:15 2004 Input: Mod(345154507061192622106247700216781134665062333599881715949805910472011109627250535887572574536169242342944939400290427370728152540591009657462420993512634062686954128751428017686266514962825793972,1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777)^20165 Output: ? Mod(391657000632796562778393311470688612049722112313688653355197367821840299754941184708752928639707922847334897379485781949988723973046972082461776904466546508558021942908100274699389616299147602887, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:56:44 2004 Input: Mod(1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777,2147483647) Output: ? Mod(234881017, 2147483647) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:57:33 2004 Input: Mod(234881017,65537) Output: ? Mod(61946, 65537) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:58:14 2004 Input: Mod(116798479811128197597213993105927457916580170019550073251329138378313304958815 197564537037428785261488414688806744251221941374876801065757257538498645740597 3985247465176041951676954461208131403777 ,65537) Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...1951676954461208131403777 ^ *** Warning: unused characters: ,65537). Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:58:36 2004 Input: Mod(1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777,65537) Output: ? Mod(32513, 65537) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 00:59:55 2004 Input: Mod(1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777,234881017) Output: ? Mod(106954746, 234881017) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 01:16:15 2004 Input: Mod(1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777,65537) Output: ? Mod(32513, 65537) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 01:18:36 2004 Input: Mod(1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403776,65536) Output: ? Mod(0, 65536) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 01:19:11 2004 Input: (1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403776/65536.0) Output: ? 1.7822033662586700072817076584766762988 E190 ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 01:25:03 2004 Input: Mod(65536,1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403776)^-1 Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(65536, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403776). Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 01:25:29 2004 Input: Mod(65536,1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777)^-1 Output: ? Mod(1167966976077619389272067113982689812402813940770143745502602399234430304027702937681874808944006669867440281822202225315845947654900794128703733140373017891008349496922483967638385171741865410561, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 01:26:00 2004 Input: Mod(65536,1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777)^1167966976077619389272067113982689812402813940770143745502602399234430304027702937681874808944006669867440281822202225315845947654900794128703733140373017891008349496922483967638385171741865410561 Output: ? Mod(1084567497794458898033947940516782864849137439777049437724645525702934819691224420588976789710245192810896115161764563570652866455165585992867127362854529135110513180149789795331638515892000203338, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 01:33:59 2004 Input: Mod(13,1167966976077619389272067113982689812402813940770143745502602399234430304027702937681874808944006669867440281822202225315845947654900794128703733140373017891008349496922483967638385171741865410561)^-1 Output: ? Mod(89843613544432260713235931844822293261754918520780288115584799941110023386746379821682677611077436143649252447861709639680457511915445702207979472336385991616026884378652612895260397826297339274, 1167966976077619389272067113982689812402813940770143745502602399234430304027702937681874808944006669867440281822202225315845947654900794128703733140373017891008349496922483967638385171741865410561) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 01:35:52 2004 Input: Mod(345154507061192622106247700216781134665062333599881715949805910472011109627250535887572574536169242342944939400290427370728152540591009657462420993512634062686954128751428017686266514962825793972,1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777)^89843613544432260713235931844822293261754918520780288115584799941110023386746379821682677611077436143649252447861709639680457511915445702207979472336385991616026884378652612895260397826297339274 Output: ? Mod(441962800684511041096522092886336679312654908098441332146218339086697270514972303917474909670220504576979700934432582327360127340096012236728586385418176021147091675188438884582057626323704595140, 1167984798111281975972139931059274579165801700195500732513291383783133049588151975645370374287852614884146888067442512219413748768010657572575384986457405973985247465176041951676954461208131403777) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '24.177.' ************** PARI ***************** Host 24.177.11.159 (24.177.11.159) Time: Thu Oct 21 01:47:17 2004 Input: factor(65536) Output: ? [2 16] ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 21 05:44:48 2004 Input: ?3 Output: ? Euler I Pi abs acos acosh agm arg asin asinh atan atanh bernfrac bernreal bernvec besselh1 besselh2 besseli besselj besseljh besselk besseln cos cosh cotan dilog eint1 erfc eta exp gamma gammah hyperu incgam incgamc lngamma log polylog psi sin sinh sqr sqrt sqrtn tan tanh teichmuller theta thetanullk weber zeta ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 21 05:45:12 2004 Input: ?Pi Output: ? Pi=Pi(): the constant pi, with current precision. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 21 05:45:22 2004 Input: ?4 Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numbpart numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfbsolve quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 21 05:45:44 2004 Input: ?primes Output: ? primes(n): returns the vector of the first n primes (n C-integer) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 21 05:45:55 2004 Input: ?primes Output: ? primes(n): returns the vector of the first n primes (n C-integer) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 21 05:46:05 2004 Input: ?4 Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numbpart numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfbsolve quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 21 05:46:35 2004 Input: ?5 Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 21 05:46:44 2004 Input: ?3 Output: ? Euler I Pi abs acos acosh agm arg asin asinh atan atanh bernfrac bernreal bernvec besselh1 besselh2 besseli besselj besseljh besselk besseln cos cosh cotan dilog eint1 erfc eta exp gamma gammah hyperu incgam incgamc lngamma log polylog psi sin sinh sqr sqrt sqrtn tan tanh teichmuller theta thetanullk weber zeta ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 21 05:46:58 2004 Input: ?4 Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numbpart numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfbsolve quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 21 05:47:41 2004 Input: ?prime Output: ? prime(n): returns the n-th prime (n C-integer) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 21 05:48:11 2004 Input: prime(1000) Output: ? 7919 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 21 05:48:26 2004 Input: prime(10000) Output: ? 104729 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 21 05:48:40 2004 Input: prime(100000) Output: ? ? Errors (if any) and Timing Info: *** not enough precomputed primes Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Oct 21 05:48:49 2004 Input: prime(10000) Output: ? 104729 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '82.254.' ************** PARI ***************** Host 82.254.238.17 (82.254.238.17) Time: Thu Oct 21 08:06:31 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '82.254.' ************** PARI ***************** Host 82.254.238.17 (82.254.238.17) Time: Thu Oct 21 08:06:42 2004 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.003s '82.254.' ************** PARI ***************** Host 82.254.238.17 (82.254.238.17) Time: Thu Oct 21 08:06:53 2004 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '129.137' ************** PARI ***************** Host 129.137.179.33 (129.137.179.33) Time: Thu Oct 21 15:57:19 2004 Input: P:=PolynomialRing(GF(2),2); B:=[1,x]; I:=ideal; Variety(I); Output: ? ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,y>:=PolynomialRing(GF(2),2);. *** incorrect type in comparison. *** unexpected character: B:=[1,x]; ^-------- *** unexpected character: I:=ideal; ^------------- *** unknown function or error in formal parameters: Variety(I); ^--- Timing: real 0m0.165s user 0m0.005s sys 0m0.011s '129.116' ************** PARI ***************** Host 129.116.42.91 (129.116.42.91) Time: Thu Oct 21 16:58:08 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '129.116' ************** PARI ***************** Host 129.116.42.91 (129.116.42.91) Time: Thu Oct 21 16:58:24 2004 Input: 6x^2+2x+5=0 Output: ? 6 ? Errors (if any) and Timing Info: *** Warning: unused characters: x^2+2x+5=0. Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '129.116' ************** PARI ***************** Host 129.116.42.91 (129.116.42.91) Time: Thu Oct 21 16:58:41 2004 Input: 6x^2-2x+8=0 Output: ? 6 ? Errors (if any) and Timing Info: *** Warning: unused characters: x^2-2x+8=0. Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '129.116' ************** PARI ***************** Host 129.116.42.91 (129.116.42.91) Time: Thu Oct 21 16:59:01 2004 Input: 6^2 Output: ? 36 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.005s sys 0m0.005s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Thu Oct 21 17:03:46 2004 Input: FindGroupOrder2 := function (p, s) K := GF(p); v := K ! (4*s); u := K ! (s^2-5); x := u^3; b := 4*x*v; a := (v-u)^3*(3*u+v); A := a/b-2; x := x/v^3; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); return FactoredOrder(E); end function; p:=2785479845775218183; s:=7939418488320203; FindGroupOrder2(p,s); Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: FindGroupOrder2:=function(p,s) ^--------------- *** unexpected character: K:=GF(p); ^-------- *** unexpected character: v:=K!(4*s); ^---------- *** unexpected character: u:=K!(s^2-5); ^------------ *** unexpected character: x:=u^3; ^------ *** unexpected character: b:=4*x*v; ^-------- *** unexpected character: a:=(v-u)^3*(3*u+v); ^------------------ *** unexpected character: A:=a/b-2; ^-------- *** unexpected character: x:=x/v^3; ^-------- *** unexpected character: b:=x^3+A*x^2+x; ^-------------- *** unexpected character: E:=EllipticCurve([0,b ^-------------------- *** expected character: '=' instead of: returnFactoredOrder(E); ^- *** unexpected character: p:=278547984577521818 ^-------------------- *** unexpected character: s:=7939418488320203; ^------------------- *** expected character: '=' instead of: FindGroupOrder2(p,s); ^- Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '62.77.2' ************** PARI ***************** Host 62.77.235.20 (62.77.235.20) Time: Thu Oct 21 18:03:29 2004 Input: s=0;for(n=10^15,10^15+10^4,if(isprime(n)==1,s++,f=factor(n);u=matsize(f);z=component(u,1);if(f[z-1,1]<1000,s++)));s Output: ? 4520 ? Errors (if any) and Timing Info: Timing: real 0m3.781s user 0m3.287s sys 0m0.020s '62.77.2' ************** PARI ***************** Host 62.77.235.20 (62.77.235.20) Time: Thu Oct 21 18:04:03 2004 Input: b=c=d=e=0;x=10^15;for(n=x,x+10^5,u=factor(n);w=matsize(u);z=component(w,1);s=1;for(i=1,z,s=s*(u[i,1]^(u[i,2]+1)-1)(u[i,1]-1));g=gcd(n,s);if(s>2*n && 1<=n/s+g/sigma(g),c++;k=s-n;m=k;test=0;np=0;while(test<1 && np<169 && s>m,np++;d++;p=prime(np);power=valuation(m,p);if(power>0,bigsig=(p^(power+1)-1)(p-1);if(s%bigsig==0,s=sbigsig;m=m(p^power),test=1)));if(np==169 && s/m<1.005,e++;if(s%2>0,b++))));print(c,",",d,",",e,",",b) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '133.44.' ************** PARI ***************** Host 133.44.1.220 (133.44.1.220) Time: Thu Oct 21 23:52:02 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '133.44.' ************** PARI ***************** Host 133.44.1.220 (133.44.1.220) Time: Thu Oct 21 23:53:05 2004 Input: A = vector [1,5] Output: ? ? Errors (if any) and Timing Info: *** bad number of components in vector. Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '133.5.1' ************** PARI ***************** Host 133.5.178.229 (133.5.178.229) Time: Fri Oct 22 01:14:03 2004 Input: 2*7; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '129.49.' ************** PARI ***************** Host 129.49.7.122 (129.49.7.122) Time: Fri Oct 22 16:21:50 2004 Input: 4 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '129.49.' ************** PARI ***************** Host 129.49.7.122 (129.49.7.122) Time: Fri Oct 22 16:21:57 2004 Input: 4 + 3 Output: ? 7 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '129.49.' ************** PARI ***************** Host 129.49.7.122 (129.49.7.122) Time: Fri Oct 22 16:22:17 2004 Input: 1152921504606846975 Output: ? 1152921504606846975 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '129.49.' ************** PARI ***************** Host 129.49.7.122 (129.49.7.122) Time: Fri Oct 22 16:22:33 2004 Input: 1152921504606846975/365.242199 Output: ? 3156594467351914.5442446533950475968961 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '129.49.' ************** PARI ***************** Host 129.49.7.122 (129.49.7.122) Time: Fri Oct 22 16:22:45 2004 Input: 1152921504606846975/365.242199 / 86400 Output: ? 36534658186.943455373202006887124964075 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '129.49.' ************** PARI ***************** Host 129.49.7.122 (129.49.7.122) Time: Fri Oct 22 16:23:32 2004 Input: 1152921504606846975/365.242199 / 86400 Output: ? 36534658186.943455373202006887124964075 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '129.49.' ************** PARI ***************** Host 129.49.7.122 (129.49.7.122) Time: Fri Oct 22 16:24:03 2004 Input: 1152921504606846975*60/365.242199 / 86400 Output: ? 2192079491216.6073223921204132274978445 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '129.49.' ************** PARI ***************** Host 129.49.7.122 (129.49.7.122) Time: Fri Oct 22 16:24:07 2004 Input: 1152921504606846975*60/365.242199 / 86400 Output: ? 2192079491216.6073223921204132274978445 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '129.49.' ************** PARI ***************** Host 129.49.7.122 (129.49.7.122) Time: Fri Oct 22 16:27:24 2004 Input: 2^64 Output: ? 18446744073709551616 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '129.49.' ************** PARI ***************** Host 129.49.7.122 (129.49.7.122) Time: Fri Oct 22 16:27:29 2004 Input: 1152921504606846975*60/365.242199 / 86400 Output: ? 2192079491216.6073223921204132274978445 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '129.49.' ************** PARI ***************** Host 129.49.7.122 (129.49.7.122) Time: Fri Oct 22 16:28:08 2004 Input: (2^60-1)*60/365.242199 / 86400 Output: ? 2192079491216.6073223921204132274978445 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '129.49.' ************** PARI ***************** Host 129.49.7.122 (129.49.7.122) Time: Fri Oct 22 16:29:05 2004 Input: (2^60-1)*60/365.242199 / 86400 + 2001 Output: ? 2192079493217.6073223921204132274978445 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '129.49.' ************** PARI ***************** Host 129.49.7.122 (129.49.7.122) Time: Fri Oct 22 16:31:13 2004 Input: (2^60-1)*60/365.242199 / 86400 + 2001 Output: ? 2192079493217.6073223921204132274978445 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '129.49.' ************** PARI ***************** Host 129.49.7.122 (129.49.7.122) Time: Fri Oct 22 16:31:34 2004 Input: (2^60-1)*59/365.242199 / 86400 + 2001 Output: ? 2155544835030.6638670189184063403728804 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '67.20.2' ************** PARI ***************** Host 67.20.208.11 (67.20.208.11) Time: Sat Oct 23 21:46:28 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.003s sys 0m0.005s '67.20.2' ************** PARI ***************** Host 67.20.208.11 (67.20.208.11) Time: Sat Oct 23 21:46:49 2004 Input: Factor[x^2-9] Output: ? ? Errors (if any) and Timing Info: *** unexpected character: Factor[x^2-9] ^------- Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '24.141.' ************** PARI ***************** Host 24.141.169.21 (24.141.169.21) Time: Sat Oct 23 23:49:06 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.005s '142.169' ************** PARI ***************** Host 142.169.57.168 (142.169.57.168) Time: Sun Oct 24 05:10:21 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '84.129.' ************** PARI ***************** Host 84.129.24.183 (84.129.24.183) Time: Sun Oct 24 07:12:08 2004 Input: 20*578 Output: ? 11560 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '84.129.' ************** PARI ***************** Host 84.129.24.183 (84.129.24.183) Time: Sun Oct 24 07:13:38 2004 Input: 25^75 Output: ? 700649232162408535461864791644958065640130970938257885878534141944895541342930300743319094181060791015625 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '84.129.' ************** PARI ***************** Host 84.129.24.183 (84.129.24.183) Time: Sun Oct 24 07:14:31 2004 Input: P:= FunctionField(Rationals()); Q:= PolynomialRing(P); f:=x^6+45*x^5+365*x^4+865*x^3+400*x^2+38*x-4; print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); t1, t2:= TransitiveGroupIdentification(G); print(t1); print(t2) Output: ? ? ? ? f ? ? G ? ? ? t1 ? t2 ? Errors (if any) and Timing Info: *** unexpected character: P:=FunctionField(Rat ^-------------------- *** unexpected character: Q:=PolynomialRing(P) ^-------------------- *** unexpected character: f:=x^6+45*x^5+365*x^4 ^-------------------- *** Warning: unused characters: ,R:=GaloisGroup(f);. *** expected character: '=' instead of: print(Order(G)); ^-- *** Warning: unused characters: ,t2:=TransitiveGroupIdentification(G);. Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '203.173' ************** PARI ***************** Host 203.173.27.45 (203.173.27.45) Time: Sun Oct 24 08:26:34 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 24 19:02:36 2004 Input: primes(100) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 09:59:31 2004 Input: 5^6-1 Output: ? 15624 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:00:06 2004 Input: gcd(15624,54) Output: ? 18 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:01:33 2004 Input: 3^3*5^2 Output: ? 675 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:02:25 2004 Input: gcd(4^24-1,675) Output: ? 45 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:09:55 2004 Input: 11! Output: ? 39916800 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:10:56 2004 Input: gcd(37^39916800 - 1, 7621) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m4.227s user 0m4.217s sys 0m0.008s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:11:40 2004 Input: 5! Output: ? 120 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:12:05 2004 Input: gcd(37^120 -1, 7621) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:12:11 2004 Input: gcd(37^120 -1, 7621) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:12:24 2004 Input: gcd(12^120 -1, 7621) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:12:34 2004 Input: gcd(47^120 -1, 7621) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:12:43 2004 Input: gcd(47^{120} -1, 7621) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: gcd(47^{120}-1,7621) ^-------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:13:06 2004 Input: ?isprime Output: ? isprime(x,{flag=0}): if flag is omitted or 0, true(1) if x is a (proven) prime number, false(0) if not. If flag is 1, the primality is certified by the Pocklington-Lehmer Test. If flag is 2, the primality is certified using the APRCL test. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:13:31 2004 Input: isprime(7621) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:13:46 2004 Input: ?isprime Output: ? isprime(x,{flag=0}): if flag is omitted or 0, true(1) if x is a (proven) prime number, false(0) if not. If flag is 1, the primality is certified by the Pocklington-Lehmer Test. If flag is 2, the primality is certified using the APRCL test. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:14:22 2004 Input: isprime(7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:14:58 2004 Input: gcd(37^120 -1, 7627) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:15:07 2004 Input: gcd(11^120 -1, 7627) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:15:15 2004 Input: gcd(57^120 -1, 7627) Output: ? 29 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:16:12 2004 Input: 7627:29 Output: ? 29 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:16:25 2004 Input: 29^2 Output: ? 841 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:16:41 2004 Input: 7627/29 Output: ? 263 ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.004s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:16:59 2004 Input: isprime(263) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:18:30 2004 Input: factor(7626) Output: ? [2 1] [3 1] [31 1] [41 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:27:19 2004 Input: ?sqrt Output: ? sqrt(x): square root of x. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:27:39 2004 Input: sqrt(7627) Output: ? 87.332697198701014355012458245101104585 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.005s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:28:27 2004 Input: ?issquare Output: ? issquare(x,{&n}): true(1) if x is a square, false(0) if not. If n is given puts the exact square root there if it was computed. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:29:01 2004 Input: issquare(86^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:29:16 2004 Input: issquare(85^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:29:25 2004 Input: issquare(84^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:29:31 2004 Input: issquare(83^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:29:38 2004 Input: issquare(82^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:29:43 2004 Input: issquare(81^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:29:48 2004 Input: issquare(80^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:29:56 2004 Input: issquare(79^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:30:01 2004 Input: issquare(78^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:30:11 2004 Input: issquare(88^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:30:16 2004 Input: issquare(87^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:30:22 2004 Input: issquare(89^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:30:32 2004 Input: issquare(90^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:30:37 2004 Input: issquare(91^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:30:41 2004 Input: issquare(92^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.008s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:30:47 2004 Input: issquare(93^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:31:19 2004 Input: factor(7627) Output: ? [29 1] [263 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:33:48 2004 Input: issquare(116^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:33:56 2004 Input: issquare(117^2-7627) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:34:59 2004 Input: 263^2-117^2 Output: ? 55480 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:35:58 2004 Input: 146^2-117^2 Output: ? 7627 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Mon Oct 25 10:36:45 2004 Input: issquare(146^2-7627) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '140.228' ************** PARI ***************** Host 140.228.166.17 (140.228.166.17) Time: Mon Oct 25 15:48:44 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.182s user 0m0.004s sys 0m0.009s '195.95.' ************** PARI ***************** Host 195.95.93.202 (195.95.93.202) Time: Mon Oct 25 16:27:43 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '171.66.' ************** PARI ***************** Host 171.66.36.62 (171.66.36.62) Time: Mon Oct 25 16:50:38 2004 Input: 2 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.008s '194.108' ************** PARI ***************** Host 194.108.139.114 (194.108.139.114) Time: Tue Oct 26 10:14:11 2004 Input: Z4 := IntegerRing(4); P := PolynomialRing(Z4); n := 7; L := Z4CyclotomicFactors(n); L; Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: Z4:=IntegerRing(4); ^----------------- *** unexpected character: P:=PolynomialRing(Z4 ^-------------------- *** unexpected character: n:=7;L:=Z4CyclotomicF ^-------------------- Timing: real 0m0.023s user 0m0.004s sys 0m0.004s '4.27.22' ************** PARI ***************** Host 4.27.227.5 (4.27.227.5) Time: Tue Oct 26 23:34:50 2004 Input: (5*x-3)^8 Output: ? 390625*x^8 - 1875000*x^7 + 3937500*x^6 - 4725000*x^5 + 3543750*x^4 - 1701000*x^3 + 510300*x^2 - 87480*x + 6561 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '4.27.22' ************** PARI ***************** Host 4.27.227.5 (4.27.227.5) Time: Tue Oct 26 23:35:08 2004 Input: (5*x-3)^8 Output: ? 390625*x^8 - 1875000*x^7 + 3937500*x^6 - 4725000*x^5 + 3543750*x^4 - 1701000*x^3 + 510300*x^2 - 87480*x + 6561 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s '4.27.22' ************** PARI ***************** Host 4.27.227.5 (4.27.227.5) Time: Tue Oct 26 23:50:33 2004 Input: (5*x+3)^8 Output: ? 390625*x^8 + 1875000*x^7 + 3937500*x^6 + 4725000*x^5 + 3543750*x^4 + 1701000*x^3 + 510300*x^2 + 87480*x + 6561 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '4.27.22' ************** PARI ***************** Host 4.27.227.5 (4.27.227.5) Time: Tue Oct 26 23:50:43 2004 Input: (5*x-3)^8 Output: ? 390625*x^8 - 1875000*x^7 + 3937500*x^6 - 4725000*x^5 + 3543750*x^4 - 1701000*x^3 + 510300*x^2 - 87480*x + 6561 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '137.226' ************** PARI ***************** Host 137.226.37.186 (137.226.37.186) Time: Wed Oct 27 10:01:37 2004 Input: P:= PolynomialRing(FiniteField(5)); P; 85*x^2+13*x^1+x; Factorization(x^8+1); Output: ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: P:=PolynomialRing(Fi ^-------------------- *** expected character: ',' instead of: Factorization(x^8+1); ^------ Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Wed Oct 27 18:12:41 2004 Input: factor(18864295) Output: ? [5 1] [73 1] [51683 1] ? Errors (if any) and Timing Info: Timing: real 0m0.181s user 0m0.006s sys 0m0.002s '83.135.' ************** PARI ***************** Host 83.135.131.224 (83.135.131.224) Time: Thu Oct 28 02:41:49 2004 Input: 45+9*89-5893+987456/258974563*85-965896589/13*1,1 Output: ? -250159637528379720/3366669319 ? Errors (if any) and Timing Info: *** Warning: unused characters: ,1. Timing: real 0m0.029s user 0m0.003s sys 0m0.006s '80.132.' ************** PARI ***************** Host 80.132.27.67 (80.132.27.67) Time: Thu Oct 28 09:22:51 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.001s sys 0m0.008s '216.47.' ************** PARI ***************** Host 216.47.153.154 (216.47.153.154) Time: Thu Oct 28 14:57:28 2004 Input: 232345^324434%53453455 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '216.47.' ************** PARI ***************** Host 216.47.153.154 (216.47.153.154) Time: Thu Oct 28 14:57:43 2004 Input: 232345^324434 mod 53453455 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** Warning: unused characters: mod53453455. *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m1.263s user 0m1.223s sys 0m0.007s '68.102.' ************** PARI ***************** Host 68.102.195.50 (68.102.195.50) Time: Fri Oct 29 02:52:53 2004 Input: 2x+5=5 Output: ? 2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+5=5. Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.2.222 (147.162.2.222) Time: Fri Oct 29 08:04:33 2004 Input: 658678686798 Output: ? 658678686798 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '63.149.' ************** PARI ***************** Host 63.149.68.2 (63.149.68.2) Time: Fri Oct 29 15:05:29 2004 Input: sin(exp(28)) Output: ? -0.37596981679757431867934877323771245641 ? Errors (if any) and Timing Info: Timing: real 0m0.048s user 0m0.006s sys 0m0.003s '151.25.' ************** PARI ***************** Host 151.25.31.30 (151.25.31.30) Time: Sat Oct 30 05:07:47 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '83.76.2' ************** PARI ***************** Host 83.76.248.52 (83.76.248.52) Time: Sat Oct 30 15:27:17 2004 Input: (a+b)^2 Output: ? a^2 + 2*b*a + b^2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '83.76.2' ************** PARI ***************** Host 83.76.248.52 (83.76.248.52) Time: Sat Oct 30 15:27:41 2004 Input: (a+b)^2 Output: ? a^2 + 2*b*a + b^2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '83.76.2' ************** PARI ***************** Host 83.76.248.52 (83.76.248.52) Time: Sat Oct 30 15:27:51 2004 Input: (3*a+b)^2 Output: ? 9*a^2 + 6*b*a + b^2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '83.76.2' ************** PARI ***************** Host 83.76.248.52 (83.76.248.52) Time: Sat Oct 30 15:28:02 2004 Input: (1/4*a+b)^2 Output: ? 1/16*a^2 + 1/2*b*a + b^2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '132.216' ************** PARI ***************** Host 132.216.136.64 (132.216.136.64) Time: Sat Oct 30 17:41:02 2004 Input: 1-2*t+O(t^10) Output: ? 1 - 2*t + O(t^10) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '132.216' ************** PARI ***************** Host 132.216.136.64 (132.216.136.64) Time: Sat Oct 30 17:41:21 2004 Input: 1/(1-2*t+O(t^10)) Output: ? 1 + 2*t + 4*t^2 + 8*t^3 + 16*t^4 + 32*t^5 + 64*t^6 + 128*t^7 + 256*t^8 + 512*t^9 + O(t^10) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '132.216' ************** PARI ***************** Host 132.216.136.64 (132.216.136.64) Time: Sat Oct 30 17:43:09 2004 Input: (1-2*t+O(t^10))/(1-t)^5(1-t^2)^10(1-t^3)^40 Output: ? 1 + 3*t + 5*t^2 + 5*t^3 - 14*t^5 - 42*t^6 - 90*t^7 - 165*t^8 - 275*t^9 + O(t^10) ? Errors (if any) and Timing Info: *** Warning: unused characters: (1-t^2)^10(1-t^3)^40. Timing: real 0m0.011s user 0m0.003s sys 0m0.008s '132.216' ************** PARI ***************** Host 132.216.136.64 (132.216.136.64) Time: Sat Oct 30 17:43:26 2004 Input: (1-2*t+O(t^10))/(1-t)^5*(1-t^2)^10*(1-t^3)^40 Output: ? 1 + 3*t - 5*t^2 - 65*t^3 - 125*t^4 + 271*t^5 + 1843*t^6 + 2455*t^7 - 6875*t^8 - 31875*t^9 + O(t^10) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '132.216' ************** PARI ***************** Host 132.216.136.64 (132.216.136.64) Time: Sat Oct 30 17:44:29 2004 Input: (1-2*t+O(t^10))/(1-t)^5 Output: ? 1 + 3*t + 5*t^2 + 5*t^3 - 14*t^5 - 42*t^6 - 90*t^7 - 165*t^8 - 275*t^9 + O(t^10) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '132.216' ************** PARI ***************** Host 132.216.136.64 (132.216.136.64) Time: Sat Oct 30 17:45:11 2004 Input: (1-5*t+O(t^10))/(1-t)^5*(1-t^2)^10 Output: ? 1 - 20*t^2 - 40*t^3 + 40*t^4 + 176*t^5 + 60*t^6 - 280*t^7 - 270*t^8 + 160*t^9 + O(t^10) ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '132.216' ************** PARI ***************** Host 132.216.136.64 (132.216.136.64) Time: Sat Oct 30 17:45:46 2004 Input: (1-5*t+O(t^10))/(1-t)^5* Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: (1-5*t+O(t^10))/(1-t)^5* ^- Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '132.216' ************** PARI ***************** Host 132.216.136.64 (132.216.136.64) Time: Sat Oct 30 17:46:09 2004 Input: (1-5*t+O(t^10))/(1-t)^5 Output: ? 1 - 10*t^2 - 40*t^3 - 105*t^4 - 224*t^5 - 420*t^6 - 720*t^7 - 1155*t^8 - 1760*t^9 + O(t^10) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '132.216' ************** PARI ***************** Host 132.216.136.64 (132.216.136.64) Time: Sat Oct 30 17:46:50 2004 Input: ((1-5*t+O(t^10))/(1-t)^5)/(1-t^2)^10 Output: ? 1 - 40*t^3 - 150*t^4 - 624*t^5 - 1800*t^6 - 5160*t^7 - 12615*t^8 - 30080*t^9 + O(t^10) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '132.216' ************** PARI ***************** Host 132.216.136.64 (132.216.136.64) Time: Sat Oct 30 17:47:15 2004 Input: (((1-5*t+O(t^10))/(1-t)^5)/(1-t^2)^10)/(1-t^3)^40 Output: ? 1 - 150*t^4 - 624*t^5 - 2580*t^6 - 11160*t^7 - 37575*t^8 - 123400*t^9 + O(t^10) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '132.216' ************** PARI ***************** Host 132.216.136.64 (132.216.136.64) Time: Sat Oct 30 17:47:45 2004 Input: ((((1-5*t+O(t^10))/(1-t)^5)/(1-t^2)^10)/(1-t^3)^40)/(1-t^4)^50 Output: ? 1 - 100*t^4 - 624*t^5 - 2580*t^6 - 11160*t^7 - 43800*t^8 - 154600*t^9 + O(t^10) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.008s '132.216' ************** PARI ***************** Host 132.216.136.64 (132.216.136.64) Time: Sat Oct 30 17:48:07 2004 Input: ((((1-5*t+O(t^10))/(1-t)^5)/(1-t^2)^10)/(1-t^3)^40)/(1-t^4)^150 Output: ? 1 - 624*t^5 - 2580*t^6 - 11160*t^7 - 48750*t^8 - 217000*t^9 + O(t^10) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '132.216' ************** PARI ***************** Host 132.216.136.64 (132.216.136.64) Time: Sat Oct 30 17:48:42 2004 Input: (((((1-5*t+O(t^10))/(1-t)^5)/(1-t^2)^10)/(1-t^3)^40)/(1-t^4)^150)/(1-t^5)^624 Output: ? 1 - 2580*t^6 - 11160*t^7 - 48750*t^8 - 217000*t^9 + O(t^10) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.084s user 0m0.076s sys 0m0.008s '132.216' ************** PARI ***************** Host 132.216.136.64 (132.216.136.64) Time: Sat Oct 30 17:49:26 2004 Input: ((((((1-5*t+O(t^10))/(1-t)^5)/(1-t^2)^10)/(1-t^3)^40)/(1-t^4)^150)/(1-t^5)^624)/(1-t^6)^2580 Output: ? 1 - 11160*t^7 - 48750*t^8 - 217000*t^9 + O(t^10) ? ? ? Errors (if any) and Timing Info: Timing: real 0m6.261s user 0m6.249s sys 0m0.012s '132.216' ************** PARI ***************** Host 132.216.136.64 (132.216.136.64) Time: Sat Oct 30 17:50:19 2004 Input: (((((((1-5*t+O(t^10))/(1-t)^5)/(1-t^2)^10)/(1-t^3)^40)/(1-t^4)^150)/(1-t^5)^624)/(1-t^6)^2580)/(1-t^7)^11160 Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31893 Killed /usr/bin/gp -q --emacs Timing: real 0m21.004s user 0m20.991s sys 0m0.011s '63.149.' ************** PARI ***************** Host 63.149.68.2 (63.149.68.2) Time: Sat Oct 30 21:40:23 2004 Input: Arccos(Exp(-10^7)) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Arccos(Exp(-10^7)) ^----------- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '63.149.' ************** PARI ***************** Host 63.149.68.2 (63.149.68.2) Time: Sat Oct 30 21:40:32 2004 Input: acos(exp(-10^7)) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m0.039s user 0m0.014s sys 0m0.015s '68.6.62' ************** PARI ***************** Host 68.6.62.167 (68.6.62.167) Time: Sun Oct 31 04:19:09 2004 Input: .98(1.0225)^(1000) Output: ? 0.98000000000000000000000000000000000000 ? Errors (if any) and Timing Info: *** Warning: unused characters: (1.0225)^(1000). Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '211.30.' ************** PARI ***************** Host 211.30.110.38 (211.30.110.38) Time: Sun Oct 31 06:56:26 2004 Input: > R := PolynomialRing(RationalField()); > f := x^3 - x - 1; > GaloisGroup(f); Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: ^- *** unexpected character: ^- *** unexpected character: ^- Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '193.195' ************** PARI ***************** Host 193.195.0.101 (193.195.0.101) Time: Sun Oct 31 08:40:03 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '218.171' ************** PARI ***************** Host 218.171.152.122 (218.171.152.122) Time: Sun Oct 31 12:03:55 2004 Input: k=polcyclo(7) Output: ? x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 31 18:58:28 2004 Input: isprime(1105) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 31 18:58:38 2004 Input: factor(1105) Output: ? [5 1] [13 1] [17 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 31 18:59:19 2004 Input: Mod(3,1105)^1104 Output: ? Mod(1, 1105) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 31 18:59:25 2004 Input: Mod(4,1105)^1104 Output: ? Mod(1, 1105) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 31 18:59:30 2004 Input: Mod(5,1105)^1104 Output: ? Mod(885, 1105) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 31 18:59:35 2004 Input: Mod(6,1105)^1104 Output: ? Mod(1, 1105) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 31 18:59:40 2004 Input: Mod(7,1105)^1104 Output: ? Mod(1, 1105) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 31 18:59:44 2004 Input: Mod(8,1105)^1104 Output: ? Mod(1, 1105) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 31 18:59:56 2004 Input: Mod(9,1105)^1104 Output: ? Mod(1, 1105) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 31 19:00:04 2004 Input: Mod(128,1105)^1104 Output: ? Mod(1, 1105) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 31 19:00:11 2004 Input: Mod(150,1105)^1104 Output: ? Mod(885, 1105) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 31 19:00:18 2004 Input: Mod(153,1105)^1104 Output: ? Mod(391, 1105) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Sun Oct 31 19:00:25 2004 Input: Mod(172,1105)^1104 Output: ? Mod(1, 1105) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Mon Nov 1 11:40:42 2004 Input: x*eta(x^2)^2*eta(x^4)^3*eta(x^8)^(-3)*eta(x^16)^2 Output: ? x - 2*x^3 - 4*x^5 + 8*x^7 + 7*x^9 - 10*x^11 - 12*x^13 + 8*x^15 + 18*x^17 + O(x^19) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Mon Nov 1 11:42:45 2004 Input: allocatmem x*eta(x^2)^2*eta(x^4)^3*eta(x^8)^(-3)*eta(x^16)^2 Output: ? allocatmem ? x - 2*x^3 - 4*x^5 + 8*x^7 + 7*x^9 - 10*x^11 - 12*x^13 + 8*x^15 + 18*x^17 + O(x^19) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Mon Nov 1 11:42:54 2004 Input: x*eta(x^2)^2*eta(x^4)^3*eta(x^8)^(-3)*eta(x^16)^2 Output: ? ? x - 2*x^3 - 4*x^5 + 8*x^7 + 7*x^9 - 10*x^11 - 12*x^13 + 8*x^15 + 18*x^17 + O(x^19) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Mon Nov 1 11:43:07 2004 Input: x*eta(x^2)^2*eta(x^4)^3*eta(x^8)^(-3)*eta(x^16)^2 eta(x,100) Output: ? x - 2*x^3 - 4*x^5 + 8*x^7 + 7*x^9 - 10*x^11 - 12*x^13 + 8*x^15 + 18*x^17 + O(x^19) ? ? ? Errors (if any) and Timing Info: *** incorrect type in trueeta. Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '80.135.' ************** PARI ***************** Host 80.135.199.10 (80.135.199.10) Time: Mon Nov 1 18:13:02 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '80.135.' ************** PARI ***************** Host 80.135.199.10 (80.135.199.10) Time: Mon Nov 1 18:13:26 2004 Input: Sl(2,3) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Sl(2,3) ^------- Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '80.135.' ************** PARI ***************** Host 80.135.199.10 (80.135.199.10) Time: Mon Nov 1 18:13:50 2004 Input: SL(2,3) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: SL(2,3) ^------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '66.122.' ************** PARI ***************** Host 66.122.165.197 (66.122.165.197) Time: Mon Nov 1 18:33:25 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" how does magma 3 gv3 21ng x1vcs.b Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? 3 ? ? gv3 ? 21 ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: howdoesmagma. *** Warning: unused characters: ng. *** unknown member function: x1vcs.b ^- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.210' ************** PARI ***************** Host 147.210.16.146 (147.210.16.146) Time: Tue Nov 2 04:51:59 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '203.195' ************** PARI ***************** Host 203.195.202.126 (203.195.202.126) Time: Tue Nov 2 08:37:25 2004 Input: 107^309 Output: ? 1201122506283399201947418765787223384533068272562760122825444350020511467041539614885899563525701762886640091287982683086324746910950590309420407110715637939171970763135407640891703776346794770750658288205747875398146372074065263714993152822252190312135040008335148590687202915617243289915317346490514410295446278311309261691651245270708101522224408677189926127690331193003042746733273783624099494137871755482359375532357936358713970210346764605893420820513024477097527586725274560040204699514548829717287183678690003524858665944284584494106725284208345192942735701075012293033039433252364868209559112533022156366000012809944507 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '203.195' ************** PARI ***************** Host 203.195.202.126 (203.195.202.126) Time: Tue Nov 2 08:40:00 2004 Input: (a+5)^11 Output: ? a^11 + 55*a^10 + 1375*a^9 + 20625*a^8 + 206250*a^7 + 1443750*a^6 + 7218750*a^5 + 25781250*a^4 + 64453125*a^3 + 107421875*a^2 + 107421875*a + 48828125 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '203.195' ************** PARI ***************** Host 203.195.202.126 (203.195.202.126) Time: Tue Nov 2 08:40:31 2004 Input: (a+2*b+3*c)^11 Output: ? a^11 + (22*b + 33*c)*a^10 + (220*b^2 + 660*c*b + 495*c^2)*a^9 + (1320*b^3 + 5940*c*b^2 + 8910*c^2*b + 4455*c^3)*a^8 + (5280*b^4 + 31680*c*b^3 + 71280*c^2*b^2 + 71280*c^3*b + 26730*c^4)*a^7 + (14784*b^5 + 110880*c*b^4 + 332640*c^2*b^3 + 498960*c^3*b^2 + 374220*c^4*b + 112266*c^5)*a^6 + (29568*b^6 + 266112*c*b^5 + 997920*c^2*b^4 + 1995840*c^3*b^3 + 2245320*c^4*b^2 + 1347192*c^5*b + 336798*c^6)*a^5 + (42240*b^7 + 443520*c*b^6 + 1995840*c^2*b^5 + 4989600*c^3*b^4 + 7484400*c^4*b^3 + 6735960*c^5*b^2 + 3367980*c^6*b + 721710*c^7)*a^4 + (42240*b^8 + 506880*c*b^7 + 2661120*c^2*b^6 + 7983360*c^3*b^5 + 14968800*c^4*b^4 + 17962560*c^5*b^3 + 13471920*c^6*b^2 + 5773680*c^7*b + 1082565*c^8)*a^3 + (28160*b^9 + 380160*c*b^8 + 2280960*c^2*b^7 + 7983360*c^3*b^6 + 17962560*c^4*b^5 + 26943840*c^5*b^4 + 26943840*c^6*b^3 + 17321040*c^7*b^2 + 6495390*c^8*b + 1082565*c^9)*a^2 + (11264*b^10 + 168960*c*b^9 + 1140480*c^2*b^8 + 4561920*c^3*b^7 + 11975040*c^4*b^6 + 21555072*c^5*b^5 + 26943840*c^6*b^4 + 23094720*c^7*b^3 + 12990780*c^8*b^2 + 4330260*c^9*b + 649539*c^10)*a + (2048*b^11 + 33792*c*b^10 + 253440*c^2*b^9 + 1140480*c^3*b^8 + 3421440*c^4*b^7 + 7185024*c^5*b^6 + 10777536*c^6*b^5 + 11547360*c^7*b^4 + 8660520*c^8*b^3 + 4330260*c^9*b^2 + 1299078*c^10*b + 177147*c^11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '193.13.' ************** PARI ***************** Host 193.13.178.170 (193.13.178.170) Time: Tue Nov 2 09:27:47 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Tue Nov 2 09:51:20 2004 Input: 8! Output: ? 40320 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.004s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Tue Nov 2 09:52:05 2004 Input: ?cong Output: ? ? Errors (if any) and Timing Info: *** cong: unknown identifier. Timing: real 0m0.018s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Tue Nov 2 09:52:21 2004 Input: ?3 Output: ? Euler I Pi abs acos acosh agm arg asin asinh atan atanh bernfrac bernreal bernvec besselh1 besselh2 besseli besselj besseljh besselk besseln cos cosh cotan dilog eint1 erfc eta exp gamma gammah hyperu incgam incgamc lngamma log polylog psi sin sinh sqr sqrt sqrtn tan tanh teichmuller theta thetanullk weber zeta ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Tue Nov 2 09:52:29 2004 Input: ?4 Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numbpart numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfbsolve quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Tue Nov 2 09:53:06 2004 Input: ?5 Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Tue Nov 2 09:53:49 2004 Input: ?40320/9 Output: ? ? Errors (if any) and Timing Info: *** no such section in help: ?: 40320/9 ^------- Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Tue Nov 2 09:53:57 2004 Input: 40320/9 Output: ? 4480 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Tue Nov 2 09:54:32 2004 Input: 4480*9 Output: ? 40320 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Tue Nov 2 09:54:43 2004 Input: 8! Output: ? 40320 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Tue Nov 2 09:55:01 2004 Input: 9! Output: ? 362880 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '194.44.' ************** PARI ***************** Host 194.44.66.49 (194.44.66.49) Time: Tue Nov 2 15:28:46 2004 Input: 12365 Output: ? 12365 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '128.196' ************** PARI ***************** Host 128.196.227.20 (128.196.227.20) Time: Tue Nov 2 15:40:49 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.001s sys 0m0.008s '128.61.' ************** PARI ***************** Host 128.61.42.30 (128.61.42.30) Time: Tue Nov 2 15:42:07 2004 Input: 5+5 Output: ? 10 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '128.61.' ************** PARI ***************** Host 128.61.42.30 (128.61.42.30) Time: Tue Nov 2 15:47:17 2004 Input: ispower(n)= { local( greatexp, k, flag); flag =0; k = 2; greatexp = log(n)/log(2); while( (k <= greatexp && flag != 1), if( n==(floor(0.5 + 2^((greatexp/k)))^k, flag = 1; ); k = k+1; ); return(flag) } Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...r(0.5+2^((greatexp/k)))^k *** ,flag=1;);k=k+1;);re ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '128.61.' ************** PARI ***************** Host 128.61.42.30 (128.61.42.30) Time: Tue Nov 2 15:47:49 2004 Input: ispower(n)= { local( greatexp, k, flag); flag =0; k = 2; greatexp = log(n)/log(2); while( (k <= greatexp && flag != 1), if( n==(floor(0.5 + 2^(greatexp/k)))^k, flag = 1; ); k = k+1; ); return(flag) } Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '128.61.' ************** PARI ***************** Host 128.61.42.30 (128.61.42.30) Time: Tue Nov 2 15:48:09 2004 Input: ispower(45)= { local( greatexp, k, flag); flag =0; k = 2; greatexp = log(n)/log(2); while( (k <= greatexp && flag != 1), if( n==(floor(0.5 + 2^(greatexp/k)))^k, flag = 1; ); k = k+1; ); return(flag) } Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: ispower(45)=local(gr ^-------------------- Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '128.61.' ************** PARI ***************** Host 128.61.42.30 (128.61.42.30) Time: Tue Nov 2 15:53:50 2004 Input: is_prime(n)= { local(d, flag, s); d = 3; flag = 0; s = sqrt(n); if( Mod(n,2)==0, flag = 1 ); while( d < s && flag == 0, if( Mod(n,d) == 0, flag =1 ); d = d+2; ); return(!flag); } Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '128.61.' ************** PARI ***************** Host 128.61.42.30 (128.61.42.30) Time: Tue Nov 2 15:53:57 2004 Input: is_prime(5)= { local(d, flag, s); d = 3; flag = 0; s = sqrt(n); if( Mod(n,2)==0, flag = 1 ); while( d < s && flag == 0, if( Mod(n,d) == 0, flag =1 ); d = d+2; ); return(!flag); } Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: is_prime(5)=local(d, ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '128.61.' ************** PARI ***************** Host 128.61.42.30 (128.61.42.30) Time: Tue Nov 2 16:02:48 2004 Input: lpf(n)= { local(d,s); d = 2; s= sqrt(n); if( Mod(n,d) == 0, return(d) ); d = 3; while( d=2*sqrt(r)*twolgn&& ( Mod(n^((r-1)/q), r) != 1), flag = "BREAK"; ); ); ); end = sqrt(r)*twolgn; a =1; while( a <= end && flag != "COMPOSITE", comp_poly = Mod(x^n - Mod(a,n), x^r - 1); fx = Mod(x - Mod(a,n), x^r - 1); fx = polypower(fx, n); if( fx != comp_poly, flag = "COMPOSITE"; subflag = "POLY"; ); a = a + 1; ); if( flag == "COMPOSITE", print(flag, " ", subflag), print("PRIME") ); } Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '128.61.' ************** PARI ***************** Host 128.61.42.30 (128.61.42.30) Time: Tue Nov 2 16:25:06 2004 Input: aks(n) = { flag = "TBD"; if(ispower(n), flag = "COMPOSITE"; subflag = "POWER"; ); twolgn = 2*(log(n)/log(2)); r = 1; while(r=2*sqrt(r)*twolgn&& ( Mod(n^((r-1)/q), r) != 1), flag = "BREAK"; ); ); ); end = sqrt(r)*twolgn; a =1; while( a <= end && flag != "COMPOSITE", comp_poly = Mod(x^n - Mod(a,n), x^r - 1); fx = Mod(x - Mod(a,n), x^r - 1); fx = polypower(fx, n); if( fx != comp_poly, flag = "COMPOSITE"; subflag = "POLY"; ); a = a + 1; ); if( flag == "COMPOSITE", print(flag, " ", subflag), print("PRIME") ); } Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '139.168' ************** PARI ***************** Host 139.168.24.55 (139.168.24.55) Time: Wed Nov 3 03:54:58 2004 Input: 23! Output: ? 25852016738884976640000 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.24.55 (139.168.24.55) Time: Wed Nov 3 03:55:16 2004 Input: factor(123) Output: ? [3 1] [41 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.003s '139.168' ************** PARI ***************** Host 139.168.24.55 (139.168.24.55) Time: Wed Nov 3 03:55:36 2004 Input: factor(101) Output: ? [101 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '139.168' ************** PARI ***************** Host 139.168.24.55 (139.168.24.55) Time: Wed Nov 3 03:55:44 2004 Input: factor(102) Output: ? [2 1] [3 1] [17 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.24.55 (139.168.24.55) Time: Wed Nov 3 03:56:07 2004 Input: factor(1020000000000000000000000000000000001) Output: ? [101 1] [103 1] [743 1] [186191 1] [5112421 1] [41825893 1] [3314532203 1] ? Errors (if any) and Timing Info: Timing: real 0m0.080s user 0m0.021s sys 0m0.007s '171.16.' ************** PARI ***************** Host 171.16.2.5 (171.16.2.5) Time: Wed Nov 3 08:24:41 2004 Input: p 1000 Output: ? p1000 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '171.16.' ************** PARI ***************** Host 171.16.2.5 (171.16.2.5) Time: Wed Nov 3 08:24:59 2004 Input: p 1000 Output: ? p1000 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '171.16.' ************** PARI ***************** Host 171.16.2.8 (171.16.2.8) Time: Wed Nov 3 08:25:54 2004 Input: Pi Output: ? 3.1415926535897932384626433832795028842 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.140.39 (193.170.140.39) Time: Wed Nov 3 10:07:13 2004 Input: 3x4= Output: ? 3 ? Errors (if any) and Timing Info: *** Warning: unused characters: x4=. Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 14:16:27 2004 Input: gcd(12,8) Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 14:25:16 2004 Input: x=MOD(21,4) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: x=MOD(21,4) ^--------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 14:25:43 2004 Input: MOD(21,4) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: MOD(21,4) ^--------- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 14:25:56 2004 Input: Mod(21,4) Output: ? Mod(1, 4) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 14:26:16 2004 Input: Inv(Mod(21,4)) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Inv(Mod(21,4)) ^---------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 14:26:58 2004 Input: 1/Mod(21,4) Output: ? Mod(1, 4) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 14:27:16 2004 Input: 1/Mod(2,7) Output: ? Mod(4, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 14:27:49 2004 Input: 2/Mod(7,55) Output: ? Mod(16, 55) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 14:29:21 2004 Input: 27+2/Mod(7,55) Output: ? Mod(43, 55) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 14:33:30 2004 Input: 29+2/Mod(7,55) Int(Mod(7,55)) Output: ? Mod(45, 55) ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Int(Mod(7,55)) ^---------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 14:33:54 2004 Input: 29+2/Mod(7,55) int(Mod(7,55)) int x = 0 Output: ? Mod(45, 55) ? ? 0 ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: int(Mod(7,55)) ^---------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 14:35:36 2004 Input: 29+2/Mod(7,55) simplify(Mod(7,55)) Output: ? Mod(45, 55) ? Mod(7, 55) ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 14:59:39 2004 Input: 29+2/Mod(7,55) gtolong(Mod(7,55)) Output: ? Mod(45, 55) ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: gtolong(Mod(7,55)) ^---------- Timing: real 0m0.011s user 0m0.003s sys 0m0.008s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:03:12 2004 Input: 29+2/Mod(7,55) t_INT x = 1 x = Mod(7,55)) Output: ? Mod(45, 55) ? 1 ? ? Mod(7, 55) ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:03:58 2004 Input: 29+2/Mod(7,55) t_INT x = 1 x = Mod(7,55) Output: ? Mod(45, 55) ? 1 ? ? Mod(7, 55) ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:04:11 2004 Input: 29+2/Mod(7,55) t_INT x = Mod(7,55) x = Mod(7,55) Output: ? Mod(45, 55) ? Mod(7, 55) ? ? Mod(7, 55) ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:04:36 2004 Input: 29+2/Mod(7,55) t_INT (Mod(7,55)) x = Mod(7,55) Output: ? Mod(45, 55) ? ? ? Mod(7, 55) ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: t_INT(Mod(7,55)) ^---------- Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:04:51 2004 Input: 29+2/Mod(7,55) (t_INT) Mod(7,55) x = Mod(7,55) Output: ? Mod(45, 55) ? t_INT ? ? Mod(7, 55) ? ? Errors (if any) and Timing Info: *** Warning: unused characters: Mod(7,55). Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:06:23 2004 Input: x = 29+2/Mod(7,55) Mod(x*x, 55) Output: ? Mod(45, 55) ? ? ? ? ? Errors (if any) and Timing Info: *** forbidden division t_INTMOD % t_INT. Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:06:56 2004 Input: x = 29+2/Mod(7,55) x*x Output: ? Mod(45, 55) ? Mod(45, 55) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:07:18 2004 Input: x = 29+2/Mod(7,55) x*x == x Output: ? Mod(45, 55) ? 1 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:07:29 2004 Input: x = 29+2/Mod(7,55) x*x == x + 1 Output: ? Mod(45, 55) ? 0 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:12:09 2004 Input: x = 36+66/Mod(72,221) x*x == x + 1 Output: ? Mod(129, 221) ? 0 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:12:19 2004 Input: x = 36+66/Mod(72,221) x*x == x Output: ? Mod(129, 221) ? 0 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:12:45 2004 Input: x = 36+66/Mod(72,221) x*x Output: ? Mod(129, 221) ? Mod(66, 221) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:14:52 2004 Input: x = 124-3/Mod(25,221) x*x Output: ? Mod(62, 221) ? Mod(87, 221) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:19:02 2004 Input: x = 124-3/Mod(25,221) x*x x = 62 - 25/Mod(112,221) x*x Output: ? Mod(62, 221) ? Mod(87, 221) ? Mod(119, 221) ? Mod(17, 221) ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:20:05 2004 Input: x = 3/Mod(25,221) Output: ? Mod(62, 221) ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:20:47 2004 Input: x = 3/Mod(25,221) (3*25*62)%221 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:21:18 2004 Input: x = 3/Mod(25,221) Output: ? Mod(62, 221) ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:21:42 2004 Input: x = 3/Mod(25,221) 25*x Output: ? Mod(62, 221) ? Mod(3, 221) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:21:54 2004 Input: x = 3/Mod(25,221) 25*x/3 Output: ? Mod(62, 221) ? Mod(1, 221) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '63.149.' ************** PARI ***************** Host 63.149.68.2 (63.149.68.2) Time: Wed Nov 3 15:23:31 2004 Input: gamma(exp(-2^13)) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 12030 Killed /usr/bin/gp -q --emacs Timing: real 0m21.017s user 0m20.990s sys 0m0.011s '194.108' ************** PARI ***************** Host 194.108.142.48 (194.108.142.48) Time: Wed Nov 3 15:24:05 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:29:52 2004 Input: x = 67+2/Mod(87,221) x*x Output: ? Mod(34, 221) ? Mod(51, 221) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:32:13 2004 Input: x = 13-2/Mod(24,77) x*x Output: ? Mod(45, 77) ? Mod(23, 77) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:35:24 2004 Input: x = 23+1/Mod(12,55) x*x Output: ? Mod(46, 55) ? Mod(26, 55) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '140.247' ************** PARI ***************** Host 140.247.161.171 (140.247.161.171) Time: Wed Nov 3 15:35:55 2004 Input: h:= ClassNumber(NumberField(x^2+84)); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: h:=ClassNumber(Number ^-------------------- Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:37:05 2004 Input: x = 24+2/Mod(7,55) x*x Output: ? Mod(40, 55) ? Mod(5, 55) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:39:23 2004 Input: x = 24+2/Mod(7,55) x*x x = 29+2/Mod(7,55) x*x Output: ? Mod(40, 55) ? Mod(5, 55) ? Mod(45, 55) ? Mod(45, 55) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:41:40 2004 Input: x = 24+2/Mod(7,55) x = x + x*x x = 29+2/Mod(7,55) x*x Output: ? Mod(40, 55) ? Mod(45, 55) ? Mod(45, 55) ? Mod(45, 55) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 15:42:25 2004 Input: x = 24+2/Mod(7,55) x = x + x*x x = 32-2/Mod(7,55) x = x + x*x Output: ? Mod(40, 55) ? Mod(45, 55) ? Mod(16, 55) ? Mod(52, 55) ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 18:36:09 2004 Input: x = 7/Mod(4,35) x = x + x*x Output: ? Mod(28, 35) ? Mod(7, 35) ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 18:46:23 2004 Input: p=1; fordiv(n,d, p *= d); p Output: ? ? ? Errors (if any) and Timing Info: *** not an integer argument in an arithmetic function Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 18:47:19 2004 Input: { int d; int p; p=1; fordiv(n,d, p *= d); p } Output: ? ? ? Errors (if any) and Timing Info: *** not an integer argument in an arithmetic function Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 18:47:37 2004 Input: { int d; int p; //p=1; fordiv(n,d, p *= d); p } Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: intd;intp;//p=1;fordiv(n,d,p* ^-------------------- Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 18:47:58 2004 Input: { int d; int p; /*p=1; fordiv(n,d, p *= d); p */ } Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 18:48:23 2004 Input: { int d; int p; p=1; /* fordiv(n,d, p *= d); p */ } Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 18:48:40 2004 Input: p=1; /* fordiv(n,d, p *= d); p */ Output: ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 18:49:16 2004 Input: p = x * exp(-x) Output: ? x - x^2 + 1/2*x^3 - 1/6*x^4 + 1/24*x^5 - 1/120*x^6 + 1/720*x^7 - 1/5040*x^8 + 1/40320*x^9 - 1/362880*x^10 + 1/3628800*x^11 - 1/39916800*x^12 + 1/479001600*x^13 - 1/6227020800*x^14 + 1/87178291200*x^15 - 1/1307674368000*x^16 + 1/20922789888000*x^17 + O(x^18) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.004s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 18:51:39 2004 Input: [a,b,c; d,e,f] Output: ? [a b c] [d e f] ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 18:58:32 2004 Input: ?Pi Output: ? Pi=Pi(): the constant pi, with current precision. ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 18:58:44 2004 Input: ??Pi Output: ? Pi:  the constant Pi (3.14159...).  The library syntax is mppi(prec) where prec must be given. Note that this creates Pi on the PARI stack, but a copy is also created on the heap for quicker computations next time the function is called.  ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.067s user 0m0.022s sys 0m0.009s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:01:08 2004 Input: matrix(12, i, 1/Mod(i,13)) Output: ? ? ? ? ? Errors (if any) and Timing Info: *** variable name expected: matrix(12,i,1/Mod(i,13)) ^------------ Timing: real 0m0.010s user 0m0.006s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:01:26 2004 Input: vector(12, i, 1/Mod(i,13)) Output: ? [Mod(1, 13), Mod(7, 13), Mod(9, 13), Mod(10, 13), Mod(8, 13), Mod(11, 13), Mod(2, 13), Mod(5, 13), Mod(3, 13), Mod(4, 13), Mod(6, 13), Mod(12, 13)] ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:01:48 2004 Input: vector(13, i, 1/Mod(i,13)) Output: ? ? ? ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(0, 13). Timing: real 0m0.010s user 0m0.002s sys 0m0.007s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:01:58 2004 Input: vector(12, i, 1/Mod(i,13)) Output: ? [Mod(1, 13), Mod(7, 13), Mod(9, 13), Mod(10, 13), Mod(8, 13), Mod(11, 13), Mod(2, 13), Mod(5, 13), Mod(3, 13), Mod(4, 13), Mod(6, 13), Mod(12, 13)] ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:04:34 2004 Input: lift(Mod(4,13)) Output: ? 4 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:04:50 2004 Input: truncate(Mod(4,13)) Output: ? ? ? ? ? Errors (if any) and Timing Info: *** incorrect type in gtrunc. Timing: real 0m0.010s user 0m0.004s sys 0m0.004s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:05:17 2004 Input: vector(12, i, lift(1/Mod(i,13)) Output: ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...or(12,i,lift(1/Mod(i,13)) ^ Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:05:29 2004 Input: vector(12, i, lift(1/Mod(i,13))) Output: ? [1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12] ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:11:04 2004 Input: contfrac(2^(1/2)) Output: ? [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:12:42 2004 Input: contfrac(1357^(1/2)) Output: ? [36, 1, 5, 6, 1, 1, 7, 1, 1, 1, 5, 2, 17, 1, 23, 1, 1, 1, 1, 2, 1, 1, 1, 1, 23, 1, 17, 2, 5, 1, 1, 1, 7, 1, 1, 6, 5, 1, 73] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:16:53 2004 Input: znstar(35) Output: ? [24, [12, 2], [Mod(12, 35), Mod(34, 35)]] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:22:04 2004 Input: gbezout(5, 7, &x, &y) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: gbezout(5,7,&x,&y) ^------------------ Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:22:33 2004 Input: int x int y gbezout(5, 7, &x, &y) Output: ? intx ? inty ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: gbezout(5,7,&x,&y) ^------------------ Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:22:58 2004 Input: x = 0 y = 0 gbezout(5, 7, &x, &y) Output: ? 0 ? 0 ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: gbezout(5,7,&x,&y) ^------------------ Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:23:09 2004 Input: x = 0 y = 0 gbezout(5, 7, x, y) Output: ? 0 ? 0 ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: gbezout(5,7,x,y) ^---------------- Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:23:37 2004 Input: vecbezout(5, 7) x = 0 y = 0 gbezout(5, 7, x, y) Output: ? ? 0 ? 0 ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: vecbezout(5,7) ^-------------- *** unknown function or error in formal parameters: gbezout(5,7,x,y) ^---------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:24:26 2004 Input: bezout(5, 7) vecbezout(5, 7) x = 0 y = 0 gbezout(5, 7, x, y) Output: ? ? [3, -2, 1] ? ? 0 ? 0 ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: vecbezout(5,7) ^-------------- *** unknown function or error in formal parameters: gbezout(5,7,x,y) ^---------------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:25:52 2004 Input: bezout(5, 7) 1/Mod(5, 7) Output: ? [3, -2, 1] ? Mod(3, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:26:24 2004 Input: x=5 y=17 bezout(x, y) 1/Mod(x, y) Output: ? 5 ? 17 ? [7, -2, 1] ? Mod(7, 17) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '66.123.' ************** PARI ***************** Host 66.123.255.107 (66.123.255.107) Time: Wed Nov 3 19:29:45 2004 Input: x=5 y=17 bezout(x, y) 1/Mod(x, y) bezoutres(x, y) Output: ? 5 ? 17 ? [7, -2, 1] ? Mod(7, 17) ? [1/5, 0, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '133.5.1' ************** PARI ***************** Host 133.5.165.4 (133.5.165.4) Time: Thu Nov 4 01:41:00 2004 Input: ellj(x) Output: ? x^-1 + 744 + 196884*x + 21493760*x^2 + 864299970*x^3 + 20245856256*x^4 + 333202640600*x^5 + 4252023300096*x^6 + 44656994071935*x^7 + 401490886656000*x^8 + 3176440229784420*x^9 + 22567393309593600*x^10 + 146211911499519294*x^11 + 874313719685775360*x^12 + 4872010111798142520*x^13 + 25497827389410525184*x^14 + O(x^15) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '203.101' ************** PARI ***************** Host 203.101.28.63 (203.101.28.63) Time: Thu Nov 4 05:12:28 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.004s '203.101' ************** PARI ***************** Host 203.101.28.63 (203.101.28.63) Time: Thu Nov 4 05:12:38 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '203.101' ************** PARI ***************** Host 203.101.28.63 (203.101.28.63) Time: Thu Nov 4 05:12:41 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '130.234' ************** PARI ***************** Host 130.234.4.91 (130.234.4.91) Time: Thu Nov 4 10:59:58 2004 Input: 1+1 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '130.234' ************** PARI ***************** Host 130.234.4.91 (130.234.4.91) Time: Thu Nov 4 11:00:09 2004 Input: 1 1 + Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 11+ ^- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '155.207' ************** PARI ***************** Host 155.207.127.17 (155.207.127.17) Time: Thu Nov 4 13:21:31 2004 Input: x := PolynomialRing(Integers()).1; O := MaximalOrder(NumberField([x^2-229, x^2-2])); NormEquation(O, 3); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: x:=PolynomialRing(Int ^-------------------- *** expected character: '(' instead of: O:=MaximalOrder(Numbe ^-------------------- *** expected character: '(' instead of: NormEquation(O,3); ^---- Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '202.141' ************** PARI ***************** Host 202.141.68.23 (202.141.68.23) Time: Thu Nov 4 15:39:46 2004 Input: factor(28164327154783624632476) Output: ? [2 2] [11 1] [19 1] [107 1] [383 1] [2029 1] [405161811559 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '68.67.9' ************** PARI ***************** Host 68.67.93.236 (68.67.93.236) Time: Thu Nov 4 22:42:32 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '213.119' ************** PARI ***************** Host 213.119.138.197 (213.119.138.197) Time: Fri Nov 5 07:26:51 2004 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '213.119' ************** PARI ***************** Host 213.119.138.197 (213.119.138.197) Time: Fri Nov 5 07:27:02 2004 Input: 2+2**100 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 2+2**100 ^----- Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '213.119' ************** PARI ***************** Host 213.119.138.197 (213.119.138.197) Time: Fri Nov 5 07:27:13 2004 Input: 2+2*100 Output: ? 202 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '213.119' ************** PARI ***************** Host 213.119.138.197 (213.119.138.197) Time: Fri Nov 5 07:27:28 2004 Input: 2+2^100 Output: ? 1267650600228229401496703205378 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '213.119' ************** PARI ***************** Host 213.119.138.197 (213.119.138.197) Time: Fri Nov 5 07:27:35 2004 Input: 2+2^10000 Output: ? 19950631168807583848837421626835850838234968318861924548520089498529438830221946631919961684036194597899331129423209124271556491349413781117593785932096323957855730046793794526765246551266059895520550086918193311542508608460618104685509074866089624888090489894838009253941633257850621568309473902556912388065225096643874441046759871626985453222868538161694315775629640762836880760732228535091641476183956381458969463899410840960536267821064621427333394036525565649530603142680234969400335934316651459297773279665775606172582031407994198179607378245683762280037302885487251900834464581454650557929601414833921615734588139257095379769119277800826957735674444123062018757836325502728323789270710373802866393031428133241401624195671690574061419654342324638801248856147305207431992259611796250130992860241708340807605932320161268492288496255841312844061536738951487114256315111089745514203313820202931640957596464756010405845841566072044962867016515061920631004186422275908670900574606417856951911456055068251250406007519842261898059237118054444788072906395242548339221982707404473162376760846613033778706039803413197133493654622700563169937455508241780972810983291314403571877524768509857276937926433221599399876886660808368837838027643282775172273657572744784112294389733810861607423253291974813120197604178281965697475898164531258434135959862784130128185406283476649088690521047580882615823961985770122407044330583075869039319604603404973156583208672105913300903752823415539745394397715257455290510212310947321610753474825740775273986348298498340756937955646638621874569499279016572103701364433135817214311791398222983845847334440270964182851005072927748364550578634501100852987812389473928699540834346158807043959118985815145779177143619698728131459483783202081474982171858011389071228250905826817436220577475921417653715687725614904582904992461028630081535583308130101987675856234343538955409175623400844887526162643568648833519463720377293240094456246923254350400678027273837755376406726898636241037491410966718557050759098100246789880178271925953381282421954028302759408448955014676668389697996886241636313376393903373455801407636741877711055384225739499110186468219696581651485130494222369947714763069155468217682876200362777257723781365331611196811280792669481887201298643660768551639860534602297871557517947385246369446923087894265948217008051120322365496288169035739121368338393591756418733850510970271613915439590991598154654417336311656936031122249937969999226781732358023111862644575299135758175008199839236284615249881088960232244362173771618086357015468484058622329792853875623486556440536962622018963571028812361567512543338303270029097668650568557157505516727518899194129711337690149916181315171544007728650573189557450920330185304847113818315407324053319038462084036421763703911550639789000742853672196280903477974533320468368795868580237952218629120080742819551317948157624448298518461509704888027274721574688131594750409732115080498190455803416826949787141316063210686391511681774304792596709378 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '213.119' ************** PARI ***************** Host 213.119.138.197 (213.119.138.197) Time: Fri Nov 5 07:27:48 2004 Input: 2+2^100000 Output: ? 9990020930143845079440327643300335909804291390541816917715292738631458324642573483274873313324496504031643944455558549300187996607656176562908471354247492875198889629873671093246350427373112479265800278531241088737085605287228390164568691026850675923517914697052857644696801524832345475543250292786520806957770971741102232042976351205330777996897925116619870771785775955521720081320295204617949229259295623920965797873558158667525495797313144806249260261837941305080582686031535134178739622834990886357758062104606636372130587795322344972010808486369541401835851359858035603574021872908155566580607186461268972839794621842267579349638893357247588761959137656762411125020708704870465179396398710109200363934745618090601613377898560296863598558024761448933047052222860131377095958357319485898496404572383875170702242332633436894423297381877733153286944217936125301907868903603663283161502726139934152804071171914923903341874935394455896301292197256417717233543544751552379310892268182402452755752094704642185943862865632744231332084742221551493315002717750064228826211822549349600557457334964678483269180951895955769174509673224417740432840455882109137905375646772139976621785265057169854834562487518322383250318645505472114369934167981678170255122812978065194806295405339154657479941297499190348507544336414505631657396006693382427316434039580121280260984212247514207834712224831410304068603719640161855741656439472253464945249700314509890093162268952744428705476425472253167514521182231455388374308232642200633025137533129365164341725206256155311794738619142904761445654927128418175183531327052975495370561438239573227939673030106077456848477427832195349227983836436163764742969545906672369124136325932123335643135894465219101882123829740907916386023235450959388766736403229577993901152154448003637215069115591111996001530589107729421032230424262035693493216052927569625858445822354594645276923108197305806280326516736449343761732409753342333289730282959173569273013286423311759605230495171677033163709522256952460402143387655197644016528148022348331881097559421960476479388520198541017348985948511005469246617234143135309938405923268953586538886974427008607028635502085562029549352480050796521564919683265106744100967822951954161617717542997520009887307377876210685890770969411610438028623950445323789591870760289260393489826100774887672852918106468489143893649064784591211612193300707900537059042188012856559403699070888032966871611655961232331998310923225082866180321880439447572986762096935819784385927969250123326935194693207724335527365566248223787833888074999276831633440318604463618703789784313032843823470410944306591471928341190975185239212327674384990561563688432939039442002617530976850605132937101449086396141620556053547335569926700941375271829142407234267937565069765567475934101310225342830080409079587329544213551307302050171598424230760469209732907290141606353960880559202357376885647852240092777111489134492416995607171786298436533978180869474106751111353523711540436599310889697485658800887861974934357929246204051767246012250618404011966289872673803070498361217974484679100747846356194664829224736134115135567179291781968056053726484141128347858241259121954601184412409[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.203s user 0m0.195s sys 0m0.008s '24.141.' ************** PARI ***************** Host 24.141.170.56 (24.141.170.56) Time: Fri Nov 5 23:17:04 2004 Input: x^2 Output: ? x^2 ? Errors (if any) and Timing Info: Timing: real 0m0.211s user 0m0.004s sys 0m0.006s '24.141.' ************** PARI ***************** Host 24.141.170.56 (24.141.170.56) Time: Fri Nov 5 23:17:04 2004 Input: x^2 Output: ? x^2 ? Errors (if any) and Timing Info: Timing: real 0m0.217s user 0m0.002s sys 0m0.008s '24.141.' ************** PARI ***************** Host 24.141.170.56 (24.141.170.56) Time: Fri Nov 5 23:17:20 2004 Input: 4^2 Output: ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '217.72.' ************** PARI ***************** Host 217.72.92.185 (217.72.92.185) Time: Sat Nov 6 05:47:30 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.003s sys 0m0.008s '200.217' ************** PARI ***************** Host 200.217.27.3 (200.217.27.3) Time: Sat Nov 6 11:25:50 2004 Input: for (i=0;i<4;i++) printf("%d",i); Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '200.217' ************** PARI ***************** Host 200.217.27.3 (200.217.27.3) Time: Sat Nov 6 11:26:12 2004 Input: void main (void) { for (i=0;i<4;i++) printf("%d",i); } Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '200.217' ************** PARI ***************** Host 200.217.27.3 (200.217.27.3) Time: Sat Nov 6 11:26:57 2004 Input: schoof Output: ? schoof ? Errors (if any) and Timing Info: Timing: real 0m0.198s user 0m0.002s sys 0m0.010s '200.217' ************** PARI ***************** Host 200.217.27.3 (200.217.27.3) Time: Sat Nov 6 11:27:49 2004 Input: schoof(1447,1,1) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: schoof(1447,1,1) ^---------------- Timing: real 0m0.016s user 0m0.004s sys 0m0.007s '68.230.' ************** PARI ***************** Host 68.230.144.166 (68.230.144.166) Time: Sat Nov 6 20:43:12 2004 Input: Mod(1,2)*divrem(x^15-1,x^4+x^2+x) Output: ? [Mod(1, 2)*x^11 + Mod(1, 2)*x^9 + Mod(1, 2)*x^8 + Mod(1, 2)*x^7 + Mod(1, 2)*x^4 + Mod(1, 2)*x^2 + Mod(1, 2)*x + Mod(1, 2), Mod(1, 2)*x + Mod(1, 2)]~ ? Errors (if any) and Timing Info: Timing: real 0m0.105s user 0m0.006s sys 0m0.007s '68.230.' ************** PARI ***************** Host 68.230.144.166 (68.230.144.166) Time: Sat Nov 6 20:43:27 2004 Input: Mod(1,2)*divrem(x^15-1,x^4+x^2+x) Output: ? [Mod(1, 2)*x^11 + Mod(1, 2)*x^9 + Mod(1, 2)*x^8 + Mod(1, 2)*x^7 + Mod(1, 2)*x^4 + Mod(1, 2)*x^2 + Mod(1, 2)*x + Mod(1, 2), Mod(1, 2)*x + Mod(1, 2)]~ ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s '68.230.' ************** PARI ***************** Host 68.230.144.166 (68.230.144.166) Time: Sat Nov 6 20:43:49 2004 Input: Mod(1,2)*(divrem(x^15-1,x^4+x^2+x)) Output: ? [Mod(1, 2)*x^11 + Mod(1, 2)*x^9 + Mod(1, 2)*x^8 + Mod(1, 2)*x^7 + Mod(1, 2)*x^4 + Mod(1, 2)*x^2 + Mod(1, 2)*x + Mod(1, 2), Mod(1, 2)*x + Mod(1, 2)]~ ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.004s sys 0m0.005s '68.230.' ************** PARI ***************** Host 68.230.144.166 (68.230.144.166) Time: Sat Nov 6 20:43:58 2004 Input: Mod(1,2)*(divrem(x^15-1,x^4+x^2+x)) Output: ? [Mod(1, 2)*x^11 + Mod(1, 2)*x^9 + Mod(1, 2)*x^8 + Mod(1, 2)*x^7 + Mod(1, 2)*x^4 + Mod(1, 2)*x^2 + Mod(1, 2)*x + Mod(1, 2), Mod(1, 2)*x + Mod(1, 2)]~ ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.230.' ************** PARI ***************** Host 68.230.144.166 (68.230.144.166) Time: Sat Nov 6 20:44:10 2004 Input: Mod(1,2)*(divrem(x^15-1,x^4+x^2+x)) Output: ? [Mod(1, 2)*x^11 + Mod(1, 2)*x^9 + Mod(1, 2)*x^8 + Mod(1, 2)*x^7 + Mod(1, 2)*x^4 + Mod(1, 2)*x^2 + Mod(1, 2)*x + Mod(1, 2), Mod(1, 2)*x + Mod(1, 2)]~ ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.008s sys 0m0.002s '68.230.' ************** PARI ***************** Host 68.230.144.166 (68.230.144.166) Time: Sat Nov 6 20:49:43 2004 Input: Mod(1,2)*(divrem(x^4+x^2+x,x+1)) Output: ? [Mod(1, 2)*x^3 + Mod(1, 2)*x^2 + Mod(1, 2), Mod(1, 2)]~ ? Errors (if any) and Timing Info: Timing: real 0m0.168s user 0m0.007s sys 0m0.004s '172.211' ************** PARI ***************** Host 172.211.119.30 (172.211.119.30) Time: Sun Nov 7 05:28:06 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.240s user 0m0.004s sys 0m0.009s '172.211' ************** PARI ***************** Host 172.211.119.30 (172.211.119.30) Time: Sun Nov 7 05:28:44 2004 Input: diff(sin(x)/x, x) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: diff(sin(x)/x,x) ^----------- Timing: real 0m0.010s user 0m0.003s sys 0m0.008s '172.211' ************** PARI ***************** Host 172.211.119.30 (172.211.119.30) Time: Sun Nov 7 05:29:02 2004 Input: integrate(sin(x)/x, x) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: integrate(sin(x)/x,x) ^----------- Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '213.119' ************** PARI ***************** Host 213.119.140.149 (213.119.140.149) Time: Sun Nov 7 06:54:18 2004 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.192s user 0m0.006s sys 0m0.005s '213.119' ************** PARI ***************** Host 213.119.140.149 (213.119.140.149) Time: Sun Nov 7 06:54:28 2004 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '144.32.' ************** PARI ***************** Host 144.32.128.112 (144.32.128.112) Time: Sun Nov 7 07:22:04 2004 Input: 4^6 Output: ? 4096 ? Errors (if any) and Timing Info: Timing: real 0m0.229s user 0m0.008s sys 0m0.009s '69.110.' ************** PARI ***************** Host 69.110.132.179 (69.110.132.179) Time: Sun Nov 7 17:33:35 2004 Input: 4x+2x+16 Output: ? 4 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2x+16. Timing: real 0m0.020s user 0m0.005s sys 0m0.006s '219.165' ************** PARI ***************** Host 219.165.137.23 (219.165.137.23) Time: Mon Nov 8 11:14:48 2004 Input: factor(243116320964027224524719021) Output: ? [243116320964027224524719021 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.004s '219.165' ************** PARI ***************** Host 219.165.137.23 (219.165.137.23) Time: Mon Nov 8 11:15:08 2004 Input: factor(2) Output: ? [2 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.007s '219.165' ************** PARI ***************** Host 219.165.137.23 (219.165.137.23) Time: Mon Nov 8 11:15:24 2004 Input: factor(1028482569210646198463262943523919512285451094438068047692482435826458280758245850867391209810067116107639173738835019545155224537244343341801897782308906221) Output: ? [1028482569210646198463262943523919512285451094438068047692482435826458280758245850867391209810067116107639173738835019545155224537244343341801897782308906221 1] ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.035s sys 0m0.003s '156.35.' ************** PARI ***************** Host 156.35.192.2 (156.35.192.2) Time: Mon Nov 8 12:25:56 2004 Input: 1+1 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '198.204' ************** PARI ***************** Host 198.204.133.209 (198.204.133.209) Time: Mon Nov 8 17:36:05 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '198.204' ************** PARI ***************** Host 198.204.133.209 (198.204.133.209) Time: Mon Nov 8 17:36:21 2004 Input: g='c800:5' ; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '198.204' ************** PARI ***************** Host 198.204.133.208 (198.204.133.208) Time: Mon Nov 8 17:36:32 2004 Input: g='c800:5' ; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 20:42:42 2004 Input: Chinese(Mod(x,x^2+x),Mod(1,x^2+x+1)) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Chinese( *** Mod(x,x^2+x),Mod(1,x ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 20:43:04 2004 Input: Chinese(Mod(x,(x^2+x)),Mod(1,(x^2+x+1))) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Chinese( *** Mod(x,(x^2+x)),Mod(1 ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:07:06 2004 Input: Chinese(Mod(2,3),Mod(1,3)) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Chinese( *** Mod(2,3),Mod(1,3)) ^------------------ Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:07:19 2004 Input: chinese(Mod(2,3),Mod(1,3)) Output: ? ? Errors (if any) and Timing Info: *** incompatible arguments in chinois. Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:07:36 2004 Input: chinese(Mod(x,x^2+x),Mod(1,x^2+x+1)) Output: ? Mod(x^3, x^4 + 2*x^3 + 2*x^2 + x) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:09:02 2004 Input: Mod(1,2)(chinese(Mod(x,x^2+x),Mod(1,x^2+x+1))) Output: ? Mod(1, 2) ? Errors (if any) and Timing Info: *** Warning: unused characters: (chinese(Mod(x,x^2+x),Mod(1,x^2+x+1))). Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:09:10 2004 Input: Mod(1,2)*(chinese(Mod(x,x^2+x),Mod(1,x^2+x+1))) Output: ? Mod(Mod(1, 2)*x^3, x^4 + 2*x^3 + 2*x^2 + x) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:10:34 2004 Input: chinese(Mod(x^2,x^4+x+1),Mod(x,x^4+x^3+1)) Output: ? Mod(-x^7 - x^4 - x^3 + x^2, x^8 + x^7 + x^5 + 3*x^4 + x^3 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:11:58 2004 Input: chinese(Mod(x,x^2+1),Mod(1,x)) Output: ? Mod(x^2 + x + 1, x^3 + x) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:14:56 2004 Input: bezout(x^2+x+1,x^3) Output: ? [-x + 1, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:17:53 2004 Input: bezout(x^2-1,x^2+x+3) Output: ? [1/15*x - 1/5, -1/15*x + 4/15, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:18:48 2004 Input: bezout(x^2+x+1,x^3) Output: ? [-x + 1, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:20:09 2004 Input: bezout(x^6+x^5+x^3+x,x^8+x^7+x^6+x^4+x^3+x+1) Output: ? [-136/257*x^7 - 69/257*x^6 - 85/257*x^5 + 74/257*x^4 - 146/257*x^3 - 151/257*x^2 - 56/257*x - 184/257, 136/257*x^5 + 69/257*x^4 - 51/257*x^3 + 129/257*x^2 - 73/257*x + 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:20:23 2004 Input: factor(bezout(x^6+x^5+x^3+x,x^8+x^7+x^6+x^4+x^3+x+1)) Output: ? [Mat([136*x^7 + 69*x^6 + 85*x^5 - 74*x^4 + 146*x^3 + 151*x^2 + 56*x + 184, 1]), Mat([136*x^5 + 69*x^4 - 51*x^3 + 129*x^2 - 73*x + 257, 1]), matrix(0,2)] ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.001s sys 0m0.009s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:21:25 2004 Input: bezout((x^6)+(x^5)+(x^3)+x,(x^8)+(x^7)+(x^6)+(x^4)+(x^3)+x+1) Output: ? [-136/257*x^7 - 69/257*x^6 - 85/257*x^5 + 74/257*x^4 - 146/257*x^3 - 151/257*x^2 - 56/257*x - 184/257, 136/257*x^5 + 69/257*x^4 - 51/257*x^3 + 129/257*x^2 - 73/257*x + 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:22:01 2004 Input: 257*bezout((x^6)+(x^5)+(x^3)+x,(x^8)+(x^7)+(x^6)+(x^4)+(x^3)+x+1) Output: ? [-136*x^7 - 69*x^6 - 85*x^5 + 74*x^4 - 146*x^3 - 151*x^2 - 56*x - 184, 136*x^5 + 69*x^4 - 51*x^3 + 129*x^2 - 73*x + 257, 257] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:24:35 2004 Input: bezout((x^15)-1,(x^4)+(x^2)+x) Output: ? [-113/279*x^3 - 125/279*x^2 - 34/279*x - 1, 113/279*x^14 + 125/279*x^13 - 79/279*x^12 + 41/279*x^11 - 46/279*x^10 + 38/279*x^9 + 5/279*x^8 + 8/279*x^7 - 43/279*x^6 - 13/279*x^5 + 35/279*x^4 + 56/279*x^3 - 22/279*x^2 - 91/279*x - 34/279, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:24:47 2004 Input: 279*bezout((x^15)-1,(x^4)+(x^2)+x) Output: ? [-113*x^3 - 125*x^2 - 34*x - 279, 113*x^14 + 125*x^13 - 79*x^12 + 41*x^11 - 46*x^10 + 38*x^9 + 5*x^8 + 8*x^7 - 43*x^6 - 13*x^5 + 35*x^4 + 56*x^3 - 22*x^2 - 91*x - 34, 279] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:26:22 2004 Input: bezout((x^6)+(x^5)+(x^3)+x,(x^8)+(x^7)+(x^6)+(x^4)+(x^3)+x+1) Output: ? [-136/257*x^7 - 69/257*x^6 - 85/257*x^5 + 74/257*x^4 - 146/257*x^3 - 151/257*x^2 - 56/257*x - 184/257, 136/257*x^5 + 69/257*x^4 - 51/257*x^3 + 129/257*x^2 - 73/257*x + 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:26:29 2004 Input: 257*bezout((x^6)+(x^5)+(x^3)+x,(x^8)+(x^7)+(x^6)+(x^4)+(x^3)+x+1) Output: ? [-136*x^7 - 69*x^6 - 85*x^5 + 74*x^4 - 146*x^3 - 151*x^2 - 56*x - 184, 136*x^5 + 69*x^4 - 51*x^3 + 129*x^2 - 73*x + 257, 257] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.202.85 (68.118.202.85) Time: Mon Nov 8 21:27:07 2004 Input: bezout(x^2+x+1,x^3) Output: ? [-x + 1, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '217.95.' ************** PARI ***************** Host 217.95.160.94 (217.95.160.94) Time: Tue Nov 9 05:13:29 2004 Input: binom(24,12) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: binom(24,12) ^------------ Timing: real 0m0.173s user 0m0.008s sys 0m0.011s '217.95.' ************** PARI ***************** Host 217.95.160.94 (217.95.160.94) Time: Tue Nov 9 05:13:47 2004 Input: binomial(24,12) Output: ? 2704156 ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.005s sys 0m0.006s '217.95.' ************** PARI ***************** Host 217.95.160.94 (217.95.160.94) Time: Tue Nov 9 05:14:04 2004 Input: binomial(24,12)%25 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '217.95.' ************** PARI ***************** Host 217.95.160.94 (217.95.160.94) Time: Tue Nov 9 05:14:24 2004 Input: (binomial(24,12))%25 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '217.95.' ************** PARI ***************** Host 217.95.160.94 (217.95.160.94) Time: Tue Nov 9 05:14:47 2004 Input: binomial(24,12) Output: ? ? 2704156 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '217.95.' ************** PARI ***************** Host 217.95.160.94 (217.95.160.94) Time: Tue Nov 9 05:15:12 2004 Input: binomial(24,12) 2704156%25 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '193.61.' ************** PARI ***************** Host 193.61.167.27 (193.61.167.27) Time: Tue Nov 9 13:27:58 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.139s user 0m0.006s sys 0m0.008s '193.61.' ************** PARI ***************** Host 193.61.167.27 (193.61.167.27) Time: Tue Nov 9 13:28:14 2004 Input: 428 Output: ? 428 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '193.61.' ************** PARI ***************** Host 193.61.167.27 (193.61.167.27) Time: Tue Nov 9 13:28:22 2004 Input: fdhsihgio Output: ? fdhsihgio ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '217.83.' ************** PARI ***************** Host 217.83.54.3 (217.83.54.3) Time: Tue Nov 9 14:48:39 2004 Input: e^4*i Output: ? i*e^4 ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.005s sys 0m0.003s '207.112' ************** PARI ***************** Host 207.112.57.139 (207.112.57.139) Time: Tue Nov 9 23:18:17 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '195.75.' ************** PARI ***************** Host 195.75.243.98 (195.75.243.98) Time: Wed Nov 10 14:44:34 2004 Input: 85*x^2+13*x^1+x Output: ? 85*x^2 + 14*x ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.005s sys 0m0.004s '193.174' ************** PARI ***************** Host 193.174.3.15 (193.174.3.15) Time: Wed Nov 10 15:05:43 2004 Input: 541*412 Output: ? 222892 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Nov 10 18:36:37 2004 Input: 3/2 Output: ? 3/2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Nov 10 18:36:49 2004 Input: 10/5 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Nov 10 18:37:01 2004 Input: 712! Output: ? 37451146351495595471486682764120873933944687174376454641329443505629242211265974502293635932917830538326536540571080604574363301618438383555783615830735327673567446643849314235425520018866642666855130656412039098871995925826670244965209848797831122637059142865849756641009049752164675822292167956946779978529026723698597244543511393035033827020555069010174205246519146371038692665241172836816067270322765668627268282917765013434642701171629829406558168312819246229377331234201466643167333207484673207922788190804669602704891732619496694312384916812595400287534440401663443158522640479272066383656457588534265707333761956189442299884827174452236547744560865956210662453495790000629298605396157075589189491811588391235487945394942275837980339118288957420066060782323875947895064398797820514246226549429890533471550036717548631326544159966861112446361806031887028829893267707768210080414830579539190470448431974941117943646253900504023164127951891726525685566821250114507104229606637108084112808067160879166472649860892324951045970253979021493199216213033522309240497931946862138249682564874963246094176688857720919595994273062416858927625348655163232353807135894188457960745790428594141724510302290186183394969693034491486818035056545422635122129518594160147563003983534189091439994024254234778498521565220137850312195785506636424141906340394597511987682514860918557098150400434995239340255663551042384744086683793442914639422724534828080663032447455452975995312780064769573873033760946131655161721869814826038191130892944382087642171237069958309478400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Nov 10 18:37:19 2004 Input: (713!)/2047 Output: ? 13044781313442286063102102985255585302834666319164832515519244367129286612912867523270817010342165693124973401771949424065227666855860560564374068435424664695287537595048637542676304725672650816545045509536777663652043524726143568471028149581267020244368914930801600627767197104686572477427609063655619992521346386906252972818526440270629759973451765610285397333057230758451679467668273684733686352584334109297138390679221521533414873441803648444980935030307827338322441216407252426271767746427245724107937459718480423414063412485442668805437442934724240549590647780354682448474178144465551212284833542073732999183669894852502374117186993348531831236869515108343039730992915618196721986149223251047919935350103821666293554013968657876150455198505142472157841396090338813311764004075645347658798011599175354355259001553303455855313134370479713324013662775151661727266194370121511376324266831075448366111251586777243328685773830512637281887264142062048272500802907343255283495705682588209073000562718957911917439839187214308791293009812917598754783175326283051533207144835423890851013028214874838527185138815610657387368791740841827266925683239438878685033946210335305581832803407712566218649655853885075115101803191789169565832435425933726840292304229426568252282286399549009377975446650351439701732230582295206288517633153996956723585354519466549119305145625713205281378229364998341792673321012160830641198732557266633189012409669434500006224785068753283773648271707953447079371309992472823708015482744489968358708513272762300189969756732232669593600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Nov 10 18:37:42 2004 Input: (711!)/2047 Output: ? 25696103884209555413709486316039966636530773435485510888316585181952516296296837865150450325303287448833409635209569913613209864270018596380962833957295224906802121111635906091282885902407635912005463364043323950966882149971917141668823277142921624573271890671639063908960392676707401227263361535479970674081162020947753937348374569138609136843555016803278986819927728143569029948761117143762087619538297802640249284316981423510043953862071261730346799861141850659348931592273611316071843426310820169776260813855209873248939069932085248289072606124470587463933545117864621807826910633313801496061966256822992339662428681730349634628935722907897929379086458366183084078574695498914071706331104628031422725920906719641437418279245508525754556625953682163035286485514479910237964298807943464981794781503962041924569002539718738388422739749908822754017804921347648264309284968800745733969985248033015203427619464316866793036571675529565851457018418106056606246755494553901231337176518327783130703789020434924274390215396280766486150089456083644741287752584984815570400319971445015622809595897369160469264893580713430723499361262039308639956354774569548444288940168805855898153086751092405523917093177043263775276571520457100016216562841636318373647320684531588816604721306453601214159680276311990209378458212441508203424431414179989448731728807433673825001862729315137182222271311672356463182393219347019716498440986153287243748541668835786450322236058971594492428478552313864269054852089747434695966329058437147120704794728639669756626055305625600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Nov 10 18:38:04 2004 Input: (713!-700!)/2047 Output: ? 13044781313442286063102102985255585301651451798036218846800204262677722265775113060286348373580719838249576156918189081884221779378339886773792018278366995011688355819828892870552028341876139224727347170517592869250401946290466695748196524215326945770592295838910522409562317995169821008166290415336976652558107302766020896568398340860325717161953819043592664954889365678800394706116026288275986005309986728712622556001858448237033198413488601940303782612233066238805374152734026098947455943546749473271871154122139435134750805674758428661622091206089695232321539325807113700573864563837329261180607069890424283585443574878843252377914904375232402008716711393940179569975097583846567974047485502560041715094698748520841093267541520845543128643812587311857643033060517148899148769741454402475274167158876192549879525239539432940846036978050193929657621523904991064794159685877581102457093156386606787071999089373530947977882135555929065567651421888510116837581446720846570176822599006756825021872758882757663471315631995510920009015128237284664109305453616217353410505442782268432409025784473654055992542018987649709277073257936872056899030518598390213378481525647017764774797980062466203724470672483795186069728010408155142878317103277973466019494596415609409582109014079073739629666835521325777716521196961245627704852683127535884509631432980229790985836500685897955669487444772821891241211527266048462260101052997490866003856339715927823936570472901993789519307689844652875199268139731316764631450005482948821488134141040872650963069399628437782528000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Nov 10 18:38:23 2004 Input: (713!-710!)/2047 Output: ? 13044781277301492977012714217731694562975360219965432465609946352619321518746177936355433233759253843190673192442259360479334680058097038384319783792720256879119851368885316710558293345527944905985782623453144240243711666826168673995757908134258191632664801606931149612803675432449733269681615776365378733055846142066362647997494179583745696487362965549026583263747825948426745369821536766644913998488570931324848935488997492958194868505032967907609258897611906295928839726465013899867251127479505321420426672410096718976356136467244258211787304694115793117142564146130287064698338752303932881323087415404300851753300922050211682513319715389409858089333749455619469595714316351565645335074579500933848728554853855532810122732059490113498544473111954531294715990977418299226700839183993731895164446223936561803976242165723986741784669689153778373368342446012695593162610313427720984199448639837775724714605731042194855666270605426038582126974618212514632407896288149506346007799590693446037377801634986338049036288871616256194554941618613675469152170064274960696378993540908672888361810742568796477439484147164956148671983409619096940569412297165524571715312674063941068744398487666030703751757789304072053156284520514104136216261000875269960353741115998550411872175546377812041191197403994646064162624099343788268206088564089176956806185111967633778329514366920149403297867645979676094118670571679264931849900325904550226771499340674244494500753493053936292675564967547710718873610598584142850424154058180082200569065845610690163753624866373238784000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Nov 10 18:38:35 2004 Input: (713!-711!)/2047 Output: ? 13044755617338401853546689275769269262868029788391397030008356050544104660396571226432951859891840389837524568362314214495314053645996290545777687472590707400062630792927525906770213442786748408909133504073413620328092557843993596553886480757989877322744341658910928988703288144293895770026381800294084512550672305744232025064589091896060621364314922055268594054070410830723535898638324923616542590496714570999335750429937204551991363397849786373719204683507966196471781867475660152660451674583819413287767683457666568204190163546372736720189153862118116079003183846809564583852370317554917898483337480107476176191330232423820643767552364412808923338940136021884673547908837043501223072077516919943291903927377900759573912576550378630641929443948516518475678360803853298831853766111346539715333029804393850393217076984300916136574745947739963415190908757346740379617930060836542575578532861090200333096048159157779011818980793940961752321412685043630166444196660587760729594474345411690745217432015168891482515564796998912510526523662828142671138434038530466548391574435103919405997405405278941158024669550717076673938068241480565227617043283084104115485501921395136775976905254625815126244131936791898071838027915217649108732419209370885203973930582105883720693469794827702924374232490671163389742021203836993847009429729565542543595905787737741685631320623850475966241047142727030120316857829767611294179016058825647035725165920892831170438334746517224802053779279474894765507040937620733960580786778160909921561392567967571550300000106177363968000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Nov 10 18:38:50 2004 Input: (713!-711!)/2047 4! Output: ? 13044755617338401853546689275769269262868029788391397030008356050544104660396571226432951859891840389837524568362314214495314053645996290545777687472590707400062630792927525906770213442786748408909133504073413620328092557843993596553886480757989877322744341658910928988703288144293895770026381800294084512550672305744232025064589091896060621364314922055268594054070410830723535898638324923616542590496714570999335750429937204551991363397849786373719204683507966196471781867475660152660451674583819413287767683457666568204190163546372736720189153862118116079003183846809564583852370317554917898483337480107476176191330232423820643767552364412808923338940136021884673547908837043501223072077516919943291903927377900759573912576550378630641929443948516518475678360803853298831853766111346539715333029804393850393217076984300916136574745947739963415190908757346740379617930060836542575578532861090200333096048159157779011818980793940961752321412685043630166444196660587760729594474345411690745217432015168891482515564796998912510526523662828142671138434038530466548391574435103919405997405405278941158024669550717076673938068241480565227617043283084104115485501921395136775976905254625815126244131936791898071838027915217649108732419209370885203973930582105883720693469794827702924374232490671163389742021203836993847009429729565542543595905787737741685631320623850475966241047142727030120316857829767611294179016058825647035725165920892831170438334746517224802053779279474894765507040937620733960580786778160909921561392567967571550300000106177363968000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? 24 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Nov 10 18:39:45 2004 Input: a=713!; b=711!; (a-b)/2047 4! Output: ? ? ? 13044755617338401853546689275769269262868029788391397030008356050544104660396571226432951859891840389837524568362314214495314053645996290545777687472590707400062630792927525906770213442786748408909133504073413620328092557843993596553886480757989877322744341658910928988703288144293895770026381800294084512550672305744232025064589091896060621364314922055268594054070410830723535898638324923616542590496714570999335750429937204551991363397849786373719204683507966196471781867475660152660451674583819413287767683457666568204190163546372736720189153862118116079003183846809564583852370317554917898483337480107476176191330232423820643767552364412808923338940136021884673547908837043501223072077516919943291903927377900759573912576550378630641929443948516518475678360803853298831853766111346539715333029804393850393217076984300916136574745947739963415190908757346740379617930060836542575578532861090200333096048159157779011818980793940961752321412685043630166444196660587760729594474345411690745217432015168891482515564796998912510526523662828142671138434038530466548391574435103919405997405405278941158024669550717076673938068241480565227617043283084104115485501921395136775976905254625815126244131936791898071838027915217649108732419209370885203973930582105883720693469794827702924374232490671163389742021203836993847009429729565542543595905787737741685631320623850475966241047142727030120316857829767611294179016058825647035725165920892831170438334746517224802053779279474894765507040937620733960580786778160909921561392567967571550300000106177363968000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? 24 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Nov 10 18:40:09 2004 Input: a=713!; b=711!; (a-b)/2047 89!/2047 Output: ? ? ? 13044755617338401853546689275769269262868029788391397030008356050544104660396571226432951859891840389837524568362314214495314053645996290545777687472590707400062630792927525906770213442786748408909133504073413620328092557843993596553886480757989877322744341658910928988703288144293895770026381800294084512550672305744232025064589091896060621364314922055268594054070410830723535898638324923616542590496714570999335750429937204551991363397849786373719204683507966196471781867475660152660451674583819413287767683457666568204190163546372736720189153862118116079003183846809564583852370317554917898483337480107476176191330232423820643767552364412808923338940136021884673547908837043501223072077516919943291903927377900759573912576550378630641929443948516518475678360803853298831853766111346539715333029804393850393217076984300916136574745947739963415190908757346740379617930060836542575578532861090200333096048159157779011818980793940961752321412685043630166444196660587760729594474345411690745217432015168891482515564796998912510526523662828142671138434038530466548391574435103919405997405405278941158024669550717076673938068241480565227617043283084104115485501921395136775976905254625815126244131936791898071838027915217649108732419209370885203973930582105883720693469794827702924374232490671163389742021203836993847009429729565542543595905787737741685631320623850475966241047142727030120316857829767611294179016058825647035725165920892831170438334746517224802053779279474894765507040937620733960580786778160909921561392567967571550300000106177363968000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? 8064462706843410396295515028067229755661781258669536812366155695082154877566443448656527880208891383844201457254400000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Nov 10 18:40:26 2004 Input: a=713!; b=711!; (a-b)/2047 88!/2047 Output: ? ? ? 13044755617338401853546689275769269262868029788391397030008356050544104660396571226432951859891840389837524568362314214495314053645996290545777687472590707400062630792927525906770213442786748408909133504073413620328092557843993596553886480757989877322744341658910928988703288144293895770026381800294084512550672305744232025064589091896060621364314922055268594054070410830723535898638324923616542590496714570999335750429937204551991363397849786373719204683507966196471781867475660152660451674583819413287767683457666568204190163546372736720189153862118116079003183846809564583852370317554917898483337480107476176191330232423820643767552364412808923338940136021884673547908837043501223072077516919943291903927377900759573912576550378630641929443948516518475678360803853298831853766111346539715333029804393850393217076984300916136574745947739963415190908757346740379617930060836542575578532861090200333096048159157779011818980793940961752321412685043630166444196660587760729594474345411690745217432015168891482515564796998912510526523662828142671138434038530466548391574435103919405997405405278941158024669550717076673938068241480565227617043283084104115485501921395136775976905254625815126244131936791898071838027915217649108732419209370885203973930582105883720693469794827702924374232490671163389742021203836993847009429729565542543595905787737741685631320623850475966241047142727030120316857829767611294179016058825647035725165920892831170438334746517224802053779279474894765507040937620733960580786778160909921561392567967571550300000106177363968000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? 8064462706843410396295515028067229755661781258669536812366155695082154877566443448656527880208891383844201457254400000000000000000000/89 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.006s '69.172.' ************** PARI ***************** Host 69.172.204.83 (69.172.204.83) Time: Thu Nov 11 02:38:11 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.003s sys 0m0.007s '130.232' ************** PARI ***************** Host 130.232.111.30 (130.232.111.30) Time: Thu Nov 11 04:12:33 2004 Input: R:=PolynomialRing(RationalField()); W:={R|}; l:=79; L:=CyclotomicField(l); M:=Divisors(l-1); g:=PrimitiveRoot(l); for m in M do d:=(l-1) div m; g_d:=g^d; w:=&+[z^g_d^i:i in [0..m-1]]; Include(~W,MinimalPolynomial(w)); end for; W := { R | MinimalPolynomial(&+[z^(g^((l-1) div m))^i : i in [2..m-1] ]) : m in M }; W; Output: ? ? ? ? ? ? ? forminMdo ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: R:=PolynomialRing(Ra ^-------------------- *** unexpected character: W:={R|}; ^------- *** unexpected character: l:=79; ^----- *** unexpected character: L:=CyclotomicField(l ^-------------------- *** unexpected character: M:=Divisors(l-1); ^---------------- *** unexpected character: g:=PrimitiveRoot(l); ^------------------- *** unexpected character: d:=(l-1)divm; ^------------ *** unexpected character: g_d:=g^d; ^------ *** unexpected character: w:=&+[z^g_d^i:iin[0.. ^-------------------- *** unexpected character: Include(~W,MinimalPolynomia ^-------------------- *** unexpected character: W:={R|MinimalPolynomi ^-------------------- Timing: real 0m0.020s user 0m0.005s sys 0m0.007s '128.125' ************** PARI ***************** Host 128.125.3.220 (128.125.3.220) Time: Thu Nov 11 15:25:10 2004 Input: poldisc(x^2+1); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.002s sys 0m0.008s '128.125' ************** PARI ***************** Host 128.125.3.220 (128.125.3.220) Time: Thu Nov 11 15:25:36 2004 Input: t=poldisc(x^2+1) Output: ? -4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '128.125' ************** PARI ***************** Host 128.125.3.220 (128.125.3.220) Time: Thu Nov 11 15:26:20 2004 Input: t=poldisc(x^4+x^3+x^2+x+1) Output: ? 125 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '128.125' ************** PARI ***************** Host 128.125.3.220 (128.125.3.220) Time: Thu Nov 11 15:26:33 2004 Input: t=poldisc(x^6+x^5+x^4+x^3+x^2+x+1) Output: ? -16807 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '128.125' ************** PARI ***************** Host 128.125.3.220 (128.125.3.220) Time: Thu Nov 11 15:26:51 2004 Input: factor(-16807) Output: ? [-1 1] [7 5] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '128.125' ************** PARI ***************** Host 128.125.3.220 (128.125.3.220) Time: Thu Nov 11 15:27:05 2004 Input: t=poldisc(x^6+x^5+x^4+x^3+x^2+x+1) Output: ? -16807 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '128.125' ************** PARI ***************** Host 128.125.3.220 (128.125.3.220) Time: Thu Nov 11 15:27:27 2004 Input: t=poldisc(x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) Output: ? -2357947691 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.008s '128.125' ************** PARI ***************** Host 128.125.3.220 (128.125.3.220) Time: Thu Nov 11 15:27:53 2004 Input: factor(2357947691) Output: ? [11 9] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '128.125' ************** PARI ***************** Host 128.125.3.220 (128.125.3.220) Time: Thu Nov 11 15:28:35 2004 Input: t=poldisc(x^{12}+x^{11}+x^{10}+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: t=poldisc(x^{12}+x^{11}+x^{10}+ ^-------------------- Timing: real 0m0.021s user 0m0.004s sys 0m0.005s '128.125' ************** PARI ***************** Host 128.125.3.220 (128.125.3.220) Time: Thu Nov 11 15:28:53 2004 Input: t=poldisc(x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) Output: ? 1792160394037 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.004s '128.125' ************** PARI ***************** Host 128.125.3.220 (128.125.3.220) Time: Thu Nov 11 15:29:39 2004 Input: 1792160394037 Output: ? 1792160394037 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '128.125' ************** PARI ***************** Host 128.125.3.220 (128.125.3.220) Time: Thu Nov 11 15:29:46 2004 Input: factor(1792160394037) Output: ? [13 11] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '24.150.' ************** PARI ***************** Host 24.150.21.49 (24.150.21.49) Time: Thu Nov 11 20:43:58 2004 Input: 1+2; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Fri Nov 12 05:01:51 2004 Input: e=ellinit([0,1,0,-18,25]); ellglobalred(e) Output: ? ? [5692, [1, 0, 0, 0], 3] ? Errors (if any) and Timing Info: Timing: real 0m0.074s user 0m0.006s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Fri Nov 12 05:02:11 2004 Input: e=ellinit([0,1,0,-18,25]); elltors(e) Output: ? ? [1, [], []] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Fri Nov 12 05:34:38 2004 Input: e=ellinit([0,1,0,-18,25]); elllseries(e,1) Output: ? ? -9.4493856450315515073076523381030683794 E-38 ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.052s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Fri Nov 12 05:36:11 2004 Input: e=ellinit([0,1,0,-18,25]); factor(ellglobalred(e)[1]) Output: ? ? [2 2] [1423 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '131.193' ************** PARI ***************** Host 131.193.156.235 (131.193.156.235) Time: Fri Nov 12 09:43:21 2004 Input: 25*5^10 mod 12 Output: ? 244140625 ? Errors (if any) and Timing Info: *** Warning: unused characters: mod12. Timing: real 0m0.026s user 0m0.007s sys 0m0.003s '217.233' ************** PARI ***************** Host 217.233.185.114 (217.233.185.114) Time: Fri Nov 12 10:10:35 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.003s '217.233' ************** PARI ***************** Host 217.233.185.114 (217.233.185.114) Time: Fri Nov 12 10:10:55 2004 Input: Intgrate[x*x,x] Output: ? ? Errors (if any) and Timing Info: *** unexpected character: Intgrate[x*x,x] ^------- Timing: real 0m0.018s user 0m0.003s sys 0m0.008s '82.120.' ************** PARI ***************** Host 82.120.179.195 (82.120.179.195) Time: Fri Nov 12 15:42:35 2004 Input: max(2.3,4.5,1.265); Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: max(2.3,4.5,1.265); ^-------- Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '82.120.' ************** PARI ***************** Host 82.120.179.195 (82.120.179.195) Time: Fri Nov 12 15:42:42 2004 Input: max(2.3,4.5,1.265) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: max(2.3,4.5,1.265) ^------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '82.120.' ************** PARI ***************** Host 82.120.179.195 (82.120.179.195) Time: Fri Nov 12 15:43:08 2004 Input: (max(2.3,4.5,1.265)) Output: ? ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (max(2.3,4.5,1.265)) ^-------- Timing: real 0m0.009s user 0m0.007s sys 0m0.003s '82.120.' ************** PARI ***************** Host 82.120.179.195 (82.120.179.195) Time: Fri Nov 12 15:43:33 2004 Input: max(max(2.3,4.5),1.265) Output: ? 4.5000000000000000000000000000000000000 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '82.120.' ************** PARI ***************** Host 82.120.179.195 (82.120.179.195) Time: Fri Nov 12 15:43:58 2004 Input: max(max(2.3,4.5),1.265); Output: ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '82.120.' ************** PARI ***************** Host 82.120.179.195 (82.120.179.195) Time: Fri Nov 12 15:44:04 2004 Input: max(max(2.3,4.5),1.265) Output: ? 4.5000000000000000000000000000000000000 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '80.12.6' ************** PARI ***************** Host 80.12.68.48 (80.12.68.48) Time: Fri Nov 12 17:00:52 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s 'form' ************** PARI ***************** Host form (140.247.29.178) Time: Fri Nov 12 17:44:25 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.003s '83.130.' ************** PARI ***************** Host 83.130.123.160 (83.130.123.160) Time: Sat Nov 13 01:54:39 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.008s '83.130.' ************** PARI ***************** Host 83.130.123.160 (83.130.123.160) Time: Sat Nov 13 01:56:45 2004 Input: factor(1234567890) Output: ? [2 1] [3 2] [5 1] [3607 1] [3803 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '83.130.' ************** PARI ***************** Host 83.130.123.160 (83.130.123.160) Time: Sat Nov 13 02:04:42 2004 Input: factor(1234567890) Output: ? [2 1] [3 2] [5 1] [3607 1] [3803 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '83.130.' ************** PARI ***************** Host 83.130.123.160 (83.130.123.160) Time: Sat Nov 13 02:06:07 2004 Input: factor(31074182404900437213507500358885679300373460228427 27545720161948823206440518081504556346829671723286 78243791627283803341547107310850191954852900733772 4822783525742386454014691736602477652346609) Output: ? ? 27545720161948823206440518081504556346829671723286 ? 78243791627283803341547107310850191954852900733772 ? 4822783525742386454014691736602477652346609 ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...0358885679300373460228427 ^ *** Warning: unused characters: ). Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '83.130.' ************** PARI ***************** Host 83.130.123.160 (83.130.123.160) Time: Sat Nov 13 02:07:03 2004 Input: factor(3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 28544 Killed /usr/bin/gp -q --emacs Timing: real 0m21.023s user 0m20.996s sys 0m0.006s '83.130.' ************** PARI ***************** Host 83.130.123.160 (83.130.123.160) Time: Sat Nov 13 02:07:11 2004 Input: factor(3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 28548 Killed /usr/bin/gp -q --emacs Timing: real 0m21.007s user 0m20.995s sys 0m0.005s '83.130.' ************** PARI ***************** Host 83.130.123.160 (83.130.123.160) Time: Sat Nov 13 02:34:18 2004 Input: factor(3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 28588 Killed /usr/bin/gp -q --emacs Timing: real 0m21.011s user 0m20.993s sys 0m0.007s '83.130.' ************** PARI ***************** Host 83.130.123.160 (83.130.123.160) Time: Sat Nov 13 02:34:29 2004 Input: factor(3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 28592 Killed /usr/bin/gp -q --emacs Timing: real 0m21.008s user 0m20.994s sys 0m0.007s '83.130.' ************** PARI ***************** Host 83.130.123.160 (83.130.123.160) Time: Sat Nov 13 02:59:49 2004 Input: a1=31074182404900437213507500358885679300373460228427 a2=27545720161948823206440518081504556346829671723286 a3=78243791627283803341547107310850191954852900733772 a4=4822783525742386454014691736602477652346609 m=10^50 r=a1 factor(r) Output: ? 31074182404900437213507500358885679300373460228427 ? 27545720161948823206440518081504556346829671723286 ? 78243791627283803341547107310850191954852900733772 ? 4822783525742386454014691736602477652346609 ? 100000000000000000000000000000000000000000000000000 ? 31074182404900437213507500358885679300373460228427 ? [17 2] [23 1] [29 1] [254537 1] [138825019 1] [64013620507439 1] [71266426140890437 1] ? Errors (if any) and Timing Info: Timing: real 0m0.157s user 0m0.092s sys 0m0.017s '83.130.' ************** PARI ***************** Host 83.130.123.160 (83.130.123.160) Time: Sat Nov 13 03:00:56 2004 Input: a1=31074182404900437213507500358885679300373460228427 a2=27545720161948823206440518081504556346829671723286 a3=78243791627283803341547107310850191954852900733772 a4=4822783525742386454014691736602477652346609 m=10^50 r=a1*m+a2 factor(r) Output: ? 31074182404900437213507500358885679300373460228427 ? 27545720161948823206440518081504556346829671723286 ? 78243791627283803341547107310850191954852900733772 ? 4822783525742386454014691736602477652346609 ? 100000000000000000000000000000000000000000000000000 ? 3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286 ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 28620 Killed /usr/bin/gp -q --emacs Timing: real 0m21.018s user 0m20.992s sys 0m0.007s '217.185' ************** PARI ***************** Host 217.185.234.103 (217.185.234.103) Time: Sat Nov 13 09:04:31 2004 Input: 1000! Output: ? 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.162s user 0m0.004s sys 0m0.009s '217.185' ************** PARI ***************** Host 217.185.234.103 (217.185.234.103) Time: Sat Nov 13 09:06:02 2004 Input: 2^1000 Output: ? 10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376 ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.002s sys 0m0.009s '217.185' ************** PARI ***************** Host 217.185.234.103 (217.185.234.103) Time: Sat Nov 13 09:06:18 2004 Input: 2^1000 Output: ? 10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '217.185' ************** PARI ***************** Host 217.185.234.103 (217.185.234.103) Time: Sat Nov 13 09:06:28 2004 Input: 2^100000 Output: ? 9990020930143845079440327643300335909804291390541816917715292738631458324642573483274873313324496504031643944455558549300187996607656176562908471354247492875198889629873671093246350427373112479265800278531241088737085605287228390164568691026850675923517914697052857644696801524832345475543250292786520806957770971741102232042976351205330777996897925116619870771785775955521720081320295204617949229259295623920965797873558158667525495797313144806249260261837941305080582686031535134178739622834990886357758062104606636372130587795322344972010808486369541401835851359858035603574021872908155566580607186461268972839794621842267579349638893357247588761959137656762411125020708704870465179396398710109200363934745618090601613377898560296863598558024761448933047052222860131377095958357319485898496404572383875170702242332633436894423297381877733153286944217936125301907868903603663283161502726139934152804071171914923903341874935394455896301292197256417717233543544751552379310892268182402452755752094704642185943862865632744231332084742221551493315002717750064228826211822549349600557457334964678483269180951895955769174509673224417740432840455882109137905375646772139976621785265057169854834562487518322383250318645505472114369934167981678170255122812978065194806295405339154657479941297499190348507544336414505631657396006693382427316434039580121280260984212247514207834712224831410304068603719640161855741656439472253464945249700314509890093162268952744428705476425472253167514521182231455388374308232642200633025137533129365164341725206256155311794738619142904761445654927128418175183531327052975495370561438239573227939673030106077456848477427832195349227983836436163764742969545906672369124136325932123335643135894465219101882123829740907916386023235450959388766736403229577993901152154448003637215069115591111996001530589107729421032230424262035693493216052927569625858445822354594645276923108197305806280326516736449343761732409753342333289730282959173569273013286423311759605230495171677033163709522256952460402143387655197644016528148022348331881097559421960476479388520198541017348985948511005469246617234143135309938405923268953586538886974427008607028635502085562029549352480050796521564919683265106744100967822951954161617717542997520009887307377876210685890770969411610438028623950445323789591870760289260393489826100774887672852918106468489143893649064784591211612193300707900537059042188012856559403699070888032966871611655961232331998310923225082866180321880439447572986762096935819784385927969250123326935194693207724335527365566248223787833888074999276831633440318604463618703789784313032843823470410944306591471928341190975185239212327674384990561563688432939039442002617530976850605132937101449086396141620556053547335569926700941375271829142407234267937565069765567475934101310225342830080409079587329544213551307302050171598424230760469209732907290141606353960880559202357376885647852240092777111489134492416995607171786298436533978180869474106751111353523711540436599310889697485658800887861974934357929246204051767246012250618404011966289872673803070498361217974484679100747846356194664829224736134115135567179291781968056053726484141128347858241259121954601184412409[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.202s user 0m0.189s sys 0m0.012s '217.185' ************** PARI ***************** Host 217.185.234.103 (217.185.234.103) Time: Sat Nov 13 09:06:49 2004 Input: 2^100 Output: ? 1267650600228229401496703205376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '217.185' ************** PARI ***************** Host 217.185.234.103 (217.185.234.103) Time: Sat Nov 13 09:06:58 2004 Input: 2^1000 Output: ? 10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '217.185' ************** PARI ***************** Host 217.185.234.103 (217.185.234.103) Time: Sat Nov 13 09:07:11 2004 Input: 2^1000 Output: ? 10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '217.185' ************** PARI ***************** Host 217.185.234.103 (217.185.234.103) Time: Sat Nov 13 09:07:20 2004 Input: 2^10000 Output: ? 19950631168807583848837421626835850838234968318861924548520089498529438830221946631919961684036194597899331129423209124271556491349413781117593785932096323957855730046793794526765246551266059895520550086918193311542508608460618104685509074866089624888090489894838009253941633257850621568309473902556912388065225096643874441046759871626985453222868538161694315775629640762836880760732228535091641476183956381458969463899410840960536267821064621427333394036525565649530603142680234969400335934316651459297773279665775606172582031407994198179607378245683762280037302885487251900834464581454650557929601414833921615734588139257095379769119277800826957735674444123062018757836325502728323789270710373802866393031428133241401624195671690574061419654342324638801248856147305207431992259611796250130992860241708340807605932320161268492288496255841312844061536738951487114256315111089745514203313820202931640957596464756010405845841566072044962867016515061920631004186422275908670900574606417856951911456055068251250406007519842261898059237118054444788072906395242548339221982707404473162376760846613033778706039803413197133493654622700563169937455508241780972810983291314403571877524768509857276937926433221599399876886660808368837838027643282775172273657572744784112294389733810861607423253291974813120197604178281965697475898164531258434135959862784130128185406283476649088690521047580882615823961985770122407044330583075869039319604603404973156583208672105913300903752823415539745394397715257455290510212310947321610753474825740775273986348298498340756937955646638621874569499279016572103701364433135817214311791398222983845847334440270964182851005072927748364550578634501100852987812389473928699540834346158807043959118985815145779177143619698728131459483783202081474982171858011389071228250905826817436220577475921417653715687725614904582904992461028630081535583308130101987675856234343538955409175623400844887526162643568648833519463720377293240094456246923254350400678027273837755376406726898636241037491410966718557050759098100246789880178271925953381282421954028302759408448955014676668389697996886241636313376393903373455801407636741877711055384225739499110186468219696581651485130494222369947714763069155468217682876200362777257723781365331611196811280792669481887201298643660768551639860534602297871557517947385246369446923087894265948217008051120322365496288169035739121368338393591756418733850510970271613915439590991598154654417336311656936031122249937969999226781732358023111862644575299135758175008199839236284615249881088960232244362173771618086357015468484058622329792853875623486556440536962622018963571028812361567512543338303270029097668650568557157505516727518899194129711337690149916181315171544007728650573189557450920330185304847113818315407324053319038462084036421763703911550639789000742853672196280903477974533320468368795868580237952218629120080742819551317948157624448298518461509704888027274721574688131594750409732115080498190455803416826949787141316063210686391511681774304792596709376 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '217.42.' ************** PARI ***************** Host 217.42.16.210 (217.42.16.210) Time: Sun Nov 14 15:29:45 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.004s sys 0m0.005s '217.42.' ************** PARI ***************** Host 217.42.16.210 (217.42.16.210) Time: Sun Nov 14 15:29:57 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:36:32 2004 Input: A*B Output: ? B*A ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.004s sys 0m0.006s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:36:51 2004 Input: prime(1001); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:37:51 2004 Input: isprime(1001) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:37:54 2004 Input: isprime(1001) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:37:58 2004 Input: isprime(1000) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:38:01 2004 Input: isprime(2) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:38:15 2004 Input: isprime(2) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:38:21 2004 Input: isprime(10000000) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:38:26 2004 Input: isprime(10000000) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:38:29 2004 Input: isprime(34) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:38:33 2004 Input: isprime(32) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:39:35 2004 Input: factor(2) Output: ? [2 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:39:40 2004 Input: factor(1001) Output: ? [7 1] [11 1] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:39:51 2004 Input: factor(1001A) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: factor(1001A) ^-- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:39:57 2004 Input: factor(1001) Output: ? [7 1] [11 1] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:40:03 2004 Input: factor(1) Output: ? [;] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:40:06 2004 Input: factor(3) Output: ? [3 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:40:12 2004 Input: factor(5) Output: ? [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '67.85.3' ************** PARI ***************** Host 67.85.35.27 (67.85.35.27) Time: Sun Nov 14 17:40:16 2004 Input: factor(6) Output: ? [2 1] [3 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.177.214 (140.247.177.214) Time: Sun Nov 14 23:18:45 2004 Input: Generators(Gamma0(11)) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Generators(Gamma0(11)) ^----------- Timing: real 0m0.040s user 0m0.004s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.177.214 (140.247.177.214) Time: Sun Nov 14 23:18:57 2004 Input: Generators(Gamma0(11)); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Generators(Gamma0(11)); ^------------ Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '219.65.' ************** PARI ***************** Host 219.65.137.253 (219.65.137.253) Time: Mon Nov 15 00:30:00 2004 Input: 10001000*10001000 Output: ? 100020001000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '219.65.' ************** PARI ***************** Host 219.65.137.253 (219.65.137.253) Time: Mon Nov 15 00:30:51 2004 Input: 1000100010001000*1000100010001000 Output: ? 1000200030004000300020001000000 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '219.65.' ************** PARI ***************** Host 219.65.137.253 (219.65.137.253) Time: Mon Nov 15 00:33:36 2004 Input: FFFFFFFF*FFFFFFFF Output: ? FFFFFFFF^2 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.003s sys 0m0.008s '219.65.' ************** PARI ***************** Host 219.65.137.253 (219.65.137.253) Time: Mon Nov 15 00:34:04 2004 Input: FFFFFFFF*EEEEEEEE Output: ? EEEEEEEE*FFFFFFFF ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.002s sys 0m0.008s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Mon Nov 15 02:56:15 2004 Input: Mod(15,11)^203 Output: ? Mod(9, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.003s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Mon Nov 15 02:56:26 2004 Input: Mod(15^203,11) Output: ? Mod(9, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.003s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Mon Nov 15 03:00:29 2004 Input: Mod(2^902,77) Output: ? Mod(4, 77) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Mon Nov 15 03:37:35 2004 Input: Mod(Mod(1,3)(x^2+x+1)*(2*x^2)),Mod(1,3)*(x^3+2*x+1)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Mod(Mod(1,3)(x^2+x+1)*(2*x^2)),M ^-------------------- Timing: real 0m0.014s user 0m0.003s sys 0m0.008s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Mon Nov 15 03:37:49 2004 Input: Mod(Mod(1,3)((x^2+x+1)*(2*x^2)),Mod(1,3)*(x^3+2*x+1)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Mod(Mod(1,3)((x^2+x+1)*(2*x^2)), ^-------------------- Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Mon Nov 15 03:37:58 2004 Input: Mod(Mod(1,3)*((x^2+x+1)*(2*x^2)),Mod(1,3)*(x^3+2*x+1)) Output: ? Mod(Mod(1, 3)*x^2 + Mod(1, 3), Mod(1, 3)*x^3 + Mod(2, 3)*x + Mod(1, 3)) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.002s sys 0m0.007s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Mon Nov 15 03:46:41 2004 Input: Mod(Mod(1,3)*((x^2+x+1)*(2*x^2+x+1)),Mod(1,3)*(x^3+2*x+1)) Output: ? Mod(Mod(1, 3), Mod(1, 3)*x^3 + Mod(2, 3)*x + Mod(1, 3)) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.008s '61.10.7' ************** PARI ***************** Host 61.10.7.92 (61.10.7.92) Time: Mon Nov 15 10:44:39 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.004s sys 0m0.006s '217.84.' ************** PARI ***************** Host 217.84.23.182 (217.84.23.182) Time: Mon Nov 15 15:55:40 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '217.84.' ************** PARI ***************** Host 217.84.23.182 (217.84.23.182) Time: Mon Nov 15 15:55:56 2004 Input: 3434523532523^32423432 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m5.247s user 0m5.197s sys 0m0.015s '217.84.' ************** PARI ***************** Host 217.84.23.182 (217.84.23.182) Time: Mon Nov 15 15:56:24 2004 Input: 3434523532523^324 Output: ? 4175849467130703316819935498317888543717454937575774959287699750703748851501655029544708694296987204149709522223044514001139945013480926282909395959276536886343504270638292658506710278734734715681622489153680611324920861339565397371358008036399451926926875043069166413141427648940777569597124608391288520028800185272605484011135377586095588602989807035921138033403507535575232037854384230060604232190380040231548254199025672006142095563270292830250585622636105926761905608185553120682869532900329207339097587466369957396706818197525829326633398018874124697426176580958112168983681506922017623596591729621140738502431139668219130797219500108084398044101535438870474865049481243813256254379206754403302504344736142125823151791674969118157735660607217834244911723430213453299020856801299062229594500582638149797327625416351677896514827681406280619065160753260782423136161097874948611374898225593128438121671652240336769672571899875100513424754592515413075100117039457424261225924354613662438766991023888341680675346447636266116295959721967740592888437234429633105055656219916098676073539228965717671373628958197925267855874798315024431786304121194955742818015729417078848374247976823595390949127531317686110287262893686927087820817326750169725066570772535280781051298855645964178443186279093092563995996015015253300879486866606078819274246146969055091163471074442202591558125843742736286884894679574028391181933017443047094872472649160319664914304482194133279650144715732696512316301392439248104584433797832576635864212848521181045566486322997966372154330691548548453379874652030730583386753974338438277617423808861698885154039279828336080104081923562590980724018019078717406967728867374874365265704440327463847525535310255003455482175497386579266957307758515422099736803622255794718354440818240874549951301343736779540320953244399756216989680107052075877568502015551774495795859949245742537131891368428406379168211373836609609992270311165775434110766223400080122632446795870922400059030475547485254535659083755185935408949810386189648928593918763549262149071771044036912069315317586521283468279300998833629707125151243077618781116868152828425684320168344152267289248173278797461558888649788442010776321288910718653058583272638030939737261195573759802357427586631001914779702916956668306741691987812972974335898315776501847464604381316820855867718986364566792065189646903469114475115340325291161122416208352428177367292683265902361434545510398308721882805710619285847251972125331374774857462461229495709611073989834348520742578360593209549147924480444152085309235834077536234634930595597695683103846199763824805754884737212053984788579584622988570642200787058286438845206886160704183907413242860785348484884971468085688053185578073904740039035423597066596959272429622474623861244676610062987363371773816948467911191365723062661689309365792660521362237969636621070359314051077388667343789397663437167176758560343596595953907259781459267793991146331183886662813819549493767477377051896343344534263862743967339815449574141705640853687869994327004091446427919404094232103677048425815668907209587895770155798596821533167650922984990906663030091390373904511424588775912089963272479562527164035677304[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '129.92.' ************** PARI ***************** Host 129.92.250.40 (129.92.250.40) Time: Tue Nov 16 00:21:02 2004 Input: Input: F:=GF(4); A:=GL(2,F)![a,a^2,a,0]; Order(A); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: Input:F:=GF(4); ^--------- *** unexpected character: A:=GL(2,F)![a,a^2,a,0 ^-------------------- *** expected character: '=' instead of: Order(A); ^- Timing: real 0m0.023s user 0m0.005s sys 0m0.004s '129.92.' ************** PARI ***************** Host 129.92.250.40 (129.92.250.40) Time: Tue Nov 16 00:21:35 2004 Input: Input: 2+2 Output: ? 4 ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.004s '129.92.' ************** PARI ***************** Host 129.92.250.40 (129.92.250.40) Time: Tue Nov 16 00:23:06 2004 Input: Input: R:=PolynomialRing(GF(2)); g:=x^3+x+1; Factorization(x^7-1); C:=CyclicCode(7,g); C; G:=GeneratorMatrix(C); G; H:=ParityCheckMatrix(C); H; Output: ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: Input:R:=PolynomialRing(GF ^-------------------- *** unexpected character: g:=x^3+x+1; ^---------- *** expected character: ',' instead of: Factorization(x^7-1); ^------ *** unexpected character: C:=CyclicCode(7,g); ^------------------ *** unexpected character: G:=GeneratorMatrix(C) ^-------------------- *** unexpected character: H:=ParityCheckMatrix( ^-------------------- Timing: real 0m0.010s user 0m0.003s sys 0m0.008s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Tue Nov 16 00:51:26 2004 Input: Mod(-23^2,3) Output: ? Mod(2, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Tue Nov 16 00:52:44 2004 Input: Mod(-23,3) Output: ? Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Tue Nov 16 00:52:53 2004 Input: Mod(-19,3) Output: ? Mod(2, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Tue Nov 16 00:53:02 2004 Input: Mod(-17,3) Output: ? Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Tue Nov 16 00:53:09 2004 Input: Mod(-13,3) Output: ? Mod(2, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Tue Nov 16 00:53:28 2004 Input: Mod(-23,41) Output: ? Mod(18, 41) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Tue Nov 16 00:55:05 2004 Input: Mod(-23,41) vector(n,41,Mod(n^2,41)) Output: ? Mod(18, 41) ? ? Errors (if any) and Timing Info: *** variable name expected: vector(n,41,Mod(n^2,41)) ^--------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Tue Nov 16 00:55:14 2004 Input: Mod(-23,41) vector(41,n,Mod(n^2,41)) Output: ? Mod(18, 41) ? [Mod(1, 41), Mod(4, 41), Mod(9, 41), Mod(16, 41), Mod(25, 41), Mod(36, 41), Mod(8, 41), Mod(23, 41), Mod(40, 41), Mod(18, 41), Mod(39, 41), Mod(21, 41), Mod(5, 41), Mod(32, 41), Mod(20, 41), Mod(10, 41), Mod(2, 41), Mod(37, 41), Mod(33, 41), Mod(31, 41), Mod(31, 41), Mod(33, 41), Mod(37, 41), Mod(2, 41), Mod(10, 41), Mod(20, 41), Mod(32, 41), Mod(5, 41), Mod(21, 41), Mod(39, 41), Mod(18, 41), Mod(40, 41), Mod(23, 41), Mod(8, 41), Mod(36, 41), Mod(25, 41), Mod(16, 41), Mod(9, 41), Mod(4, 41), Mod(1, 41), Mod(0, 41)] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Tue Nov 16 00:55:46 2004 Input: Mod(-19,41) vector(41,n,Mod(n^2,41)) Output: ? Mod(22, 41) ? [Mod(1, 41), Mod(4, 41), Mod(9, 41), Mod(16, 41), Mod(25, 41), Mod(36, 41), Mod(8, 41), Mod(23, 41), Mod(40, 41), Mod(18, 41), Mod(39, 41), Mod(21, 41), Mod(5, 41), Mod(32, 41), Mod(20, 41), Mod(10, 41), Mod(2, 41), Mod(37, 41), Mod(33, 41), Mod(31, 41), Mod(31, 41), Mod(33, 41), Mod(37, 41), Mod(2, 41), Mod(10, 41), Mod(20, 41), Mod(32, 41), Mod(5, 41), Mod(21, 41), Mod(39, 41), Mod(18, 41), Mod(40, 41), Mod(23, 41), Mod(8, 41), Mod(36, 41), Mod(25, 41), Mod(16, 41), Mod(9, 41), Mod(4, 41), Mod(1, 41), Mod(0, 41)] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.3.37 (24.177.3.37) Time: Tue Nov 16 00:56:24 2004 Input: Mod(-5,41) vector(41,n,Mod(n^2,41)) Output: ? Mod(36, 41) ? [Mod(1, 41), Mod(4, 41), Mod(9, 41), Mod(16, 41), Mod(25, 41), Mod(36, 41), Mod(8, 41), Mod(23, 41), Mod(40, 41), Mod(18, 41), Mod(39, 41), Mod(21, 41), Mod(5, 41), Mod(32, 41), Mod(20, 41), Mod(10, 41), Mod(2, 41), Mod(37, 41), Mod(33, 41), Mod(31, 41), Mod(31, 41), Mod(33, 41), Mod(37, 41), Mod(2, 41), Mod(10, 41), Mod(20, 41), Mod(32, 41), Mod(5, 41), Mod(21, 41), Mod(39, 41), Mod(18, 41), Mod(40, 41), Mod(23, 41), Mod(8, 41), Mod(36, 41), Mod(25, 41), Mod(16, 41), Mod(9, 41), Mod(4, 41), Mod(1, 41), Mod(0, 41)] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:46:46 2004 Input: 3e-2pi Output: ? 0.030000000000000000000000000000000000000 ? Errors (if any) and Timing Info: *** Warning: unused characters: pi. Timing: real 0m0.011s user 0m0.003s sys 0m0.007s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:47:19 2004 Input: 3000e-2000pi Output: ? 3.0000000000000000000000000000000000000 E-1997 ? Errors (if any) and Timing Info: *** Warning: unused characters: pi. Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:47:39 2004 Input: 3000*e-2000*pi Output: ? 3000*e - 2000*pi ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:48:14 2004 Input: 3000*exp(1)-2000*pi Output: ? -2000*pi + 8154.8454853771357060808624140579874933 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.004s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:48:36 2004 Input: 3*exp(1)-2*3.141592653589793 Output: ? 1.8716601781975497060808624140579874932 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:48:50 2004 Input: 4*exp(1)-3*3.141592653589793 Output: ? 1.4483493530668019414411498854106499910 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:48:58 2004 Input: 5*exp(1)-4*3.141592653589793 Output: ? 1.0250385279360541768014373567633124887 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:49:15 2004 Input: 7*exp(1)-5*3.141592653589793 Output: ? 3.3200095312643516475220122994686374842 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:49:23 2004 Input: 7*exp(1)-6*3.141592653589793 Output: ? 0.17841687767455864752201229946863748426 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:49:42 2004 Input: 6*exp(1)-5*3.141592653589793 Output: ? 0.60172770280530641216172482811597498650 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:49:48 2004 Input: 6*exp(1)-4*3.141592653589793 Output: ? 3.7433203563950994121617248281159749865 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:49:58 2004 Input: 3*exp(1)-2*3.141592653589793 Output: ? 1.8716601781975497060808624140579874932 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.002s sys 0m0.007s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:50:07 2004 Input: 4*exp(1)-3*3.141592653589793 Output: ? 1.4483493530668019414411498854106499910 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:50:15 2004 Input: 5*exp(1)-4*3.141592653589793 Output: ? 1.0250385279360541768014373567633124887 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:53:40 2004 Input: 6*exp(1)-5*3.141592653589793 Output: ? 0.60172770280530641216172482811597498650 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:53:54 2004 Input: 8*exp(1)-6*3.141592653589793 Output: ? 2.8966987061336038828822997708212999821 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:54:06 2004 Input: 10*exp(1)-8*3.141592653589793 Output: ? 2.0500770558721083536028747135266249775 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:54:14 2004 Input: 12*exp(1)-10*3.141592653589793 Output: ? 1.2034554056106128243234496562319499730 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:54:22 2004 Input: 13*exp(1)-11*3.141592653589793 Output: ? 0.78014458047986505968373712758461247076 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:54:38 2004 Input: 18*exp(1)-15*3.141592653589793 Output: ? 1.8051831084159192364851744843479249597 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:54:51 2004 Input: 20*exp(1)-17*3.141592653589793 Output: ? 0.95856145815442370720574942705324995502 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:55:21 2004 Input: 25*exp(1)-21*3.141592653589793 Output: ? 1.9835999860904778840071867838165624441 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:55:31 2004 Input: 27*exp(1)-23*3.141592653589793 Output: ? 1.1369783358289823547277617265218874396 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:55:41 2004 Input: 28*exp(1)-24*3.141592653589793 Output: ? 0.71366751069823459008804919787454993703 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.009s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:56:11 2004 Input: 35*exp(1)-30*3.141592653589793 Output: ? 0.89208438837279323761006149734318742147 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:56:30 2004 Input: 42*exp(1)-36*3.141592653589793 Output: ? 1.0705012660473518851320737968118249055 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:56:51 2004 Input: 49*exp(1)-42*3.141592653589793 Output: ? 1.2489181437219105326540860962804623904 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:57:18 2004 Input: 57*exp(1)-49*3.141592653589793 Output: ? 1.0040241962657214155363858671017623718 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:57:51 2004 Input: 64*exp(1)-55*3.141592653589793 Output: ? 1.1824410739402800630583981665703998570 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:57:56 2004 Input: 64*exp(1)-56*3.141592653589793 Output: ? -1.9591515796495129369416018334296001432 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:58:03 2004 Input: 64*exp(1)-55*3.141592653589793 Output: ? 1.1824410739402800630583981665703998570 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:58:11 2004 Input: 65*exp(1)-56*3.141592653589793 Output: ? 0.75913024880953229841868563792306235401 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:58:31 2004 Input: 72*exp(1)-62*3.141592653589793 Output: ? 0.93754712648409094594069793739169983845 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:58:52 2004 Input: 80*exp(1)-69*3.141592653589793 Output: ? 0.69265317902790182882299770821299982065 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.003s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:59:13 2004 Input: 79*exp(1)-68*3.141592653589793 Output: ? 1.1159640041586495934627102368603373221 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:59:28 2004 Input: 87*exp(1)-75*3.141592653589793 Output: ? 0.87107005670246047634501000768163730434 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:59:40 2004 Input: 95*exp(1)-82*3.141592653589793 Output: ? 0.62617610924627135922730977850293728579 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 03:59:53 2004 Input: 94*exp(1)-81*3.141592653589793 Output: ? 1.0494869343770191238670223071502747888 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:00:12 2004 Input: 101*exp(1)-88*3.141592653589793 Output: ? -1.9136888415382152286109653933810877277 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:00:17 2004 Input: 101*exp(1)-87*3.141592653589793 Output: ? 1.2279038120515777713890346066189122725 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:00:27 2004 Input: 109*exp(1)-94*3.141592653589793 Output: ? 0.98300986459538865427133437744021225618 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:00:39 2004 Input: 116*exp(1)-100*3.141592653589793 Output: ? 1.1614267422699473017933466769088497391 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:00:48 2004 Input: 124*exp(1)-107*3.141592653589793 Output: ? 0.91653279481375818467564644773014972132 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:01:02 2004 Input: 131*exp(1)-113*3.141592653589793 Output: ? 1.0949496724883168321976587471987872058 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:01:09 2004 Input: 139*exp(1)-120*3.141592653589793 Output: ? 0.85005572503212771507995851802008718796 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:01:21 2004 Input: 146*exp(1)-126*3.141592653589793 Output: ? 1.0284726027066863626019708174887246724 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:01:34 2004 Input: 153*exp(1)-132*3.141592653589793 Output: ? 1.2068894803812450101239831169573621568 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:01:44 2004 Input: 161*exp(1)-139*3.141592653589793 Output: ? 0.96199553292505589300628288777866213905 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:01:55 2004 Input: 168*exp(1)-145*3.141592653589793 Output: ? 1.1404124105996145405282951872472996220 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:02:04 2004 Input: 176*exp(1)-152*3.141592653589793 Output: ? 0.89551846314342542341059495806859960419 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:02:14 2004 Input: 183*exp(1)-158*3.141592653589793 Output: ? 1.0739353408179840709326072575372370886 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:02:30 2004 Input: 190*exp(1)-164*3.141592653589793 Output: ? 1.2523522184925427184546195570058745716 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:02:39 2004 Input: 198*exp(1)-171*3.141592653589793 Output: ? 1.0074582710363536013369193278271745553 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:02:55 2004 Input: 205*exp(1)-176*3.141592653589793 Output: ? 4.3274678023007052488589316272958120384 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:03:02 2004 Input: 205*exp(1)-177*3.141592653589793 Output: ? 1.1858751487109122488589316272958120397 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:03:11 2004 Input: 213*exp(1)-184*3.141592653589793 Output: ? 0.94098120125472313174123139811711202343 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.008s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:03:19 2004 Input: 220*exp(1)-190*3.141592653589793 Output: ? 1.1193980789292817792632436975857495049 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:03:26 2004 Input: 228*exp(1)-197*3.141592653589793 Output: ? 0.87450413147309266214554346840704948857 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:03:45 2004 Input: 235*exp(1)-203*3.141592653589793 Output: ? 1.0529210091476513096675557678756869730 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:03:54 2004 Input: 242*exp(1)-209*3.141592653589793 Output: ? 1.2313378868222099571895680673443244544 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:04:03 2004 Input: 250*exp(1)-216*3.141592653589793 Output: ? 0.98644393936602084007186783816562443815 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:04:36 2004 Input: 257*exp(1)-222*3.141592653589793 Output: ? 1.1648608170405794875938801376342619226 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:04:45 2004 Input: 265*exp(1)-229*3.141592653589793 Output: ? 0.91996686958439037047617990845556190630 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:04:55 2004 Input: 272*exp(1)-235*3.141592653589793 Output: ? 1.0983837472589490179981922079241993907 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:05:08 2004 Input: 279*exp(1)-241*3.141592653589793 Output: ? 1.2768006249335076655202045073928368722 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:05:17 2004 Input: 287*exp(1)-248*3.141592653589793 Output: ? 1.0319066774773185484025042782141368559 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:05:30 2004 Input: 294*exp(1)-254*3.141592653589793 Output: ? 1.2103235551518771959245165776827743373 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:05:41 2004 Input: 302*exp(1)-261*3.141592653589793 Output: ? 0.96542960769568807880681634850407432102 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:05:49 2004 Input: 309*exp(1)-267*3.141592653589793 Output: ? 1.1438464853702467263288286479727118085 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:06:00 2004 Input: 317*exp(1)-264*3.141592653589793 Output: ? 32.314879073811987609211128418794011788 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:06:08 2004 Input: 317*exp(1)-274*3.141592653589793 Output: ? 0.89895253791405760921112841879401178616 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:06:17 2004 Input: 324*exp(1)-280*3.141592653589793 Output: ? 1.0773694155886162567331407182626492736 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:06:37 2004 Input: 331*exp(1)-286*3.141592653589793 Output: ? 1.2557862932631749042551530177312867550 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:06:45 2004 Input: 339*exp(1)-293*3.141592653589793 Output: ? 1.0108923458069857871374527885525867387 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:07:13 2004 Input: 354*exp(1)-306*3.141592653589793 Output: ? 0.94441527602535531754176485884252420389 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:07:24 2004 Input: 361*exp(1)-312*3.141592653589793 Output: ? 1.1228321536999139650637771583111616913 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:07:52 2004 Input: 369*exp(1)-318*3.141592653589793 Output: ? 4.0195308598335178479460769291324616707 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:07:57 2004 Input: 369*exp(1)-319*3.141592653589793 Output: ? 0.87793820624372484794607692913246166903 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:08:07 2004 Input: 376*exp(1)-325*3.141592653589793 Output: ? 1.0563550839182834954680892286010991565 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:08:15 2004 Input: 383*exp(1)-331*3.141592653589793 Output: ? 1.2347719615928421429901015280697366409 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:10:08 2004 Input: 391*exp(1)-338*3.141592653589793 Output: ? 0.98987801413665302587240129889103661861 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:10:21 2004 Input: 398*exp(1)-364*3.141592653589793 Output: ? -61.663558179984648326605586401640325894 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.008s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:10:27 2004 Input: 398*exp(1)-346*3.141592653589793 Output: ? -5.1148904153683743266055864016403258943 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:10:33 2004 Input: 398*exp(1)-344*3.141592653589793 Output: ? 1.1682948918112116733944135983596741091 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:10:46 2004 Input: 406*exp(1)-351*3.141592653589793 Output: ? 0.92340094435502255627671336918097408676 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:10:53 2004 Input: 413*exp(1)-357*3.141592653589793 Output: ? 1.1018178220295812037987256686496115772 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:11:10 2004 Input: 421*exp(1)-363*3.141592653589793 Output: ? 3.9985165281631850866810254394709115506 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:11:16 2004 Input: 421*exp(1)-364*3.141592653589793 Output: ? 0.85692387457339208668102543947091154889 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:11:29 2004 Input: 428*exp(1)-370*3.141592653589793 Output: ? 1.0353407522479507342030377389395490393 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:11:45 2004 Input: 443*exp(1)-383*3.141592653589793 Output: ? 0.96886368246632026460734980922948650750 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.003s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:12:05 2004 Input: 458*exp(1)-396*3.141592653589793 Output: ? 0.90238661268468979501166187951942396963 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:12:26 2004 Input: 465*exp(1)-402*3.141592653589793 Output: ? 1.0808034903592484425336741789880614541 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.007s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:12:40 2004 Input: 480*exp(1)-415*3.141592653589793 Output: ? 1.0143264205776179729379862492779989222 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:12:56 2004 Input: 495*exp(1)-418*3.141592653589793 Output: ? 32.363775886693917503342298319567936383 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:13:03 2004 Input: 495*exp(1)-428*3.141592653589793 Output: ? 0.94784935079598750334229831956793638435 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:13:21 2004 Input: 502*exp(1)-434*3.141592653589793 Output: ? 1.1262662284705461508643106190365738748 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:13:45 2004 Input: 517*exp(1)-447*3.141592653589793 Output: ? 1.0597891586889156812686226893265113369 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:13:56 2004 Input: 532*exp(1)-460*3.141592653589793 Output: ? 0.99331208890728521167293475961644880509 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.003s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:16:54 2004 Input: 539*exp(1)-466*3.141592653589793 Output: ? 1.1717289665818438591949470590850862895 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:17:18 2004 Input: 547*exp(1)-473*3.141592653589793 Output: ? 0.92683501912565474207724682990638627324 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:18:14 2004 Input: 555*exp(1)-479*3.141592653589793 Output: ? 3.8235337252592586249595466007276862526 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:18:21 2004 Input: 555*exp(1)-480*3.141592653589793 Output: ? 0.68194107166946562495954660072768625694 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:18:38 2004 Input: 554*exp(1)-479*3.141592653589793 Output: ? 1.1052518968002133895992591293750237517 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:18:48 2004 Input: 569*exp(1)-492*3.141592653589793 Output: ? 1.0387748270185829200035711996649612198 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.001s sys 0m0.008s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:19:03 2004 Input: 584*exp(1)-505*3.141592653589793 Output: ? 0.97229775723695245040788326995489869398 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '217.114' ************** PARI ***************** Host 217.114.114.122 (217.114.114.122) Time: Tue Nov 16 04:45:08 2004 Input: 814*exp(1)-704*3.141592653589793 Output: ? 1.0001802384485495832740016810672731720 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.004s '212.98.' ************** PARI ***************** Host 212.98.201.1 (212.98.201.1) Time: Tue Nov 16 06:32:23 2004 Input: set(GF81); Output: ? ? Errors (if any) and Timing Info: *** obsolete function: set(GF81); ^---------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file) New syntax: set(x) ===> Set(x) Set({x=[]}): convert x into a set, i.e. a row vector with strictly increasing coefficients. Empty set if x is omitted. Timing: real 0m0.115s user 0m0.003s sys 0m0.009s '212.98.' ************** PARI ***************** Host 212.98.201.1 (212.98.201.1) Time: Tue Nov 16 06:33:23 2004 Input: GF81 := GF(3, 4); GF81, PrimeField(GF81); Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: GF81:=GF(3,4); ^----------- *** Warning: unused characters: ,PrimeField(GF81);. Timing: real 0m0.024s user 0m0.003s sys 0m0.008s '193.253' ************** PARI ***************** Host 193.253.180.90 (193.253.180.90) Time: Tue Nov 16 07:15:30 2004 Input: Pi Output: ? 3.1415926535897932384626433832795028842 ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.004s sys 0m0.007s '137.222' ************** PARI ***************** Host 137.222.103.110 (137.222.103.110) Time: Tue Nov 16 14:39:51 2004 Input: p := 2^174 - 3; IsPrime(p); print p mod 3; F := FiniteField(p); D := PrimitiveElement(F); for i:=0 to 6 do ec := #EllipticCurve([0,0,0,0,D^i]); print Factorization(ec); end for; Output: ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: p:=2^174-3; ^---------- *** expected character: '=' instead of: IsPrime(p); ^- *** unexpected character: F:=FiniteField(p); ^----------------- *** unexpected character: D:=PrimitiveElement(F ^-------------------- *** unexpected character: fori:=0to6do ^-------- *** unexpected character: ec:=#EllipticCurve([0, ^-------------------- *** expected character: '=' instead of: printFactorization(ec); ^- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '62.252.' ************** PARI ***************** Host 62.252.0.8 (62.252.0.8) Time: Tue Nov 16 16:39:51 2004 Input: ax^2 - 8 + 16 = 0 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ax^2-8+16=0 ^--- Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '62.245.' ************** PARI ***************** Host 62.245.109.94 (62.245.109.94) Time: Tue Nov 16 17:38:10 2004 Input: plot(x=-2,2,exp(x)/(x+1)) Output: WARNING: PARI command contains unsafe command 'plot', so it will not be executed. '60.34.5' ************** PARI ***************** Host 60.34.52.213 (60.34.52.213) Time: Tue Nov 16 17:52:27 2004 Input: (x^5-1)/(x-1) Output: ? x^4 + x^3 + x^2 + x + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.003s sys 0m0.008s '60.34.5' ************** PARI ***************** Host 60.34.52.213 (60.34.52.213) Time: Tue Nov 16 17:53:43 2004 Input: solve(x^5-1) Output: ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: solve(x^5-1) ^----- Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '80.223.' ************** PARI ***************** Host 80.223.251.161 (80.223.251.161) Time: Wed Nov 17 03:56:35 2004 Input: revisite Output: ? revisite ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.005s '80.223.' ************** PARI ***************** Host 80.223.251.161 (80.223.251.161) Time: Wed Nov 17 03:56:52 2004 Input: 121332 Output: ? 121332 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 14:55:18 2004 Input: logarithm(2) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: logarithm(2) ^------------ Timing: real 0m0.019s user 0m0.005s sys 0m0.005s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 14:55:26 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 14:56:32 2004 Input: sqrt(3) Output: ? 1.7320508075688772935274463415058723669 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.005s sys 0m0.004s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 14:56:41 2004 Input: log(3) Output: ? 1.0986122886681096913952452369225257046 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 14:56:49 2004 Input: 2^200 Output: ? 1606938044258990275541962092341162602522202993782792835301376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 14:57:03 2004 Input: log2(2^2) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: log2(2^2) ^--------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 14:57:10 2004 Input: log(2^2) Output: ? 1.3862943611198906188344642429163531361 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 14:57:18 2004 Input: log(10^2) Output: ? 4.6051701859880913680359829093687284152 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.002s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 14:57:28 2004 Input: log(1.7^2) Output: ? 1.0612565021243407924630863263775246560 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 14:57:34 2004 Input: log(1.67^2) Output: ? 1.0256472528573274784475357347521019012 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 14:57:39 2004 Input: log(1.61^2) Output: ? 0.95246835799274325575224533176929486575 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 14:57:44 2004 Input: log(1.63^2) Output: ? 0.97716002963734193205789891350404292286 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 14:57:50 2004 Input: log(1.65^2) Output: ? 1.0015505758249784840439304774902284576 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 14:57:57 2004 Input: log(1.648^2) Output: ? 0.99912486297455991276711287366610894025 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.008s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 14:58:12 2004 Input: logn(1.648^2) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: logn(1.648^2) ^------------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 15:09:53 2004 Input: ((5^31)*(5^32))/(5-1) Output: ? 108420217248550443400745280086994171142578125/4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Wed Nov 17 15:10:02 2004 Input: ((5^31)*(5^32)) Output: ? 108420217248550443400745280086994171142578125 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.003s sys 0m0.007s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Wed Nov 17 20:34:07 2004 Input: ?forprimes Output: ? ? Errors (if any) and Timing Info: *** forprimes: unknown identifier. Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Wed Nov 17 20:34:14 2004 Input: ?forprime Output: ? forprime(X=a,b,seq): the sequence is evaluated, X running over the primes between a and b. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Wed Nov 17 20:35:37 2004 Input: s=0; forprime(p=2,100,s+=log(p)/p); s Output: ? ? ? 3.3694708749989818713880714936006244994 ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.004s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Wed Nov 17 20:36:17 2004 Input: s=0; n=100; forprime(p=2,n,s+=log(p)/p); s/log(n); Output: ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Wed Nov 17 20:36:23 2004 Input: s=0; n=100; forprime(p=2,n,s+=log(p)/p); s/log(n) Output: ? ? ? ? 0.73167130397288971671148509276720354326 ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Wed Nov 17 20:36:28 2004 Input: s=0; n=1000; forprime(p=2,n,s+=log(p)/p); s/log(n) Output: ? ? ? ? 0.81205981521389517750534452460833495363 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Wed Nov 17 20:36:34 2004 Input: s=0; n=10000; forprime(p=2,n,s+=log(p)/p); s/log(n) Output: ? ? ? ? 0.85673963019827502252296443485365010165 ? ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.025s sys 0m0.006s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Wed Nov 17 20:36:40 2004 Input: s=0; n=100000; forprime(p=2,n,s+=log(p)/p); s/log(n) Output: ? ? ? ? 0.88459662011224455274489827720714468947 ? ? Errors (if any) and Timing Info: Timing: real 0m0.176s user 0m0.171s sys 0m0.006s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Wed Nov 17 20:36:48 2004 Input: s=0; n=1000000; forprime(p=2,n,s+=log(p)/p); s/log(n) Output: ? ? ? ? 0 ? ? Errors (if any) and Timing Info: *** not enough precomputed primes, need primelimit ~ 1000000. Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Thu Nov 18 01:19:35 2004 Input: s=0; n=100000; forprime(p=2,n,s+=log(p)/p); s/log(n) Output: ? ? ? ? 0.88459662011224455274489827720714468947 ? ? Errors (if any) and Timing Info: Timing: real 0m0.176s user 0m0.170s sys 0m0.007s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Thu Nov 18 01:19:48 2004 Input: s=0; n=10000; forprime(p=2,n,s+=log(p)/p); s/log(n) Output: ? ? ? ? 0.85673963019827502252296443485365010165 ? ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.024s sys 0m0.007s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Thu Nov 18 01:21:07 2004 Input: s=0; n=10000; forprime(p=2,n,s+=log(p)/p); ll=s/log(n) exp(ll) Output: ? ? ? ? 0.85673963019827502252296443485365010165 ? 2.3554684625165925022001505292256990281 ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.027s sys 0m0.006s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Thu Nov 18 01:22:21 2004 Input: s=0; n=10000; forprime(p=2,n,s+=log(p)/p); ll=s-log(n) exp(ll) Output: ? ? ? ? -1.3194767676890651252595359069087099212 ? 0.26727511236069856049344884426828887525 ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.027s sys 0m0.002s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Thu Nov 18 01:22:40 2004 Input: s=0; n=1000; forprime(p=2,n,s+=log(p)/p); ll=s-log(n) exp(ll) Output: ? ? ? ? -1.2982448035890939076970136798101082768 ? 0.27301055990103503950282804797433027513 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Thu Nov 18 01:24:55 2004 Input: s=0; n=10000; forprime(p=2,n,s+=log(p)/p); ll=s-log(n) exp(ll) Output: ? ? ? ? -1.3194767676890651252595359069087099212 ? 0.26727511236069856049344884426828887525 ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.027s sys 0m0.005s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Thu Nov 18 01:25:40 2004 Input: s=0; n=1000; forprime(p=2,n,s+=log(p)/p); ll=s-log(n) exp(ll) Output: ? ? ? ? -1.2982448035890939076970136798101082768 ? 0.27301055990103503950282804797433027513 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Thu Nov 18 01:25:48 2004 Input: s=0; n=10000; forprime(p=2,n,s+=log(p)/p); ll=s-log(n) exp(ll) Output: ? ? ? ? -1.3194767676890651252595359069087099212 ? 0.26727511236069856049344884426828887525 ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.027s sys 0m0.004s '198.161' ************** PARI ***************** Host 198.161.29.182 (198.161.29.182) Time: Thu Nov 18 01:25:55 2004 Input: s=0; n=100000; forprime(p=2,n,s+=log(p)/p); ll=s-log(n) exp(ll) Output: ? ? ? ? -1.3286305110533727894495076465872088830 ? 0.26483970811261282354011622407694474982 ? Errors (if any) and Timing Info: Timing: real 0m0.177s user 0m0.171s sys 0m0.006s '129.247' ************** PARI ***************** Host 129.247.192.54 (129.247.192.54) Time: Thu Nov 18 03:50:49 2004 Input: factor(2*3*7*43*13*139*3263443*547+1) Output: ? [31 1] [1201073 1] [156461741 1] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.005s sys 0m0.005s '218.47.' ************** PARI ***************** Host 218.47.118.26 (218.47.118.26) Time: Thu Nov 18 04:23:56 2004 Input: IsPrime(7) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: IsPrime(7) ^---------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '131.211' ************** PARI ***************** Host 131.211.220.116 (131.211.220.116) Time: Thu Nov 18 07:28:27 2004 Input: prime(41561) Output: ? 500257 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.002s '216.180' ************** PARI ***************** Host 216.180.93.134 (216.180.93.134) Time: Thu Nov 18 09:17:32 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.132s user 0m0.004s sys 0m0.005s '69.162.' ************** PARI ***************** Host 69.162.12.202 (69.162.12.202) Time: Thu Nov 18 14:24:55 2004 Input: 3*4 Output: ? 12 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.004s sys 0m0.006s '69.162.' ************** PARI ***************** Host 69.162.12.202 (69.162.12.202) Time: Thu Nov 18 14:25:24 2004 Input: atan(1)*4 Output: ? 3.1415926535897932384626433832795028842 ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.002s sys 0m0.006s '68.40.6' ************** PARI ***************** Host 68.40.63.160 (68.40.63.160) Time: Thu Nov 18 20:31:46 2004 Input: cout>> Output: ? ? Errors (if any) and Timing Info: *** unexpected character: cout>> ^- Timing: real 0m0.018s user 0m0.006s sys 0m0.003s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 08:56:20 2004 Input: ((2^100)^2-1)*((2^100)^3-1)/2^100-1 Output: ? 3273390607896141870013189696827599152216642046043064789483289331060157461918588286437581681340805061423502742649347342526337649042154406532332805685249/1267650600228229401496703205376 ? Errors (if any) and Timing Info: Timing: real 0m0.324s user 0m0.005s sys 0m0.008s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:06:43 2004 Input: ((2^200)^2)*((2^200)^3)/(2^200); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:06:49 2004 Input: ((2^200)^2)*((2^200)^3)/(2^200) Output: ? 6668014432879854274079851790721257797144758322315908160396257811764037237817632071521432200871554290742929910593433240445888801654119365080363356052330830046095157579514014558463078285911814024728965016135886601981690748037476461291163877376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:27:10 2004 Input: 2^1000 Output: ? 10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:28:22 2004 Input: ((2^200)^2)*((2^200)^3)/(2^200) Output: ? 6668014432879854274079851790721257797144758322315908160396257811764037237817632071521432200871554290742929910593433240445888801654119365080363356052330830046095157579514014558463078285911814024728965016135886601981690748037476461291163877376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:29:31 2004 Input: ((2^200)^3)*((2^200)^4)/(2^200) Output: ? 17218479456385750618067377696052635483579924745448689921733236816400740691241745619397484537236046173286370919031961587788584927290816661024991609882728717344659503471655990880884679896520055123906467064419056526231345685268240569209892573766037966584735183775739433978714578587782701380797240772477647874555986712746271362892227516205318914435913511141036261376 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:30:18 2004 Input: ((2^200)^3)*((2^200)^5)/(2^200) Output: ? 27669029702758120146491942186874884129832195596687593922941153328644615037061218897472958124908361305229397532165999293867885545372978607205176630181452676933921073841230450143984178961558051196639818353232501575334232440224365258413261224549068647496733893492858693838936019366894056124879628942806188005563423883960767413509787430715244414672882018609567819742394979958289448147350615740681597522011228581960985268453376 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.008s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:31:25 2004 Input: ((2^200)^4)*((2^200)^5)/(2^200) Output: ? 44462416477094044620016814065517364315819234512137839319418223093753683069769152238984782576173969417485953521141049383745107056455283979316385016701612810119562585078620415976730705698345087039035930761275083827265405596065418173652685035788898113991627042329246850314029877161622487411877779578892097029690461532001915311366862468942148892205997883828265721290296220249202674740669814705818564765009960300389641843321936008416473775144511929246788246559538970957296160626364645376 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:32:22 2004 Input: ((2^200)^3)*((2^200)^7)/(2^200) Output: ? 71448348576730208360402604523024658663907311448489024669693316988935593287322878666163481950176220037593478347105937422686501991894419788796088422137966026262523598150372719976137911322484446114613284904383977643176193557817897027023063420124852033989626806764509137929914787205373413116077254242653423277386226627159120168223623660139965116969572411841665962582988716865792650075294655252525257343163566042824495509307872827973214736884381496689456792434150079470111661811761376161068055664012337698456291039551943299284254570579952324837376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:33:07 2004 Input: ((2^200)^5)*((2^200)^6)/(2^200) Output: ? 114813069527425452423283320117768198402231770208869520047764273682576626139237031385665948631650626991844596463898746277344711896086305533142593135616665318539129989145312280000688779148240044871428926990063486244781615463646388363947317026040466353970904996558162398808944629605623311649536164221970332681344168908984458505602379484807914058900934776500429002716706625830522008132236281291761267883317206598995396418127021779858404042159853183251540889433902091920554957783589672039160081957216630582755380425583726015528348786419432054508915275783882625175435528800822842770817965453762184851149029376 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.009s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:34:09 2004 Input: ((2^160)^5)*((2^160)^6)/(2^160) Output: ? 44462416477094044620016814065517364315819234512137839319418223093753683069769152238984782576173969417485953521141049383745107056455283979316385016701612810119562585078620415976730705698345087039035930761275083827265405596065418173652685035788898113991627042329246850314029877161622487411877779578892097029690461532001915311366862468942148892205997883828265721290296220249202674740669814705818564765009960300389641843321936008416473775144511929246788246559538970957296160626364645376 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.008s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:35:04 2004 Input: ((2^160)^3)*((2^160)^7)/(2^160) Output: ? 30422419887462074119071134929958489032043186702245995987957913005836841367216067357323144240859877069545506861679635202642345411084305213453789078664403403059928208689481185220549258184013586200335791339139627558484226201606636463934347727908649520193900630877843276694401765022011544615205503550967713779282527138661579516950283671253463206314672846846606637692828053410669727717058223014832711195154653927501539142641927787722571776 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:35:54 2004 Input: ((2^160)^4)*((2^160)^5)/(2^160) Output: ? 20815864389328798163850480654728171077230524494533409610638224700807216119346720596024478883464648369684843227908562015582767132496646929816279813211354641525848259018778440691546366699323167100945918841095379622423387354295096957733925002768876520583464697770622321657076833170056511209332449663781837603694136444406281042053396870977465916057756101739472373801429441421111406337458176 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:36:24 2004 Input: ((2^160)^3)*((2^160)^5)/(2^160) Output: ? 14242792383964888162918480513432465216409371640403009729971037612045113415478719007639881209041451055630074000655093473974722206675223109929434400259100512062680086347153555148539548552831624261944567042435944993535084132588196941322891072406503377213352323037077384970994853089450777507879083442634420291861180736024127002634265953304576 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:36:54 2004 Input: ((2^160)^3)*((2^160)^4)/(2^160) Output: ? 9745314011399999080353382387875188310876226857595007526867906457212948690766426102465615065882010259225304916231408668183459169865203094046577987296312653419531277699956473029870789655490053648352799593479218378873685597925394874945746363615468965612827738803104277547081828589991914110976 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:37:34 2004 Input: ((2^160)^2)*((2^160)^3)/(2^160) Output: ? 4562440617622195218641171605700291324893228507248559930579192517899275167208677386505912811317371399778642309573594407310688704721375437998252661319722214188251994674360264950082874192246603776 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:38:24 2004 Input: ((2^100)^2)*((2^100)^3)/(2^100) Output: ? 2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:38:56 2004 Input: ((2^100)^3)*((2^100)^4)/(2^100) Output: ? 4149515568880992958512407863691161151012446232242436899995657329690652811412908146399707048947103794288197886611300789182395151075411775307886874834113963687061181803401509523685376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:39:24 2004 Input: ((2^100)^3)*((2^100)^5)/(2^100) Output: ? 5260135901548373507240989882880128665550339802823173859498280903068732154297080822113666536277588451226982968856178217713019432250183803863127814770651880849955223671128444598191663757884322717271293251735781376 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:39:58 2004 Input: ((2^100)^4)*((2^100)^5)/(2^100) Output: ? 6668014432879854274079851790721257797144758322315908160396257811764037237817632071521432200871554290742929910593433240445888801654119365080363356052330830046095157579514014558463078285911814024728965016135886601981690748037476461291163877376 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:40:38 2004 Input: ((2^100)^3)*((2^100)^7)/(2^100) Output: ? 8452712498170643941637436558664265704301557216577944354047371344426782440907597751590676094202515006314790319892114058862117560952042968596008623655407033230534186943984081346699704282822823056848387726531379014466368452684024987821414350380272583623832617294363807973376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:41:16 2004 Input: ((2^100)^5)*((2^100)^6)/(2^100) Output: ? 10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:42:26 2004 Input: ((2^100)^1)*((2^100)^2)/(2^100) Output: ? 1606938044258990275541962092341162602522202993782792835301376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:43:00 2004 Input: ((2^100)^1)*((2^100)^3)/(2^100) Output: ? 2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:43:30 2004 Input: ((2^160)^1)*((2^160)^3)/(2^160) Output: ? 3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290176 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:44:10 2004 Input: ((2^160)^1)*((2^160)^2)/(2^160) Output: ? 2135987035920910082395021706169552114602704522356652769947041607822219725780640550022962086936576 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:44:50 2004 Input: ((2^200)^1)*((2^200)^2)/(2^200) Output: ? 2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:45:20 2004 Input: ((2^200)^1)*((2^200)^3)/(2^200) Output: ? 4149515568880992958512407863691161151012446232242436899995657329690652811412908146399707048947103794288197886611300789182395151075411775307886874834113963687061181803401509523685376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:46:03 2004 Input: ((2^200)^1)*((2^200)^5)/(2^200) Output: ? 10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:47:06 2004 Input: ((2^160)^1)*((2^160)^5)/(2^160) Output: ? 6668014432879854274079851790721257797144758322315908160396257811764037237817632071521432200871554290742929910593433240445888801654119365080363356052330830046095157579514014558463078285911814024728965016135886601981690748037476461291163877376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:47:41 2004 Input: ((2^100)^1)*((2^100)^5)/(2^100) Output: ? 3273390607896141870013189696827599152216642046043064789483291368096133796404674554883270092325904157150886684127560071009217256545885393053328527589376 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:49:32 2004 Input: (5^31-1)*(5^32-1)/(5-1) Output: ? 27105054312137610850179335102438926696777344 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:50:18 2004 Input: (13^31-1)*(13^32-1)/(13-1) Output: ? 1256753054043340213658075387330551341189061455950935970059014575379840 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.001s sys 0m0.008s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:51:03 2004 Input: (29^31-1)*(29^32-1)/(29-1) Output: ? 4829651971646134451483406376431970838344885649327943001154487347396054819016277974701677440 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '193.145' ************** PARI ***************** Host 193.145.234.39 (193.145.234.39) Time: Fri Nov 19 09:51:31 2004 Input: (29^47-1)*(29^48-1)/(29-1) Output: ? 302448732673863911251957779239079078682828739532453698417217351339057658237388462515407710232419534634898126736699128458885095769885783360 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '201.128' ************** PARI ***************** Host 201.128.34.78 (201.128.34.78) Time: Sat Nov 20 13:59:22 2004 Input: Pi Output: ? 3.1415926535897932384626433832795028842 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.005s sys 0m0.005s '80.60.9' ************** PARI ***************** Host 80.60.97.177 (80.60.97.177) Time: Sat Nov 20 17:10:02 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '195.121' ************** PARI ***************** Host 195.121.142.246 (195.121.142.246) Time: Sat Nov 20 20:30:38 2004 Input: incgam(0.5,1.05) Output: ? 0.26108092548682760924896501819234526427 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.003s sys 0m0.007s '195.121' ************** PARI ***************** Host 195.121.142.246 (195.121.142.246) Time: Sat Nov 20 20:31:14 2004 Input: incgam(0.5+I*0.25,1.05+I*1.05) Output: ? ? Errors (if any) and Timing Info: *** impossible assignment t_COMPLEX --> t_REAL. Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '212.238' ************** PARI ***************** Host 212.238.233.143 (212.238.233.143) Time: Sun Nov 21 16:04:57 2004 Input: Factor(-223591); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(-223591); ^---------------- Timing: real 0m0.010s user 0m0.002s sys 0m0.008s '212.238' ************** PARI ***************** Host 212.238.233.143 (212.238.233.143) Time: Sun Nov 21 16:06:18 2004 Input: factor(-223591) Output: ? [-1 1] [37 1] [6043 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:08:58 2004 Input: ? Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) Extended help looks available: ?? (opens the full user's manual in a dvi previewer) ?? tutorial (same with the GP tutorial) ?? refcard (same with the GP reference card) ?? keyword (long help text about "keyword" from the user's manual) ??? keyword (a propos: list of related functions). ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:09:10 2004 Input: ?5 Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:09:37 2004 Input: ?ellinit Output: ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:11:37 2004 Input: ellinit([0,8,12,0]) Output: ? ? Errors (if any) and Timing Info: *** bad argument for an elliptic curve related function Timing: real 0m0.023s user 0m0.004s sys 0m0.006s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:11:49 2004 Input: ?ellinit Output: ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:12:24 2004 Input: ?5 Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:12:58 2004 Input: ?ellwp Output: ? ellwp(e,{z=x},{flag=0}): Complex value of Weierstrass P function at z on the lattice generated over Z by e=[om1,om2] (e as given by ellinit is also accepted). Optional flag means 0 (default), compute only P(z), 1 compute [P(z),P'(z)], 2 consider om as an elliptic curve and compute P(z) for that curve (identical to ellztopoint in that case). If z is omitted or is a simple variable, return formal expansion in z. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:13:09 2004 Input: ?5 Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:13:26 2004 Input: ?ellminimalmodel Output: ? ellminimalmodel(e,{&v}): return the standard minimal integral model of the rational elliptic curve e. Sets v to the corresponding change of variables. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:13:43 2004 Input: ? Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) Extended help looks available: ?? (opens the full user's manual in a dvi previewer) ?? tutorial (same with the GP tutorial) ?? refcard (same with the GP reference card) ?? keyword (long help text about "keyword" from the user's manual) ??? keyword (a propos: list of related functions). ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:13:50 2004 Input: ?8 Output: ? algdep charpoly concat lindep listcreate listinsert listkill listput listsort matadjoint matcompanion matdet matdetint matdiagonal mateigen mathess mathilbert mathnf mathnfmod mathnfmodid matid matimage matimagecompl matindexrank matintersect matinverseimage matisdiagonal matker matkerint matmuldiagonal matmultodiagonal matpascal matrank matrix matrixqz matsize matsnf matsolve matsolvemod matsupplement mattranspose qfgaussred qfjacobi qflll qflllgram qfminim qfperfection qfrep qfsign setintersect setisset setminus setsearch setunion trace vecextract vecsort vector vectorsmall vectorv ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:14:08 2004 Input: ?vector Output: ? vector(n,{X},{expr=0}): row vector with n components of expression expr (X ranges from 1 to n). By default, fill with 0s. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:15:58 2004 Input: ? Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) Extended help looks available: ?? (opens the full user's manual in a dvi previewer) ?? tutorial (same with the GP tutorial) ?? refcard (same with the GP reference card) ?? keyword (long help text about "keyword" from the user's manual) ??? keyword (a propos: list of related functions). ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:16:16 2004 Input: ?5 Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:16:36 2004 Input: ?ellchangecurve Output: ? ellchangecurve(x,y): change data on elliptic curve according to y=[u,r,s,t] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:16:51 2004 Input: ?5 Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:17:05 2004 Input: ?ellan Output: ? ellan(e,n): computes the first n Fourier coefficients of the L-function of the elliptic curve e (n<2^24 on a 32-bit machine) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:17:14 2004 Input: ?5 Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '140.180' ************** PARI ***************** Host 140.180.164.210 (140.180.164.210) Time: Sun Nov 21 22:17:29 2004 Input: ?ellj Output: ? ellj(x): elliptic j invariant of x. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Mon Nov 22 05:10:03 2004 Input: g(p)=(sum(i=0,((p-1)/2), (1/p^2)*((binomial(((p-1)/2)*(p^2+p+1), m*(p^2+p+1))^2)/(binomial(((p-1)/2)*(p+1), m*(p+1))^2))*4^((m+1)*p^2)) + sum(i=0,p-3, ((binomial((p-1)/2,p-1-m)^2/(binomial(((p-1)/2)*(p+1), (p-1-m)*(p+1)^2))*4^(m+1))*binomial(((p-1)/2)*(p+1), p+1)))); g(3); Output: ? ? (p^2 + p + 1)*m ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: ...omial(((p-1)/2)*(p^2+p+1), ^- *** Warning: unused characters: )^2)/(binomial(((p-1)/2)*(p+1),m*(p+1))^2))*4^((m+1)*p^2)). *** unexpected character: ...(binomial(((p-1)/2)*(p+1), ^- *** Warning: unused characters: ))*4^(m+1))*binomial(((p-1)/2)*(p+1),p+1))));. *** unknown function or error in formal parameters: g(3); ^----- Timing: real 0m0.016s user 0m0.004s sys 0m0.006s '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Mon Nov 22 05:11:21 2004 Input: g(p)=(sum(i=0,((p-1)/2), (1/p^2)*((binomial(((p-1)/2)*(p^2+p+1),m*(p^2+p+1))^2)/(binomial(((p-1)/2)*(p+1),m*(p+1))^2))*4^((m+1)*p^2))+ sum(i=0,p-3,((binomial((p-1)/2,p-1-m)^2/(binomial(((p-1)/2)*(p+1),(p-1-m)*(p+1)^2))*4^(m+1))*binomial(((p-1)/2)*(p+1), p+1)))); g(3); Output: ? ? ? ? Errors (if any) and Timing Info: *** this should be an integer: ...mial(((p-1)/2)*(p^2+p+1), *** m*(p^2+p+1))^2)/(bin ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Mon Nov 22 05:11:33 2004 Input: g(p)=(sum(i=0,((p-1)/2), (1/p^2)*((binomial(((p-1)/2)*(p^2+p+1),m*(p^2+p+1))^2)/(binomial(((p-1)/2)*(p+1),m*(p+1))^2))*4^((m+1)*p^2))+ sum(i=0,p-3,((binomial((p-1)/2,p-1-m)^2/(binomial(((p-1)/2)*(p+1),(p-1-m)*(p+1)^2))*4^(m+1))*binomial(((p-1)/2)*(p+1), p+1)))); g(5); Output: ? ? ? ? Errors (if any) and Timing Info: *** this should be an integer: ...mial(((p-1)/2)*(p^2+p+1), *** m*(p^2+p+1))^2)/(bin ^-------------------- Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Mon Nov 22 05:11:59 2004 Input: g(p)=(sum(m=0,((p-1)/2), (1/p^2)*((binomial(((p-1)/2)*(p^2+p+1),m*(p^2+p+1))^2)/(binomial(((p-1)/2)*(p+1),m*(p+1))^2))*4^((m+1)*p^2))+ sum(i=0,p-3,((binomial((p-1)/2,p-1-m)^2/(binomial(((p-1)/2)*(p+1),(p-1-m)*(p+1)^2))*4^(m+1))*binomial(((p-1)/2)*(p+1), p+1)))); g(5); Output: ? ? ? ? Errors (if any) and Timing Info: *** this should be an integer: ((binomial((p-1)/2,p-1-m)^2/(binomial(( ^-------------------- Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Mon Nov 22 05:12:32 2004 Input: g(p)=(sum(m=0,((p-1)/2), (1/p^2)*((binomial(((p-1)/2)*(p^2+p+1),m*(p^2+p+1))^2)/(binomial(((p-1)/2)*(p+1),m*(p+1))^2))*4^((m+1)*p^2))+ sum(i=0,p-3,((binomial((p-1)/2,p-1-m)^2/(binomial(((p-1)/2)*(p+1),(p-1-m)*(p+1)^2))*4^(m+1))*binomial(((p-1)/2)*(p+1), p+1)))); g(5)%p^3 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Mon Nov 22 05:12:49 2004 Input: g(p)=(sum(m=0,((p-1)/2), (1/p^2)*((binomial(((p-1)/2)*(p^2+p+1),m*(p^2+p+1))^2)/(binomial(((p-1)/2)*(p+1),m*(p+1))^2))*4^((m+1)*p^2))+ sum(i=0,p-3,((binomial((p-1)/2,p-1-m)^2/(binomial(((p-1)/2)*(p+1),(p-1-m)*(p+1)^2))*4^(m+1))*binomial(((p-1)/2)*(p+1), p+1)))); (g(5))%5^3; Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Mon Nov 22 05:12:53 2004 Input: g(p)=(sum(m=0,((p-1)/2), (1/p^2)*((binomial(((p-1)/2)*(p^2+p+1),m*(p^2+p+1))^2)/(binomial(((p-1)/2)*(p+1),m*(p+1))^2))*4^((m+1)*p^2))+ sum(i=0,p-3,((binomial((p-1)/2,p-1-m)^2/(binomial(((p-1)/2)*(p+1),(p-1-m)*(p+1)^2))*4^(m+1))*binomial(((p-1)/2)*(p+1), p+1)))); (g(5))%5^3; Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Mon Nov 22 05:14:34 2004 Input: g(p)=(sum(m=0,((p-1)/2), (1/p^2)*((binomial(((p-1)/2)*(p^2+p+1),m*(p^2+p+1))^2)/(binomial(((p-1)/2)*(p+1),m*(p+1))^2))*4^((m+1)*p^2))+ sum(m=0,p-3,((binomial((p-1)/2,p-1-m)^2/(binomial(((p-1)/2)*(p+1),(p-1-m)*(p+1)^2))*4^(m+1))*binomial(((p-1)/2)*(p+1), p+1)))); (g(5))%5^3; Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Mon Nov 22 05:15:04 2004 Input: g(p)=(sum(m=0,((p-1)/2), (1/p^2)*((binomial(((p-1)/2)*(p^2+p+1),m*(p^2+p+1))^2)/(binomial(((p-1)/2)*(p+1),m*(p+1))^2))*4^((m+1)*p^2))+ sum(m=0,p-3,((binomial((p-1)/2,p-1-m)^2/(binomial(((p-1)/2)*(p+1),(p-1-m)*(p+1)^2))*4^(m+1))*binomial(((p-1)/2)*(p+1), p+1)))); print(g(5)%5^3); Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Mon Nov 22 05:15:11 2004 Input: g(p)=(sum(m=0,((p-1)/2), (1/p^2)*((binomial(((p-1)/2)*(p^2+p+1),m*(p^2+p+1))^2)/(binomial(((p-1)/2)*(p+1),m*(p+1))^2))*4^((m+1)*p^2))+ sum(m=0,p-3,((binomial((p-1)/2,p-1-m)^2/(binomial(((p-1)/2)*(p+1),(p-1-m)*(p+1)^2))*4^(m+1))*binomial(((p-1)/2)*(p+1), p+1)))); print(g(5)%5); Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Mon Nov 22 05:15:17 2004 Input: g(p)=(sum(m=0,((p-1)/2), (1/p^2)*((binomial(((p-1)/2)*(p^2+p+1),m*(p^2+p+1))^2)/(binomial(((p-1)/2)*(p+1),m*(p+1))^2))*4^((m+1)*p^2))+ sum(m=0,p-3,((binomial((p-1)/2,p-1-m)^2/(binomial(((p-1)/2)*(p+1),(p-1-m)*(p+1)^2))*4^(m+1))*binomial(((p-1)/2)*(p+1), p+1)))); print(g(5)); Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:32:07 2004 Input: isprime(1233331111) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.004s sys 0m0.005s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:32:45 2004 Input: isprime(1233331111,{flag=0}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: isprime(1233331111,{flag=0}) ^---------- Timing: real 0m0.022s user 0m0.005s sys 0m0.005s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:34:21 2004 Input: isprime(1233331111.{flag=0}) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: isprime(1233331111.{flag=0}) ^--------- Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:34:35 2004 Input: isprime(1233331111,{flag = 0}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: isprime(1233331111,{flag=0}) ^---------- Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:35:00 2004 Input: isprime(1233331111,{flag = 0}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: isprime(1233331111,{flag=0}) ^---------- Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:36:45 2004 Input: 5+3 Output: ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.005s sys 0m0.005s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:37:01 2004 Input: ? 5+3 Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:37:11 2004 Input: print 5+3 Output: ? print5 + 3 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.005s sys 0m0.006s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:37:30 2004 Input: a=5 b=3 a+b Output: ? 5 ? 3 ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:39:29 2004 Input: a=5 b=3 gcd(5,25) Output: ? 5 ? 3 ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.005s sys 0m0.005s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:39:54 2004 Input: a=11123 isprime(a) Output: ? 11123 ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:40:04 2004 Input: a=11123 isprime(11123) Output: ? 11123 ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:40:09 2004 Input: isprime(11123) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:40:15 2004 Input: isprime(111234) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:40:27 2004 Input: isprime(1093) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:40:39 2004 Input: isprime(12333321) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:40:45 2004 Input: isprime(1233332111111) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.005s sys 0m0.003s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:41:01 2004 Input: isprime(13) isprime(111111111111111111) Output: ? 1 ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '222.150' ************** PARI ***************** Host 222.150.220.115 (222.150.220.115) Time: Mon Nov 22 08:41:38 2004 Input: isprime(13) isprime(8074761184358972350337234593060752060672283522143889240748412763971308992513797981530407650744043792313533321819710620433300521178420412887991185069018099838407880087260566373454070788737614547736891437676861852612949714898186481036249129222685685292388724566909223027557755397260071915123018202088868914480371131661778642850412974832089112451463481079651685610303663287701787687413216646454679160649128179779371718190018691405533318674611173588868565498790711647897937380652941648128464853018079134609633641046546924689820689825379486632895732573073070142225709423345193032587093878415961968603981818777198314118262618166237718308957349292421368374995599547166846076005678559896615257033139624357273204054756912488280732908211524415165169563761556035548060500252039993848840016911364796660826965208965890694031462906687492606991398827962478836151110562518221768712326898449683711364896683553865823996962782208433801549946154658945762694751502438511027824742591879044243260655030449337076496586526701601764587736015711993848881277176297765508079191774619059618697033772353870778074156071592738029172607497550766301600450769092712944435115710491882195210018824926464185804915191201033160302614984375841264175362190500496248033211523391010829592072990419655103614883214154203975006183522211442758742983708601160702494928168675208103178413292163437022343738905873779688310109339510277613385300904325580949695004298898119212673013377499947970645510950754993020477868062407694482032771165305905544160051929844321001113752476516646669599698655444459281866902390739410428463200182827604857999644055973759883691676926978249819362976527581864683332706498570740723954444801439179104180039342532760612835894012946205034441628722799) Output: ** WARNING: Computation used more memory than allowed. ** ? 1 ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m20.318s user 0m20.229s sys 0m0.015s '141.44.' ************** PARI ***************** Host 141.44.72.31 (141.44.72.31) Time: Mon Nov 22 09:27:48 2004 Input: <<73642736487326*6343486823764= Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ^- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '141.44.' ************** PARI ***************** Host 141.44.72.31 (141.44.72.31) Time: Mon Nov 22 09:28:03 2004 Input: 73642736487326*6343486823764= Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...642736487326*6343486823764= ^-- Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:02:19 2004 Input: log(3) Output: ? 1.0986122886681096913952452369225257046 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:02:49 2004 Input: log(2.7182) Output: ? 0.99996989653910988646358475975126720858 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:04:59 2004 Input: 1.442695*log((2^100)^2*(2^100)^3/(2^100)) Output: ? 399.99998866317211926787747818684161755 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:06:15 2004 Input: 1.442695*log((5^31-1)*(5^32-1)/4) Output: ? 144.28146588866834911954271746306675667 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:06:47 2004 Input: 1.442695*log((13^31-1)*(13^32-1)/12) Output: ? 229.54273323645132060193637134605572009 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:12:39 2004 Input: 1.442695*log((29^31-1)*(29^32-1)/28) Output: ? 301.24543923305996141372339635075122174 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:12:44 2004 Input: 1.442695*log((29^31-1)*(29^32-1)/28) Output: ? 301.24543923305996141372339635075122174 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:13:05 2004 Input: 1.442695*log((29^47-1)*(29^48-1)/28) Output: ? 456.70082667121471810643285698205899978 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:14:12 2004 Input: 1.442695*log((29^60-1)*(29^61-1)/28) Output: ? 583.00832896471545791925929374499656944 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:14:33 2004 Input: 1.442695*log((29^130-1)*(29^131-1)/28) Output: ? 1263.1256490066425184498631840069680983 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:14:54 2004 Input: 1.442695*log((29^216-1)*(29^217-1)/28) Output: ? 2098.6983564867243356731765349002474053 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:15:22 2004 Input: 1.442695*log((13^216-1)*(13^217-1)/12) Output: ? 1598.7053901437508649275902152144143302 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:15:39 2004 Input: 1.442695*log((13^130-1)*(13^131-1)/12) Output: ? 962.22977666251972540323221211885303040 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:15:53 2004 Input: 1.442695*log((13^60-1)*(13^61-1)/12) Output: ? 444.16823080570368160433616308758220496 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:16:11 2004 Input: 1.442695*log((13^47-1)*(13^48-1)/12) Output: ? 347.95680086086641632739832541034619452 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:16:28 2004 Input: 1.442695*log((5^47-1)*(5^48-1)/4) Output: ? 218.58316281920001119745164880269749325 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:16:43 2004 Input: 1.442695*log((5^60-1)*(5^61-1)/4) Output: ? 278.95329157525698663575235344516511988 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:16:59 2004 Input: 1.442695*log((5^130-1)*(5^131-1)/4) Output: ? 604.02321564633300822660230151999078860 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '193.145' ************** PARI ***************** Host 193.145.231.148 (193.145.231.148) Time: Mon Nov 22 14:17:24 2004 Input: 1.442695*log((5^216-1)*(5^217-1)/4) Output: ? 1003.3948366479406918953608091547766102 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.002s '80.58.1' ************** PARI ***************** Host 80.58.16.235 (80.58.16.235) Time: Mon Nov 22 20:50:46 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Mon Nov 22 23:28:36 2004 Input: X:=[1 0 0 0 0 0 0 0 0 0 6701514300] [0 1 0 0 0 0 0 0 0 0 24893436301800] [0 0 1 0 0 0 0 0 0 0 10921000] [0 0 0 1 0 0 0 0 0 0 2559001105500] [0 0 0 0 1 0 0 0 0 0 7463144900] [0 0 0 0 0 1 0 0 0 0 1023024800] [0 0 0 0 0 0 1 0 0 0 70948700] [0 0 0 0 0 0 0 1 0 0 6896501213900] [0 0 0 0 0 0 0 0 1 0 97206500] [0 0 0 0 0 0 0 0 0 1 86497227100] Output: ? ? [10000000024893436301800] ? [1000000010921000] ? [10000002559001105500] ? [1000007463144900] ? [100001023024800] ? [100070948700] ? [1006896501213900] ? [1097206500] ? [186497227100] ? Errors (if any) and Timing Info: *** unexpected character: X:=[10000000006701514 ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Nov 23 00:10:32 2004 Input: Q := [ 67015142, 248934363018, 109210, 25590011058, 74631448, 10230248, 709488, 68965012138, 972064, 864972272 ]; n := #Q; S := 1000; X := RMatrixSpace(IntegerRing(), n, n + 1) ! 0; for i := 1 to n do X[i][i] := 1; end for; for i := 1 to n do X[i][n + 1] := S * Q[i]; end for; X; L:=LLL(X); L; Output: ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: Q:=[67015142,24893436 ^-------------------- *** unexpected character: n:=#Q; ^----- *** unexpected character: S:=1000; ^------- *** unexpected character: X:=RMatrixSpace(Integ ^-------------------- *** unexpected character: fori:=1tondoX[i][i]:=1;e ^-------------------- *** unexpected character: fori:=1tondoX[i][n+1]:=S ^-------------------- *** unexpected character: L:=LLL(X); ^--------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '148.233' ************** PARI ***************** Host 148.233.239.24 (148.233.239.24) Time: Tue Nov 23 01:32:19 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '144.138' ************** PARI ***************** Host 144.138.154.204 (144.138.154.204) Time: Tue Nov 23 02:43:14 2004 Input: p=y/1+y Output: ? 2*y ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '147.210' ************** PARI ***************** Host 147.210.13.50 (147.210.13.50) Time: Tue Nov 23 13:22:27 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '146.50.' ************** PARI ***************** Host 146.50.160.25 (146.50.160.25) Time: Tue Nov 23 13:35:39 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '131.122' ************** PARI ***************** Host 131.122.54.239 (131.122.54.239) Time: Tue Nov 23 15:50:14 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.005s sys 0m0.005s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Nov 23 20:23:02 2004 Input: mat:=Matrix([[Random(2^16),Random(2^16),14111,157845645,91121],[5,Random(2^16),71112312,932222,1200123],[1,1,Random(2^16),14112222,37373737.0],[Random(2^16),Random(2^16),14111,157845645,91121],[Random(2^16),Random(2^16),14111,157845645,91121]]); mat; SetVerbose("LLL",2); B,T:=LLL(mat); B; T; Output: ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: mat:=Matrix([[Random(2^ ^-------------------- *** unknown function or error in formal parameters: SetVerbose("LLL",2); ^-------------------- *** Warning: unused characters: ,T:=LLL(mat);. Timing: real 0m0.018s user 0m0.004s sys 0m0.006s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Wed Nov 24 00:40:13 2004 Input: R := PolynomialRing(Integers()); K := NumberField(101*x^4+35*x^3+177*x^2+19*x+370); Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: R:=PolynomialRing(In ^-------------------- *** unexpected character: K:=NumberField(101*x ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Wed Nov 24 00:42:08 2004 Input: R := PolynomialRing(Integers()); K := NumberField(101*x^4+35*x^3+177*x^2+19*x+370); z:=x^2+10*x+1; z; Norm(z); Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: R:=PolynomialRing(In ^-------------------- *** unexpected character: K:=NumberField(101*x ^-------------------- *** unexpected character: z:=x^2+10*x+1; ^------------- *** expected character: '=' instead of: Norm(z); ^- Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '146.50.' ************** PARI ***************** Host 146.50.160.25 (146.50.160.25) Time: Thu Nov 25 08:40:15 2004 Input: q:=(((-x)^3*(3-x)*(1-x))/((-2-x)*(-4-x)*(2-x)) Norm(q) Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: q:=(((-x)^3*(3-x)*(1- ^-------------------- *** expected character: '=' instead of: Norm(q) ^ Timing: real 0m0.018s user 0m0.004s sys 0m0.005s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Thu Nov 25 16:44:43 2004 Input: P:=PolynomialRing(RationalField()); j^24 - 34520162587049780604302863237461310701/8796093022208*j^23 + 72024719986066924493072915162959204486096840735993014054423789/17592186 044416*j^22 + 505566599669222326029938120598919707544844756182182471410 47256359340445/8796093022208*j^21 + 13360025480197375525435640270158541 86866189486517449554269188824613615618712731/549755813888*j^20 + 10281635479870031224142934761068186635277652652195026619846529177369952 031067272465495/34359738368*j^19 + 437931915889683096662230101333838537 8609266858963429349452598836221451914820839698896499311547/274877906944 *j^18 - 608284230965684193910905580620837949045046545210671586697009911 576139585419985033859659424546924764583/1099511627776*j^17 - 56080253930195044645151610384082389207199472043882280007074204153127077 31070322137789377450953317411437029455/1099511627776*j^16 + 25136944560537721351948661022480496791805113921371336738849907055568564 048401845797039915621291810345128018185499545/274877906944*j^15 + 27040685928565486059060801531753967743235625683269550672331121704436626 6097834280779660244915909840862127989337999598446843/274877906944*j^14 + 15221651890746247989334719847503516665330189168978866375658087420657585 6904308631670728030974208266200129173321126765607414944333/137438953472 *j^13 + 531402889344786733133195466280323357268088763083403946899834710 05859504026205122885816653187722325302272556498990189437262482553619041 /68719476736*j^12 + 243437712000485235518872901642109435838134984811325 46158976433965306052586331274264395083234527263646036619776993932255397 85244748887555879/17179869184*j^11 + 10510740830012148549518819299943478657015969520378529166736058567303984 80168948413053185741840922740900695348574992522539638811829262113540669 921/68719476736*j^10 + 604055531577859897231228293776838408388441018134 80086956390200906549193434778733551499510085214216570144669689370162547 90838316817207256897620377057/34359738368*j^9 - 47297741301545967587442271366087332361986445516622156367183596359759207 21431185015264812462604486852228818002577948640026018078088014461268655 606584251/17179869184*j^8 - 1048534178915981985938259211269579382436074 78576597863842471739031600683017417536967838554449149927942582452722308 76246574959593822449833121854894113041817/2147483648*j^7 + 80279000416890495136316913620824502851914372155534097069205158928046520 25481975771173808907372321984185863356398390394361064558043789248273990 9314371065864529/4294967296*j^6 - 9332398638266331386424198317592034843 51085913997177114780627497119104422418156146386888481853425630347064713 07421878670981463365734000624948615497798442372962037/4294967296*j^5 + 15313926997831182707254833531280252178346681983508434387135005436195285 03771095959876795641302014606838686600671635640994147505913482208582216 6094609803324359408929/4294967296*j^4 + 14997377184935340635240282994593002542683681949721874650036286869514128 80830553685601498992249982939529558966491980095257486178597373951387225 28295905706799281009525/134217728*j^3 + 10300761344436275075526648456065847103807858120283568521163270656381556 91264913060657909801804876757419088835562148680406098475408974147831146 15462329956000721963873825/16777216*j^2 - 49019130247987411928332481753850935772080901610631212745989284726367826 91128290012057807454270747231316607984837054379740457009771127438752620 416932533565283157280625/131072*j + 45451176859474359734207884509751140 95516878362912558017466455813325026779367343574450782603602689796500588 081608843558394480177552835571767925633304060842742778165625/4096 G1, r1, pr:= GaloisGroup(f1); G1; Order(G1); Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4901913024798741192833248175385093577208090161063121274598928472636782691128290012057807454270747231316607984837054379740457009771127438752620416932533565283157280625/131072*j + 4545117685947435973420788450975114095516878362912558017466455813325026779367343574450782603602689796500588081608843558394480177552835571767925633304060842742778165625/4096 ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: P:=PolynomialRing(Ra ^-------------------- *** unexpected character: ...310701/8796093022208*j^23+ ^- *** unexpected character: ...8712731/549755813888*j^20+ ^- *** unexpected character: ...764583/1099511627776*j^17- ^- *** unexpected character: ...029455/1099511627776*j^16+ ^- *** unexpected character: ...5499545/274877906944*j^15+ ^- *** unexpected character: ...8446843/274877906944*j^14+ ^- *** unexpected character: ...87555879/17179869184*j^11+ ^- *** unexpected character: ...620377057/34359738368*j^9- ^- *** unexpected character: ...4113041817/2147483648*j^7+ ^- *** unexpected character: ...2372962037/4294967296*j^5+ ^- *** unexpected character: ...4359408929/4294967296*j^4+ ^- *** unexpected character: ...99281009525/134217728*j^3+ ^- *** unexpected character: ...721963873825/16777216*j^2- ^- *** Warning: unused characters: ,r1,pr:=GaloisGroup(f1);. *** expected character: '=' instead of: G1;Order(G1); ^- Timing: real 0m0.010s user 0m0.004s sys 0m0.008s '195.121' ************** PARI ***************** Host 195.121.141.201 (195.121.141.201) Time: Thu Nov 25 18:21:19 2004 Input: polylog(2,1.5) Output: ? 2.3743952702724802006774997630716384242 - 1.2738062049196005309331316855804716978*I ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.006s sys 0m0.005s '195.121' ************** PARI ***************** Host 195.121.141.201 (195.121.141.201) Time: Thu Nov 25 18:22:02 2004 Input: polylog(2,0.5+0.75*I) Output: ? 0.33413601897125028776013525639833671130 + 0.90606166546980373319386164264201313134*I ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.006s sys 0m0.005s '195.121' ************** PARI ***************** Host 195.121.141.201 (195.121.141.201) Time: Thu Nov 25 18:23:28 2004 Input: polylog(12,1.2+3.05*I) Output: ? 1.1980227489045881863096108894071243708 + 3.0517517497474608170002138571322757472*I ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '195.121' ************** PARI ***************** Host 195.121.141.201 (195.121.141.201) Time: Thu Nov 25 18:23:56 2004 Input: polylog(12,1.2) Output: ? 1.2003549495472056932233851165647085304 - 5.8238794962183049804884424530447896459 E-16*I ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '195.121' ************** PARI ***************** Host 195.121.141.201 (195.121.141.201) Time: Thu Nov 25 18:24:18 2004 Input: polylog(34,1.07) Output: ? 1.0700000000666420244405087140634761846 - 9.1019341039022584485757810905872504818 E-76*I ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '195.121' ************** PARI ***************** Host 195.121.141.201 (195.121.141.201) Time: Thu Nov 25 18:24:59 2004 Input: polylog(3,0.995+0.8992*I) Output: ? 0.90801162636320557148732270980823341113 + 1.1587066677908962848426920480141357311*I ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '195.121' ************** PARI ***************** Host 195.121.141.201 (195.121.141.201) Time: Thu Nov 25 18:25:33 2004 Input: polylog(2,-1.6) Output: ? -1.2077769923691381940737201652556163352 + 0.E-38*I ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '195.121' ************** PARI ***************** Host 195.121.141.201 (195.121.141.201) Time: Thu Nov 25 18:26:01 2004 Input: polylog(3,-1.6) Output: ? -1.3738230324761534310142654103662156417 - 4.701977403289150032 E-38*I ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '195.121' ************** PARI ***************** Host 195.121.141.201 (195.121.141.201) Time: Thu Nov 25 18:26:25 2004 Input: polylog(5,1.1) Output: ? 1.1457965144814728028514473726208651921 - 0.000010801791407204528757132759391277486721*I ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s '195.121' ************** PARI ***************** Host 195.121.141.201 (195.121.141.201) Time: Thu Nov 25 18:26:46 2004 Input: polylog(5,2.1) Output: ? 2.3118781289102276677336477424201105756 - 0.039665008962192420316707074792000513318*I ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '195.121' ************** PARI ***************** Host 195.121.141.201 (195.121.141.201) Time: Thu Nov 25 18:27:06 2004 Input: polylog(5,-2.1) Output: ? -1.9886259024724241069988519596244344996 + 9.403954806578300064 E-38*I ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.002s '195.121' ************** PARI ***************** Host 195.121.141.201 (195.121.141.201) Time: Thu Nov 25 18:27:25 2004 Input: polylog(5,-1.1) Output: ? -1.0665975586008613725802614395089317164 + 1.8684221641752694386142508874389698781 E-38*I ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.006s '195.121' ************** PARI ***************** Host 195.121.141.201 (195.121.141.201) Time: Thu Nov 25 18:28:06 2004 Input: polylog(5,0.0+1.1*I) Output: ? -0.036562857660403386400287724109138297091 + 1.0949501863653270371091835205992544289*I ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '195.121' ************** PARI ***************** Host 195.121.141.201 (195.121.141.201) Time: Thu Nov 25 18:28:29 2004 Input: polylog(5,0.0-1.1*I) Output: ? -0.036562857660403386400287724109138297088 - 1.0949501863653270371091835205992544289*I ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '195.121' ************** PARI ***************** Host 195.121.141.201 (195.121.141.201) Time: Thu Nov 25 18:29:20 2004 Input: polylog(2,0.0+1.5*I) Output: ? -0.39270711221755170287932806159835544523 + 1.2749694484943800618149431804918900805*I ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.005s '195.121' ************** PARI ***************** Host 195.121.141.201 (195.121.141.201) Time: Thu Nov 25 18:29:37 2004 Input: polylog(2,0.0-1.5*I) Output: ? -0.39270711221755170287932806159835544523 - 1.2749694484943800618149431804918900805*I ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.003s '146.50.' ************** PARI ***************** Host 146.50.160.25 (146.50.160.25) Time: Thu Nov 25 19:52:01 2004 Input: GCD(x^4-5*x^2+x-4,2-x); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: GCD(x^4-5*x^2+x-4,2-x); ^------------------ Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '146.50.' ************** PARI ***************** Host 146.50.160.25 (146.50.160.25) Time: Thu Nov 25 19:52:09 2004 Input: gcd(x^4-5*x^2+x-4,2-x); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.002s sys 0m0.008s '146.50.' ************** PARI ***************** Host 146.50.160.25 (146.50.160.25) Time: Thu Nov 25 19:52:22 2004 Input: gcd(x^4-5*x^2+x-4,2-x); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '146.50.' ************** PARI ***************** Host 146.50.160.25 (146.50.160.25) Time: Thu Nov 25 19:52:26 2004 Input: gcd(x^4-5*x^2+x-4,2-x) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '146.50.' ************** PARI ***************** Host 146.50.160.25 (146.50.160.25) Time: Thu Nov 25 19:52:36 2004 Input: extendedgcd(x^4-5*x^2+x-4,2-x) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: extendedgcd(x^4-5*x^2+x-4,2-x) ^----------------- Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '141.26.' ************** PARI ***************** Host 141.26.64.5 (141.26.64.5) Time: Fri Nov 26 04:30:15 2004 Input: factor(21) Output: ? [3 1] [7 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '141.26.' ************** PARI ***************** Host 141.26.64.5 (141.26.64.5) Time: Fri Nov 26 04:31:21 2004 Input: factor(8733733665192721) Output: ? [79213427 1] [110255723 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '141.26.' ************** PARI ***************** Host 141.26.64.5 (141.26.64.5) Time: Fri Nov 26 04:31:54 2004 Input: factor(68772246400360545131) Output: ? [2581179961 1] [26643723971 1] ? Errors (if any) and Timing Info: Timing: real 0m0.043s user 0m0.011s sys 0m0.009s '141.26.' ************** PARI ***************** Host 141.26.64.5 (141.26.64.5) Time: Fri Nov 26 04:46:20 2004 Input: factor(195648318974882871956483189748828719564831897488287) Output: ? [3 1] [37 1] [613 1] [210631 1] [52986961 1] [91705483 1] [213344189 1] [13168164561429877 1] ? Errors (if any) and Timing Info: Timing: real 0m0.217s user 0m0.197s sys 0m0.020s '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Fri Nov 26 05:49:31 2004 Input: check(p)= { (sum(m=0,((p-1)/2), ((binomial(((p-1)/2)*(p^2+p+1),m*(p^2+p+1))^2)/(binomial(((p-1)/2)*(p+1),m*(p+1))^2))*4^(m*(p^2)+1) ) + p^2*sum(m=(p+1)/2,p-3, (binomial((p-1)/2, p-1-m)^2/(binomial(((p-1)/2)*(p+1),(p-1-m)*(p+1))^2))*4^(m+1)))*binomial(((p-1)/2)*(p+1), p+1); } check1(p)= { (-1)^((p+1)/2)*p^2*binomial(p-1,(p-1)/2); } find(k)= { for(i=3,100+k, if(isprime(i)==1, if((check1(i)-check(i))%i^3==0, print(i) ), next ) ); } Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '148.240' ************** PARI ***************** Host 148.240.200.104 (148.240.200.104) Time: Fri Nov 26 09:16:56 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.155s user 0m0.003s sys 0m0.009s '64.12.1' ************** PARI ***************** Host 64.12.116.139 (64.12.116.139) Time: Fri Nov 26 11:57:29 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '200.50.' ************** PARI ***************** Host 200.50.106.91 (200.50.106.91) Time: Sat Nov 27 19:26:59 2004 Input: 762 Output: ? 762 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Sun Nov 28 01:40:46 2004 Input: for i in [1..100] do Log(2,Prime(i)); end for Output: ? ? ? endfor ? Errors (if any) and Timing Info: *** Warning: unused characters: do. *** unexpected character: foriin[1..100]do ^---------- *** unknown function or error in formal parameters: Log(2,Prime(i)); ^---------- Timing: real 0m0.020s user 0m0.005s sys 0m0.004s '128.135' ************** PARI ***************** Host 128.135.149.114 (128.135.149.114) Time: Sun Nov 28 19:04:59 2004 Input: isprime(467) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '128.135' ************** PARI ***************** Host 128.135.149.114 (128.135.149.114) Time: Sun Nov 28 19:05:05 2004 Input: isprime(467); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '128.135' ************** PARI ***************** Host 128.135.149.114 (128.135.149.114) Time: Sun Nov 28 19:05:13 2004 Input: Isprime(467) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Isprime(467) ^------------ Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '128.135' ************** PARI ***************** Host 128.135.149.114 (128.135.149.114) Time: Sun Nov 28 19:05:19 2004 Input: isprime(467) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '128.135' ************** PARI ***************** Host 128.135.149.114 (128.135.149.114) Time: Sun Nov 28 19:05:27 2004 Input: isprime(4) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '139.124' ************** PARI ***************** Host 139.124.3.53 (139.124.3.53) Time: Mon Nov 29 07:49:37 2004 Input: disc(x^3-8*x^2+3*x-7) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: disc(x^3-8*x^2+3*x-7 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file) New syntax: disc(x) ===> poldisc(x) poldisc(x,{v}): discriminant of the polynomial x, with respect to main variable if v is omitted, with respect to v otherwise. Timing: real 0m0.146s user 0m0.005s sys 0m0.007s '139.124' ************** PARI ***************** Host 139.124.3.53 (139.124.3.53) Time: Mon Nov 29 07:49:47 2004 Input: poldisc(x^3-8*x^2+3*x-7) Output: ? -12167 ? Errors (if any) and Timing Info: Timing: real 0m0.069s user 0m0.006s sys 0m0.005s '139.124' ************** PARI ***************** Host 139.124.3.53 (139.124.3.53) Time: Mon Nov 29 07:50:18 2004 Input: factor(12167) Output: ? [23 3] ? ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.004s sys 0m0.009s '139.124' ************** PARI ***************** Host 139.124.3.53 (139.124.3.53) Time: Mon Nov 29 07:52:21 2004 Input: a=(1+sqrt(29))/2;poldisc(x^3+2*a*x^2+(3*a+4)*x+2*a+4) Output: ? -16.000000000000000000000000000000000000 ? ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.005s sys 0m0.004s '198.30.' ************** PARI ***************** Host 198.30.180.2 (198.30.180.2) Time: Mon Nov 29 10:53:25 2004 Input: 2^123456789 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m0.161s user 0m0.007s sys 0m0.004s '198.30.' ************** PARI ***************** Host 198.30.180.2 (198.30.180.2) Time: Mon Nov 29 10:53:41 2004 Input: 3^123 Output: ? 48519278097689642681155855396759336072749841943521979872827 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.004s sys 0m0.005s '148.87.' ************** PARI ***************** Host 148.87.1.170 (148.87.1.170) Time: Tue Nov 30 13:14:26 2004 Input: b6b4d387490046548b31d0badd6cc914 Output: ? b6b4d387490046548b31d0badd6cc914 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '129.64.' ************** PARI ***************** Host 129.64.72.207 (129.64.72.207) Time: Tue Nov 30 17:25:09 2004 Input: # Output: ? timer = 1 (on) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '129.64.' ************** PARI ***************** Host 129.64.72.207 (129.64.72.207) Time: Tue Nov 30 17:25:40 2004 Input: { b=bnfinit((x^5-1)/(x-1)); eh=Mod(-1220*x^3-705*x^2+300*x-456,b.pol)/11^3; er=Mod(-3607*x^3+2096*x^2-3280*x-14848,b.pol)/11^4; z=cos(2*Pi/5)+I*sin(2*Pi/5); ehsig=Mod(subst(lift(eh),x,x^2),b.pol); ersig=Mod(subst(lift(er),x,x^2),b.pol); P11=idealprimedec(b,11); W1=Mod(x+2,b.pol); W2=Mod(x^2+2,b.pol); w1=P11[4]; w2=P11[3]; H1=norm(Mod(x+2,b.pol))^(-idealval(b,eh,w1)); H2=norm(Mod(x^2+2,b.pol))^(-idealval(b,eh,w2)); H1sig=norm(Mod(x+2,b.pol))^(-idealval(b,ehsig,w1)); H2sig=norm(Mod(x^2+2,b.pol))^(-idealval(b,ehsig,w2)); R1=norm(Mod(x+2,b.pol))^(-idealval(b,er,w1)); R2=norm(Mod(x^2+2,b.pol))^(-idealval(b,er,w2)); R1sig=norm(Mod(x+2,b.pol))^(-idealval(b,ersig,w1)); R2sig=norm(Mod(x^2+2,b.pol))^(-idealval(b,ersig,w2)); } Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.141s user 0m0.012s sys 0m0.006s '129.64.' ************** PARI ***************** Host 129.64.72.207 (129.64.72.207) Time: Tue Nov 30 17:26:19 2004 Input: { b=bnfinit((x^5-1)/(x-1)); eh=Mod(-1220*x^3-705*x^2+300*x-456,b.pol)/11^3; er=Mod(-3607*x^3+2096*x^2-3280*x-14848,b.pol)/11^4; z=cos(2*Pi/5)+I*sin(2*Pi/5); ehsig=Mod(subst(lift(eh),x,x^2),b.pol); ersig=Mod(subst(lift(er),x,x^2),b.pol); P11=idealprimedec(b,11); W1=Mod(x+2,b.pol); W2=Mod(x^2+2,b.pol); w1=P11[4]; w2=P11[3]; H1=norm(Mod(x+2,b.pol))^(-idealval(b,eh,w1)); H2=norm(Mod(x^2+2,b.pol))^(-idealval(b,eh,w2)); H1sig=norm(Mod(x+2,b.pol))^(-idealval(b,ehsig,w1)); H2sig=norm(Mod(x^2+2,b.pol))^(-idealval(b,ehsig,w2)); R1=norm(Mod(x+2,b.pol))^(-idealval(b,er,w1)); R2=norm(Mod(x^2+2,b.pol))^(-idealval(b,er,w2)); R1sig=norm(Mod(x+2,b.pol))^(-idealval(b,ersig,w1)); R2sig=norm(Mod(x^2+2,b.pol))^(-idealval(b,ersig,w2)); (log(norm(W1)^(-idealval(b,eh,w1)))-I*log(norm(W1)^(-idealval(b,nfgaloisapply(b,x^2,eh),w1)))-log(norm(W1)^(-idealval(b,nfgaloisapply(b,x^4,eh),w1)))+I*log(norm(W1)^(-idealval(b,nfgaloisapply(b,x^3,eh),w1))))/10 } Output: ? -0.47957905455967410881238871559302585996 - 1.4387371636790223264371661467790775799*I ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.015s sys 0m0.003s '131.236' ************** PARI ***************** Host 131.236.1.5 (131.236.1.5) Time: Tue Nov 30 23:13:12 2004 Input: 1+1 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.159s user 0m0.004s sys 0m0.007s '131.236' ************** PARI ***************** Host 131.236.1.5 (131.236.1.5) Time: Tue Nov 30 23:13:36 2004 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.005s sys 0m0.004s '131.236' ************** PARI ***************** Host 131.236.1.5 (131.236.1.5) Time: Tue Nov 30 23:14:08 2004 Input: 2001!/2000! Output: ? 2001 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '131.236' ************** PARI ***************** Host 131.236.1.5 (131.236.1.5) Time: Tue Nov 30 23:14:19 2004 Input: 2001!/1000! Output: ? 1649124392934891847880268160758353580541049399729080565041904808841735726309201635831110912347469988829334035537751039752306856070077104540081980047171391486852755132000966811002214714390647720843943929647687970980586795451403935185796192058788589822462966800665434242417073469829619863309822470597475277699254958432193083115828237627291969846935394394080215380045974037891303039075322132495601465228504087951222866005373340048564974595130369534927515391656859119235401740128298531327547722634407324306432908474993893823837191408056862948288237278224679694482100876712906255826835902936178766747137369807939954355696189717788568692154262761377175926404845510650546827074642365014931158425292907616318583465976845564003710047977939822040925848491771950520602260603367650865906120149578880539062634471399971916745274188896219561318135825114731597610654118792358129676908345046791405635620164506073478188374414696554547523323328838299010189444524149287366130447907570351066714706747940494346134614623487226344736015849336952772494591699229902902223268096087373409454836657717367977063754276380853214645982307685352444352133742625998532313587091117058319642197616042838572594490097739118336854870852171503547044498338864190294997647595344410505612228538494500489102238181092146783273230985215630728981302392346166612016878404834705043243556175722016284772883326280314212815161050717150812715448949990761446071205026719160967296625237199485422013375792657931499059270042689010313280657273096902415360870132710525732925884181542027320854136681502434485374615988450452978468629419426684535504864464644738101621313229071754267367586526126540105703865711037479191750220965902045628210555120172125296685255271201110826146873353011177835705449690640001206659053013815935559355781611818845422324005336655173403937639247764146560284733945846571664554566477037900263709702205460599965984134940738725708785429474281376562690973185730534619507436716113738957886966682522137710437782612824069437090619635815202440811314652768987267865879188450155831649391240419286359613874531228430155654556619361316218126118073320467767913829937929680097317070544581670751225512780451472502559755140351135456730775501277796837015234284291031345655308656633172968467134454016414326634459016310995471161002240039771957481277560796094013770856983749228987372254924692105761375611715228328592056594090581344562099232963788830763471958979103304153480974086686978500089719929483220785759705068646241135484090287117660077820469879699206329414300509287716990606814978287039888756805968118893987929950249590268914583170019685353629717380251392728332301602872848448484813086191991786700555943911345216058262126778312954674409917708706936940711894166160113422191311132156080304327783199680963748020988928739773307279911451811896135661817300697728160904328254790307303708867578421359135125892431724969901811607793762096805552337357303712387563293350802454464839024640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '203.160' ************** PARI ***************** Host 203.160.1.66 (203.160.1.66) Time: Tue Nov 30 23:25:38 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '204.39.' ************** PARI ***************** Host 204.39.210.65 (204.39.210.65) Time: Thu Dec 2 16:30:04 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '204.39.' ************** PARI ***************** Host 204.39.210.65 (204.39.210.65) Time: Thu Dec 2 16:30:19 2004 Input: 2x+4y=12 Output: ? 2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+4y=12. Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '204.39.' ************** PARI ***************** Host 204.39.210.65 (204.39.210.65) Time: Thu Dec 2 16:31:08 2004 Input: 4y=12 Output: ? 4 ? Errors (if any) and Timing Info: *** Warning: unused characters: y=12. Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '204.39.' ************** PARI ***************** Host 204.39.210.65 (204.39.210.65) Time: Thu Dec 2 16:31:31 2004 Input: x=9 Output: ? 9 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '204.39.' ************** PARI ***************** Host 204.39.210.65 (204.39.210.65) Time: Thu Dec 2 16:31:42 2004 Input: 2+x=7 Output: ? 9 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '204.39.' ************** PARI ***************** Host 204.39.210.65 (204.39.210.65) Time: Thu Dec 2 16:36:54 2004 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '204.39.' ************** PARI ***************** Host 204.39.210.65 (204.39.210.65) Time: Thu Dec 2 16:37:01 2004 Input: 22/7 Output: ? 22/7 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.007s '204.39.' ************** PARI ***************** Host 204.39.210.65 (204.39.210.65) Time: Thu Dec 2 16:39:47 2004 Input: 8/9 Output: ? 8/9 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '204.39.' ************** PARI ***************** Host 204.39.211.22 (204.39.211.22) Time: Thu Dec 2 16:50:52 2004 Input: 1./7 Output: ? 0.14285714285714285714285714285714285714 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '204.39.' ************** PARI ***************** Host 204.39.211.22 (204.39.211.22) Time: Thu Dec 2 16:51:16 2004 Input: Pi? Output: ? 3.1415926535897932384626433832795028842 ? Errors (if any) and Timing Info: *** Warning: unused characters: ?. Timing: real 0m0.023s user 0m0.004s sys 0m0.007s '204.39.' ************** PARI ***************** Host 204.39.211.22 (204.39.211.22) Time: Thu Dec 2 16:51:37 2004 Input: Pi? Output: ? 3.1415926535897932384626433832795028842 ? Errors (if any) and Timing Info: *** Warning: unused characters: ?. Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '204.39.' ************** PARI ***************** Host 204.39.211.22 (204.39.211.22) Time: Thu Dec 2 16:52:57 2004 Input: /p 100 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ^- Timing: real 0m0.020s user 0m0.003s sys 0m0.007s '204.39.' ************** PARI ***************** Host 204.39.211.22 (204.39.211.22) Time: Thu Dec 2 16:53:10 2004 Input: /p 100 Pi? Output: ? ? 3.1415926535897932384626433832795028842 ? Errors (if any) and Timing Info: *** unexpected character: ^- *** Warning: unused characters: ?. Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '204.39.' ************** PARI ***************** Host 204.39.211.22 (204.39.211.22) Time: Thu Dec 2 16:53:20 2004 Input: (/p 100) Pi? Output: ? ? 3.1415926535897932384626433832795028842 ? Errors (if any) and Timing Info: *** unexpected character: (/p100) ^------- *** Warning: unused characters: ?. Timing: real 0m0.010s user 0m0.002s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 3 16:27:15 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 3 16:27:40 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" nextprime(138) Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? 139 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 3 16:28:45 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" nextprime(2 ) Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: nextprime(2 ^ *** Warning: unused characters: ). Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 3 16:28:53 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" nextprime(2) Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 3 16:29:03 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" nextprime(2) Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 3 16:29:10 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" nextprime(3) Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 3 16:29:31 2004 Input: nextprime(3) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 3 16:29:50 2004 Input: nextprime(138) Output: ? 139 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Fri Dec 3 19:59:17 2004 Input: s=2m^2+n^2 r=2m^2+2mn Output: ? 2 ? 2 ? Errors (if any) and Timing Info: *** Warning: unused characters: m^2+n^2. *** Warning: unused characters: m^2+2mn. Timing: real 0m0.009s user 0m0.002s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Fri Dec 3 19:59:41 2004 Input: s=2m^2+n^2 r=2m^2+2mn s^2-r^2= Output: ? 2 ? 2 ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: m^2+n^2. *** Warning: unused characters: m^2+2mn. *** unexpected character: s^2-r^2= ^-- Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '80.142.' ************** PARI ***************** Host 80.142.84.63 (80.142.84.63) Time: Sat Dec 4 08:21:51 2004 Input: a^2+b^2 ; Output: ? a^2 + b^2 ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.003s sys 0m0.007s '80.142.' ************** PARI ***************** Host 80.142.84.63 (80.142.84.63) Time: Sat Dec 4 08:22:50 2004 Input: a^2+b^2; Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '80.142.' ************** PARI ***************** Host 80.142.84.63 (80.142.84.63) Time: Sat Dec 4 08:23:01 2004 Input: 34+3 Output: ? 37 ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '80.142.' ************** PARI ***************** Host 80.142.84.63 (80.142.84.63) Time: Sat Dec 4 08:23:21 2004 Input: 34+3+a Output: ? a + 37 ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '80.142.' ************** PARI ***************** Host 80.142.84.63 (80.142.84.63) Time: Sat Dec 4 08:23:51 2004 Input: 34+(3+a*5â)*b Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: 34+(3+a*5â)*b ^---- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '80.142.' ************** PARI ***************** Host 80.142.84.63 (80.142.84.63) Time: Sat Dec 4 08:24:07 2004 Input: 34+(3+a*5^a)*b Output: ? (3*b + 34) + b*a + 1.6094379124341003746007593332261876395*b*a^2 + 1.2951451969901174725900855024963274477*b*a^3 + 0.69481859404760878829862955905644443859*b*a^4 + 0.27956684688109503219695907351715128656*b*a^5 + 0.089989096486018674769936612712314957070*b*a^6 + 0.024138643931714788934883074071207055487*b*a^7 + 0.0055499498140641592651415220955242805490*b*a^8 + 0.0011165374553576805018781864815814938655*b*a^9 + 0.00019966641236726087197027647067819097611*b*a^10 + 0.000032135069390357057934695871967032070832*b*a^11 + 0.0000047017635450492019924595772942507957056*b*a^12 + 0.00000063059970872522857568336954920840106393*b*a^13 + 0.000000078070082984021817719332900683721903621*b*a^14 + 0.0000000089749250986686468529374274145592197734*b*a^15 + 0.00000000096297231433691195454685338424699746040*b*a^16 + 9.6865259457389617689846266491425208585 E-11*b*a^17 + O(a^18) ? ? Errors (if any) and Timing Info: Timing: real 0m0.048s user 0m0.004s sys 0m0.005s '66.171.' ************** PARI ***************** Host 66.171.23.227 (66.171.23.227) Time: Sat Dec 4 10:14:55 2004 Input: zeta(2) Output: ? 1.6449340668482264364724151666460251892 ? Errors (if any) and Timing Info: Timing: real 0m0.048s user 0m0.004s sys 0m0.008s '65.110.' ************** PARI ***************** Host 65.110.147.104 (65.110.147.104) Time: Sat Dec 4 18:31:36 2004 Input: m:=[[4,2,0],[0,4,2],[0,0,4]];SmithNormalFormIntegerMat(m); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: m:=[[4,2,0],[0,4,2],[ ^-------------------- Timing: real 0m0.016s user 0m0.005s sys 0m0.005s '65.110.' ************** PARI ***************** Host 65.110.147.104 (65.110.147.104) Time: Sat Dec 4 18:32:08 2004 Input: m:=[[4,2,0],[0,4,2],[0,0,4]]; Output: ? ? Errors (if any) and Timing Info: *** unexpected character: m:=[[4,2,0],[0,4,2],[ ^-------------------- Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '65.110.' ************** PARI ***************** Host 65.110.147.104 (65.110.147.104) Time: Sat Dec 4 18:32:09 2004 Input: m:=[[4,2,0],[0,4,2],[0,0,4]]; Output: ? ? Errors (if any) and Timing Info: *** unexpected character: m:=[[4,2,0],[0,4,2],[ ^-------------------- Timing: real 0m0.015s user 0m0.005s sys 0m0.002s '65.110.' ************** PARI ***************** Host 65.110.147.104 (65.110.147.104) Time: Sat Dec 4 18:37:59 2004 Input: Mat([[1,2],[2,3]]}); Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: Mat([[1,2],[2,3]]}); ^--- Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '65.110.' ************** PARI ***************** Host 65.110.147.104 (65.110.147.104) Time: Sat Dec 4 18:38:23 2004 Input: m:=Mat([[1,2],[2,3]]); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: m:=Mat([[1,2],[2,3]]) ^-------------------- Timing: real 0m0.015s user 0m0.003s sys 0m0.004s '65.110.' ************** PARI ***************** Host 65.110.147.104 (65.110.147.104) Time: Sat Dec 4 18:38:23 2004 Input: m:=Mat([[1,2],[2,3]]); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: m:=Mat([[1,2],[2,3]]) ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '65.110.' ************** PARI ***************** Host 65.110.147.104 (65.110.147.104) Time: Sat Dec 4 18:38:31 2004 Input: Mat([[1,2],[2,3]]); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.003s '65.110.' ************** PARI ***************** Host 65.110.147.104 (65.110.147.104) Time: Sat Dec 4 18:38:46 2004 Input: m:=([[1,2],[2,3]]); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: m:=([[1,2],[2,3]]); ^------------------ Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '146.186' ************** PARI ***************** Host 146.186.133.120 (146.186.133.120) Time: Sun Dec 5 00:37:18 2004 Input: g:=5; K := FiniteField(2); GL := GeneralLinearGroup(5, K); Exponent(GL); 2^g-1; 7%3; Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '65.110.' ************** PARI ***************** Host 65.110.147.104 (65.110.147.104) Time: Sun Dec 5 01:28:28 2004 Input: M := Matrix(2,3 [3,9,9, 9,-3,9]);S:=SmithForm(M);S Output: ? ? Errors (if any) and Timing Info: *** unexpected character: M:=Matrix(2,3[3,9,9,9 ^-------------------- Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '220.108' ************** PARI ***************** Host 220.108.9.104 (220.108.9.104) Time: Sun Dec 5 02:23:52 2004 Input: factor(1000009) Output: ? [293 1] [3413 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '129.31.' ************** PARI ***************** Host 129.31.75.196 (129.31.75.196) Time: Sun Dec 5 18:37:22 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.228.' ************** PARI ***************** Host 68.228.163.38 (68.228.163.38) Time: Sun Dec 5 20:48:27 2004 Input: y=1/6x^2-6 Output: ? 1/6 ? Errors (if any) and Timing Info: *** Warning: unused characters: x^2-6. Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '158.110' ************** PARI ***************** Host 158.110.147.131 (158.110.147.131) Time: Mon Dec 6 06:47:37 2004 Input: for(i=1,10,print(i," ",kronecker(21,19+i*21))) Output: ? 1 -1 2 -1 3 -1 4 -1 5 -1 6 -1 7 -1 8 -1 9 -1 10 -1 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.004s sys 0m0.004s '158.110' ************** PARI ***************** Host 158.110.147.131 (158.110.147.131) Time: Mon Dec 6 06:48:52 2004 Input: for(i=1,10,print(i," ",kronecker(21,1+i*21))) Output: ? 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.004s sys 0m0.004s '158.110' ************** PARI ***************** Host 158.110.147.131 (158.110.147.131) Time: Mon Dec 6 06:49:17 2004 Input: for(i=1,10,print(i," ",kronecker(21,2+i*21))) Output: ? 1 -1 2 -1 3 -1 4 -1 5 -1 6 -1 7 -1 8 -1 9 -1 10 -1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '158.110' ************** PARI ***************** Host 158.110.147.131 (158.110.147.131) Time: Mon Dec 6 06:49:32 2004 Input: for(i=1,10,print(i," ",kronecker(21,5+i*21))) Output: ? 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '158.110' ************** PARI ***************** Host 158.110.147.131 (158.110.147.131) Time: Mon Dec 6 06:49:47 2004 Input: for(i=1,10,print(i," ",kronecker(21,1+i*21))) Output: ? 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '158.110' ************** PARI ***************** Host 158.110.147.131 (158.110.147.131) Time: Mon Dec 6 06:50:03 2004 Input: for(i=0,10,print(i," ",kronecker(21,1+i*21))) Output: ? 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.004s sys 0m0.004s '158.110' ************** PARI ***************** Host 158.110.147.131 (158.110.147.131) Time: Mon Dec 6 06:51:02 2004 Input: for(i=0,10,print(i," ",kronecker(21,-1+i*21))) Output: ? 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.008s sys 0m0.003s '158.110' ************** PARI ***************** Host 158.110.147.131 (158.110.147.131) Time: Mon Dec 6 06:54:43 2004 Input: for(i=0,10,print(i," ",kronecker(-20,1+i*20))) Output: ? 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '158.110' ************** PARI ***************** Host 158.110.147.131 (158.110.147.131) Time: Mon Dec 6 06:55:09 2004 Input: kronecker(-20,1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.001s sys 0m0.007s '158.110' ************** PARI ***************** Host 158.110.147.131 (158.110.147.131) Time: Mon Dec 6 06:55:43 2004 Input: kronecker(-20,41) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.006s sys 0m0.002s '158.110' ************** PARI ***************** Host 158.110.147.131 (158.110.147.131) Time: Mon Dec 6 06:57:38 2004 Input: kronecker(-20,19) Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '158.110' ************** PARI ***************** Host 158.110.147.131 (158.110.147.131) Time: Mon Dec 6 06:57:49 2004 Input: kronecker(-20,39) Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '193.226' ************** PARI ***************** Host 193.226.241.240 (193.226.241.240) Time: Mon Dec 6 10:33:06 2004 Input: n:=8; Z:=IntegerRing(n); E:=UnitGroup(Z); Generators(E); Parent(E.1); Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: n:=8; ^---- *** unexpected character: Z:=IntegerRing(n); ^----------------- *** unexpected character: E:=UnitGroup(Z); ^--------------- *** expected character: '=' instead of: Generators(E); ^- *** expected character: ',' instead of: Parent(E.1); ^---- Timing: real 0m0.039s user 0m0.003s sys 0m0.007s '83.115.' ************** PARI ***************** Host 83.115.241.166 (83.115.241.166) Time: Mon Dec 6 14:43:16 2004 Input: x*(x+1) Output: ? x^2 + x ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.003s sys 0m0.006s '83.115.' ************** PARI ***************** Host 83.115.241.166 (83.115.241.166) Time: Mon Dec 6 14:43:30 2004 Input: x(x+1) Output: ? x ? Errors (if any) and Timing Info: *** Warning: unused characters: (x+1). Timing: real 0m0.010s user 0m0.006s sys 0m0.005s '62.10.9' ************** PARI ***************** Host 62.10.95.43 (62.10.95.43) Time: Mon Dec 6 15:38:40 2004 Input: cia0 Output: ? cia0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '206.168' ************** PARI ***************** Host 206.168.253.164 (206.168.253.164) Time: Tue Dec 7 02:07:07 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Tue Dec 7 10:26:20 2004 Input: check1(p)= { (1/4 + sum(m=2, (p-1)/2, (4^((p*m)-1))*((binomial(((p-1)/2)*(p+1), m*(p+1)))^2)/((binomial((p-1)/2,m))^2))); } check1(3511); Output: ** WARNING: Computation used more memory than allowed. ** ? ? ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m0.081s user 0m0.050s sys 0m0.007s '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Tue Dec 7 10:26:59 2004 Input: allocatemem allocatemem check1(p)= { (1/4 + sum(m=2, (p-1)/2, (4^((p*m)-1))*((binomial(((p-1)/2)*(p+1), m*(p+1)))^2)/((binomial((p-1)/2,m))^2))); } check1(3511); Output: WARNING: PARI command contains unsafe command 'allocatemem', so it will not be executed. '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Tue Dec 7 10:27:13 2004 Input: check1(p)= { (1/4 + sum(m=2, (p-1)/2, (4^((p*m)-1))*((binomial(((p-1)/2)*(p+1), m*(p+1)))^2)/((binomial((p-1)/2,m))^2))); } check1(3511); Output: ** WARNING: Computation used more memory than allowed. ** ? ? ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m0.062s user 0m0.046s sys 0m0.013s '192.68.' ************** PARI ***************** Host 192.68.254.6 (192.68.254.6) Time: Tue Dec 7 10:28:50 2004 Input: allocatemem(2); check1(p)= { (1/4 + sum(m=2, (p-1)/2, (4^((p*m)-1))*((binomial(((p-1)/2)*(p+1), m*(p+1)))^2)/((binomial((p-1)/2,m))^2))); } check1(3511); Output: WARNING: PARI command contains unsafe command 'allocatemem', so it will not be executed. '208.58.' ************** PARI ***************** Host 208.58.5.212 (208.58.5.212) Time: Tue Dec 7 13:06:39 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.004s sys 0m0.004s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Dec 8 01:39:13 2004 Input: 58476762826968385237118095373190503384806789444413648200593209481080439644701406154056603450452131728212673903968212225225503269444248471980457946917018207218500351299629592361816503464418599260181494127405304047251480108627581863536943588327193441613266507636621694902123935493222456320010315463919482372072296928470728798902515149410234536706177749441721107742326522439295256797562390628953285003550811948129776240196537562681383208322979782832687269546543297554234726163199736790760097140053933125106367183002240008058293566077855595036722207415380752151683063378028929384176539066876300043694094637624850299081955122698003124750249035698880373825381434874609855552431334123779461487905222057245379294872001504276712239968047337300138486014577247170712366776237226719802794485855869779197538275258909647590841207339792273092572853545926644682531495102599603038604033837199859133629633979610263080196784408081692692139366491002860334860678273831923846500448687497584610051520088288764429743451800195445507842292247615152366160125446156593344785887484312532483815002457230703629881404396344020030053949033395660611557754752693668891417221218766861370684978562976741602290422558244188375926540787195088692824622222873604336216809336164692710729019536856412407070537321024652312717154922184070980743318456011158018841747853845102668665025298616229528797121841873503439426098011566822161789323539117116351291879418353625566126010243720422345616296641610512504542439515780553413868103123481286335416582209044703493432822558251325085043164768151381877650134051624245119591215951643555718852454718404097589379523013242938102653546675144499167598286916463556725981976943876336280505473752758589682114909005063733679765104535626876706899270470947433897039507105905533419817570298681186596046411927692174827013325929553365578041966091742159447002375834182893637166785106787344213751908819218063307378584381757682075794196160719487911122929067407238318571606326134507988261202615513306008527723462643214610955380897202007526455631384734457539485739288909857816520548972189573120995493812960282960586083266254277951432466354677128982366614847816414239147642778158225313852220366570897080047633574900956804260147228886495784692242122257153651589323537522535056131712401676185720295216443123428105454143876011902560690956237355696159293586056380185373966300998373417273147891194861919542565535860483360606492650698581211470427576647840505144740393822120930899955919180473637752114752973763657362172456527542488115381056144487818717923767464328873494323463348297396684576407802829138015971941/(13*2789*59369*433494437*198160071001853267796700692507490184570501064382201*63806927452714047340778156846369278969435365966728521*1473869*952077737766937*13812722702652253529*425523658238268276603571021441) Output: ? 600938340889789568962245962195544400998423758921171968388287604368789339996714078981801829656638513359589840561279507654013657702035433833786791075113042077630591695134536911336864037118806501961083735880647529524454690990208325539688902892850122985884730408600007466711597716194783859621304611310430400569882179445047418795163670060134848440774817444911536707050193563970630313384578036419465029479642013339354068330820002797637518342963470202060207787395439595099304407216202383913881224655080099827500016432170933494683426400154324912405183232231973500551826215010233485375121801914682135486119433870946862140717232074887171488748281194695197662519866955898689643415954112272027163933453770643575314469882122423265699081966748046886511226970815992010400886824588647137749123489638720853837476758307889491031670024145660576434992239338694367594313539909153858029244407161330601181247246149447809164093022410728190318896176819771480648640568115197095369838758900169498823482925857936532208053373086724316866373218708506353902202832580422977105331740409887465372153774014180379086628964137486671679225138818410162048605990301088341503711545822523582481223227399469916250869686505087938260595868319125038167110958770148247248279450001798196776965658637646448126598498745444483033438232577196839026818600599124637409402639234265088879880152357230280198689723782140129047921818456901741047423163400878824515256714922015056460993230999169743102108837136995377435032833361602468252976250047983109913829690519399399090187801361252337729736610220327075675977711239918967989989089664050855712763406849475035470877523221788948861135878342101595296312542099061117012499365153046092870421909101982197717255657478528284151503167615513709929137451636003873463943412726435952248017313990477708907601682971810742569554549858745922174451468607135023139298798163550986205185935830111591933984428066337868120245079352192908068889902969059560650296623501165684291061291882599532583595320514159377255630035615321535245179350003463963512962302450172532218145859824165161431199422903203553966524726523893719205807578978731405224649010047290414851394663384864333533312265525320755994478892660626545448885976006046879716397407475125092496987213543397075708829868264079778374006515946497621060667837978442483189104425606748174937190211751734604680180273826881013774952083505552418503026480973917440121327493983853 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Dec 8 02:28:36 2004 Input: 124659321435381971396290243033354856707490000293069074131180211845908149782247100761827220664277986659254760443131482038902800585716173458609594766697232635560296084509585797210411987775940257433812964435237344966079889709441871711290995269529524523727979893257113791552886038256935929800873600749011154928233723086586315093514607499398452448645141590391719779685843017/(1473869*952077737766937*13812722702652253529*2789*59369*433494437) Output: ? 89602967705708072792663403998986146825018568639870394696204823153960013146219431199991728701888274781082374520622853618071798283068073811605141368131916788051393389366308929605616269561967194188759375233624257781364851241986998788228090477655661641309234572617940393640909884173573967039169913040964487507613373 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Dec 8 02:30:38 2004 Input: 600938340889789568962245962195544400998423758921171968388287604368789339996714078981801829656638513359589840561279507654013657702035433833786791075113042077630591695134536911336864037118806501961083735880647529524454690990208325539688902892850122985884730408600007466711597716194783859621304611310430400569882179445047418795163670060134848440774817444911536707050193563970630313384578036419465029479642013339354068330820002797637518342963470202060207787395439595099304407216202383913881224655080099827500016432170933494683426400154324912405183232231973500551826215010233485375121801914682135486119433870946862140717232074887171488748281194695197662519866955898689643415954112272027163933453770643575314469882122423265699081966748046886511226970815992010400886824588647137749123489638720853837476758307889491031670024145660576434992239338694367594313539909153858029244407161330601181247246149447809164093022410728190318896176819771480648640568115197095369838758900169498823482925857936532208053373086724316866373218708506353902202832580422977105331740409887465372153774014180379086628964137486671679225138818410162048605990301088341503711545822523582481223227399469916250869686505087938260595868319125038167110958770148247248279450001798196776965658637646448126598498745444483033438232577196839026818600599124637409402639234265088879880152357230280198689723782140129047921818456901741047423163400878824515256714922015056460993230999169743102108837136995377435032833361602468252976250047983109913829690519399399090187801361252337729736610220327075675977711239918967989989089664050855712763406849475035470877523221788948861135878342101595296312542099061117012499365153046092870421909101982197717255657478528284151503167615513709929137451636003873463943412726435952248017313990477708907601682971810742569554549858745922174451468607135023139298798163550986205185935830111591933984428066337868120245079352192908068889902969059560650296623501165684291061291882599532583595320514159377255630035615321535245179350003463963512962302450172532218145859824165161431199422903203553966524726523893719205807578978731405224649010047290414851394663384864333533312265525320755994478892660626545448885976006046879716397407475125092496987213543397075708829868264079778374006515946497621060667837978442483189104425606748174937190211751734604680180273826881013774952083505552418503026480973917440121327493983853/89602967705708072792663403998986146825018568639870394696204823153960013146219431199991728701888274781082374520622853618071798283068073811605141368131916788051393389366308929605616269561967194188759375233624257781364851241986998788228090477655661641309234572617940393640909884173573967039169913040964487507613373 Output: ? 2853850578151875077061785275057259128763318556772402239241246410329576208063285587328220781056284381070685741593728109459667374757412699643261769054260143279065292684612144889579843130359514168808360490413092292037543567613575701556692583743406755639126672922060362087485009074143128426397370306329109283145094598044773624465119355105283964537274432343358585463895711089015261534330103813043668944645698076509240414869303546273655820540407167769393545956755326724670065902669488022995745904806956066583797532831676421249498328292643673400636994761594765945172279340957820781725353274870088644278638898862579792013025406370370966829326465899682334219427723087614750865436098065939883946189195152520117916655179241714417079071646013264974652534004836537333425641732482414218583427696509604768540691890713917660985464452720514669397921563617783416168213807114302167362621737236525154580048887307889943734525851540703145166149892271118908368609633830649306178412472655114865492189292067045474039147506739188865966297030388420394542187975996518320207903117636587396340854217559575409350307357640793329603769169511148520038544766491144298630103586935049218669669486229611942013235932004156525164342977935007023104230625040151345602347847516853483230726129704625539299434601026076190260756008764052843647305662032331430698239910937238977615459263594918852951525333150250585995493758542976288006835588127248482248609158493893692427250625639103032507847249003696030888010283893369779298494951264000492118705214892350371061400548086201889315932559909263417889116069686192754905170225033005571306081961053351560643323748337692326497826599830528387746212415641889440267702052148639116509001749166695201459774949106491917816275675702653084634251280643622814127024553415109516365092179876749298362582221099155970800932419631187695553815580156348968369269878668259631585586450665833132234419040917302346000767983294565499405107376612123502320360297228025247574979137337931386726747144919583811397924941787619400876724497535607882704818563605842170838039928893227949158587089459365757005445055233538407881990802456042735601/425523658238268276603571021441 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Dec 8 02:33:52 2004 Input: 124659321435381971396290243033354856707490000293069074131180211845908149782247100761827220664277986659254760443131482038902800585716173458609594766697232635560296084509585797210411987775940257433812964435237344966079889709441871711290995269529524523727979893257113791552886038256935929800873600749011154928233723086586315093514607499398452448645141590391719779685843017/(1473869*952077737766937*13812722702652253529*425523658238268276603571021441*2789*59369*433494437) Output: ? 210571059848182798945692173671950856913747637637506204222980261300245334254344826561899602272351391100242409883004854300985262242101935161886021098015750729481776536284383546045113241911825894461066651342314487406759013903505804344325933698066893610891623385384370339503798955797053 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Dec 8 02:35:40 2004 Input: 600938340889789568962245962195544400998423758921171968388287604368789339996714078981801829656638513359589840561279507654013657702035433833786791075113042077630591695134536911336864037118806501961083735880647529524454690990208325539688902892850122985884730408600007466711597716194783859621304611310430400569882179445047418795163670060134848440774817444911536707050193563970630313384578036419465029479642013339354068330820002797637518342963470202060207787395439595099304407216202383913881224655080099827500016432170933494683426400154324912405183232231973500551826215010233485375121801914682135486119433870946862140717232074887171488748281194695197662519866955898689643415954112272027163933453770643575314469882122423265699081966748046886511226970815992010400886824588647137749123489638720853837476758307889491031670024145660576434992239338694367594313539909153858029244407161330601181247246149447809164093022410728190318896176819771480648640568115197095369838758900169498823482925857936532208053373086724316866373218708506353902202832580422977105331740409887465372153774014180379086628964137486671679225138818410162048605990301088341503711545822523582481223227399469916250869686505087938260595868319125038167110958770148247248279450001798196776965658637646448126598498745444483033438232577196839026818600599124637409402639234265088879880152357230280198689723782140129047921818456901741047423163400878824515256714922015056460993230999169743102108837136995377435032833361602468252976250047983109913829690519399399090187801361252337729736610220327075675977711239918967989989089664050855712763406849475035470877523221788948861135878342101595296312542099061117012499365153046092870421909101982197717255657478528284151503167615513709929137451636003873463943412726435952248017313990477708907601682971810742569554549858745922174451468607135023139298798163550986205185935830111591933984428066337868120245079352192908068889902969059560650296623501165684291061291882599532583595320514159377255630035615321535245179350003463963512962302450172532218145859824165161431199422903203553966524726523893719205807578978731405224649010047290414851394663384864333533312265525320755994478892660626545448885976006046879716397407475125092496987213543397075708829868264079778374006515946497621060667837978442483189104425606748174937190211751734604680180273826881013774952083505552418503026480973917440121327493983853/210571059848182798945692173671950856913747637637506204222980261300245334254344826561899602272351391100242409883004854300985262242101935161886021098015750729481776536284383546045113241911825894461066651342314487406759013903505804344325933698066893610891623385384370339503798955797053 Output: ? 2853850578151875077061785275057259128763318556772402239241246410329576208063285587328220781056284381070685741593728109459667374757412699643261769054260143279065292684612144889579843130359514168808360490413092292037543567613575701556692583743406755639126672922060362087485009074143128426397370306329109283145094598044773624465119355105283964537274432343358585463895711089015261534330103813043668944645698076509240414869303546273655820540407167769393545956755326724670065902669488022995745904806956066583797532831676421249498328292643673400636994761594765945172279340957820781725353274870088644278638898862579792013025406370370966829326465899682334219427723087614750865436098065939883946189195152520117916655179241714417079071646013264974652534004836537333425641732482414218583427696509604768540691890713917660985464452720514669397921563617783416168213807114302167362621737236525154580048887307889943734525851540703145166149892271118908368609633830649306178412472655114865492189292067045474039147506739188865966297030388420394542187975996518320207903117636587396340854217559575409350307357640793329603769169511148520038544766491144298630103586935049218669669486229611942013235932004156525164342977935007023104230625040151345602347847516853483230726129704625539299434601026076190260756008764052843647305662032331430698239910937238977615459263594918852951525333150250585995493758542976288006835588127248482248609158493893692427250625639103032507847249003696030888010283893369779298494951264000492118705214892350371061400548086201889315932559909263417889116069686192754905170225033005571306081961053351560643323748337692326497826599830528387746212415641889440267702052148639116509001749166695201459774949106491917816275675702653084634251280643622814127024553415109516365092179876749298362582221099155970800932419631187695553815580156348968369269878668259631585586450665833132234419040917302346000767983294565499405107376612123502320360297228025247574979137337931386726747144919583811397924941787619400876724497535607882704818563605842170838039928893227949158587089459365757005445055233538407881990802456042735601 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Dec 8 03:33:08 2004 Input: 278746716758510745417137740065731399563587857282282345443277769556310588776367830202012078015254993967006336465981066199712011604390377973529672605210334641938246425356114192554026278393127277749534079410096920750001807358427627445146938582981096069222986340499675485212749031990978619925970309156049882780542741146668366500540876489713985310439724085858028663123379479/(370248451*6709*144481*116359*141041*233801980384836959) Output: ? 202420473076700002472831337135056887503504907638783092300771934200834098639167879222334073790150469216607142854345183277199538386958083037454426674213008572218325810795499790004452771523152812490404840935943106446916327045096843269948296788223996281463765352559459965959920034012007885496365625551939711771272150540727992481 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.003s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Dec 8 12:07:37 2004 Input: 130758016785234081760401106271932660230310451811077082354693258568123194576910752379390993971422781148228186254851889917944381946181685488718622651121974064164929296134025880056603777961462599683293800459709477561242534014636110626368832445630171111753881952379574330573682168206667103288801083269943545880820042640799377985736755421158467857413409305329123611550481893006261395970743724371326235400747381642749402469256769853193505243676004056037454898218243726778121654944140204632334747310346018213106551754283243192339661143237559925395538912207453523677024484889035209566968981480691365213853879792566581220431609233629145746043561105039081256675269545600526369380904685828601761818830647702409506360638397224629589695830975499278082855286429213510584668676627612682182173776555402598238626610267049752722931090331374047712201402445675949631208504626283649266375422626257607660678155728224274476891146916824927395462201451234743222285864652272217370340519077476895082505568407896709488214557176292504710496099603099298484050421126553576437560387396285520356332582398333154367871586355138644609525173867710974418349761411714194634777589122377190041025574699022424756922754054973937046418975971851865694579339221708540461422525620034267099915878968439950267767576655041107452992304085866075825021080218995080582238367036280265961184416149645628219687611725256957462948559247878684628845590870382637206313866477569144596427266602383955732138529471190132903707340499873544238004822051284167704229349432912479884039465984409957671088870134669477662575743381971348963262703568847891212854341580083114207809390461167071552870441884066539047854365853997836522946505007319027389617920140686405295133825794756410022529133309467961880513934960317443645786942952374280924171427996535091758792421268858601689712176521316176910418555025962522352540033582022151438988700881790874989159300666863539553641045261833868286521247592822734665917543891577051196356515744452144278829618597210517747780543379248359770591826392759060851388563824424273909934409211858177646693334003600582645145163024129266670195298524277385017300500474606243253350746830083178930194838166506125840719854601073336527697570860088217792199142853472881342204343303257430213187552735174662240732987092215480408585962029697368803120257601533696366754637216248370122197430326435088650180664581359908704797319579979251851998834314180197817759382899511977704940706468416017221946809035545455286258975207881649604910617224065683437160102816426839732216128937991721127513634444080017973864624433840428927913344858928961896017451/(29*370248451*6709*144481*256579*319973431*101731310703289*10635841025639256246541*39488879317091*1050474234583201*689529693448123842995171*116359*141041*233801980384836959*202420473076700002472831337135056887503504907638783092300771934200834098639167879222334073790150469216607142854345183277199538386958083037454426674213008572218325810795499790004452771523152812490404840935943106446916327045096843269948296788223996281463765352559459965959920034012007885496365625551939711771272150540727992481) Output: ? 6366282058954182757781986570211602659601672773266671456556771127849433729944192959680172771078438225031017361749953385096090803358208938945168020011429558016771248029293050086910594869073398420701288994355788502591400028971331370803612916789605420223186293763130683725854232076113169602588430066080585476884492530109340028070610619848311580909708424352011077896716753521296776999632182432521815942859240024912210841984110482711173411622999922584152375506602078411025743275663117373946501226850417255175292710361524186454279818906628359794244012228590835612032237102450100662586745544420472785909084153643336193200252787832442570499827902344023243180625817830777985387147391896169808793605987053673371404056044309352192731284097686147121492754550009962009361252268295821982541123510927090626734434965101724995790023026016254643238744506076969916035982480734647284021886209251619640530355073261541801573484256770954768114699413753859937863984450064005486225846857932994216171475446945203596787873665643937188640186934572721137760520255726543643940643751737478255513154098534675874798712776919286768806835121614601877343189937904998120672043228745262491591917927088439789181479132626109468723639636629792123600726826091205116195698398085573140018469499143315121745513286436915258860196624431098672727343666262928393379102273251104689450543558050565811472231275895082629073410219751253187152086527860910971052993505515285684803955683171284683004005573366981013952796331653516591077395765436035604208758402290342817718072249272656700676788339009781659023486140604020992455036990943864137565242965643769997899292056382621187303011418490901144295973931290526471258155109406751589718799558049568605450826566282898647384665898649823996184592400918626628797524388908691036554635139750228049753649228261774840657271921905245777747692557917167916212063257181630826128016591361016020997035757198110734916193112985380000082000690710505086426085907943948976630450867950678005050391951688382002688851574873648923506915742392479919681044099223829598086728991609119364511346380454347930925078834417726190960302275337314906801 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.007s sys 0m0.004s '137.82.' ************** PARI ***************** Host 137.82.36.148 (137.82.36.148) Time: Wed Dec 8 12:45:42 2004 Input: thueinit(x^19-2,1) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m6.290s user 0m6.038s sys 0m0.056s '137.82.' ************** PARI ***************** Host 137.82.36.148 (137.82.36.148) Time: Wed Dec 8 12:46:13 2004 Input: allocatemem(64): thueinit(x^19-2,1) Output: WARNING: PARI command contains unsafe command 'allocatemem', so it will not be executed. '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Wed Dec 8 13:31:20 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.002s sys 0m0.008s '69.119.' ************** PARI ***************** Host 69.119.90.61 (69.119.90.61) Time: Wed Dec 8 21:08:10 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.003s sys 0m0.007s '193.204' ************** PARI ***************** Host 193.204.167.87 (193.204.167.87) Time: Thu Dec 9 06:37:23 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.181s user 0m0.003s sys 0m0.009s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Thu Dec 9 09:23:01 2004 Input: ellinit([0,0,0,1,1]) Output: ? [0, 0, 0, 1, 1, 0, 2, 4, -1, -48, -864, -496, 6912/31, [-0.68232780382801932736948373971104825689, 0.34116390191400966368474186985552412844 - 1.1615413999972519360879176872471740748*I, 0.34116390191400966368474186985552412844 + 1.1615413999972519360879176872471740748*I]~, 3.7499429780943428558514068688792391676, -1.8749714890471714279257034344396195838 + 1.3217205335652045388339957273859485673*I, -1.2567898718619115702891347357889582326 - 5.925211778913298466 E-39*I, 0.62839493593095578514456736789447911630 - 1.2807441770880269044452305771781743234*I, 4.9563766338459469553082572514616457857] ? Errors (if any) and Timing Info: Timing: real 0m0.259s user 0m0.009s sys 0m0.006s '24.52.1' ************** PARI ***************** Host 24.52.133.80 (24.52.133.80) Time: Thu Dec 9 09:24:02 2004 Input: E=ellinit([0,0,0,1,1]); V=vector(100); forprime(i=1,100,V[i]=ellap(E,prime(i))); V Output: ? ? ? ? [0, 0, -3, 0, -2, 0, 0, 0, 0, 0, -1, 0, 7, 0, 0, 0, -3, 0, 12, 0, 0, 0, -6, 0, 0, 0, 0, 0, -13, 0, 2, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, -25, 0, 0, 0, -11, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 22, 0, 20, 0, 0, 0, 0, 0, -10, 0, 0, 0, -4, 0, 22, 0, 0, 0, 0, 0, -30, 0, 0, 0, -32, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.003s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Dec 9 10:16:46 2004 Input: 2^3445 Output: ? 111772525111414845557497756854783872555110476858396833211054348506204763808371363973228263394928941910432362404073351781944601771370655956999411263454156490308872384642472468453754569278115601507466606238794182675481414119201944045151576707897322943915377409131989915881773092659597052592761223947745734584748394077319611094746288641691651741005647105359588635140243948908364425595823436158386518746126513336765392938922260779019464112894731505837498921310987484821853780794369740604346317238996489615701848842278808457234830063526232001851192422534515937537407818937884504259572700538217784039988198053695936032707526545159999152006036372089155437218559876455171386721422424766404989220673986720638108840240354490741925305883766499187435245900507347695933777521728461501061825869768619208850977803664268629588333588642399805282641515013855700752350776602118150200506177511493603384845000632688109738367062098707989744657570903332294654837431229032678480676047555301517381525878139787257642880145137388228796025166208514199062684559736832 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.002s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Dec 9 10:17:01 2004 Input: 2^34 Output: ? 17179869184 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Dec 9 11:19:21 2004 Input: factorint(1522330095375761149454243191044233437108888810626723674002983687652207223896709 ) Output: ? ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...4002983687652207223896709 ^ *** Warning: unused characters: ). Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Dec 9 11:45:01 2004 Input: 2853850578151875077061785275057259128763318556772402239241246410329576208063285587328220781056284381070685741593728109459667374757412699643261769054260143279065292684612144889579843130359514168808360490413092292037543567613575701556692583743406755639126672922060362087485009074143128426397370306329109283145094598044773624465119355105283964537274432343358585463895711089015261534330103813043668944645698076509240414869303546273655820540407167769393545956755326724670065902669488022995745904806956066583797532831676421249498328292643673400636994761594765945172279340957820781725353274870088644278638898862579792013025406370370966829326465899682334219427723087614750865436098065939883946189195152520117916655179241714417079071646013264974652534004836537333425641732482414218583427696509604768540691890713917660985464452720514669397921563617783416168213807114302167362621737236525154580048887307889943734525851540703145166149892271118908368609633830649306178412472655114865492189292067045474039147506739188865966297030388420394542187975996518320207903117636587396340854217559575409350307357640793329603769169511148520038544766491144298630103586935049218669669486229611942013235932004156525164342977935007023104230625040151345602347847516853483230726129704625539299434601026076190260756008764052843647305662032331430698239910937238977615459263594918852951525333150250585995493758542976288006835588127248482248609158493893692427250625639103032507847249003696030888010283893369779298494951264000492118705214892350371061400548086201889315932559909263417889116069686192754905170225033005571306081961053351560643323748337692326497826599830528387746212415641889440267702052148639116509001749166695201459774949106491917816275675702653084634251280643622814127024553415109516365092179876749298362582221099155970800932419631187695553815580156348968369269878668259631585586450665833132234419040917302346000767983294565499405107376612123502320360297228025247574979137337931386726747144919583811397924941787619400876724497535607882704818563605842170838039928893227949158587089459365757005445055233538407881990802456042735601/(98729*222137*740461*4121893*1070211521*88646853289637*1838241818746901*130409341500760573) Output: ? 1874659501786602246627156607480533549200407924112704754291557931705372019377609902704976937812940794885346853837725782823747506859051032909097873028017297701708388605077575483430138695411679288005254757463057149971852065780495105618704980378178981335294533014481477182771728674890661603341314955402682349345995926372923526353231586528894830747131884892223561426109933428991795604206444279819459455725812461091002753078942811722460762195155028028497058877857841586719790851026118977605891421011542408398141391327340529590886910063392005940699434296410538372810378065494257435366419739096208110564153658454786313469113410671512772249240069528449228591040571041206991650096065707910521353769409923080054981090136328461574514914490783722260343570618108089709868441288957299284260173003145241667362840383338162119791184424560786772157734962180464868172593656328465424557333180594971407562242141819287456859013949837663107703622953918307769126733694588954672583490391636241959975668127557676074329202127066270021159593079003640591780276613349598786663508554500595382453364003245125835495234362139815093418466775943658815308475605307524015202839993468911137408703127405459360031845269137272425183723908064397163669129747764781298587539590567215581196301178065861126289196727300639256835899163581315079182601815621646549629437570936403178577087491015247894465307251639311920790088272195145527464470722885224786623447760320614888116670298011773424466913206491349974536547171303267692004146049576774934543096715027147543226788783420078772738747677159628874639512077359590027399760265962538900353864715204241733701147305428679528419252934513944784047715578255963000829303459963092466171487072259943570836857207930797837006602084858836083579304500550849143433131909422351076299282356495601889667697708332080354273880911523190058462837438110467267494714482424989015042750253573502333680605344103025491280084903182543510897207154897831749716847892524812565089502969183567597879331097822780791693184609324764215101330520648168420034498363486589 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Dec 9 12:27:48 2004 Input: 35357329823156284558903850387502927465575535429805539394079518959532027779334148382452844314847467801459027172958970023945677499120047751481455645926035934191182782274010354858263741885647664429313868157266626011445531218758992117401949582729242077222654564319162794287281117487364909085865024224043093668495780601898336897904922268994335471184100190089543912772154784932226281299398650516530829970277260408489741978650340109090403065219401876190788409016021726064982466175052310331456587591865247622359263676666039320593517321019329610746365230247449425967677919903602217817490342255425832844425580377440886550499099475815709173088485949426196882666854624505415169210642823850466814972857754886382044117723823312126931060456645282013943441729554863317819212589062301825700876861638628137593436414969213274527978403915090985587330089698176291613272922894901573653609811341957690822093127222673562460719970119086157853050890448998306874588839225572274619227916023351643417248337431416969170798207028511031701747644298068539337481365165856451985367431380041368321036135328579078751642490088734987953092083080646585869399718531269604407386333150336509021518718398285739051287734803089362979984699219388568961456575620526935553970921763167548123230521837360822266252644219328419138061065615720566928697310681661983297965220203646140838577121528593122971789818484775856448119034736905851802935240271156564192425252841644434947847009869115453284564050001822325424485426233031714848813552571787142852497420538854757322605672074470051751678299100323143092165401678348825452398055614863821007527755745931909634621242315600178305570197275721837271011186927405095510162956799215803842400306683223222324367106955480609145174442926140789607915758240902110440129266746665501468780828583182546000768298912272098254005678079931812641695886692324416123041618585401716663634307885130697670335549637148267388745641817766446595196866047082938268077339495057544861543844266470842135098884818939855978959201600786802986447882835338673605957187245224395005515053574709265918396741207062032484228768500408064634077816698322573304651785581672708331986630340061129704521111783413150784568017810395451801987047657543627458568831318156012577849016864281795194283006352581940812780030172028844106383210669330255835037863960320409337262374089472324104787471648748122070700901139559226031617282470601218509367140493661163196433524082728498560589429455079938397022556256067653141221402995649965491181992802503903157413652214356443357453538839128721109772839302427267306122084103645796565285984415951200046669185018827669359586753990466345686670949574424763933929929425607306637617506813313314239640183297913343749729534613486044143632301081447126405660924368023757898395779093336562347346398168643811115127948949416907066324675696230821230241863062947042109665293435462625722988387668015089757613880046912194237567795146330227759339821028372521234399305328650815036036384089675076126525853030036708063662868156152220281318289617860379620968367673522355866627085536899137405251758742070982061575551203620486216141563503641016209/(353*2710260697*582416774750273*21937080329465122026187124199656961913) Output: ? 2892550744623512551026196477013263808503097641970759030287059737346596805185440023446791257418259834609398054229667985121131838119306444515164834908507448579832398776467545183450393621811150802757047087038885097664275535185543571400705550822855174256056970904282334923670761957640442574680602824574668548296834065689500095962642798350574159064776841476864038130149180452650320767359191683530400170990285592588894120258869971757264756109033443623966180283413901767255725593647931748349331260030682465593270330733422557197243469219216264806443773419946227645857349839967194110442661422661172067817418812371066960430233493647801538726867368710336219411453815028151211822305206322985255594242778414075031271594072430597952285980715872894886554426850901108509711064319996352437091822267366202980413333795866800170836369606210685900806588845841502195256265268577555091896376670635700299684304481306247190528976659004846533447095208380255479104837761482838865854838751322111684411853407918926879927931211119965711334118672125736485348430677034256935410163567720774141025079117261996979286476733568891541839946849536069330238459926528703303094287914799777218730951024372032378055723261286900988497424328446890418341840225312108609570961741076276842215356014816610854360980700182608517485198414436052247779189120458220026929333856575856008267449785893894343633190826944000386894299422308091336178980653514257947948153823144251694084155327936426597279645243376486070790638097198887707589680476412718427574173708215328060155870394944997253754584748046652961413867060347897523690539201813149577696541513719675360755374864024614994066823327012890039454343924345500420244747570582358667620344966810881371784312255974186648631364489763118131103196306265792060051211304441747259242697258823268580297488337069867580296437625060562710011740968170696208905251346721719316423934651700486524598878430370574944255871267725673505235561541698823294215299506683561468226551555861044324866748227746499292831350258523955289563757324881754222641256705282119729782926444658891398176208838595159674491582902857146371351069885693829473630064883544857423756827190512611756638224081612669562805939843856196465972189276382390157623628757472790652230080731027091993874110928458976518684792157786955470531778282433722268686727391490560109232189598642983546304529201707916701581496120715795670331123483040947612597157857255975175908924664855822684788196685159301401008824410388756477267353955746430561299425204833867569807689599828962281317086430483361798265485536100924143402368179599185166275809344540080378230548746428343238593346938506240494857294492819182706525369296859083786113849891247974472915900148476315696053939265592212686543401995759294867493098764433274493473599327126276016466645939300928380196862537999767986441383282187360896784927239755823214110044688237002657330220305058258279395525938013323689806646558725666903598514731944871291327961720540877301558294544043453035048299382350919865562173855410109782516116773579069881088627515164889518975900001 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Dec 9 12:47:24 2004 Input: 2892550744623512551026196477013263808503097641970759030287059737346596805185440023446791257418259834609398054229667985121131838119306444515164834908507448579832398776467545183450393621811150802757047087038885097664275535185543571400705550822855174256056970904282334923670761957640442574680602824574668548296834065689500095962642798350574159064776841476864038130149180452650320767359191683530400170990285592588894120258869971757264756109033443623966180283413901767255725593647931748349331260030682465593270330733422557197243469219216264806443773419946227645857349839967194110442661422661172067817418812371066960430233493647801538726867368710336219411453815028151211822305206322985255594242778414075031271594072430597952285980715872894886554426850901108509711064319996352437091822267366202980413333795866800170836369606210685900806588845841502195256265268577555091896376670635700299684304481306247190528976659004846533447095208380255479104837761482838865854838751322111684411853407918926879927931211119965711334118672125736485348430677034256935410163567720774141025079117261996979286476733568891541839946849536069330238459926528703303094287914799777218730951024372032378055723261286900988497424328446890418341840225312108609570961741076276842215356014816610854360980700182608517485198414436052247779189120458220026929333856575856008267449785893894343633190826944000386894299422308091336178980653514257947948153823144251694084155327936426597279645243376486070790638097198887707589680476412718427574173708215328060155870394944997253754584748046652961413867060347897523690539201813149577696541513719675360755374864024614994066823327012890039454343924345500420244747570582358667620344966810881371784312255974186648631364489763118131103196306265792060051211304441747259242697258823268580297488337069867580296437625060562710011740968170696208905251346721719316423934651700486524598878430370574944255871267725673505235561541698823294215299506683561468226551555861044324866748227746499292831350258523955289563757324881754222641256705282119729782926444658891398176208838595159674491582902857146371351069885693829473630064883544857423756827190512611756638224081612669562805939843856196465972189276382390157623628757472790652230080731027091993874110928458976518684792157786955470531778282433722268686727391490560109232189598642983546304529201707916701581496120715795670331123483040947612597157857255975175908924664855822684788196685159301401008824410388756477267353955746430561299425204833867569807689599828962281317086430483361798265485536100924143402368179599185166275809344540080378230548746428343238593346938506240494857294492819182706525369296859083786113849891247974472915900148476315696053939265592212686543401995759294867493098764433274493473599327126276016466645939300928380196862537999767986441383282187360896784927239755823214110044688237002657330220305058258279395525938013323689806646558725666903598514731944871291327961720540877301558294544043453035048299382350919865562173855410109782516116773579069881088627515164889518975900001/(88853*1806697*125395237117) Output: ? 143695287760641253314511554589272131561697118106322094493856882998252182231338957832944822135680815516281413470596963285666976292153798679071194490730867499484181652586433542167878495465561550921325119728159615945094056163428278059961794721109713269998423453933699849750829354791569591843440706496453609520649795083045104381502554067536767729693776087886735297336221133296989357457396606520536349905254626122684755791087185413736870740719550552951722225832461631243570799851860666675529556418420965032379596442366783995211020876614210344836474591099909852540529351550358251024873833692932869290419303208160915303371146835853385516347937429633083116615887906490912944491200522290432494432802843947860646290622108540860875597770120215713677484745884466286757666614288178913500422336297341624967718523165966146336071266073172984131857708843022015858714846643263078615606555946821472712647648685108252370417638400600016930464722749058690279945694684085604785042751030831566359456517255221578470141338878618396859214817248300206565440601144319828464376565482283747894042572059233066812853444983163554869530960479258482345331900898374187186765780209324417232936016887420342271038992863782556830576791126494901371752777514240419909674178435728638602941912307782328119362399984610307498432615061345449745640933997764506070574686847269020411958657627227965028233703461378155429831231350525924955014630864541886756085697940466783432387313643976585033094695691526927225030284745789503363037619332607118725029245847633609159679667960941860965322289823382800499159784829478264192296485656794239911437481871296901166862969047159720228920077850605707502841214730922733198547168521927449049825199182591460308331820850060967518932054023705683524829261879444961636924766393686561621882502020564778573321180550513789614036299341229176539745700092115115058342493225833011037995259648829492317700905097407848181583307389008307837204375781580338465052659995482636611179678394698096487449135818197082248491210523807953754187568631670095796298620736577925577532133200950279910055286587286382969984021192832489256273112204268329191993790653438306187760074626208682183998465505969857033941529753399115754163111537499148849900769100626251887354195542787360385695750184601435860045787575800577947173061094882525760473816850607389605516983502793768864151141765871036606684842221082447688151856584784670067141622637844552104858597589246990594432214719951479906013145461629749899670226019782543350650509608755187367437484748356861959928889504650517407891075540239292157796640515236994080811921922162209029610784061906356823252809796779721981087141169740278092754972299779274021988974848205281873174472877785327771289321616424821158277863871669448576837896321012718829719597872889578018738170007215461620817122600691541378509386989622540643355040746182503494726853235443111773721811324244199271477958641236244241434515150426509673726021967219800602228001743323934493999863352600271643110113046159587282007794119858837537645018687406805152633 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Dec 9 12:52:52 2004 Input: 790613929874580701066187716539610099164552777444715819552887485519596621623752814533644990919186006712014988169248846606532021486473079737728856010146089300778270414971479636071389353333498449102781001518152649144640007989550053402108654322288459320988998259627372394198876750247218823169731812272654959884732243425842805913591872325173578278728541918775857350280777404235535588759854531284573791704266143266791445985957507213045506721253489556055433425939805903359133280040847317408629575765286570787384841540058817191752016795221723262106063120567356527853690397380392541237932609153137118045488886184589955175295330464940511124559900800943670377000669766243784736321146150963592400390075366591449744109182887747623934211744441270518239577060989706048189082121041283325619313178695697047132905906437804889323001763045981105863008279710933607104302220558858388838162252294307028521618933611455644206033442616329109969256947953188552194864386156196661091151721291003376533388231343138606236617976913066793808241168708677601977613835465383735366259594114784372482926471587219269004374631442382710633629260044243200540439374454587583395467410418809375633510736535490508082696934559899384227967157946189511739875071743889577360953095071302048245307888495838309448031809235281688620024878980159220433042453110108380233111220677353237776641717953218020080356983570223627431130759964656957035549719548642841591761035197813821922594109950300143770045135866961415704668820522320999866059370132580000702507890803776787931724791640951871726722076591466849155633910155534118052892649872819833113565544398221883193309531468196055310789362929864639528630631891004509043574213186856105234898122325553137778508703312543121191290500280093405022914093213485438931318458186852375714099361373831410619051337584512504739901971745708242699212240735446536128142907748105997472265633699978279607238607998544101547398496631008184502539540926391028196581933215465961286632330889321040653091242578814068396421530694043314527539134355730845055545396230621907409122758338188894731258924988878239835567524161820414216973897255652417486461983408541966218288843748377209749788318048580736172649973149413341474448100778372812800309680651083450861405873133958547537076830132944065102705722720533685064213017515910651822160187360524844016594095445154649623712743321984746862631058423665636951044390031104070383116717659687849211977137014905218391909738075976650085997855556598947082372522673680828674090419374653959825682350374700106416971456356655601555274073420784789520021202714221600646181436265426741639512839703264194603359048935053767876408827010290426728436855548147551735883767678536634402706942581245855996098526118272411745205872378260009344318892297089081263047889264225494983368438089243683992832272411740370643170361818431259713652513584953936916064018451099660535264154661079131907892906981573965862263848665994430638672123190739033482007265422021106767918139799048546176804813059509201/(709*8969*336419*15061*170179*712841*15636705475517134545061743537722067281) Output: ? 790613929874580701066187716539610099164552777444715819552887485519596621623752814533644990919186006712014988169248846606532021486473079737728856010146089300778270414971479636071389353333498449102781001518152649144640007989550053402108654322288459320988998259627372394198876750247218823169731812272654959884732243425842805913591872325173578278728541918775857350280777404235535588759854531284573791704266143266791445985957507213045506721253489556055433425939805903359133280040847317408629575765286570787384841540058817191752016795221723262106063120567356527853690397380392541237932609153137118045488886184589955175295330464940511124559900800943670377000669766243784736321146150963592400390075366591449744109182887747623934211744441270518239577060989706048189082121041283325619313178695697047132905906437804889323001763045981105863008279710933607104302220558858388838162252294307028521618933611455644206033442616329109969256947953188552194864386156196661091151721291003376533388231343138606236617976913066793808241168708677601977613835465383735366259594114784372482926471587219269004374631442382710633629260044243200540439374454587583395467410418809375633510736535490508082696934559899384227967157946189511739875071743889577360953095071302048245307888495838309448031809235281688620024878980159220433042453110108380233111220677353237776641717953218020080356983570223627431130759964656957035549719548642841591761035197813821922594109950300143770045135866961415704668820522320999866059370132580000702507890803776787931724791640951871726722076591466849155633910155534118052892649872819833113565544398221883193309531468196055310789362929864639528630631891004509043574213186856105234898122325553137778508703312543121191290500280093405022914093213485438931318458186852375714099361373831410619051337584512504739901971745708242699212240735446536128142907748105997472265633699978279607238607998544101547398496631008184502539540926391028196581933215465961286632330889321040653091242578814068396421530694043314527539134355730845055545396230621907409122758338188894731258924988878239835567524161820414216973897255652417486461983408541966218288843748377209749788318048580736172649973149413341474448100778372812800309680651083450861405873133958547537076830132944065102705722720533685064213017515910651822160187360524844016594095445154649623712743321984746862631058423665636951044390031104070383116717659687849211977137014905218391909738075976650085997855556598947082372522673680828674090419374653959825682350374700106416971456356655601555274073420784789520021202714221600646181436265426741639512839703264194603359048935053767876408827010290426728436855548147551735883767678536634402706942581245855996098526118272411745205872378260009344318892297089081263047889264225494983368438089243683992832272411740370643170361818431259713652513584953936916064018451099660535264154661079131907892906981573965862263848665994430638672123190739033482007265422021106767918139799048546176804813059509201/61117907592245731858557395364806077987990440280661464347114409201 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Dec 9 12:56:15 2004 Input: 79061392987458070106618771653961009916455277744471581955288748551959662162375281453364499091918600671201498816924884660653202148647307973772885601014608930077827041497147963607138935333349844910278100151815264914464000798955005340210865432228845932098899825962737239419887675024721882316973181227265495988473224342584280591359187232517357827872854191877585735028077740423553558875985453128457379170426614326679144598595750721304550672125348955605543342593980590335913328004084731740862957576528657078738484154005881719175201679522172326210606312056735652785369039738039254123793260915313711804548888618458995517529533046494051112455990080094367037700066976624378473632114615096359240039007536659144974410918288774762393421174444127051823957706098970604818908212104128332561931317869569704713290590643780488932300176304598110586300827971093360710430222055885838883816225229430702852161893361145564428206593717660078435432295725768574413312585921506073632437497226251450152060234286919125842186147409246775783529782390201648033206033442616329109969256947953188552194864386156196661091151721291003376533388231343138606236617976913066793808241168708677601977613835465383735366259594114784372482926471587219269004374631442382710633629260044243200540439374454587583395467410418809375633510736535490508082696934559899384227967157946189511739875071743889577360953095071302048245307888495838309448031809235281688620024878980159220433042453110108380233111220677353237776641717953218020080356983570223627431130759964656957035549719548642841591761035197813821922594109950300143770045135866961415704668820522320999866059370132580000702507890803776787931724791640951871726722076591466849155633910155534118052892649872819833113565544398221883193309531468196055310789362929864639528630631891004509043574213186856105234898122325553137778508703312543121191290500280093405022914093213485438931318458186852375714099361373831410619051337584512504739901971745708242699212240735446536128142907748105997472265633699978279607238607998544101547398496631008184502539540926391028196581933215465961286632330889321040653091242578814068396421530694043314527539134355730845055545396230621907409122758338188894731258924988878239835567524161820414216973897255652417486461983408541966218288843748377209749788318048580736172649973149413341474448100778372812800309680651083450861405873133958547537076830132944065102705722720533685064213017515910651822160187360524844016594095445154649623712743321984746862631058423665636951044390031104070383116717659687849211977137014905218391909738075976650085997855556598947082372522673680828674090419374653959825682350374700106416971456356655601555274073420784789520021202714221600646181436265426741639512839703264194603359048935053767876408827010290426728436855548147551735883767678536634402706942581245855996098526118272411745205872378260009344318892297089081263047889264225494983368438089243683992832272411740370643170361818431259713652513584953936916064018451099660535264154661079131907892906981573965862263848665994430638672123190739033482007265422021106767918139799048546176804813059509201/(709*8969*336419*15061*170179*712841*15636705475517134545061743537722067281) Output: ? 1293588018669161679022154765878713840862432830592184596646160257295523326603117107962397306090536657375194184630373778094171902869000212094034157949483727395241952451876313144387225850017569356993663269887295394725226596648935944068756991108655665081145950299001167936182761387659554652251207459409376571846973187509002277458024548595196397630316450273889050184485351139794830167098457994132563298341670677575833009699951633575215484173165994296047904631397513039450210115718035608442264934011990230423562083223741234658750338003558127522803818557085454554734137068670341983772678520928614242412656440472368599688334981834987360290207991448415137899716951290522929027824657094267932568001850154110436562210553405657827650782967025853420776608297043258923259746191318637281860385207705754210884621940589990704574643092921231926523785655874542011532082916106614134816192335339690138184007631936838075663303701920301412286701973361870952216994696604772188771532933911201081634794629492095191111214440338970871137210400037794070457123614302988023338181916455039054214306123060736221505629762429526139879667925527620263474846859963834126455766623073956528884909740865863915670007829946811647260808711671429378107828546286233755530021118744933315139466394085729146010779476394979780649123129859402459253873844150565035584246389205057890903071955516729227763192780290036635825709327824223743528194657183481659887561711253508090925364658757346031519985436561063646460635390360336107282303924162231963408232571234165453208248129057802750938092523510609813868282574856139920442368524567493159436079904645913350674379320302488931453857815555279252423949749342401620035528544404694769969293807761191511283199357971599777265831576049828827453794897906239729918031377358871768108548665901079631731700112636975012234815935525891962828941249970964148965416407128041136353299719186032268546603393456268795492298878000672551507830467745426054689636277576210485155856204712112564001041879368239563232303696483681171211063466678609985856122375271118649970595933168617539896731418127351378665362666971832672554979564562817662834706694831401521737925500877350387648451521226816833536007861012106462588812899679572872659400294835954580667111233025941482601774234526352906508231706257493948823560406092736037475663904624570799308093901749473010100666050740514538464584392228812451926671693744986065995460443548049541602686624803098112991461350499080046068574188701283778505999030357054168230081014153216399754445359801754444613844797218139842638037977450357599220234882803561772261117274706326804293777163280560218469459515304550440762638914871252421096592967444900562025618178067654935454304797286579149978858533855461911815741999738571174060979955068436855327740166504974330174307084982945962228457926007628082887918784806574844566763673171883629820930272337450476933638569967226211123562950097126107360904594561254756944971014026141615147870617711863205768420441996759512898327889918969165660819052942225535752249639887555903493172294830654795025100001 ? ? Errors (if any) and Timing Info: Timing: real 0m0.175s user 0m0.007s sys 0m0.005s '217.230' ************** PARI ***************** Host 217.230.139.23 (217.230.139.23) Time: Thu Dec 9 13:57:25 2004 Input: 79061392987458070106618771653961009916455277744471581955288748551959662162375281453364499091918600671201498816924884660653202148647307973772885601014608930077827041497147963607138935333349844910278100151815264914464000798955005340210865432228845932098899825962737239419887675024721882316973181227265495988473224342584280591359187232517357827872854191877585735028077740423553558875985453128457379170426614326679144598595750721304550672125348955605543342593980590335913328004084731740862957576528657078738484154005881719175201679522172326210606312056735652785369039738039254123793260915313711804548888618458995517529533046494051112455990080094367037700066976624378473632114615096359240039007536659144974410918288774762393421174444127051823957706098970604818908212104128332561931317869569704713290590643780488932300176304598110586300827971093360710430222055885838883816225229430702852161893361145564428206593717660078435432295725768574413312585921506073632437497226251450152060234286919125842186147409246775783529782390201648033206033442616329109969256947953188552194864386156196661091151721291003376533388231343138606236617976913066793808241168708677601977613835465383735366259594114784372482926471587219269004374631442382710633629260044243200540439374454587583395467410418809375633510736535490508082696934559899384227967157946189511739875071743889577360953095071302048245307888495838309448031809235281688620024878980159220433042453110108380233111220677353237776641717953218020080356983570223627431130759964656957035549719548642841591761035197813821922594109950300143770045135866961415704668820522320999866059370132580000702507890803776787931724791640951871726722076591466849155633910155534118052892649872819833113565544398221883193309531468196055310789362929864639528630631891004509043574213186856105234898122325553137778508703312543121191290500280093405022914093213485438931318458186852375714099361373831410619051337584512504739901971745708242699212240735446536128142907748105997472265633699978279607238607998544101547398496631008184502539540926391028196581933215465961286632330889321040653091242578814068396421530694043314527539134355730845055545396230621907409122758338188894731258924988878239835567524161820414216973897255652417486461983408541966218288843748377209749788318048580736172649973149413341474448100778372812800309680651083450861405873133958547537076830132944065102705722720533685064213017515910651822160187360524844016594095445154649623712743321984746862631058423665636951044390031104070383116717659687849211977137014905218391909738075976650085997855556598947082372522673680828674090419374653959825682350374700106416971456356655601555274073420784789520021202714221600646181436265426741639512839703264194603359048935053767876408827010290426728436855548147551735883767678536634402706942581245855996098526118272411745205872378260009344318892297089081263047889264225494983368438089243683992832272411740370643170361818431259713652513584953936916064018451099660535264154661079131907892906981573965862263848665994430638672123190739033482007265422021106767918139799048546176804813059509201/(709*8969*336419*15061*170179*712841*15636705475517134545061743537722067281) Output: ? 1293588018669161679022154765878713840862432830592184596646160257295523326603117107962397306090536657375194184630373778094171902869000212094034157949483727395241952451876313144387225850017569356993663269887295394725226596648935944068756991108655665081145950299001167936182761387659554652251207459409376571846973187509002277458024548595196397630316450273889050184485351139794830167098457994132563298341670677575833009699951633575215484173165994296047904631397513039450210115718035608442264934011990230423562083223741234658750338003558127522803818557085454554734137068670341983772678520928614242412656440472368599688334981834987360290207991448415137899716951290522929027824657094267932568001850154110436562210553405657827650782967025853420776608297043258923259746191318637281860385207705754210884621940589990704574643092921231926523785655874542011532082916106614134816192335339690138184007631936838075663303701920301412286701973361870952216994696604772188771532933911201081634794629492095191111214440338970871137210400037794070457123614302988023338181916455039054214306123060736221505629762429526139879667925527620263474846859963834126455766623073956528884909740865863915670007829946811647260808711671429378107828546286233755530021118744933315139466394085729146010779476394979780649123129859402459253873844150565035584246389205057890903071955516729227763192780290036635825709327824223743528194657183481659887561711253508090925364658757346031519985436561063646460635390360336107282303924162231963408232571234165453208248129057802750938092523510609813868282574856139920442368524567493159436079904645913350674379320302488931453857815555279252423949749342401620035528544404694769969293807761191511283199357971599777265831576049828827453794897906239729918031377358871768108548665901079631731700112636975012234815935525891962828941249970964148965416407128041136353299719186032268546603393456268795492298878000672551507830467745426054689636277576210485155856204712112564001041879368239563232303696483681171211063466678609985856122375271118649970595933168617539896731418127351378665362666971832672554979564562817662834706694831401521737925500877350387648451521226816833536007861012106462588812899679572872659400294835954580667111233025941482601774234526352906508231706257493948823560406092736037475663904624570799308093901749473010100666050740514538464584392228812451926671693744986065995460443548049541602686624803098112991461350499080046068574188701283778505999030357054168230081014153216399754445359801754444613844797218139842638037977450357599220234882803561772261117274706326804293777163280560218469459515304550440762638914871252421096592967444900562025618178067654935454304797286579149978858533855461911815741999738571174060979955068436855327740166504974330174307084982945962228457926007628082887918784806574844566763673171883629820930272337450476933638569967226211123562950097126107360904594561254756944971014026141615147870617711863205768420441996759512898327889918969165660819052942225535752249639887555903493172294830654795025100001 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.179s user 0m0.008s sys 0m0.005s '158.109' ************** PARI ***************** Host 158.109.16.7 (158.109.16.7) Time: Thu Dec 9 14:42:58 2004 Input: E:=Ellipticurve([1/17^2,0]); IE := IntegralModel(E); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: E:=Ellipticurve([1/17 ^-------------------- Timing: real 0m0.021s user 0m0.004s sys 0m0.004s '83.176.' ************** PARI ***************** Host 83.176.167.231 (83.176.167.231) Time: Thu Dec 9 16:47:00 2004 Input: prime(50) Output: ? 229 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.005s sys 0m0.006s '83.176.' ************** PARI ***************** Host 83.176.167.231 (83.176.167.231) Time: Thu Dec 9 16:47:14 2004 Input: prime(5000) Output: ? 48611 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '83.176.' ************** PARI ***************** Host 83.176.167.231 (83.176.167.231) Time: Thu Dec 9 16:47:21 2004 Input: prime(50000) Output: ? ? Errors (if any) and Timing Info: *** not enough precomputed primes Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Dec 9 21:15:50 2004 Input: 6366282058954182757781986570211602659601672773266671456556771127849433729944192959680172771078438225031017361749953385096090803358208938945168020011429558016771248029293050086910594869073398420701288994355788502591400028971331370803612916789605420223186293763130683725854232076113169602588430066080585476884492530109340028070610619848311580909708424352011077896716753521296776999632182432521815942859240024912210841984110482711173411622999922584152375506602078411025743275663117373946501226850417255175292710361524186454279818906628359794244012228590835612032237102450100662586745544420472785909084153643336193200252787832442570499827902344023243180625817830777985387147391896169808793605987053673371404056044309352192731284097686147121492754550009962009361252268295821982541123510927090626734434965101724995790023026016254643238744506076969916035982480734647284021886209251619640530355073261541801573484256770954768114699413753859937863984450064005486225846857932994216171475446945203596787873665643937188640186934572721137760520255726543643940643751737478255513154098534675874798712776919286768806835121614601877343189937904998120672043228745262491591917927088439789181479132626109468723639636629792123600726826091205116195698398085573140018469499143315121745513286436915258860196624431098672727343666262928393379102273251104689450543558050565811472231275895082629073410219751253187152086527860910971052993505515285684803955683171284683004005573366981013952796331653516591077395765436035604208758402290342817718072249272656700676788339009781659023486140604020992455036990943864137565242965643769997899292056382621187303011418490901144295973931290526471258155109406751589718799558049568605450826566282898647384665898649823996184592400918626628797524388908691036554635139750228049753649228261774840657271921905245777747692557917167916212063257181630826128016591361016020997035757198110734916193112985380000082000690710505086426085907943948976630450867950678005050391951688382002688851574873648923506915742392479919681044099223829598086728991609119364511346380454347930925078834417726190960302275337314906801/(15956419361*152642517761609) Output: ? 2613815406834986431912133885935068848723329999879056019523947181322091217587402903072124491792506017060509917605421411595929566255561754240690270100896398222179904394305315383925403457519557588300639114240413142686096763891477865185427460755568975972977394092323794156472021611018995975779068292068689095975562036437409125705394428779467363228111807443584398596934948346686740360394721283670931400114061752908512381962896207460794019079668380166663388266438802964752803632829612984031397110831959465949148629420287209226964351136295191904984830686267442599722949390446399336349733248646628460601947250071812999771009109527617305043242954559286037534502187116355096498415704182661494584485993642026377077058246955812470168354411715843677803703970396622893638114160863499223073720409075144714712795020127024349096542618070088317555193433169810022178479539745787439402541163217630008394063877817287853118366153890184982225010224202183924480326862222321860524582440915329698070477384327977767095123587435506134993345877564497115371362283769375945894570979575021117830691472674745272831624833405987992554941705894288834434896185859126013012605707154480054023348705405426559337288658736340390832821986148688583005455203968122171162068127956215285813310383810171671513282689045785588825512192190953087784865666631508352194751356740789155142552749262957051175141166430237472218424869952012758690863134366809596852045347737057132194153325973631480726044139357599893459138491849463278454385568631959648902798224421202598072418651146146337323939560784550539847427859862375417724187954494153737822650610187870250600533543285329963948914753405948978094031839214565960941346504227598684951367665879006951113582653711393594226341133253713056763892229681499175852241464550917348065611694161749124015005655522850986159806026853841948085919496006892119238375617334029236565332660946462939379126983128649919300566914447307300417914436958576692658185472845416166897980247324809623709703061067250037707891308838650847110237294684908871602552424914248815726328372549569614019411529124553800498869745603849 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Dec 10 00:25:19 2004 Input: 77699732103649415246816941239230444676620336682710873480762466409244297046070070245946271951162900235334718407163121061310508122256153342564471236729590109957551820990360792820463825423325139534242190661436244183370789897323367936987869174578419352727743906784284602840918333460633586423223967902185572506067117148179013093662437867971624490712397771027689775283651844318038146573469965940044731184753722125531793674671951135829452296064957487024432280875974808743806412608639327104528899070130302967807261905934046373391194685865849122280321476446557168525789123837914509462231840631677204536077051862565796467533216347627808018111700279628622430768097124015099044451266347492549656350161226574080756450522733763397257831235649838311443/(3*163*800483*350207569*313195711516578281) Output: ? 1809744286275915791787707538063569421362212748480652924274121791887825537777780515006007434742476694984105444713607892539717076769012477293874872796577896682545875601616937804558605216953276398487690519727258847220349085698967474858738951387196190476675063387208324189410281711917321108178643316345879761949435501304093067304067282732261404360521956099015448974202511745957174279365209403311270342363473885741721366356443304342226835478854221496405520045530079219884599225313200617319436745675548093330682233728370762899300752632340321514309015296574547548008688407293073213922569688760081471605901229571315167915205804112664971773737830103334688102058754865798210830830023395067644249575166664570836401 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Dec 10 00:26:35 2004 Input: 77699732103649415246816941239230444676620336682710873480762466409244297046070070245946271951162900235334718407163121061310508122256153342564471236729590109957551820990360792820463825423325139534242190661436244183370789897323367936987869174578419352727743906784284602840918333460633586423223967902185572506067117148179013093662437867971624490712397771027689775283651844318038146573469965940044731184753722125531793674671951135829452296064957487024432280875974808743806412608639327104528899070130302967807261905934046373391194685865849122280321476446557168525789123837914509462231840631677204536077051862565796467533216347627808018111700279628622430768097124015099044451266347492549656350161226574080756450522733763397257831235649838311443/(3*163*800483*350207569*313195711516578281*36100799219803) Output: ? 50130310834868864795790986491859175124963036925814371002407608830087829748532304583878082318685593831041131911492429156427996812443666244847370308352215716771360224135805040183078772566557680677389235451411275614531314716833300729843374133227162807974000705804296659791614667579546988148142557188822919519720084924188499005594381326729073381491956441931907024225240890102641520818813323294413662209566821252136423758186098679468224164116150048401515738106841220793661059169469319188546823577932184559972045795796242095525346996047995384865899663796781997719347290972351626243141188804129203591640447972300274635464121955133031090797524931588531200212627744484602534971066219360473878583267 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Dec 10 00:32:37 2004 Input: 469092580912853942080319480803546179859663725488193863606031224955002227563905881463723870967855189028736523139339379806784374083514767913303038670508045464012720269414075834391645072701781589884679297489130268968060095634544626870950224740233934484230544490212274595927479769605914615239843525150035764439276314673634607200453789046420890909667185251672925162986774457819113817014216188888652836896973533776033897423540797229496358954308219768279226216328191574532214813875973613955332447872812888864136252706909784957103677035986829777543529163003659318269880938846076571215600439319669433166419540078856512849912058731241467330627751044519409430512665581580342158329327687645839853068740913579665222053571369329403548608587337959906532611058627125817556720307517436316078282385817120436844969542856326568672084995803855469929246142247812575466722904943808047597152057156683253917325696334630826323146381574378096049577638505476528990431369140361929077737641847289980634561073911442611791610906852158577943769174453610924603991115773992761081941753775410284910115509215256819031491573216842615342753497472896086482800319020467190083098000024467501583348388789051939844780176971738706843814835999076650532096501058738051704155323821130959762164672011143032559391008877697710591517949427470862234868404567071004972952522148235591579044366183594966369341552675123844048770953026091380947836326169069576998317731728583447785490132985398671437161640464576546891768781987602829997775794715587225901101720130710539660053532108490059023170523836215537673286518294362884823420687043533187034561743881274422936654506006502258131222731115480699808088324133805566720984382186683135826407656270183761729459157252215642477831289051139149667132393116351041750973820364273556546967555090279594119830638425774984608538052112052593354429274339018386885007815785080110819114712715347137647701109353357171074265910143036793741839106726986942834914750774660178149797924895400056226692133136359538833607376255776460071186458486529149760183680029720919819023363628693474013647508254200128118309406308199271573167339943405403214643437404804007389579448263809780679752761352801505770581420896649799729723261253311177216291823867320978/(3*2*3*163*800483*350207569*313195711516578281*67031206681*46724505421882309671121*7772507*73254041816089*258422401920467*36100799219803*50130310834868864795790986491859175124963036925814371002407608830087829748532304583878082318685593831041131911492429156427996812443666244847370308352215716771360224135805040183078772566557680677389235451411275614531314716833300729843374133227162807974000705804296659791614667579546988148142557188822919519720084924188499005594381326729073381491956441931907024225240890102641520818813323294413662209566821252136423758186098679468224164116150048401515738106841220793661059169469319188546823577932184559972045795796242095525346996047995384865899663796781997719347290972351626243141188804129203591640447972300274635464121955133031090797524931588531200212627744484602534971066219360473878583267) Output: ? 2183449587805549234190712272171455095092644245368937826729503557048383898355581674460470547450969894223155769792919372128320984254190201229085199092518472805599709884383279638609130207269390616416325973891965850859236491549345043713400754963749223885114233105914419020029931949845215478982026381839690107684380868579997580667418006943692252949135137233985172445184918950844089852921464254112259975690646567728438031612266086478941182983053785794310397799912045616462878081332366568263344330588204878229611618951319756242488930869212245788264975045559379597958223285298378050918807411362656285594212338917736798718878869190616085545077384453406291228099973680968451354035710902512140558757846459846177057532090787082233345303793507653593014980444165251794975808953590108880407147286935676250360004505885066686644451190139131187886369139899265227474698465836767733019952245217733578569379447539864718643165875324518675613720850608741323046769753663721239873032866413165452508392732567494486675178901636950431327221939675172977780836426818730273023907229293866927129678852734245501915677270046859367162809699561225154965148839140481302946044071602493563201247446178296774179542877555965895245482685299860041908545740128163595440229834954309420084340517853877050503283706087778629449293954157252333941439848704490851145084961753429760625645548320566748286423045676991909908784592798305770061013804402020581201 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Dec 10 00:32:45 2004 Input: 469092580912853942080319480803546179859663725488193863606031224955002227563905881463723870967855189028736523139339379806784374083514767913303038670508045464012720269414075834391645072701781589884679297489130268968060095634544626870950224740233934484230544490212274595927479769605914615239843525150035764439276314673634607200453789046420890909667185251672925162986774457819113817014216188888652836896973533776033897423540797229496358954308219768279226216328191574532214813875973613955332447872812888864136252706909784957103677035986829777543529163003659318269880938846076571215600439319669433166419540078856512849912058731241467330627751044519409430512665581580342158329327687645839853068740913579665222053571369329403548608587337959906532611058627125817556720307517436316078282385817120436844969542856326568672084995803855469929246142247812575466722904943808047597152057156683253917325696334630826323146381574378096049577638505476528990431369140361929077737641847289980634561073911442611791610906852158577943769174453610924603991115773992761081941753775410284910115509215256819031491573216842615342753497472896086482800319020467190083098000024467501583348388789051939844780176971738706843814835999076650532096501058738051704155323821130959762164672011143032559391008877697710591517949427470862234868404567071004972952522148235591579044366183594966369341552675123844048770953026091380947836326169069576998317731728583447785490132985398671437161640464576546891768781987602829997775794715587225901101720130710539660053532108490059023170523836215537673286518294362884823420687043533187034561743881274422936654506006502258131222731115480699808088324133805566720984382186683135826407656270183761729459157252215642477831289051139149667132393116351041750973820364273556546967555090279594119830638425774984608538052112052593354429274339018386885007815785080110819114712715347137647701109353357171074265910143036793741839106726986942834914750774660178149797924895400056226692133136359538833607376255776460071186458486529149760183680029720919819023363628693474013647508254200128118309406308199271573167339943405403214643437404804007389579448263809780679752761352801505770581420896649799729723261253311177216291823867320978/(3*2*3*163*800483*350207569*313195711516578281*67031206681*46724505421882309671121*7772507*73254041816089*258422401920467*36100799219803*50130310834868864795790986491859175124963036925814371002407608830087829748532304583878082318685593831041131911492429156427996812443666244847370308352215716771360224135805040183078772566557680677389235451411275614531314716833300729843374133227162807974000705804296659791614667579546988148142557188822919519720084924188499005594381326729073381491956441931907024225240890102641520818813323294413662209566821252136423758186098679468224164116150048401515738106841220793661059169469319188546823577932184559972045795796242095525346996047995384865899663796781997719347290972351626243141188804129203591640447972300274635464121955133031090797524931588531200212627744484602534971066219360473878583267) Output: ? 2183449587805549234190712272171455095092644245368937826729503557048383898355581674460470547450969894223155769792919372128320984254190201229085199092518472805599709884383279638609130207269390616416325973891965850859236491549345043713400754963749223885114233105914419020029931949845215478982026381839690107684380868579997580667418006943692252949135137233985172445184918950844089852921464254112259975690646567728438031612266086478941182983053785794310397799912045616462878081332366568263344330588204878229611618951319756242488930869212245788264975045559379597958223285298378050918807411362656285594212338917736798718878869190616085545077384453406291228099973680968451354035710902512140558757846459846177057532090787082233345303793507653593014980444165251794975808953590108880407147286935676250360004505885066686644451190139131187886369139899265227474698465836767733019952245217733578569379447539864718643165875324518675613720850608741323046769753663721239873032866413165452508392732567494486675178901636950431327221939675172977780836426818730273023907229293866927129678852734245501915677270046859367162809699561225154965148839140481302946044071602493563201247446178296774179542877555965895245482685299860041908545740128163595440229834954309420084340517853877050503283706087778629449293954157252333941439848704490851145084961753429760625645548320566748286423045676991909908784592798305770061013804402020581201 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Dec 10 00:43:58 2004 Input: 2613815406834986431912133885935068848723329999879056019523947181322091217587402903072124491792506017060509917605421411595929566255561754240690270100896398222179904394305315383925403457519557588300639114240413142686096763891477865185427460755568975972977394092323794156472021611018995975779068292068689095975562036437409125705394428779467363228111807443584398596934948346686740360394721283670931400114061752908512381962896207460794019079668380166663388266438802964752803632829612984031397110831959465949148629420287209226964351136295191904984830686267442599722949390446399336349733248646628460601947250071812999771009109527617305043242954559286037534502187116355096498415704182661494584485993642026377077058246955812470168354411715843677803703970396622893638114160863499223073720409075144714712795020127024349096542618070088317555193433169810022178479539745787439402541163217630008394063877817287853118366153890184982225010224202183924480326862222321860524582440915329698070477384327977767095123587435506134993345877564497115371362283769375945894570979575021117830691472674745272831624833405987992554941705894288834434896185859126013012605707154480054023348705405426559337288658736340390832821986148688583005455203968122171162068127956215285813310383810171671513282689045785588825512192190953087784865666631508352194751356740789155142552749262957051175141166430237472218424869952012758690863134366809596852045347737057132194153325973631480726044139357599893459138491849463278454385568631959648902798224421202598072418651146146337323939560784550539847427859862375417724187954494153737822650610187870250600533543285329963948914753405948978094031839214565960941346504227598684951367665879006951113582653711393594226341133253713056763892229681499175852241464550917348065611694161749124015005655522850986159806026853841948085919496006892119238375617334029236565332660946462939379126983128649919300566914447307300417914436958576692658185472845416166897980247324809623709703061067250037707891308838650847110237294684908871602552424914248815726328372549569614019411529124553800498869745603849/9883301900468179 Output: ? 264467829998309385624591250833158637145295806687743554008472218373695404656355237131379822893761217893984568494566943290755057205389966111763519149066676349377632279727288800196922155573550047117995052516887836543148877549368694974625997664914349222926748699995005907575995400911103810860610118669326443546875306057793963755226632166574726793177998380104235862038791641590274696397428481526632281774313155187508359253941613514168062437333690157012702257169615858308789499782705436207774839136871823123898210186411857871112915606681550240731214451327460041376952218340570900067239988411570035118264150425292503519400342361534860344270362233715220579701570065422264913991585506205555460546660311172231033358795100941476131250299291392792921944333603653240368574533824670514861255021674276407555692897119130561438804696530238560610838253772414700735344753312677261041814905585382770479975417700914655054154485719148778532759873319006367674522598567067099796885849778556645912739194216175612715644020269168205134738115857082192240582006311916112039587134959060519295954470217214006679265741844119528191697115850020555421194753976157145851307287371942048995674234017750767294591306803561867052228485987465717572011990424068212415662249104791886372476188675385110109348128238387728649166536517488648999444643943498008316221565862043418774734294366179457087421121314781018584729462473673166219823893579450271187194220913448746217204576682860093469292826485168873294069729259157711926169367569362380862163252780079081521236744456689645344229650549978084377103735978841986777450326794800614283996288061685452758667800049518838637270715473296450834357228342826138715142406550394056888519283896305634587393731037994719621253682781475503527110085538890631592942555720408085001530385035978474954736158479284900344806111962977774400800660006723023105981214547265226970331501686568949922597307153274173951405265173667550798399868438030071777199985348098944033844866340265105939077312212207011581189525573794433641314123019671398159083422251376060684749636134685333666020126764935731 ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Dec 10 00:48:56 2004 Input: 1293588018669161679022154765878713840862432830592184596646160257295523326603117107962397306090536657375194184630373778094171902869000212094034157949483727395241952451876313144387225850017569356993663269887295394725226596648935944068756991108655665081145950299001167936182761387659554652251207459409376571846973187509002277458024548595196397630316450273889050184485351139794830167098457994132563298341670677575833009699951633575215484173165994296047904631397513039450210115718035608442264934011990230423562083223741234658750338003558127522803818557085454554734137068670341983772678520928614242412656440472368599688334981834987360290207991448415137899716951290522929027824657094267932568001850154110436562210553405657827650782967025853420776608297043258923259746191318637281860385207705754210884621940589990704574643092921231926523785655874542011532082916106614134816192335339690138184007631936838075663303701920301412286701973361870952216994696604772188771532933911201081634794629492095191111214440338970871137210400037794070457123614302988023338181916455039054214306123060736221505629762429526139879667925527620263474846859963834126455766623073956528884909740865863915670007829946811647260808711671429378107828546286233755530021118744933315139466394085729146010779476394979780649123129859402459253873844150565035584246389205057890903071955516729227763192780290036635825709327824223743528194657183481659887561711253508090925364658757346031519985436561063646460635390360336107282303924162231963408232571234165453208248129057802750938092523510609813868282574856139920442368524567493159436079904645913350674379320302488931453857815555279252423949749342401620035528544404694769969293807761191511283199357971599777265831576049828827453794897906239729918031377358871768108548665901079631731700112636975012234815935525891962828941249970964148965416407128041136353299719186032268546603393456268795492298878000672551507830467745426054689636277576210485155856204712112564001041879368239563232303696483681171211063466678609985856122375271118649970595933168617539896731418127351378665362666971832672554979564562817662834706694831401521737925500877350387648451521226816833536007861012106462588812899679572872659400294835954580667111233025941482601774234526352906508231706257493948823560406092736037475663904624570799308093901749473010100666050740514538464584392228812451926671693744986065995460443548049541602686624803098112991461350499080046068574188701283778505999030357054168230081014153216399754445359801754444613844797218139842638037977450357599220234882803561772261117274706326804293777163280560218469459515304550440762638914871252421096592967444900562025618178067654935454304797286579149978858533855461911815741999738571174060979955068436855327740166504974330174307084982945962228457926007628082887918784806574844566763673171883629820930272337450476933638569967226211123562950097126107360904594561254756944971014026141615147870617711863205768420441996759512898327889918969165660819052942225535752249639887555903493172294830654795025100001/(21094856454809*99123275608139) Output: ? 618648215826058930494290822099419748847514792535789443383081661774090664671483850535964594892514551992482188684050238930049717370497493991614468080746817955180933218786457898135986677521991473938852999189744174885224378524039151894118149297967326503522199024128869334266201684976350151445603550760662437362323055704368214952038947736412854999338203356030422526312360271493188078651300094318556680765727424198371073954138640249049504661499569016188977506422039927789145428082176813585478971626962324519406738951032535692004045856511186662405051232663228952874873683548664466083892831832612073421216214768181603991403068332083270349023964719167408893356456924849575504656174755259983853572019746297100806299286154345434766968746061217467547075471857871145400545598725225788999698740074271240244406197978468047870358068084806948027162761683425078614269644361627593337204740879512710659059274495367971732209657147335085437150486736631171732453142801371434090882444429504414527535030393371647920786518776158875336122085884044736500763608191499302827968444543408019568568639052613972016327079254998084091156205456405567654360392544718176731145309641378510127927857378808876381059315057314199538614457910554231931891797946514688957622918055090031690714524781498339806166384447344836766830341841754187427236622479585172739068513288545875048542221496163349245392469350955050336817081789635744236456610597754693783117049471126118353178282919031410070014267091246619066555481997243742694521010561993384853501953447601624459819502932250978147046771227752244670443976139254111173050644301630641356386357173893667704632545373472451637531609741959771860476630499224179198810912347763669863057073468939460350691109280961763443002088501109012742209202304380170480128787741153469957138456050081648620346626604042185697180068466126198379875415963557011191662118364006670645705384110825551088934546650328344377086963462375523313632260633850171204367758997357035752032844130002240811592238302781449122495519546827810017972648631905160418908435994296764473064746955458554660206119157726898064177645395299664849716397083699448282353681139892244795032791743481907055498892188207677112174688832654811651873943463986077557403577359982052519355078281688789991905103961391250065997557294983952454140113061153896729129399708011624842095321767415818713469002398882371579453309055416366211874119801120877203185697831855244159758872491676346297875536165321695366392226236575109684145700141360008039893805751907380317459914891975431237143635659058487590917261027417512176020680008385464571055399813066275825284364145966685014080192325783636065812766667772262290511327295016698680197089286982621336940919745497174233275005653870113770495068355411975123060902785732348690932971280784622791150844183383415212703160201153312397100332849512016715876403746633749042655552803502459698996051014201297798369326873970025745172304518480756981858165785458566256560616744680609677676302257403994786429015879563382814962032733350847559116753317837051 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Dec 10 01:25:38 2004 Input: 2183449587805549234190712272171455095092644245368937826729503557048383898355581674460470547450969894223155769792919372128320984254190201229085199092518472805599709884383279638609130207269390616416325973891965850859236491549345043713400754963749223885114233105914419020029931949845215478982026381839690107684380868579997580667418006943692252949135137233985172445184918950844089852921464254112259975690646567728438031612266086478941182983053785794310397799912045616462878081332366568263344330588204878229611618951319756242488930869212245788264975045559379597958223285298378050918807411362656285594212338917736798718878869190616085545077384453406291228099973680968451354035710902512140558757846459846177057532090787082233345303793507653593014980444165251794975808953590108880407147286935676250360004505885066686644451190139131187886369139899265227474698465836767733019952245217733578569379447539864718643165875324518675613720850608741323046769753663721239873032866413165452508392732567494486675178901636950431327221939675172977780836426818730273023907229293866927129678852734245501915677270046859367162809699561225154965148839140481302946044071602493563201247446178296774179542877555965895245482685299860041908545740128163595440229834954309420084340517853877050503283706087778629449293954157252333941439848704490851145084961753429760625645548320566748286423045676991909908784592798305770061013804402020581201/(19040401*617818667) Output: ? 185612000935602906022948238986279707544335659681156739518282666551411612319675329943667046364530660962110648760992517423424798114618091690314687128034157628103173652835135911040625241178524593492114052430775187038391381296216640979159481045025076757661669923267935827708021965029995912918127073345809027986085967845431947245253906924164925503111494871472299555417921023387513686230888219732139159322676533423530297318316999698978551360048220085618170152129752270891587261068750936672068421368359022897959188467544682329470916390330157316031499872525891828784509405426672352508197466816613898479705871716274229973065790422201233799805898380904156237969854898243272197391411772052971904464081314305258106713121601631510080479667103422550597703329870705554878777089459954607848500860874140636226108117103435797564374044697924416436277239565411754998031732462353208760204347352141974757805395012994486359311767327667213397505505106304453908068368216408769753360547519560940039463597742544099750478128195929748905816281293002229187225064694278626892303985321239551498871827073141367665333737077427938786127668376353600062468186397023998466269032207392001240342287955653731195705520039200561014365504774981018684727488056619790975998549341444537338576094066844355426960002751332181346688960414639593301483927468543455191980123816295892898727239783350803888546821029041883101051835652343836894403 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 01:48:42 2004 Input: lcm(248,2047) Output: ? 507656 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.005s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 01:49:43 2004 Input: lcm(324,2453) Output: ? 794772 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 01:50:45 2004 Input: lcm(870,2047) Output: ? 1780890 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 07:20:29 2004 Input: 8397*7914 Output: ? 66453858 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 07:20:54 2004 Input: 66453858 % 11009 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 07:23:58 2004 Input: Mod(66453858, 11009) Output: ? Mod(3534, 11009) ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.004s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 07:24:28 2004 Input: Mod(52555112, 11009) Output: ? Mod(9155, 11009) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:30:59 2004 Input: Mod(3^12, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.183s user 0m0.006s sys 0m0.009s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:31:27 2004 Input: Mod(4^12, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:31:34 2004 Input: Mod(5^12, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:31:41 2004 Input: Mod(5^11, 13) Output: ? Mod(8, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:31:51 2004 Input: Mod(6^12, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:31:56 2004 Input: Mod(7^12, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:32:00 2004 Input: Mod(8^12, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:32:04 2004 Input: Mod(9^12, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:32:12 2004 Input: Mod(10^12, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.009s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:32:17 2004 Input: Mod(11^12, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:32:23 2004 Input: Mod(12^12, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:32:30 2004 Input: Mod(13^12, 13) Output: ? Mod(0, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:33:05 2004 Input: Mod(2^4, 13) Output: ? Mod(3, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:33:13 2004 Input: Mod(2^6, 13) Output: ? Mod(12, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:33:29 2004 Input: Mod(3^6, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:33:38 2004 Input: Mod(4^6, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:33:49 2004 Input: Mod(5^6, 13) Output: ? Mod(12, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:33:59 2004 Input: Mod(5^4, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:34:15 2004 Input: Mod(6^4, 13) Output: ? Mod(9, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:34:27 2004 Input: Mod(6^6, 13) Output: ? Mod(12, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:34:37 2004 Input: Mod(6^3, 13) Output: ? Mod(8, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:34:53 2004 Input: Mod(6^2, 13) Output: ? Mod(10, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:35:07 2004 Input: Mod(7^2, 13) Output: ? Mod(10, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:35:16 2004 Input: Mod(7^3, 13) Output: ? Mod(5, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:35:22 2004 Input: Mod(7^4, 13) Output: ? Mod(9, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:35:30 2004 Input: Mod(7^6, 13) Output: ? Mod(12, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:35:39 2004 Input: Mod(7^4, 13) Output: ? Mod(9, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:35:47 2004 Input: Mod(7^3, 13) Output: ? Mod(5, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:36:01 2004 Input: Mod(8^3, 13) Output: ? Mod(5, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:36:15 2004 Input: Mod(8^6, 13) Output: ? Mod(12, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:36:22 2004 Input: Mod(8^4, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:36:38 2004 Input: Mod(9^4, 13) Output: ? Mod(9, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:36:43 2004 Input: Mod(9^4, 13) Output: ? Mod(9, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:36:43 2004 Input: Mod(9^4, 13) Output: ? Mod(9, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:37:02 2004 Input: Mod(9^6, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:37:16 2004 Input: Mod(10^6, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:37:28 2004 Input: Mod(11^6, 13) Output: ? Mod(12, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:37:34 2004 Input: Mod(11^4, 13) Output: ? Mod(3, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:37:43 2004 Input: Mod(11^3, 13) Output: ? Mod(5, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:37:49 2004 Input: Mod(11^2, 13) Output: ? Mod(4, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:38:01 2004 Input: Mod(12^2, 13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:39:04 2004 Input: Mod(3^2, 13) Output: ? Mod(9, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:39:13 2004 Input: Mod(3^5, 13) Output: ? Mod(9, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:45:33 2004 Input: Mod(2^5, 11) Output: ? Mod(10, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:45:41 2004 Input: Mod(2^10, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:45:57 2004 Input: Mod(3^10, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:46:05 2004 Input: Mod(3^5, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:46:19 2004 Input: Mod(4^5, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:46:37 2004 Input: Mod(5^5, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:46:41 2004 Input: Mod(5^5, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:46:47 2004 Input: Mod(5^1, 11) Output: ? Mod(5, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:46:51 2004 Input: Mod(5^5, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:46:56 2004 Input: Mod(6^5, 11) Output: ? Mod(10, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:47:07 2004 Input: Mod(6^2, 11) Output: ? Mod(3, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:47:29 2004 Input: Mod(7^2, 11) Output: ? Mod(5, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:47:37 2004 Input: Mod(7^5, 11) Output: ? Mod(10, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:47:44 2004 Input: Mod(7^10, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:47:49 2004 Input: Mod(8^10, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:48:09 2004 Input: Mod(8^5, 11) Output: ? Mod(10, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:48:16 2004 Input: Mod(8^2, 11) Output: ? Mod(9, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:48:30 2004 Input: Mod(9^2, 11) Output: ? Mod(4, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:48:38 2004 Input: Mod(9^5, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:48:53 2004 Input: Mod(10^5, 11) Output: ? Mod(10, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:49:01 2004 Input: Mod(10^2, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:49:31 2004 Input: Mod(4^2, 11) Output: ? Mod(5, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:49:41 2004 Input: Mod(4^5, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:49:48 2004 Input: Mod(5^5, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:49:57 2004 Input: Mod(9^5, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:50:10 2004 Input: Mod(9^2, 11) Output: ? Mod(4, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:50:17 2004 Input: Mod(10^2, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:50:47 2004 Input: Mod(11^2, 11) Output: ? Mod(0, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:50:52 2004 Input: Mod(11^5, 11) Output: ? Mod(0, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:50:59 2004 Input: Mod(13^5, 11) Output: ? Mod(10, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:51:14 2004 Input: Mod(13^5, 11) Output: ? Mod(10, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:51:35 2004 Input: Mod(13^2, 11) Output: ? Mod(4, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:51:50 2004 Input: Mod(12^2, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:52:09 2004 Input: Mod(14^2, 11) Output: ? Mod(9, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:52:17 2004 Input: Mod(14^3, 11) Output: ? Mod(5, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:52:22 2004 Input: Mod(14^5, 11) Output: ? Mod(1, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:54:09 2004 Input: Mod(2^2, 8) Output: ? Mod(4, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:54:58 2004 Input: Mod(2^4, 8) Output: ? Mod(0, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:55:27 2004 Input: Mod(3^4, 8) Output: ? Mod(1, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:55:34 2004 Input: Mod(3^2, 8) Output: ? Mod(1, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:55:43 2004 Input: Mod(4^2, 8) Output: ? Mod(0, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:56:12 2004 Input: Mod(5^2, 8) Output: ? Mod(1, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:56:21 2004 Input: Mod(5^4, 8) Output: ? Mod(1, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:56:29 2004 Input: Mod(6^4, 8) Output: ? Mod(0, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:56:38 2004 Input: Mod(7^4, 8) Output: ? Mod(1, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 09:56:48 2004 Input: Mod(7^2, 8) Output: ? Mod(1, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:23:06 2004 Input: Mod(13431876537, 97) Output: ? Mod(96, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:23:23 2004 Input: Mod(134311876537, 97) Output: ? Mod(0, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:23:40 2004 Input: Mod(134311876537, 97) Output: ? Mod(0, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:23:41 2004 Input: Mod(134311876537, 97) Output: ? Mod(0, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:23:46 2004 Input: Mod(134311876537, 127) Output: ? Mod(0, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:23:49 2004 Input: Mod(134311876537, 127) Output: ? Mod(0, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:24:07 2004 Input: Mod(134311876537, 127) Output: ? Mod(0, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:24:09 2004 Input: Mod(134311876537, 127) Output: ? Mod(0, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:24:12 2004 Input: Mod(134311876537, 127) Output: ? Mod(0, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:24:17 2004 Input: Mod(134311876537, 12) Output: ? Mod(1, 12) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:24:26 2004 Input: Mod(134311876537, 12) Output: ? Mod(1, 12) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:24:40 2004 Input: Mod(134311876537, 100000) Output: ? Mod(76537, 100000) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:24:53 2004 Input: Mod(97*127, 100000) Output: ? Mod(12319, 100000) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:25:03 2004 Input: Mod(97*127*293, 100000) Output: ? Mod(9467, 100000) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:25:09 2004 Input: Mod(97*127*293, 10000000000) Output: ? Mod(3609467, 10000000000) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:25:28 2004 Input: Mod(97*127, 10000000000) Output: ? Mod(12319, 10000000000) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:25:47 2004 Input: Mod(97*293, 10000000000) Output: ? Mod(28421, 10000000000) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:25:59 2004 Input: Mod(127*293, 10000000000) Output: ? Mod(37211, 10000000000) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:26:21 2004 Input: Mod(127*293, 97) Output: ? Mod(60, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:26:50 2004 Input: Mod(97*293, 127) Output: ? Mod(100, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:27:05 2004 Input: Mod(127*293, 97) Output: ? Mod(60, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:27:37 2004 Input: Mod(60^-1, 97) Output: ? Mod(76, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.005s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:28:04 2004 Input: Mod(100^-1, 127) Output: ? Mod(47, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:28:33 2004 Input: Mod(60^-1, 293) Output: ? Mod(210, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:29:03 2004 Input: Mod(60^-1, 293) Output: ? Mod(210, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:29:05 2004 Input: Mod(60^-1, 293) Output: ? Mod(210, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.008s sys 0m0.002s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:29:06 2004 Input: Mod(60^-1, 293) Output: ? Mod(210, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:29:07 2004 Input: Mod(60^-1, 293) Output: ? Mod(210, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:29:09 2004 Input: Mod(60^-1, 293) Output: ? Mod(210, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:29:11 2004 Input: Mod(60^-1, 293) Output: ? Mod(210, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:29:12 2004 Input: Mod(60^-1, 293) Output: ? Mod(210, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:34:06 2004 Input: Mod(13^-1, 293) Output: ? Mod(248, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:34:26 2004 Input: Mod(13+248, 293) Output: ? Mod(261, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.006s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:34:33 2004 Input: Mod(13*248, 293) Output: ? Mod(1, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:34:53 2004 Input: Mod(100*47, 127) Output: ? Mod(1, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:35:09 2004 Input: Mod(60*76, 97) Output: ? Mod(1, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:35:45 2004 Input: Mod(12319, 293) Output: ? Mod(13, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:35:58 2004 Input: Mod(13^-1, 293) Output: ? Mod(248, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:51:15 2004 Input: Mod(5^2, 97) Output: ? Mod(25, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:51:23 2004 Input: Mod(5^3, 97) Output: ? Mod(28, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:51:34 2004 Input: Mod(5^4, 97) Output: ? Mod(43, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:52:07 2004 Input: Mod(5^3, 97) Output: ? Mod(28, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:52:20 2004 Input: Mod(5^4, 97) Output: ? Mod(43, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:52:29 2004 Input: Mod(5^5, 97) Output: ? Mod(21, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:52:38 2004 Input: Mod(5^6, 97) Output: ? Mod(8, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:52:45 2004 Input: Mod(5^7, 97) Output: ? Mod(40, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:52:53 2004 Input: Mod(5^8, 97) Output: ? Mod(6, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:52:59 2004 Input: Mod(5^9, 97) Output: ? Mod(30, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:53:09 2004 Input: Mod(5^10, 97) Output: ? Mod(53, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:53:21 2004 Input: Mod(5^11, 97) Output: ? Mod(71, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:53:29 2004 Input: Mod(3^11, 97) Output: ? Mod(25, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:53:35 2004 Input: Mod(3^11, 127) Output: ? Mod(109, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:53:54 2004 Input: Mod(3^4, 127) Output: ? Mod(81, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:54:02 2004 Input: Mod(3^5, 127) Output: ? Mod(116, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.009s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:54:16 2004 Input: Mod(3^6, 127) Output: ? Mod(94, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:54:35 2004 Input: Mod(3^7, 127) Output: ? Mod(28, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:54:45 2004 Input: Mod(3^8, 127) Output: ? Mod(84, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:54:56 2004 Input: Mod(3^9, 127) Output: ? Mod(125, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:55:04 2004 Input: Mod(3^10, 127) Output: ? Mod(121, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:55:42 2004 Input: Mod(2^8, 127) Output: ? Mod(2, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:56:00 2004 Input: Mod(2^8, 293) Output: ? Mod(256, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:56:09 2004 Input: Mod(2^9, 293) Output: ? Mod(219, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:56:19 2004 Input: Mod(2^10, 293) Output: ? Mod(145, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:56:27 2004 Input: Mod(2^11, 293) Output: ? Mod(290, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:58:33 2004 Input: 5+1 Output: ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 10:59:33 2004 Input: 5*4560+3*4700+2*3244+23632 Output: ? 67020 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 11:00:56 2004 Input: 67020-1 Output: ? 67019 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 11:01:26 2004 Input: Mod(67020-1, 97) Output: ? Mod(89, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 11:02:01 2004 Input: Mod(67020-2, 127) Output: ? Mod(89, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 11:02:30 2004 Input: Mod(67020-3, 293) Output: ? Mod(213, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 11:03:56 2004 Input: Mod(67020-3, 293) Output: ? Mod(213, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 11:05:22 2004 Input: Mod(67020-1, 97) Output: ? Mod(89, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 11:05:37 2004 Input: Mod(67020-2, 127) Output: ? Mod(89, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 11:06:47 2004 Input: Mod(67020-2, 127) Output: ? Mod(89, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 11:06:58 2004 Input: Mod(66980-2, 127) Output: ? Mod(49, 127) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 11:07:39 2004 Input: Mod(66980-1, 97) Output: ? Mod(49, 97) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 11:08:25 2004 Input: Mod(66980-3, 293) Output: ? Mod(173, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 10 11:09:22 2004 Input: Mod(66980-3, 293) Output: ? Mod(173, 293) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 18:31:57 2004 Input: gcd(1048575, 2910435) Output: ? 5115 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 18:56:34 2004 Input: gcd(1048575, 1047552 ) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: gcd(1048575,1047552 ^ *** Warning: unused characters: ). Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 18:56:41 2004 Input: gcd(1048575, 1047552) Output: ? 1023 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 18:56:58 2004 Input: gcd(1048575/1023, 1047552/1023) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 18:57:18 2004 Input: gcd(1048575/1024, 1047552/1024) Output: ? 1023/1024 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 18:57:29 2004 Input: gcd(1048575/31, 1047552/31) Output: ? 33 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 18:57:38 2004 Input: gcd(1048575/33, 1047552/33) Output: ? 31 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 18:57:43 2004 Input: gcd(1048575/11, 1047552/11) Output: ? 93 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 18:58:00 2004 Input: gcd(1048575/248, 1047552/248) Output: ? 33/8 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 18:58:07 2004 Input: gcd(1048575/93, 1047552/93) Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 18:59:17 2004 Input: gcd(1023, 5115) Output: ? 1023 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Dec 10 19:48:10 2004 Input: 618648215826058930494290822099419748847514792535789443383081661774090664671483850535964594892514551992482188684050238930049717370497493991614468080746817955180933218786457898135986677521991473938852999189744174885224378524039151894118149297967326503522199024128869334266201684976350151445603550760662437362323055704368214952038947736412854999338203356030422526312360271493188078651300094318556680765727424198371073954138640249049504661499569016188977506422039927789145428082176813585478971626962324519406738951032535692004045856511186662405051232663228952874873683548664466083892831832612073421216214768181603991403068332083270349023964719167408893356456924849575504656174755259983853572019746297100806299286154345434766968746061217467547075471857871145400545598725225788999698740074271240244406197978468047870358068084806948027162761683425078614269644361627593337204740879512710659059274495367971732209657147335085437150486736631171732453142801371434090882444429504414527535030393371647920786518776158875336122085884044736500763608191499302827968444543408019568568639052613972016327079254998084091156205456405567654360392544718176731145309641378510127927857378808876381059315057314199538614457910554231931891797946514688957622918055090031690714524781498339806166384447344836766830341841754187427236622479585172739068513288545875048542221496163349245392469350955050336817081789635744236456610597754693783117049471126118353178282919031410070014267091246619066555481997243742694521010561993384853501953447601624459819502932250978147046771227752244670443976139254111173050644301630641356386357173893667704632545373472451637531609741959771860476630499224179198810912347763669863057073468939460350691109280961763443002088501109012742209202304380170480128787741153469957138456050081648620346626604042185697180068466126198379875415963557011191662118364006670645705384110825551088934546650328344377086963462375523313632260633850171204367758997357035752032844130002240811592238302781449122495519546827810017972648631905160418908435994296764473064746955458554660206119157726898064177645395299664849716397083699448282353681139892244795032791743481907055498892188207677112174688832654811651873943463986077557403577359982052519355078281688789991905103961391250065997557294983952454140113061153896729129399708011624842095321767415818713469002398882371579453309055416366211874119801120877203185697831855244159758872491676346297875536165321695366392226236575109684145700141360008039893805751907380317459914891975431237143635659058487590917261027417512176020680008385464571055399813066275825284364145966685014080192325783636065812766667772262290511327295016698680197089286982621336940919745497174233275005653870113770495068355411975123060902785732348690932971280784622791150844183383415212703160201153312397100332849512016715876403746633749042655552803502459698996051014201297798369326873970025745172304518480756981858165785458566256560616744680609677676302257403994786429015879563382814962032733350847559116753317837051/(23648869729501*330093163200265121) Output: ? 79249557574140080255767785238580075600902379473138903746622263330930322227077522369815086150692387512656264959945724115869118295580793076184660260101424679043572264859923714804334761201091441443572016523318997922699647085901989878607217209176919709808403907008909034162862867855910039318263023253868572566547379671952396796656007338263080562586234963884478053862898932501952816796370132258613496999061028830021304737284637632341439160958243681896827218467563888038079632363790827500131271179624286052119796461563022509494212453122424867560759340835092254806694333618535599366168233238810446267391770508485218917308454175278098866041009431730928691759235194411577767203251105899100308340084729546770839717428219914053937414542990612440568579008515256098168689954125560944655561095892345210208405865573836471791489270421669754386263182272482911478499523672697058972258147390474232613341598797779863442730786593102629095838415202221030674760293302401031453418825760755405200716001370357317053996258401069301408885270344363206938787651542167104716357786579807171266741872055283249848491982684141265744842888815187386900436687235121537656921576806465852904180284641954449488065018522539668373544866642411116568262973625050713854162290942195999082474467183433961143812150634092645474475630551315272031877915052092046777162718945308989774774565123976540694315795480308728118399815643466546984673772633211143538661452928767204547349401319750563213885000451573846965869481862772348968684969784301943889998759325393420409687026147447513016042887812222613823586818549010633275950607134087358246200531438441718609661718108098714581160308734067864738885079747434810014549221806384291470257595237031900467813066160105611723050422686370712874226131768206597852547766736017191757847836024540499325354186339221403921788244940069964997167309677691782794605906387989401912363337896253020988013276368817831135775202879389187547768766681923187288676671484141682892917742248304253146110641790701482582577631779976671594973674922520094190943842117582292408842887465289068129708336675562474461753746484482617730692652549118787509374454888105644768529512785261586170756088024793025697814449209489926436920525665246358488884279682700608143540670904096328493647933382597496007816622036717545631908151317922952159214630287845578059012223214994387033272515173912619021644695870926478847153582543614405096081602692950135672908959858090506617933817637414530279242794865068143334267910327866037252954583480011282854534956610161044848776543247015965420241096806066146276933617013681267637791357797335216645081192138794674145859237832320637026341018645069116898033430917083602468419719622019885779308030885964343117591512938967518980656923114853704690288945273305135912702510648677352430497277518235136623023609900121533592006101928656218949711925951912270673579265312339782390654992696142766269852090659360226903159460774049676191744891665424275918935738889969730789852540162743520797112792292777703327831 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:13:42 2004 Input: prime 1, 100 Output: ? prime1 ? Errors (if any) and Timing Info: *** Warning: unused characters: ,100. Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:15:57 2004 Input: 2 + 2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:16:51 2004 Input: 2 * 2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:17:10 2004 Input: 2 * 2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:17:52 2004 Input: 2 * 37 q Output: ? 74 ? q ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:18:46 2004 Input: 1./7 q Output: ? 0.14285714285714285714285714285714285714 ? q ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:20:21 2004 Input: exp(1) q Output: ? 2.7182818284590452353602874713526624977 ? q ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.006s sys 0m0.004s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:20:37 2004 Input: exp(exp(1)) q Output: ? 15.154262241479264189760430272629911905 ? q ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:20:49 2004 Input: exp(exp(exp(1))) q Output: ? 3814279.1047602205922092195940982035710 ? q ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:21:29 2004 Input: ln(ln(ln(exp(exp(exp(1)))))) q Output: ? ? q ? Errors (if any) and Timing Info: *** obsolete function: ln(ln(ln(exp(exp(exp(1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file) New syntax: ln(x) ===> log(x) log(x,{flag=0}): natural logarithm of x. flag is optional, and can be 0: default, or 1: calls logagm, computed using the agm. Timing: real 0m0.010s user 0m0.003s sys 0m0.008s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:22:04 2004 Input: ln(exp(exp(exp(1)))) q Output: ? ? q ? Errors (if any) and Timing Info: *** obsolete function: ln(exp(exp(exp(1)))) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file) New syntax: ln(x) ===> log(x) log(x,{flag=0}): natural logarithm of x. flag is optional, and can be 0: default, or 1: calls logagm, computed using the agm. Timing: real 0m0.010s user 0m0.007s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 20:22:05 2004 Input: gcd(8388606, 2047) Output: ? 2047 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:22:13 2004 Input: log(exp(exp(exp(1)))) q Output: ? 15.154262241479264189760430272629911905 ? q ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:22:23 2004 Input: log(log(exp(exp(exp(1))))) q Output: ? 2.7182818284590452353602874713526624977 ? q ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:22:33 2004 Input: Log(log(log(exp(exp(exp(1)))))) q Output: ? ? q ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Log( *** log(log(exp(exp(exp( ^-------------------- Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:23:07 2004 Input: Log(exp(1)) q Output: ? ? q ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Log(exp(1)) ^------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:23:22 2004 Input: Log exp(1) q Output: ? ? q ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Logexp(1) ^--------- Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:23:30 2004 Input: Log exp(1) q Output: ? ? q ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Logexp(1) ^--------- Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:23:52 2004 Input: Log(exp(1)) q Output: ? ? q ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Log(exp(1)) ^------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:23:56 2004 Input: Log(exp(1)) q Output: ? ? q ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Log(exp(1)) ^------- Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:24:07 2004 Input: Ln(exp(1)) q Output: ? ? q ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Ln(exp(1)) ^------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 20:24:09 2004 Input: lcm(8388608/2, 1822785) Output: ? 7645314416640 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:24:15 2004 Input: Ln(exp(1)) q Output: ? ? q ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Ln(exp(1)) ^------- Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:24:24 2004 Input: Ln(exp(1)) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Ln(exp(1)) ^------- Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:24:35 2004 Input: Log(exp(1)) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Log(exp(1)) ^------- Timing: real 0m0.010s user 0m0.005s sys 0m0.003s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:24:59 2004 Input: log(exp(1)) Output: ? 1.0000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:25:20 2004 Input: log(exp(exp(1))) Output: ? 2.7182818284590452353602874713526624977 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:25:31 2004 Input: log(log(exp(exp(1)))) Output: ? 1.0000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:25:54 2004 Input: Pi Output: ? 3.1415926535897932384626433832795028842 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.004s sys 0m0.006s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:27:26 2004 Input: exp(Pi*sqrt(163)) Output: ? 262537412640768743.99999999999925007254 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.004s sys 0m0.004s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:27:57 2004 Input: p exp(Pi*sqrt(163)) Output: ? p ? 262537412640768743.99999999999925007254 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:28:12 2004 Input: p exp(Pi*sqrt(163)) q Output: ? p ? 262537412640768743.99999999999925007254 ? q ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:29:09 2004 Input: p sqr(log%/ Pi) q Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:29:42 2004 Input: p sqr(log(%)/ Pi) q Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:30:32 2004 Input: p sqr(log(%)/Pi) q Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:30:44 2004 Input: p sqrt(log(%)/Pi) q Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:31:03 2004 Input: p sqrt(log(%1)/Pi) q Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:32:46 2004 Input: Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:32:56 2004 Input: Input: L2 (x) =2 { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } Output: ? ? ? Errors (if any) and Timing Info: *** log is not analytic at 0. Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:45:47 2004 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.004s '207.218' ************** PARI ***************** Host 207.218.212.20 (207.218.212.20) Time: Fri Dec 10 20:46:13 2004 Input: 1000! Output: ? 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 22:29:01 2004 Input: gcd (244,568) gcd (568,892) Output: ? 4 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 22:31:18 2004 Input: gcd (244,2453) gcd (568,2453) gcd (892, 2453) Output: ? 1 ? 1 ? 223 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 22:31:32 2004 Input: lcm(244,2453) lcm(568,2453) lcm(892, 2453) Output: ? 598532 ? 1393304 ? 9812 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 22:40:15 2004 Input: gcd(244,568) gcd(568,892) gcd(892, 244) Output: ? 4 ? 4 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 10 22:40:53 2004 Input: gcd(244,568) gcd(568,892) gcd(892, 244) 892-568 Output: ? 4 ? 4 ? 4 ? 324 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Sat Dec 11 00:19:47 2004 Input: 9685995879751900266965751728317768534339466701207000659149731241881949753354635345084281976035888903045502320103446579505659387331923629334860466271399373437326209341972131575136093644025636838290584602169614758827377791986085345002050945133029449449670916412840913242228973349825383725536735884300286184121884036574524080954143407325374149139116277633621883265159497956689114320097584920869431906969366010597089073562607735421643706791927168419061098028425335805093731827233045382848003600234506105049739615913373130832311018452678801463727615407195189081346113083644772821388561006232108341355292189777868977995775680888853220589875078882125907087578737872571758277286558270158228271350034202047428787094010669970312848571162948469362025657801196589040534326720408822433215072639664264027121362230601587800736610522156690101146287031324186123308142390705299484158749451511117464259062850764304908544549382915990412266525961996719142422326551346787151644403530860708140786692361664163200758137417585725510911037474307939694726849939529029385963251870007674827522475410130915290139159058716474399566900514/(2*2789*59369*433494437*68541957733949701*257*5417*8513*39639893*1473869*952077737766937*13812722702652253529*425523658238268276603571021441*210571059848182798945692173671950856913747637637506204222980261300245334254344826561899602272351391100242409883004854300985262242101935161886021098015750729481776536284383546045113241911825894461066651342314487406759013903505804344325933698066893610891623385384370339503798955797053) Output: ? 1206496190850610537943692909309853797278439778920640332016002933495589769027622043124132642680978237361203459501129069858954948643681836009664941311707074615084430065652525726684246006387151927485591411763714182719156958183307180849318159827108232154115459511073856868742727877151753766356262608059818179326802990685942224909033008318383119670412819245301065036972351542195850206883164326422533820946577306820841107428687955605658229445444038102229871873516246204174938524649513937017253258406054659382072520075875162235779396983412281315424320191203907505628448887588135001938755574328923547674897904165808967054463604931403658605053050532394775883540794764633202270330217944492385274788584634376652601 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Sat Dec 11 00:31:21 2004 Input: 99981574752650161914958921024273402872845480621960394266147080899657971111785111927606850897792735478775284955262549505300398640291210654967460001872790687629215395177034019951360995694068358061645115986733036012412635288455933219247679529558331267245294374481643865292416241614199920238820227887866308113356198763322605245112053311294745403550125908095040680569103588852972530371120322127362257296295288369702743335875244213988613984280194196465285935591591792611177114408698411561987947079752437982919217219443708194832343522852274563959274554162006880661385997388853256566370298923040685773228305074070308741137287971805202504985261071018580403040056644751554934363747785673000122311324192259191849454329188591718621975063212701788288426978530278562811025435428513003799527077988933294060028215109228177902916590932656089598599944597416932668798030197616705144633702249468274503381472951108296656787730883003079916180362964437619043442374083399981024469605334796278641581775953995095549620244475198042604065364584949843280539814915721150870806814501032047908079102640417274490170006531507203309320144985400286215993347551457266909216820583817039516860867898198827812186973767716811044927557582450909863238541109659851179628872882194615562031961917308605501276623534459708821986863602888915348905454769980633780769102552750423167526436012972550873774523544078900514388435252965621001206196439566175440745057884088673006979091619194431344482933493816317593874926856442485002403223738907217201477594721914829118579615882323521288807663727724635962224336369354193651983357422984978463341030358799695648267245992429406999052036066182786908942844791762780416542652864730581848048962582383265855823780589025731823922982399014530985806488396598966901314110882434386703126647359804947206655137193644324902900935855741933239066011190617332115109700595468247812951312444105916866665373643988803421996067088700811435271635971310805491260777187735392274143755338044242229394910263485953968748598392385312771698327889909897378609583525940112698118359888422651377507515819247745805173009610257179644597749976278380675309102189330248168278504138091843991019801971561661835564936136666935584742512899980710260792662076567529644612799896188596858401681790524617294045529710520712200526461892209392254445317005953933670070076319993696928810312602997294894590677970148810042679011598675319203318437153803641351642349892833787679607919210217237086833797712429666742624566617406493290778525764108374811899771896624793937783211885852035751605247751099546748957742945465167212456748446002159739804205707143464996799530868362907063243628110443107749114527015624270466814012939157577542971135316448932454683836540410859891842880585705686484610234042154681710985071271751859693559048207687581029633858001272034759110415778955766092460721471553859668322574216566881000013239654323103056115863802171102025923196506410603217066092243430078731110183174750904275883736654183477145982674483281800605619862119534676160961989005212682413435506134435499162315468039215645415002182427115262180962205250153764187327477671089668830066580885385635219779462215292308008005344003211473074811046429666775806489714385048074046076890937679346655377519119675479368793094526847691424117146055479657391717506808666446803844692980038286845692137093632061913690517025681889167639048053909757409971155892709728256496673641570206976978056300888341971178363064171159775191385156127206262213561214800326044084745856289976032415398292357166707793075603315552467200683004721614154314886251784016187373536433812555874586161652738134982690440675820599813756714098323506037801934421317762212221116308791041590776364341187596635877642563610351830606418236794069765959622442184458620362982813394909628661150140186353832183329252516508857970179534646689096712013602993800621691257223089673776919055463142809881899827729354922461745594379574519493726860694619197996817900503102249761097467164857782921036741787936402823790433674542434295423274968903611841232137993981063115430524297919928186434704822198167435595249882254401194251584413232447547555416457056120090307243673748535118613947025447984066440561094243707738919412212352762309985208244318176154821819485657978950656709126901214515315590297519589337494867143317701368052857286101098056729991705657654291524156975065931034486497224459943868455884684104874085952025990033411636972717095185690830205551583813260649294255560827766651189397978538842267734353374810578600608011404728576184955994601081275695018594487332814296045585692025301695790121020255398435489294348866596838778474803512339450001169724410094299893459893814811940290238975740274415918628516389339076321251859913398109301753394692540867327120676286501694528983663330282413190384613970384946297930000501825168526273887136028230418054551017915933097602958721549428890578566940703130345292644051600846049183448367029543093353013870524864221530037590614145978745184827001984795392532148269049806862806505101838134445103621306631695968821700942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Output: ? 3803472231079082629443862290567020650995621652431243645353399412674706754939889792723069585841731599669236070435750490079938721347663142894119289234639423292143673480969676530142895483389187201361896156771182915251520522590120570291915017912471405411056792123295449230616417815499143388466081416070928408143667256771814468425781792934971057480193990596743645331010722505388393831386222936796703604478954101047466892070037510078399133563201336948563325140705977091065076202218025682943387824830564357522779307890593314799292247737847221747405194380345943327209408742136849580039661804965365583537873898219914015804878188155909952866908912267999194542222375887399684134166460651929008413734665339335268297897348992624641060769919785192230365960570939126150101029747795375064017705550024665396784684933765172872441305976391242020316730641123743769789516536611958736517159702238253807840636944675628097172449828042312987936069861333928245839147099837284836183741535861390369930941249844939407462823322883444909048523467972517406781416270604106879912375962124633500699207565438379727092908093656899722305826569701895849310758409853998310488036323646891539555369069815652861572083606983405369891474391975851863263968414154863061009322020831266060010983178566566391412798187274508116175593359867780824088648409059922580532235040529031939038887374732327775460058965947997121633055627389173979247996074806219856932008818825406053242458666918595252774043492945741367965433127511463857558866117965947425278052247207797685982219237942387619438516313340382072061755449980600271106577984400219753229366038918179974939954804608328390932300867126835861811309636283671228301399158117216994326010146832978623122297496031755704805982989722928317247074397491166704122428384647003198972402003363571620868695207676094915433795899644664309519166290578188147224597410909554765297507869179353376461212655697337055061099776215924596586761201347376671396797940241992966963818874521651776076288630489314535346903794016742779197406187507495071246277270726829515585494892708912357657221829437342855726598444528988019759288720388471836752666667316114159639782223259731674990578567672696292047602107838934314607650721291703213656901482161968790815158687935838959958522223608898422069577126340411258433543613716104425626062418644856740683274720182795667889488790034195130251254449615399380650820089609627358439634143824618781656847949942355389193351253492366775760009042976570010048437789824992961497727710096706596116194184469283767293041575389963348160500177480280841285668713266975956046135380727490938804689688459630274938472333466262371607363769497287304368141882492849880047576385119923421291296733957633812508506935985162062708627619900470399761062588966237655825879195293872296924554357740911559451071971204827505370538378378050919134614546017987669493682754957520482636465633202493311458947298698379997839658399244393862750575651293049492399143581800837405362202446340328664646573452476676292179102191402372572894331600433301591250094055513847662637650162075334078918247851035640356836046481051171507398895111964046801192493548280796167742682599587374937404579556383502522672851119260947556021208147330137380066932[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.012s sys 0m0.008s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Sat Dec 11 02:36:44 2004 Input: 20288869671821835462512605667060214418686361772761974176470598239533689067460333749150271823067571291914004695680154816686078997121458423266892977137981460330939159899781654113069224554335035630114843221128455570860034903306276233066560102037984505579797757966025368442834307032190389350061708464820201013147701846029484527480818442557275885015330412535428131032557469476203067887887228508791324323816107982485576970747784587482214513284784452047539505352169525157008906400969131877999716991951699486373541311651792222185775228493041339760836125129031405609577797628073039419969777542029870111330536923415257531161481083675687727768130392809292304144395260728629172142069661825738754627195682541715233449015837548827864897880094425591274261664126392724201488549160960591283083679716901772184497109267306901132367517155410402132488404723844524503769343469744333194745065971613130739260295972644059153892192460207324310326237648290499740692771404479859784103051199965799605530181698611826931339751597342565644666153711741251040089555412027456665586464822724695397979890453145815841191002829725823085300037091992647609787014878405373739750442206425821225693523088079884203763083130632494322490257758477406260630567124089686257034093121266609297550167481312490453406500738808581529795364665304177295609707014164287631696920376618613135816468552048800371265318042043563851917841747673447215023738786838376998018554821892102902466965949503239677417738686192056756698732672114342491281495810512534567802384981894553122093777838271808285077563236830880835056588923986963048987474994334479753342505276018827289370062391327245068483412538253583917532497606780093433287686190484476196068588241177780584626056149958423712042351538503213921173099257199725302430272016538226296824419742892960259402501761902086950367785967758443944085071170472428493779331218530053347509661391568179932649973781207141145254213195453046742745029999016160348706368177640438744687513467352056389373581463970014404785762508358278428099370153826784717530519049765220653894273664893665049833209263517100898668219462538683220325649545072317430524880889988935043000962971922402028589719941174783528538139473097667852675270002927854643444082942030928904952369045825698375523623657647144529877793579341317626051161117764936065892997665145780587907672691678426321632795737617892292139599828458431214768655637164925170759092130368511309868267274978645445957893231474295501875692173066391796832288199407485846831556316274484932608290740779994204794038330727373640506678599782126263085705244097177483177487277787759842445830067988536217777335264671437284309370304155513960697052340622262754899288532716251932619560717312083058438147566548181658350442180079452603112679698956633271440368270551279645865022565421923555636720937862295278188562422707900145536112869890722095619971689640986265340048546885321997816204667962300195395629670086798250850000515642240803579783166991850036191214560387851647544994314622903903436620941300166296927506397676145309335877196734020767324709861105814495778606522351891569085750125626149028130426963789459941769116640704895983679162459596754690072704602739297792945093321475509903781374153584010780406802089493333524150275534794643305107107086448534643833049685151629897486581543238066552721942142282339767457497705341144993441910143801527786851115289002711265838163309724009682907061112622673180086644187256507753631973246649856537802567323541567694760746164220402543718850143962069791001452552860434143183162318060944130468986653483385597550770705822789479281857134176466449845261145303978294900753215235560938395674608374035178803976005371307055828193569460779217352187828455721128733113682174524714575601622471398362132423906720176516262029480848613172691691938900923051169655982596916605889417319852975375470451044855769091379666354558724714253876154824443189013575591458973285285854696396359680786782907962592938133209736657404412577336585695005603286706928925509502327650015380000697478341015674298516808231951740424047188484080512073600774533306684083766512714265931020026203640841281022929421805891953032634059688884786150125823205239295181653938296781584818672522290628221976697140527014424784980003139881001285654801/592369 Output: ? 3425039067172967434574159969049733260634226600777889149579164041253625538720009613796513967318946685581791872241821367540515961693042414992495045678957112936520844254135792742879729451462692279662650007196267119120013860162546695229925958657185724705343756672956445803685592431776542889661968885073358162420332908377967876016607628447348845907758578273918474976333580838329329841346732950034745964730785706626372577016654245492626135615601838051542114012071787206455588729486035204070388050683222701791204690260934016159821872598505549709865999930622872839324440952864353033323785941200479787316780068405885103906767755178898242103845811109172205862291115964648584267925847204316693585787859010467332599953042368663428521391243367831752549789763879055825252258163570441951399158247123291763157273467603284630419133539299052133465526508619547022847134720038410719457815309648737651575334963957273110829937498452370787520318863460191154616931575501057581356055296608330214027098261153407239632686990261571021553483337538130969056374559105465793379880585028030737256657666614190790063457545841497965845619384537787698172425444006248426192194764821559066341000809981596640567464389701772767057401342487099470200258137088484754778540592310976654340481605437234300479346613142919621012471055255115864538776845878884214348981863773866143538312867832178991686823254093911709072865350427427366223374077110445853516736159706551643058121871587344995672923243146089136450208007528135755125858343450203263135374231584460551125021369833973129093109740184054336917797677458976254494660421854364383237898214798348206838990965315073048806303594255199701120838127380077862495789987403877683685099699879261167384865877511892707424316859677534428907167535303117702383188859737465379995310312135334607213156286352271464301438118429297269790463574304602113510215966488802308613324024648180430213257915455930534051277699449675243428509931987690164189275295911912801765033866956585572400578265231640144029441531943480909382390056506465516853602914697632835934067053625977228692455085177836939250402951967216923965577122549005337977659345777536475237725635865887990186812601803062538474859331446727943676200139259119677674571583258227372626246317046587241318101328335403191233469945142523937959474772948100941455916441465670990194907682825810655458471955422699751698620256707969393193880104658570109299962038926498738095387718631232465905186333429719567005648873095383417571190963640481835955554108380837777231470711799569897275859866186004608699421914344289836754743284016749269995136017885432870802798604921685000021495936598883007772076240342677277287814240890772939654048157941460801058050086569702847116940212358881315252898477145065424273160766170517577969199649298204268937946206743081348895151660175042123775647007643529648839846931539415819467252960509578702690392060841354290622264951062986110919989005178663679370460053723648739819231453197559297699780805610666940293127141127051534336979305348552388279519420779302311453819696293023565940268626667805792635773736024655505113493468703822959697490409489601910594429593835075094017270056265056863217471643981926433176802520299932964719857749744502291714590[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.006s '133.80.' ************** PARI ***************** Host 133.80.131.20 (133.80.131.20) Time: Sat Dec 11 04:04:43 2004 Input: [1,2,-1]-4/11*[-1,3,1]-25/198*[13,5,-2] Output: ? [-5/18, 5/18, -10/9] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.004s sys 0m0.005s '68.163.' ************** PARI ***************** Host 68.163.139.136 (68.163.139.136) Time: Sat Dec 11 15:53:40 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.006s sys 0m0.004s '68.163.' ************** PARI ***************** Host 68.163.139.136 (68.163.139.136) Time: Sat Dec 11 15:53:52 2004 Input: 34 Output: ? 34 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '24.0.23' ************** PARI ***************** Host 24.0.232.184 (24.0.232.184) Time: Sun Dec 12 00:44:57 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '24.0.23' ************** PARI ***************** Host 24.0.232.184 (24.0.232.184) Time: Sun Dec 12 00:45:22 2004 Input: hello Output: ? hello ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '24.0.23' ************** PARI ***************** Host 24.0.232.184 (24.0.232.184) Time: Sun Dec 12 00:45:40 2004 Input: stop the cazy kids Output: ? stopthecazykids ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '24.0.23' ************** PARI ***************** Host 24.0.232.184 (24.0.232.184) Time: Sun Dec 12 00:47:47 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '24.0.23' ************** PARI ***************** Host 24.0.232.184 (24.0.232.184) Time: Sun Dec 12 00:48:06 2004 Input: 4+4 Output: ? 8 ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '66.32.2' ************** PARI ***************** Host 66.32.248.212 (66.32.248.212) Time: Sun Dec 12 15:17:47 2004 Input: 34223^2003 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.004s sys 0m0.002s '66.32.2' ************** PARI ***************** Host 66.32.248.212 (66.32.248.212) Time: Sun Dec 12 15:17:55 2004 Input: 3422^2003 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.003s '66.32.2' ************** PARI ***************** Host 66.32.248.212 (66.32.248.212) Time: Sun Dec 12 15:17:58 2004 Input: 3422^200 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.005s '66.32.2' ************** PARI ***************** Host 66.32.248.212 (66.32.248.212) Time: Sun Dec 12 15:18:02 2004 Input: 322^200 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.001s sys 0m0.005s '66.32.2' ************** PARI ***************** Host 66.32.248.212 (66.32.248.212) Time: Sun Dec 12 15:18:06 2004 Input: 22^200 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.004s sys 0m0.002s '66.32.2' ************** PARI ***************** Host 66.32.248.212 (66.32.248.212) Time: Sun Dec 12 15:18:09 2004 Input: 22^20 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.002s '69.225.' ************** PARI ***************** Host 69.225.32.205 (69.225.32.205) Time: Sun Dec 12 20:13:00 2004 Input: Hello tigertony, I am speachless, in a trance of unbelief. Please browse this absolutely marvelous creation for Your enjoyment by Your fellow members, Ms Chandra and her husband Mr Grizz and the Elves leader Ms Jennifer (simplyjen239) and all of the TEAMS members and helpers. (Kangaroos and Joeys). Final decission will be made on the weekend. I still cannot believe that those members would go to such lenghts as they did, to crerate this masterpiece, without expecting a reward. Welcome to BGPayMail. This is a paid email. Thank You. ----------------------------------------------------------------------CQ3 Your Paid Link-- To All BG Elves Presents: Happy Holidays Bill and Fellow BG'ers! Team Elf is herebye submitting our final answer for the Christmas Wishes Stocking contest. Bill rewards his members with bonus's for their work, support of their advertisers, and much more. If you visited our site last time, you will be pleased to see many new additions. Please use the checklist so you don't miss anything. Although the timer on this ad is for 45 seconds or so, you could spend a good hour or more in here reading and looking at our creation. So grab a cup of Coffee, a bar of chocolate and put on some music... relax and enjoy! Team BG Elves Presents: Bill's Christmas Gift http://www.grizzlygraphics.net/BGELVES/page1.htm http://www.bgpaymail.com/scripts/runner.php?EA=200412121845048067 AOL Users *****************************************************1 To Complain, go ahead, send a note....and WAIT Your complaint will be solved, guaranteed!!! nothappy@bgpaymail.com ------------------------------------------------------------------------ UNSUBSCRIBE INFO : Log IN to your account and choose account information. and DELETE YOUR ACCOUNT there. Alternatively, you may email TO: nothappy@bgpaymail.com and your request will be processed within 48 hours. ------------------------------------------------------------------------ BGPayMail is owned and operated by Bill, ALL THE INFO IS ON THE SITE, and ANYONE can contact me at nothappy@bgpaymail.com Output: WARNING: PARI command contains unsafe command 'read', so it will not be executed. '12.219.' ************** PARI ***************** Host 12.219.73.164 (12.219.73.164) Time: Sun Dec 12 23:18:50 2004 Input: (14x+9x)/(7x+3x) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.005s '81.49.2' ************** PARI ***************** Host 81.49.247.100 (81.49.247.100) Time: Mon Dec 13 05:14:32 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '81.49.2' ************** PARI ***************** Host 81.49.247.100 (81.49.247.100) Time: Mon Dec 13 05:16:10 2004 Input: 1+2 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.004s '219.165' ************** PARI ***************** Host 219.165.143.227 (219.165.143.227) Time: Mon Dec 13 11:52:18 2004 Input: factor(x^15-1) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.178s user 0m0.000s sys 0m0.009s '219.165' ************** PARI ***************** Host 219.165.143.227 (219.165.143.227) Time: Mon Dec 13 11:52:34 2004 Input: factor(x^10-1) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.001s sys 0m0.007s '219.165' ************** PARI ***************** Host 219.165.143.227 (219.165.143.227) Time: Mon Dec 13 11:52:41 2004 Input: factor(x^2-1) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.001s sys 0m0.005s '219.165' ************** PARI ***************** Host 219.165.143.227 (219.165.143.227) Time: Mon Dec 13 11:52:47 2004 Input: factor(10) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.004s sys 0m0.004s '128.119' ************** PARI ***************** Host 128.119.47.38 (128.119.47.38) Time: Mon Dec 13 12:55:43 2004 Input: S6:= Sym(6); S6; gens := { S6 | (1,2), (2,3), (5,4), (6,3)}; gens; H := sub; H; Order(H); Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.004s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 13 14:36:47 2004 Input: 4*16 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.003s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 13 14:37:36 2004 Input: 4*16 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.004s sys 0m0.002s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 13 14:38:55 2004 Input: 4*4 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.003s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 13 14:39:34 2004 Input: 4+5 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.003s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 13 14:40:40 2004 Input: prime(3) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.004s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 13 14:42:16 2004 Input: prime(3) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.004s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 13 14:44:17 2004 Input: divrem(26, 3) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.003s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 13 14:44:28 2004 Input: divrem(26,3) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.004s sys 0m0.001s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Mon Dec 13 16:29:04 2004 Input: Mod(3.10600)^-1 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Mon Dec 13 16:29:21 2004 Input: Mod(3.10600)^(-1) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.001s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Mon Dec 13 16:29:30 2004 Input: Mod(3,10600)^(-1) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Mon Dec 13 16:29:44 2004 Input: Mod(3,10600) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Mon Dec 13 16:30:01 2004 Input: Mod(3,5) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Mon Dec 13 16:30:12 2004 Input: 10*2 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.004s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Mon Dec 13 16:30:18 2004 Input: 10*2 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Mon Dec 13 16:30:26 2004 Input: 20*3 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Mon Dec 13 16:31:11 2004 Input: 10*2 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.005s sys 0m0.001s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Mon Dec 13 16:33:12 2004 Input: 10*2 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Mon Dec 13 16:37:57 2004 Input: 10*8 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Mon Dec 13 16:53:48 2004 Input: 10*8 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Mon Dec 13 16:53:52 2004 Input: 10 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.004s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Mon Dec 13 16:53:58 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Mon Dec 13 16:54:08 2004 Input: 1/1 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.001s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Mon Dec 13 16:54:28 2004 Input: 1 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.003s '66.243.' ************** PARI ***************** Host 66.243.235.218 (66.243.235.218) Time: Mon Dec 13 18:02:24 2004 Input: 2+2 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 13 19:32:06 2004 Input: gcd(248,870) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.004s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 13 19:32:13 2004 Input: gcd(248,870) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 13 19:32:20 2004 Input: 1 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 13 19:32:49 2004 Input: --help Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 13 19:33:10 2004 Input: GCD(240,870) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 13 19:34:12 2004 Input: GCD(248,870) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Tue Dec 14 00:07:44 2004 Input: 1 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Tue Dec 14 00:07:49 2004 Input: 1*8 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.005s '132.77.' ************** PARI ***************** Host 132.77.4.43 (132.77.4.43) Time: Tue Dec 14 05:29:35 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.002s '212.138' ************** PARI ***************** Host 212.138.47.13 (212.138.47.13) Time: Tue Dec 14 14:22:29 2004 Input: 2410312426921032588580116606028314112912093247945688951359675039065257391591803200669085024107346049663448766280888004787862416978794958324969612987890774651455213339381625224770782077917681499676845543137387820057597683303280706012438932581187337633431914898423998167651676144654423917749992451544062530082617210605384471605940230305042798096660131146255586264079933020977903380408326503642260167962931947410634244152286818827827000403499805688783516991211156053 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.002s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Tue Dec 14 21:50:34 2004 Input: -I Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.005s sys 0m0.001s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Tue Dec 14 22:04:37 2004 Input: 6 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.004s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Tue Dec 14 22:15:07 2004 Input: 5 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Tue Dec 14 22:15:13 2004 Input: 5*7 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.007s user 0m0.002s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Tue Dec 14 22:35:36 2004 Input: lcm(248,2047) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Tue Dec 14 22:36:09 2004 Input: LCM(248^2-1,2047^2-1) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Tue Dec 14 22:36:38 2004 Input: LCM(248^2-1,2047^2-1) 248^2-1 2047^2-1 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Tue Dec 14 22:37:35 2004 Input: LCM(248^2-1,2047^2-1) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.003s '140.142' ************** PARI ***************** Host 140.142.174.171 (140.142.174.171) Time: Tue Dec 14 22:47:40 2004 Input: S3 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.004s sys 0m0.004s '133.11.' ************** PARI ***************** Host 133.11.72.233 (133.11.72.233) Time: Tue Dec 14 23:40:30 2004 Input: cos(x+y); Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.004s '133.11.' ************** PARI ***************** Host 133.11.72.233 (133.11.72.233) Time: Tue Dec 14 23:40:53 2004 Input: (x+y)^2 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.004s '133.11.' ************** PARI ***************** Host 133.11.72.233 (133.11.72.233) Time: Tue Dec 14 23:41:01 2004 Input: (x+y)^2; Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.004s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Dec 15 03:29:39 2004 Input: GCD(7747872,2047) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.004s sys 0m0.002s '195.241' ************** PARI ***************** Host 195.241.144.218 (195.241.144.218) Time: Wed Dec 15 07:39:10 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.007s user 0m0.003s sys 0m0.003s '80.163.' ************** PARI ***************** Host 80.163.33.124 (80.163.33.124) Time: Wed Dec 15 09:51:45 2004 Input: 2 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.263s user 0m0.004s sys 0m0.007s '217.224' ************** PARI ***************** Host 217.224.248.93 (217.224.248.93) Time: Wed Dec 15 11:58:42 2004 Input: solve((x² Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.004s '66.81.1' ************** PARI ***************** Host 66.81.121.161 (66.81.121.161) Time: Wed Dec 15 13:46:41 2004 Input: 1+3 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.240s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Wed Dec 15 15:47:25 2004 Input: 4 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Wed Dec 15 15:48:57 2004 Input: 4 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 01:44:55 2004 Input: 8*10 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 01:45:16 2004 Input: 41234559767*16031980213 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 01:46:19 2004 Input: 41234559766*16031980212 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 01:54:34 2004 Input: gcd( 5673, 661071646219043350392) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 01:57:53 2004 Input: GCD( 5673, 661071646219043350392) Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.004s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 02:02:28 2004 Input: 5675 div 1917 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.003s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 02:04:43 2004 Input: 1841- 76 * 24 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 02:17:53 2004 Input: (172811141519290705^5675) mod 661071646276309890371 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.004s '64.12.1' ************** PARI ***************** Host 64.12.116.139 (64.12.116.139) Time: Thu Dec 16 02:24:18 2004 Input: 8*9 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.004s sys 0m0.002s '65.96.1' ************** PARI ***************** Host 65.96.160.100 (65.96.160.100) Time: Thu Dec 16 02:47:59 2004 Input: 2+2 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] Options are: [-b buffersize] Deprecated [-emacs] Run as if in Emacs shell [-f] Faststart: do not read .gprc [--help] Print this message [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [-test] Test mode. As -q, plus wrap long lines [--version] Output version info and exit Errors (if any) and Timing Info: Timing: real 0m0.006s user 0m0.002s sys 0m0.004s '65.96.1' ************** PARI ***************** Host 65.96.160.100 (65.96.160.100) Time: Thu Dec 16 02:49:22 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.069s user 0m0.006s sys 0m0.009s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 03:47:18 2004 Input: (172811141519290705 mod 661071646276309890371)^138748739489387 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (172811141519290705 *** mod66107164627630989 ^-------------------- Timing: real 0m0.215s user 0m0.007s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 03:47:46 2004 Input: Mod(172811141519290705, 661071646276309890371)^138748739489387 Output: ? Mod(576841257919349360124, 661071646276309890371) ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.006s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 03:48:15 2004 Input: Mod(576841257919349360124, 661071646276309890371)^4959246619467 Output: ? Mod(218876460241420747658, 661071646276309890371) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 03:48:55 2004 Input: isprime(41234559767) isprime(16031980213) Output: ? 1 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.007s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 03:49:15 2004 Input: eulerphi(41234559767 * 16031980213) Output: ? 661071646219043350392 ? Errors (if any) and Timing Info: Timing: real 0m0.047s user 0m0.017s sys 0m0.009s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 03:50:00 2004 Input: gcd(138748739489387,661071646219043350392 ) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 03:50:14 2004 Input: bezout(138748739489387,661071646219043350392 ) Output: ? [-23628447644297655349, 4959246619467, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 03:50:32 2004 Input: bezout(661071646219043350392,138748739489387 ) Output: ? [4959246619467, -23628447644297655349, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 03:51:27 2004 Input: Mod(172811141519290705,661071646276309890371)^138748739489387 Output: ? Mod(576841257919349360124, 661071646276309890371) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 03:51:56 2004 Input: Mod(576841257919349360124,661071646276309890371)^-23628447644297655349 Output: ? Mod(172811141519290705, 661071646276309890371) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 03:52:23 2004 Input: Mod(576841257919349360124,661071646276309890371)^-23628447644297655349 -23628447644297655349 + 661071646276309890371 Output: ? Mod(172811141519290705, 661071646276309890371) ? 637443198632012235022 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 03:52:36 2004 Input: Mod(576841257919349360124,661071646276309890371)^ 637443198632012235022 -23628447644297655349 + 661071646276309890371 Output: ? Mod(486768848156742935253, 661071646276309890371) ? 637443198632012235022 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Dec 16 06:43:51 2004 Input: Mod(35^-1, 257) Output: ? Mod(235, 257) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Dec 16 06:44:51 2004 Input: Mod(35^-1, 257) Output: ? Mod(235, 257) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Dec 16 06:45:04 2004 Input: Mod(35, 257) Output: ? Mod(35, 257) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Dec 16 06:48:27 2004 Input: 35 + 257 Output: ? 292 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Dec 16 06:48:48 2004 Input: 5+6 Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Dec 16 06:51:51 2004 Input: 5+6 Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Dec 16 07:07:03 2004 Input: 2+6 Output: ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '80.58.5' ************** PARI ***************** Host 80.58.55.107 (80.58.55.107) Time: Thu Dec 16 08:17:50 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.393s user 0m0.006s sys 0m0.008s '24.177.' ************** PARI ***************** Host 24.177.6.36 (24.177.6.36) Time: Thu Dec 16 10:42:40 2004 Input: primes(300-500) Output: ? [] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.011s sys 0m0.002s '24.177.' ************** PARI ***************** Host 24.177.6.36 (24.177.6.36) Time: Thu Dec 16 10:42:49 2004 Input: primes(300) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '24.177.' ************** PARI ***************** Host 24.177.6.36 (24.177.6.36) Time: Thu Dec 16 10:43:15 2004 Input: 1301*1748 Output: ? 2274148 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '24.177.' ************** PARI ***************** Host 24.177.6.36 (24.177.6.36) Time: Thu Dec 16 10:48:50 2004 Input: primes(200) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '24.177.' ************** PARI ***************** Host 24.177.6.36 (24.177.6.36) Time: Thu Dec 16 10:49:30 2004 Input: primes(300) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '24.177.' ************** PARI ***************** Host 24.177.6.36 (24.177.6.36) Time: Thu Dec 16 10:49:50 2004 Input: primes(300) 1301*1747 Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987] ? 2272847 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.6.36 (24.177.6.36) Time: Thu Dec 16 10:49:56 2004 Input: 1301*1747 Output: ? ? 2272847 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '24.177.' ************** PARI ***************** Host 24.177.6.36 (24.177.6.36) Time: Thu Dec 16 10:50:08 2004 Input: 1300*1746 Output: ? 2269800 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.240.34 (140.247.240.34) Time: Thu Dec 16 11:13:55 2004 Input: factor(98098098098098328409328408324082308423894293840928342) Output: ? [2 1] [29148503 1] [1211090351 1] [1456136987 1] [954191534111726099778896761 1] ? Errors (if any) and Timing Info: Timing: real 0m0.387s user 0m0.318s sys 0m0.019s '140.247' ************** PARI ***************** Host 140.247.240.34 (140.247.240.34) Time: Thu Dec 16 11:14:13 2004 Input: factor(980980980980983284093284083240823084987987987987987987987987987987987987987987987987987987987987987987667687623894293840928342) Output: ? [2 1] [59 1] [3251 1] [123057780511 1] [20780334440171022699202817836976631086417793574774835718750244024644053753536298135935557560140012280091493429 1] ? Errors (if any) and Timing Info: Timing: real 0m7.006s user 0m6.998s sys 0m0.007s '130.34.' ************** PARI ***************** Host 130.34.108.100 (130.34.108.100) Time: Thu Dec 16 11:27:16 2004 Input: 1000! Output: ? 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '130.34.' ************** PARI ***************** Host 130.34.108.100 (130.34.108.100) Time: Thu Dec 16 11:27:39 2004 Input: 10! Output: ? 3628800 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '210.136' ************** PARI ***************** Host 210.136.161.233 (210.136.161.233) Time: Thu Dec 16 11:36:57 2004 Input: 10! Output: ? 3628800 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.008s sys 0m0.003s '67.169.' ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Dec 16 11:54:24 2004 Input: 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577093565086451991485204835850923810886856444151959519096476989697984530772874385934959102191740255674075576673757973410921270882212818568614971212311992961545684969524419262432065062483932805080688114700940498009515050746962157746562583674264775859470661647242923485286534469447682691123169606469061326764392862248786254254300973551931824906194721544791424768639405086225685216734905537653497501445885879065476800289681763707292630539398178292966891297476273692535432308002159873408493908140943158079334312089560544050504837771485283683185602911305436885032951937845774693721167760286817378508982712021831896598727004137367817076937578034580097676266758525928898817936850213652800890178157124419730169294122623110721902113264208497972136333187400702936143841019036909304429544068424594815250798142423431198921707277266808760182502588228602652309034254773478544705374894867354234153137421680355629328431501159761882067477285429828936757897415215969633806691250666490516781996948396522156669609575415351070379317308756132809150792669173534318221167665669457372313090355388762487722722996156646219260899987117328852953279556217421969907479682815822418132560218368821677449046164554080720858117312421687579120381860423682790070049669959342805248684325015164462104155682430419087805115912503692437656982759087251935714913071967124027543355016438651861876586119945862054492130897413136165411348879166740123152696350695850519940324513970633793516303485004447438466003130492113272973873278700683223489713155627298449969587875112880340600970955573546980185113948292747778810100955261909718537371506614003000522770346729442646304423929467908317958947999489260602961399567319163125982609563197067075541775364172671935280320762207846406862575255446955046217657010125000976366061127328468341463352463465737806573828548463119158465373469001814233127201/49363 Output: ? 7546300746332845304701080966110072434168838711994862153669099944306125170659824474349986176182904899426752316419701311671768874613714047551064406650984502649658558194569498344371714414880805813556812314614670541770606468546211662139486412971560321769036512792286130276312194853012711615001210801984164158438242561669934553982554906304591807835182002116293446051540610543324382326632498058757056210734263807430893290002744757951834572556929661661828058815290679885294285381688500706720098056954592597634977479846475048910394153324692771698339464376145246118303498520639341693020303913879653584345219992873214797469816855650739792643636816795765001167113869564736059003949445583924167880649816176073366307180024690258413628379262521748285366998683094130953421139789589484888413244993204523692483099315123336869509451854373000781837284040764532695597860065498078350246923500752929499966386597300258230195549380507267671880906203648805891322773330131143106710836687350762774240953483620958217885426460606121253723933883802305240433942958312533817741420810221115200561862432190438676962886747255146749910891027271647244808478689146897347911323172248398620990697623746276941654506704490845582930396592236169800166534344243206025415498391181228945066477151959164991973043386617946682713393338614279735174013022667958266052232792634929350497072682143839393319737879937810774062347375102898151339098039174766273689013675829932409665968892351424654956756382282261182715429363240059837350170529634017222314726198367000111342082453284343414544525777505703576295341112304705371370142214471456100253385645077241266375358355791481940631267198917206321579133583800827359616063373154023030512308885879535777986026908239917765005339565293341684900444205197333725543551448663051256438522743121082605906142257173521612221076159938474142463210885052562739720017083558808928753661608158332573165991692697277592469451072652300852944657534498646749139825816764335791383225336413790992587178944484157303153532543598624124004258306931062103566717263858137573025207581897770466655999757972539720780404384079717896948755686551064934600443608453030606771133944526002138981805549130560185477879357736310713492107445596186585215145671208464767586544331292831756046376796491874079699327076383035649226807639752239515438724242537696574262544255303335109536104254613731963168540442901403924970418553265414857849382638175438932793413393066580096796660138802045379282860202546534706267792224709798068035388269348247490398208198718749687154521589674261997387934787440905081116378419712703229877484204634200376675854859037367314498465905500090432505432329689185207300551937905232140399160403013899312631560437291797251527909127863609900436618376908994955029937247424984788274692212733945553597035724179803726730705492015080350840835436765607836794843046732706122226125867188058687622266051447988375616070091828003360847453397467251581473806703028635979942768645806544083915988947026341235419376298863147292535857992342976589341591538195595977037955043266475876763827802603075120176707033873777794065100374333732554820145791066357646239299746436038243734736571583664355894567681201161311162530355567937250187692896405434822546878[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.115s user 0m0.071s sys 0m0.032s '211.127' ************** PARI ***************** Host 211.127.183.55 (211.127.183.55) Time: Thu Dec 16 11:56:35 2004 Input: 10I Output: ? 10 ? Errors (if any) and Timing Info: *** Warning: unused characters: I. Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '211.127' ************** PARI ***************** Host 211.127.183.55 (211.127.183.55) Time: Thu Dec 16 11:57:19 2004 Input: 10! Output: ? 3628800 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:16:43 2004 Input: isprime(101) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.004s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:16:47 2004 Input: isprime(107) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:16:54 2004 Input: 101*107 Output: ? 10807 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:17:10 2004 Input: prime(100) Output: ? 541 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:17:15 2004 Input: prime(101) Output: ? 547 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:17:20 2004 Input: 541*547 Output: ? 295927 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.008s sys 0m0.003s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:17:29 2004 Input: prime(300) Output: ? 1987 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:17:36 2004 Input: prime(500) Output: ? 3571 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:17:40 2004 Input: prime(501) Output: ? 3581 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:17:48 2004 Input: 3571*3581 Output: ? 12787751 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:17:59 2004 Input: prime(1000) Output: ? 7919 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:18:04 2004 Input: prime(1001) Output: ? 7927 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:18:04 2004 Input: prime(1001) Output: ? 7927 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:18:12 2004 Input: 7919*7927 Output: ? 62773913 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:18:19 2004 Input: prime(5000) Output: ? 48611 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:18:24 2004 Input: prime(5001) Output: ? 48619 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:18:32 2004 Input: 48611*48619 Output: ? 2363418209 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:19:30 2004 Input: 48610*48618 Output: ? 2363320980 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:19:59 2004 Input: factor(48610*48618) Output: ? [2 2] [3 2] [5 1] [37 1] [73 1] [4861 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:26:47 2004 Input: bezout(2363320980,7) Output: ? [-1, 337617283, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Thu Dec 16 12:27:20 2004 Input: -1*2363320980+337617283*7 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:05:20 2004 Input: isprime(567894239047686465486786756657) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:08:22 2004 Input: isprime(567894239047686465486786756657) ?isprime Output: ? 0 ? isprime(x,{flag=0}): if flag is omitted or 0 true(1) if x is a strong pseudoprime for 10 random bases, false(0) if not. If flag is 1 the primality is certified by Pocklington-Lehmer Test. If flag is 2 a primality certificate is output(see manual). ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:09:15 2004 Input: isprime(567894239047686465486786756657223987560423) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:09:27 2004 Input: isprime(567894239047686465486786756657223987560423341) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:09:34 2004 Input: isprime(567894239047686465486786756657223987560423341) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:10:11 2004 Input: isprime(5678942390476864654867867) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:10:20 2004 Input: isprime(56789423904768646548678679) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:10:25 2004 Input: isprime(56789423904768646548678671) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:10:31 2004 Input: isprime(5678942390476864654867671) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:12:57 2004 Input: isprime(567894239) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:13:05 2004 Input: isprime(567894238) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:13:10 2004 Input: isprime(567894237) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:13:17 2004 Input: isprime(567894231) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:13:23 2004 Input: isprime(567894233) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:18:17 2004 Input: ?isprime Output: ? isprime(x,{flag=0}): if flag is omitted or 0 true(1) if x is a strong pseudoprime for 10 random bases, false(0) if not. If flag is 1 the primality is certified by Pocklington-Lehmer Test. If flag is 2 a primality certificate is output(see manual). ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:20:03 2004 Input: isprime(4576896453,{flag=0}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: isprime(4576896453,{flag=0}) ^--------- Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '66.168.' ************** PARI ***************** Host 66.168.42.37 (66.168.42.37) Time: Thu Dec 16 14:25:02 2004 Input: isprime(7) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:25:14 2004 Input: isprime(19) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.37 (66.168.42.37) Time: Thu Dec 16 14:25:15 2004 Input: isprime(46789) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.002s sys 0m0.011s '66.168.' ************** PARI ***************** Host 66.168.42.37 (66.168.42.37) Time: Thu Dec 16 14:25:20 2004 Input: isprime(46781) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.37 (66.168.42.37) Time: Thu Dec 16 14:25:24 2004 Input: isprime(46783) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '66.168.' ************** PARI ***************** Host 66.168.42.37 (66.168.42.37) Time: Thu Dec 16 14:25:31 2004 Input: isprime(46787) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '66.168.' ************** PARI ***************** Host 66.168.42.37 (66.168.42.37) Time: Thu Dec 16 14:25:38 2004 Input: isprime(101) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:25:42 2004 Input: isprime(101) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.37 (66.168.42.37) Time: Thu Dec 16 14:25:46 2004 Input: isprime(9001) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:26:44 2004 Input: isprime(9001) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:27:47 2004 Input: isprime(5673) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:27:55 2004 Input: isprime(5677) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:28:01 2004 Input: isprime(5679) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:28:09 2004 Input: isprime(5671) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:28:34 2004 Input: isprime(5653) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:31:44 2004 Input: 5653*9001 Output: ? 50882653 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:34:06 2004 Input: gcd(50882653,4) Output: ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:35:10 2004 Input: gcd(50882653,9001) Output: ? 9001 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:35:20 2004 Input: divrem(50882653,9001) Output: ? [5653, 0]~ ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:38:13 2004 Input: 5652*9000 Output: ? 50868000 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:42:52 2004 Input: gcd(50868000,4) Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:54:40 2004 Input: gcd(50868000,3) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:54:59 2004 Input: gcd(50868000,7) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:55:28 2004 Input: gcd(50882653,7) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:55:31 2004 Input: gcd(50882653,7) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:56:41 2004 Input: bezout(50868000,7) Output: ? [1, -7266857, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:57:14 2004 Input: gcd(50868000,9) Output: ? 9 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:57:21 2004 Input: gcd(50868000,11) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:57:36 2004 Input: bezout(50868000,11) Output: ? [-3, 13873091, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:58:03 2004 Input: bezout(50868000,7) Output: ? [1, -7266857, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.010s '68.118.' ************** PARI ***************** Host 68.118.205.174 (68.118.205.174) Time: Thu Dec 16 14:58:17 2004 Input: bezout(50868000,11) Output: ? [-3, 13873091, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:34:56 2004 Input: isprime 2571 Output: ? isprime2571 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:35:09 2004 Input: isprime 2571? Output: ? isprime2571 ? Errors (if any) and Timing Info: *** Warning: unused characters: ?. Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:36:15 2004 Input: isprime (2571) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:36:26 2004 Input: factor (2571) Output: ? [3 1] [857 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:36:37 2004 Input: isprime 4751 Output: ? isprime4751 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:36:45 2004 Input: isprime (4751) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:36:51 2004 Input: factor (4751) Output: ? [4751 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:37:29 2004 Input: isprime (8967 Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: isprime(8967 ^ Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:37:32 2004 Input: isprime (8967) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:37:38 2004 Input: factor (8967) Output: ? [3 1] [7 2] [61 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:37:56 2004 Input: isprime (13951) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:38:11 2004 Input: isprime (19761) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:38:17 2004 Input: isprime (19763) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:38:26 2004 Input: factor(19763) Output: ? [19763 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:38:56 2004 Input: 19763 * 4571 Output: ? 90336673 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:39:34 2004 Input: isprime (1379845521) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:39:43 2004 Input: isprime (1379845523) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:39:48 2004 Input: isprime (1379845527) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:39:52 2004 Input: isprime (1379845529) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:39:58 2004 Input: isprime (1379845531) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:40:07 2004 Input: isprime (1379845537) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:40:27 2004 Input: isprime (186645789137) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:40:32 2004 Input: isprime (186645789159) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:40:36 2004 Input: isprime (186645789161) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:40:41 2004 Input: isprime (186645789361) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:40:48 2004 Input: isprime (186645789371) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:40:56 2004 Input: isprime (186645789379) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:41:00 2004 Input: isprime (186645789381) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:41:05 2004 Input: isprime (186645789383) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.003s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:41:09 2004 Input: isprime (186645789387) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:41:18 2004 Input: isprime (186645789391) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:41:39 2004 Input: isprime (186645789389) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:41:54 2004 Input: isprime (186235789389) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:42:08 2004 Input: isprime (1862357571943581389) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.004s sys 0m0.007s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:42:16 2004 Input: isprime (1862357571943581381) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:42:28 2004 Input: isprime (1862357571943581379) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:42:37 2004 Input: factor (1862357571943581379) Output: ? [223 1] [1019 1] [8195661674567 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:43:06 2004 Input: factor (8195661674567) Output: ? [8195661674567 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:43:53 2004 Input: 8195661674567 * 4571 Output: ? 37462369514445757 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:44:51 2004 Input: 8195661674566 * 4570 Output: ? 37454173852766620 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:46:01 2004 Input: factor (37454173852766620) Output: ? [2 2] [5 1] [193 1] [457 1] [5897 1] [3600523 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:47:27 2004 Input: mod((13,37454173852766620)**-1) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: mod((13,37454173852766620)* ^-------------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:48:51 2004 Input: mod((13,37454173852766620)^-1) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: mod((13,37454173852766620)^ ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:50:43 2004 Input: mod((13^-1,37454173852766620) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: mod((13^-1,37454173852766620) ^------------------- Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:50:56 2004 Input: mod(13^-1,37454173852766620) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13^-1,3745417385 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:51:08 2004 Input: mod(13,37454173852766620)^-1 Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,3745417385276 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:55:40 2004 Input: bezout(13,37454173852766620) Output: ? [-2881090296366663, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:56:17 2004 Input: 13*-2881090296366663 Output: ? -37454173852766619 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:57:26 2004 Input: 13*2881090296366663 Output: ? 37454173852766619 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:58:46 2004 Input: mod(-2881090296366663, 37454173852766620) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(-288109029636666 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:59:24 2004 Input: 37454173852766620-2881090296366663 Output: ? 34573083556399957 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 17:59:39 2004 Input: 34573083556399957*3 Output: ? 103719250669199871 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 18:01:44 2004 Input: mod(103719250669199871,3745417385276620 Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(1037192506691998 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 18:01:51 2004 Input: mod(103719250669199871,3745417385276620) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(1037192506691998 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 18:01:59 2004 Input: Mod(103719250669199871,3745417385276620) Output: ? Mod(2592981266731131, 3745417385276620) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:19:46 2004 Input: factor( 661071646276309890371) Output: ? [16031980213 1] [41234559767 1] ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.012s sys 0m0.012s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:20:40 2004 Input: eulerphi(16031980213,41234559767) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: eulerphi(16031980213,41234559767) ^------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:21:30 2004 Input: eulerPhi(16031980213,41234559767) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: eulerPhi(16031980213 ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:22:02 2004 Input: eulerphi(16031980213,41234559767) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: eulerphi(16031980213,41234559767) ^------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:22:24 2004 Input: euler(16031980213,41234559767) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: euler(16031980213,41 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: euler ===> Euler Euler=Euler(): Euler's constant with current precision. Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 18:22:41 2004 Input: Mod(13,37454173852766620)^-1 Output: ? Mod(34573083556399957, 37454173852766620) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:23:44 2004 Input: eulerphi(3,4) (16031980213,41234559767) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: eulerphi(3,4) ^--- *** expected character: ')' instead of: (16031980213,41234559767) ^------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:23:57 2004 Input: eulerphi(3 4) (16031980213,41234559767) Output: ? 16 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (16031980213,41234559767) ^------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:24:09 2004 Input: eulerphi(16031980213 41234559767) Output: ? 1005928170253323645312 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 18:24:18 2004 Input: Mod(13*34573083556399957,37454173852766620) Output: ? Mod(1, 37454173852766620) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:24:36 2004 Input: eulerphi(16031980213 41234559767) Output: ? 1005928170253323645312 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:25:01 2004 Input: 16031980212 * 41234559766 eulerphi(16031980213 41234559767) Output: ? 661071646219043350392 ? 1005928170253323645312 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:26:08 2004 Input: 16031980212 * 41234559766 eulerphi(16031980213 * 41234559767) Output: ? 661071646219043350392 ? 661071646219043350392 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.017s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:27:04 2004 Input: gcd(5797,661071646219043350392) Output: ? 31 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:27:10 2004 Input: gcd(5799,661071646219043350392) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:27:21 2004 Input: gcd(5801,661071646219043350392) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:27:52 2004 Input: bezout(5801,661071646219043350392) Output: ? [167404628218544161649, -1469, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:29:06 2004 Input: (5801,661071646219043350392) Mod(172811141519290705,661071646276309890371)^5801 Output: ? ? Mod(93404254218449475291, 661071646276309890371) ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (5801,6610716462190433503 ^-------------------- Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:29:22 2004 Input: Mod(172811141519290705 661071646276309890371)^5801 Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...0705661071646276309890371)^5801 ^------ Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:29:30 2004 Input: Mod(172811141519290705, 661071646276309890371)^5801 Output: ? Mod(93404254218449475291, 661071646276309890371) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 18:30:00 2004 Input: Mod(93404254218449475291, 661071646276309890371)^167404628218544161649 Output: ? Mod(172811141519290705, 661071646276309890371) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.172 (68.118.194.172) Time: Thu Dec 16 19:39:38 2004 Input: Mod(407584658818048296306,661071646276309890371)^167404628218544161649 Output: ? Mod(1930290905, 661071646276309890371) ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.29.200 (140.247.29.200) Time: Thu Dec 16 19:46:59 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.29.200 (140.247.29.200) Time: Thu Dec 16 19:47:04 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '66.81.6' ************** PARI ***************** Host 66.81.66.65 (66.81.66.65) Time: Thu Dec 16 20:35:58 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '66.81.6' ************** PARI ***************** Host 66.81.66.65 (66.81.66.65) Time: Thu Dec 16 20:36:44 2004 Input: 2E2e2e2 Output: ? 200.00000000000000000000000000000000000 ? Errors (if any) and Timing Info: *** Warning: unused characters: e2e2. Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 20:43:29 2004 Input: Mod(23147356346213112,37462369514445757)^34573083556399957 Output: ? Mod(30291167479490441, 37462369514445757) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 20:46:15 2004 Input: Mod(34573083556399957*13, 37454173852766620) Output: ? Mod(1, 37454173852766620) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 20:48:10 2004 Input: Mod(23147356346213112,37454173852766620)^34573083556399957 Output: ? Mod(18380938370685332, 37454173852766620) ? Errors (if any) and Timing Info: Timing: real 0m0.050s user 0m0.006s sys 0m0.005s '66.168.' ************** PARI ***************** Host 66.168.42.182 (66.168.42.182) Time: Thu Dec 16 20:49:03 2004 Input: Mod(23147356346213112,37462369514445757)^34573083556399957 Output: ? Mod(30291167479490441, 37462369514445757) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '64.252.' ************** PARI ***************** Host 64.252.112.144 (64.252.112.144) Time: Thu Dec 16 21:11:03 2004 Input: Mod(3162290551924525524,21881344711792705537)^1497144637470988273 Output: ? Mod(162673592347393697, 21881344711792705537) ? Errors (if any) and Timing Info: Timing: real 0m0.073s user 0m0.007s sys 0m0.006s '64.252.' ************** PARI ***************** Host 64.252.112.144 (64.252.112.144) Time: Thu Dec 16 21:14:12 2004 Input: 1497144637470988273 - 21881344701499059376 Output: ? -20384200064028071103 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '64.252.' ************** PARI ***************** Host 64.252.112.144 (64.252.112.144) Time: Thu Dec 16 21:14:46 2004 Input: bezout(19,21881344701499059376) Output: ? [-6909898326789176645, 6, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '64.252.' ************** PARI ***************** Host 64.252.112.144 (64.252.112.144) Time: Thu Dec 16 21:15:21 2004 Input: -6909898326789176645 + 21881344701499059376 Output: ? 14971446374709882731 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '64.252.' ************** PARI ***************** Host 64.252.112.144 (64.252.112.144) Time: Thu Dec 16 21:17:56 2004 Input: Mod(19*14971446374709882731,21881344701499059376) Output: ? Mod(1, 21881344701499059376) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '64.252.' ************** PARI ***************** Host 64.252.112.144 (64.252.112.144) Time: Thu Dec 16 21:19:49 2004 Input: Mod(3162290551924525524^14971446374709882731,21881344711792705537) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m4.328s user 0m4.232s sys 0m0.026s '64.252.' ************** PARI ***************** Host 64.252.112.144 (64.252.112.144) Time: Thu Dec 16 21:19:59 2004 Input: Mod(3162290551924525524,21881344711792705537)^14971446374709882731 Output: ? Mod(1930290907, 21881344711792705537) ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.007s sys 0m0.012s '144.16.' ************** PARI ***************** Host 144.16.64.4 (144.16.64.4) Time: Fri Dec 17 01:16:14 2004 Input: prime(40) Output: ? 173 ? Errors (if any) and Timing Info: Timing: real 0m0.393s user 0m0.007s sys 0m0.008s '144.16.' ************** PARI ***************** Host 144.16.64.4 (144.16.64.4) Time: Fri Dec 17 01:16:23 2004 Input: Prime(40) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Prime(40) ^--------- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '144.16.' ************** PARI ***************** Host 144.16.64.4 (144.16.64.4) Time: Fri Dec 17 01:16:45 2004 Input: nextprime(40) Output: ? 41 ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.007s sys 0m0.006s '211.8.1' ************** PARI ***************** Host 211.8.159.203 (211.8.159.203) Time: Fri Dec 17 04:48:33 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.326s user 0m0.005s sys 0m0.010s '211.8.1' ************** PARI ***************** Host 211.8.159.203 (211.8.159.203) Time: Fri Dec 17 04:51:36 2004 Input: 1000! Output: ? 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.011s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 17 05:26:46 2004 Input: gcd(54005, 256) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.006s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Fri Dec 17 05:27:16 2004 Input: Mod(54005, 257) Output: ? Mod(35, 257) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '151.37.' ************** PARI ***************** Host 151.37.64.135 (151.37.64.135) Time: Fri Dec 17 05:38:10 2004 Input: 1+2 Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.006s sys 0m0.006s '151.37.' ************** PARI ***************** Host 151.37.64.135 (151.37.64.135) Time: Fri Dec 17 05:38:40 2004 Input: a = 12 b = 20 a+b Output: ? 12 ? 20 ? 32 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '151.37.' ************** PARI ***************** Host 151.37.64.135 (151.37.64.135) Time: Fri Dec 17 05:38:58 2004 Input: a = [1,0,1,0] Output: ? [1, 0, 1, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.004s '151.37.' ************** PARI ***************** Host 151.37.64.135 (151.37.64.135) Time: Fri Dec 17 05:44:00 2004 Input: a = [1,0,1,0; 1,1,1,1] Output: ? ? 1 ? Errors (if any) and Timing Info: *** unexpected character: a=[1,0,1,0; ^ *** Warning: unused characters: ,1,1,1]. Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '151.37.' ************** PARI ***************** Host 151.37.64.135 (151.37.64.135) Time: Fri Dec 17 05:44:09 2004 Input: a = [1,0,1,0;1,1,1,1] Output: ? [1 0 1 0] [1 1 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '151.37.' ************** PARI ***************** Host 151.37.64.135 (151.37.64.135) Time: Fri Dec 17 05:44:21 2004 Input: a = [1,0,1,0;1,1,1,1] Sum(a) Output: ? [1 0 1 0] [1 1 1 1] ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: Sum(a) ^ Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '151.37.' ************** PARI ***************** Host 151.37.64.135 (151.37.64.135) Time: Fri Dec 17 05:44:28 2004 Input: a = [1,0,1,0;1,1,1,1] sum(a) Output: ? [1 0 1 0] [1 1 1 1] ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: sum(a) ^- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '151.37.' ************** PARI ***************** Host 151.37.64.135 (151.37.64.135) Time: Fri Dec 17 05:44:36 2004 Input: a = [1,0,1,0;1,1,1,1] a' Output: ? [1 0 1 0] [1 1 1 1] ? [0 0 0 0] [0 0 0 0] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Fri Dec 17 12:25:05 2004 Input: (2243440904)^337617283 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m5.251s user 0m4.864s sys 0m0.015s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Fri Dec 17 12:27:22 2004 Input: Mod(2243440904,2363418209)^337617283 Output: ? Mod(1930290809, 2363418209) ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.005s sys 0m0.009s '69.37.5' ************** PARI ***************** Host 69.37.52.82 (69.37.52.82) Time: Fri Dec 17 12:27:32 2004 Input: lift(Mod(2243440904,2363418209)^337617283) Output: ? 1930290809 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '145.254' ************** PARI ***************** Host 145.254.200.99 (145.254.200.99) Time: Fri Dec 17 13:51:33 2004 Input: Mod(3, 2) Output: ? Mod(1, 2) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.006s sys 0m0.008s '145.254' ************** PARI ***************** Host 145.254.200.99 (145.254.200.99) Time: Fri Dec 17 13:51:57 2004 Input: Mod(54005, 257) Output: ? Mod(35, 257) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '145.254' ************** PARI ***************** Host 145.254.200.99 (145.254.200.99) Time: Fri Dec 17 13:52:17 2004 Input: Mod(54005, 256) Output: ? Mod(245, 256) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '145.254' ************** PARI ***************** Host 145.254.200.99 (145.254.200.99) Time: Fri Dec 17 13:52:34 2004 Input: Mod(54005, 256)-256 Output: ? Mod(245, 256) ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.007s sys 0m0.006s '145.254' ************** PARI ***************** Host 145.254.200.99 (145.254.200.99) Time: Fri Dec 17 13:54:14 2004 Input: Mod(2*54004+1, 256) Output: ? Mod(233, 256) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '145.254' ************** PARI ***************** Host 145.254.200.99 (145.254.200.99) Time: Fri Dec 17 13:56:09 2004 Input: Mod(202^-11*49, 257) Output: ? Mod(12, 257) ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.009s sys 0m0.005s '145.254' ************** PARI ***************** Host 145.254.200.99 (145.254.200.99) Time: Fri Dec 17 13:56:23 2004 Input: Mod(202^-23*53, 257) Output: ? Mod(46, 257) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '220.214' ************** PARI ***************** Host 220.214.79.117 (220.214.79.117) Time: Fri Dec 17 17:42:56 2004 Input: a:=3; IsInteger(a); Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: a:=3; ^--- *** expected character: '=' instead of: IsInteger(a); ^- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s 'form' ************** PARI ***************** Host form (140.247.29.178) Time: Fri Dec 17 20:00:09 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.004s sys 0m0.009s '82.225.' ************** PARI ***************** Host 82.225.97.169 (82.225.97.169) Time: Fri Dec 17 22:07:22 2004 Input: p := 11685037692629544436418522744508054167282745075683333963951114538336503311896091970659888174669185217769701714376736146487719134933981559784973709552957801; K := GF(p); E := EllipticCurve([K | 1, 0]); time SEA(E : MaxSmooth := 1); Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: p:=1168503769262954443 ^-------------------- *** unexpected character: K:=GF(p); ^------- *** unexpected character: E:=EllipticCurve([K|1, ^-------------------- *** expected character: ',' instead of: timeSEA(E:MaxSmooth:=1); ^--------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '213.41.' ************** PARI ***************** Host 213.41.184.45 (213.41.184.45) Time: Sat Dec 18 00:14:18 2004 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '213.41.' ************** PARI ***************** Host 213.41.184.45 (213.41.184.45) Time: Sat Dec 18 00:14:35 2004 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '213.41.' ************** PARI ***************** Host 213.41.184.45 (213.41.184.45) Time: Sat Dec 18 00:14:53 2004 Input: 2+3^30 Output: ? 205891132094651 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '213.41.' ************** PARI ***************** Host 213.41.184.45 (213.41.184.45) Time: Sat Dec 18 00:15:06 2004 Input: 2+3^300 Output: ? 136891479058588375991326027382088315966463695625337436471480190078368997177499076593800206155688941388250484440597994042813512732765695774566003 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '213.41.' ************** PARI ***************** Host 213.41.184.45 (213.41.184.45) Time: Sat Dec 18 00:16:12 2004 Input: 2+3^3000+4^20+5^15+45^7 Output: ? 2310809578111909272693109431184832846484968454396283812529115413319435556973292122101720139716262409469889717513948376726158501486182636383531313869623735751595188198743086350673413093292498741784795660389148326466211372843337723144590341000538769498117226562808444716579845071408688720747381120135479199680471885180482121554984483377022066232113498842614313541610752653690490275184816645775562870080222550532658199952189433551842563700110684899935346509404097452154895288699360903786484615575470777362920177718027703180305669825349020152868844727956235156059960772077214312800556301983539901820176796454299860300131486822074451633519214994291242241850066416567586776526981799888092096865174444248800546127994730384671200620078154936387315118122040519117349396356198197315367766646921156257797160661163192060277301722871797101013527586327674333920080776435765228230385762165404932957246335621254520607306174400378047735376342518713628466946614321497738427647167939078993913147690702992638955965837451910388196619417991842556404018337740923222175380153877003983519741457506625666074023573361964063311318755920947209571433341645962479076131201964416276406387762072361807631460445372486964777059883706070699922193176468574966898852772974365576953262531708962699524486008324366541931862849776343129934761158587798436540362085500749517170402734545433993099089688531543345393342814833105525138762128016370025483881594201769799957464319029 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '213.41.' ************** PARI ***************** Host 213.41.184.45 (213.41.184.45) Time: Sat Dec 18 00:16:32 2004 Input: 2+3^3000+4^20+5^15+45^ Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 2+3^3000+4^20+5^15+45^ ^ Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '133.80.' ************** PARI ***************** Host 133.80.131.20 (133.80.131.20) Time: Sat Dec 18 03:35:42 2004 Input: Matdet([x,2,1;-1,x-3,-1;1,1,x-1]) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Matdet([x,2,1;-1,x-3 ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '133.80.' ************** PARI ***************** Host 133.80.131.18 (133.80.131.18) Time: Sat Dec 18 03:35:58 2004 Input: ([x,2,1;-1,x-3,-1;1,1,x-1]) Output: ? [x 2 1] [-1 x - 3 -1] [1 1 x - 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '133.80.' ************** PARI ***************** Host 133.80.131.20 (133.80.131.20) Time: Sat Dec 18 03:36:11 2004 Input: ?Matdet ([x,2,1;-1,x-3,-1;1,1,x-1]) Output: ? ? ? [x 2 1] [-1 x - 3 -1] [1 1 x - 1] ? Errors (if any) and Timing Info: *** Matdet: unknown identifier. Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '133.80.' ************** PARI ***************** Host 133.80.131.19 (133.80.131.19) Time: Sat Dec 18 03:36:20 2004 Input: ?det ([x,2,1;-1,x-3,-1;1,1,x-1]) Output: ? ? ? [x 2 1] [-1 x - 3 -1] [1 1 x - 1] ? Errors (if any) and Timing Info: *** obsolete function: det ^--- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: det(x) ===> matdet(x) matdet(x,{flag=0}): determinant of the matrix x using Gauss-Bareiss. If (optional) flag is set to 1, use classical gaussian elimination (slightly better for integer entries). Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '133.80.' ************** PARI ***************** Host 133.80.131.20 (133.80.131.20) Time: Sat Dec 18 03:36:37 2004 Input: matdet([x,2,1;-1,x-3,-1;1,1,x-1]) Output: ? x^3 - 4*x^2 + 5*x - 2 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.005s sys 0m0.007s '133.80.' ************** PARI ***************** Host 133.80.131.20 (133.80.131.20) Time: Sat Dec 18 03:36:55 2004 Input: factor(x^3 - 4*x^2 + 5*x - 2) Output: ? [x - 2 1] [x - 1 2] ? Errors (if any) and Timing Info: Timing: real 0m0.043s user 0m0.003s sys 0m0.008s '193.249' ************** PARI ***************** Host 193.249.119.115 (193.249.119.115) Time: Sat Dec 18 08:55:32 2004 Input: 1550880802783769298423921500751307878471020215206711102793111990113875394553459999757605304671735856091597555389797408938173344043674704780986390069906679096728933081405044935969514508676239942493440750589270015739962374529363251827 Output: ? 1550880802783769298423921500751307878471020215206711102793111990113875394553459999757605304671735856091597555389797408938173344043674704780986390069906679096728933081405044935969514508676239942493440750589270015739962374529363251827 ? Errors (if any) and Timing Info: Timing: real 0m0.434s user 0m0.008s sys 0m0.003s '219.116' ************** PARI ***************** Host 219.116.197.203 (219.116.197.203) Time: Sat Dec 18 09:02:49 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '130.104' ************** PARI ***************** Host 130.104.220.180 (130.104.220.180) Time: Sat Dec 18 09:17:43 2004 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.009s sys 0m0.003s '129.79.' ************** PARI ***************** Host 129.79.94.191 (129.79.94.191) Time: Sat Dec 18 17:35:16 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(3*x^7+2*x^5 + 7*x^4 + 8*x^3 - x + 1); OrdK := MaximalOrder(K); I := (5*x^3+7*x+9)*OrdK; Factorization(I); Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: R:=PolynomialRing(Rat ^-------------------- *** unexpected character: K:=NumberField(3*x^7+ ^-------------------- *** unexpected character: OrdK:=MaximalOrder(K); ^----------------- *** unexpected character: I:=(5*x^3+7*x+9)*OrdK; ^-------------------- *** unknown function or error in formal parameters: Factorization(I); ^--- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '129.79.' ************** PARI ***************** Host 129.79.94.191 (129.79.94.191) Time: Sat Dec 18 17:37:50 2004 Input: R := PolynomialRing(RationalField()); K := NumberField(3*x^7+2*x^5 + 7*x^4 + 8*x^3 - x + 1); OrdK := MaximalOrder(K); I := 37*OrdK; Factorization(I); Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: R:=PolynomialRing(Rat ^-------------------- *** unexpected character: K:=NumberField(3*x^7+ ^-------------------- *** unexpected character: OrdK:=MaximalOrder(K); ^----------------- *** unexpected character: I:=37*OrdK; ^--------- *** unknown function or error in formal parameters: Factorization(I); ^--- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '213.140' ************** PARI ***************** Host 213.140.6.103 (213.140.6.103) Time: Sun Dec 19 10:05:52 2004 Input: P2 := PolynomialRing(Integers(),2); P2!ClassicalModularPolynomial(5); Output: ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,Y>:=PolynomialRing(Integers(),2);. *** incorrect type in comparison. *** Warning: unused characters: ClassicalModularPolynomial(5);. *** this should be an integer: P2!ClassicalModularP ^-------------------- Timing: real 0m0.345s user 0m0.010s sys 0m0.009s '213.140' ************** PARI ***************** Host 213.140.6.103 (213.140.6.103) Time: Sun Dec 19 10:06:09 2004 Input: P2 := PolynomialRing(Integers(),2); P2!ClassicalModularPolynomial(5); Output: ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,Y>:=PolynomialRing(Integers(),2);. *** incorrect type in comparison. *** Warning: unused characters: ClassicalModularPolynomial(5);. *** this should be an integer: P2!ClassicalModularP ^-------------------- Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '213.140' ************** PARI ***************** Host 213.140.6.103 (213.140.6.103) Time: Sun Dec 19 10:18:49 2004 Input: P2 := PolynomialRing(Integers(),2); P2!ClassicalModularPolynomial(1); Output: ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,Y>:=PolynomialRing(Integers(),2);. *** incorrect type in comparison. *** Warning: unused characters: ClassicalModularPolynomial(1);. *** this should be an integer: P2!ClassicalModularP ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '62.2.24' ************** PARI ***************** Host 62.2.249.226 (62.2.249.226) Time: Mon Dec 20 02:58:12 2004 Input: 3x^3+2x^2-16x+22,x=0,x Output: ? 3 ? Errors (if any) and Timing Info: *** Warning: unused characters: x^3+2x^2-16x+22,x=0,x. Timing: real 0m0.019s user 0m0.008s sys 0m0.004s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 16:11:50 2004 Input: sqrt(42025) Output: ? 205.00000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.200s user 0m0.005s sys 0m0.008s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 16:12:21 2004 Input: 205/5 Output: ? 41 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.004s sys 0m0.009s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 16:14:12 2004 Input: factor(48041) Output: ? [7 1] [6863 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.006s sys 0m0.004s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 16:14:20 2004 Input: factor(48841) Output: ? [13 2] [17 2] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 16:15:13 2004 Input: factor(198025) Output: ? [5 2] [89 2] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 16:16:03 2004 Input: factor(356409) Output: ? [3 2] [199 2] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 16:16:22 2004 Input: factor(638401) Output: ? [17 2] [47 2] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.008s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 16:27:31 2004 Input: issquare(Mod(5,41)) issquare(Mod(41,5)) Output: ? 1 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.006s sys 0m0.006s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 16:27:51 2004 Input: issquare(Mod(5,41)) issquare(Mod(41,5)) factor(48841) Output: ? 1 ? 1 ? [13 2] [17 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 16:28:08 2004 Input: issquare(Mod(13,17)) issquare(Mod(17,13)) factor(48841) Output: ? 1 ? 1 ? [13 2] [17 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 16:28:22 2004 Input: issquare(Mod(13,17)) issquare(Mod(17,13)) factor(198025) Output: ? 1 ? 1 ? [5 2] [89 2] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 16:28:35 2004 Input: issquare(Mod(5,89)) issquare(Mod(89,5)) factor(198025) Output: ? 1 ? 1 ? [5 2] [89 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 16:28:52 2004 Input: issquare(Mod(5,89)) issquare(Mod(89,5)) factor(356409) Output: ? 1 ? 1 ? [3 2] [199 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 16:29:05 2004 Input: issquare(Mod(3,199)) issquare(Mod(199,3)) factor(356409) Output: ? 0 ? 1 ? [3 2] [199 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:03:26 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) Output: ? 1 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.005s sys 0m0.008s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:04:18 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) Output: ? 1 ? 1 ? 1 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:04:50 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) Mod(54833,16) Mod(57793,16) Output: ? 1 ? 1 ? 1 ? 1 ? Mod(1, 16) ? Mod(1, 16) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:05:02 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) Mod(54833,32) Mod(57793,32) Output: ? 1 ? 1 ? 1 ? 1 ? Mod(17, 32) ? Mod(1, 32) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:05:10 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) Mod(54833,16) Mod(57793,16) Output: ? 1 ? 1 ? 1 ? 1 ? Mod(1, 16) ? Mod(1, 16) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:06:22 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) Mod(54833,16) Mod(57793,16) Mod(119513,16) Output: ? 1 ? 1 ? 1 ? 1 ? Mod(1, 16) ? Mod(1, 16) ? Mod(9, 16) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:06:34 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) Mod(54833,16) Mod(57793,16) Mod(119513,8) Output: ? 1 ? 1 ? 1 ? 1 ? Mod(1, 16) ? Mod(1, 16) ? Mod(1, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:06:47 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) Mod(54833,16) Mod(57793,16) Mod(119513,16) Output: ? 1 ? 1 ? 1 ? 1 ? Mod(1, 16) ? Mod(1, 16) ? Mod(9, 16) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:07:11 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) issquare(Mod(7,119513)) Mod(54833,16) Mod(57793,16) Mod(119513,16) Output: ? 1 ? 1 ? 1 ? 1 ? 1 ? Mod(1, 16) ? Mod(1, 16) ? Mod(9, 16) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:16:14 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) issquare(Mod(7,119513)) Mod(54833,16) Mod(57793,16) Mod(119513,16) Mod(54833,7) Mod(57793,7) Mod(119513,7) Output: ? 1 ? 1 ? 1 ? 1 ? 1 ? Mod(1, 16) ? Mod(1, 16) ? Mod(9, 16) ? Mod(2, 7) ? Mod(1, 7) ? Mod(2, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:16:39 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) issquare(Mod(7,119513)) Mod(54833,16) Mod(57793,16) Mod(119513,16) Mod(54833,7) Mod(57793,7) Mod(119513,7) Mod(953,7) Output: ? 1 ? 1 ? 1 ? 1 ? 1 ? Mod(1, 16) ? Mod(1, 16) ? Mod(9, 16) ? Mod(2, 7) ? Mod(1, 7) ? Mod(2, 7) ? Mod(1, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.005s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:17:07 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) issquare(Mod(7,119513)) Mod(54833,16) Mod(57793,16) Mod(119513,16) Mod(54833,7) Mod(57793,7) Mod(119513,7) Mod(953,7) Mod(113,7) Output: ? 1 ? 1 ? 1 ? 1 ? 1 ? Mod(1, 16) ? Mod(1, 16) ? Mod(9, 16) ? Mod(2, 7) ? Mod(1, 7) ? Mod(2, 7) ? Mod(1, 7) ? Mod(1, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:18:45 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) issquare(Mod(7,119513)) Mod(54833,16) Mod(57793,16) Mod(119513,16) Mod(54833,7) Mod(57793,7) Mod(119513,7) Mod(953,7) Mod(953,16) Output: ? 1 ? 1 ? 1 ? 1 ? 1 ? Mod(1, 16) ? Mod(1, 16) ? Mod(9, 16) ? Mod(2, 7) ? Mod(1, 7) ? Mod(2, 7) ? Mod(1, 7) ? Mod(9, 16) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:21:50 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) issquare(Mod(7,119513)) Mod(54833,16) Mod(57793,16) Mod(119513,16) Mod(54833,7) Mod(57793,7) Mod(119513,7) Mod(953,7) Mod(953,32) Output: ? 1 ? 1 ? 1 ? 1 ? 1 ? Mod(1, 16) ? Mod(1, 16) ? Mod(9, 16) ? Mod(2, 7) ? Mod(1, 7) ? Mod(2, 7) ? Mod(1, 7) ? Mod(25, 32) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.010s sys 0m0.006s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:22:10 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) issquare(Mod(7,119513)) Mod(54833,32) Mod(57793,32) Mod(119513,32) Mod(54833,7) Mod(57793,7) Mod(119513,7) Mod(953,7) Mod(953,32) Output: ? 1 ? 1 ? 1 ? 1 ? 1 ? Mod(17, 32) ? Mod(1, 32) ? Mod(25, 32) ? Mod(2, 7) ? Mod(1, 7) ? Mod(2, 7) ? Mod(1, 7) ? Mod(25, 32) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:22:34 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) issquare(Mod(7,119513)) Mod(54833,32) Mod(57793,32) Mod(119513,32) Mod(54833,7) Mod(57793,7) Mod(119513,7) Mod(953,7) Mod(953,32) sqrt(Mod(17,32)) Output: ? 1 ? 1 ? 1 ? 1 ? 1 ? Mod(17, 32) ? Mod(1, 32) ? Mod(25, 32) ? Mod(2, 7) ? Mod(1, 7) ? Mod(2, 7) ? Mod(1, 7) ? Mod(25, 32) ? ? Errors (if any) and Timing Info: *** composite modulus in mpsqrtmod: 32. Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:23:12 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) issquare(Mod(7,119513)) Mod(54833,32) Mod(57793,32) Mod(119513,32) Mod(54833,7) Mod(57793,7) Mod(119513,7) Mod(953,7) Mod(953,32) issquare(Mod(17,32)) Output: ? 1 ? 1 ? 1 ? 1 ? 1 ? Mod(17, 32) ? Mod(1, 32) ? Mod(25, 32) ? Mod(2, 7) ? Mod(1, 7) ? Mod(2, 7) ? Mod(1, 7) ? Mod(25, 32) ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '24.233.' ************** PARI ***************** Host 24.233.85.150 (24.233.85.150) Time: Mon Dec 20 17:24:47 2004 Input: issquare(Mod(7,54833)) issquare(Mod(54833,7)) issquare(Mod(7,57793)) issquare(Mod(57793,7)) issquare(Mod(7,119513)) Mod(54833,64) Mod(57793,64) Mod(119513,64) Mod(54833,7) Mod(57793,7) Mod(119513,7) Mod(953,7) Mod(953,64) issquare(Mod(17,64)) Output: ? 1 ? 1 ? 1 ? 1 ? 1 ? Mod(49, 64) ? Mod(1, 64) ? Mod(25, 64) ? Mod(2, 7) ? Mod(1, 7) ? Mod(2, 7) ? Mod(1, 7) ? Mod(57, 64) ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '213.140' ************** PARI ***************** Host 213.140.17.109 (213.140.17.109) Time: Mon Dec 20 18:20:37 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '66.169.' ************** PARI ***************** Host 66.169.67.211 (66.169.67.211) Time: Tue Dec 21 02:36:17 2004 Input: Mod(23026759675658040866,31999668921654488407)^-9142762539246047177 Output: ? Mod(1930290907, 31999668921654488407) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '66.169.' ************** PARI ***************** Host 66.169.67.211 (66.169.67.211) Time: Tue Dec 21 02:38:46 2004 Input: (Mod(23026759675658040866,31999668921654488407))^-9142762539246047177 Output: ? Mod(1930290907, 31999668921654488407) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '66.169.' ************** PARI ***************** Host 66.169.67.211 (66.169.67.211) Time: Tue Dec 21 02:38:54 2004 Input: (Mod(23026759675658040866,31999668921654488407))^-9142762539246047177 Output: ? Mod(1930290907, 31999668921654488407) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '217.25.' ************** PARI ***************** Host 217.25.80.204 (217.25.80.204) Time: Tue Dec 21 09:19:53 2004 Input: 1111111111111111111111111111111111111111111111/11 Output: ? 101010101010101010101010101010101010101010101 ? Errors (if any) and Timing Info: Timing: real 0m0.287s user 0m0.005s sys 0m0.007s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 12:50:48 2004 Input: f1:=j^7 - 98373700603090523199715*j^6 - 4546951697981923176956448676986*j^5 - 209903939873446020495519316596118272758*j^4 - 12543980353722772760179537174109237891242365*j^3 - 282310474518147042483634599702449209357160103606*j^2 + 904330206367752622526324160408849797910089300094965*j - 709822597815616788561460999971455889888479357689323263; f2:=j^7 + 313645809715*j^6 - 3091990138604570*j^5 + 98394038810047812049302*j^4 - 823534263439730779968091389*j^3 + 5138800366453976780323726329446*j^2 - 425319473946139603274605151187659*j + 737707086760731113357714241006081263; polgalois(f1); Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? -823534263439730779968091389*j^3 + 5138800366453976780323726329446*j^2 ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: f1:=j^7-983737006030905 ^-------------------- *** unexpected character: ...95519316596118272758*j^4- ^ *** unexpected character: ...37174109237891242365*j^3- ^ *** unexpected character: ...02449209357160103606*j^2+ ^ *** unexpected character: ...8849797910089300094965*j- ^ *** unexpected character: f2:=j^7+313645809715*j^ ^-------------------- *** unexpected character: ...6139603274605151187659*j+ ^ Timing: real 0m0.087s user 0m0.004s sys 0m0.007s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 12:52:32 2004 Input: f1:=j^2+1; polgalois(f1); Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: f1:=j^2+1; ^------- Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 12:56:04 2004 Input: f1:=j^2+1; polgalois(f1); Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: f1:=j^2+1; ^------- Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 12:56:15 2004 Input: f1:=j^2+1 polgalois(f1) Output: ? ? [1, -1, 1] ? Errors (if any) and Timing Info: *** unexpected character: f1:=j^2+1 ^------ Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 12:56:35 2004 Input: f1=j^2+1 polgalois(f1) Output: ? j^2 + 1 ? [2, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 12:57:50 2004 Input: f1=j^7 - 98373700603090523199715*j^6 - 4546951697981923176956448676986*j^5 - 209903939873446020495519316596118272758*j^4 - 12543980353722772760179537174109237891242365*j^3 - 282310474518147042483634599702449209357160103606*j^2 + 904330206367752622526324160408849797910089300094965*j - 709822597815616788561460999971455889888479357689323263 f2=j^7 + 313645809715*j^6 - 3091990138604570*j^5 + 98394038810047812049302*j^4 - 823534263439730779968091389*j^3 + 5138800366453976780323726329446*j^2 - 425319473946139603274605151187659*j + 737707086760731113357714241006081263 polgalois(f1) polgalois(f2) Output: ? ? ? ? ? ? ? ? ? ? ? 709822597815616788561460999971455889888479357689323263 ? ? j^7 + 313645809715*j^6 - 3091990138604570*j^5 + 98394038810047812049302*j^4 ? ? -823534263439730779968091389*j^3 + 5138800366453976780323726329446*j^2 ? ? ? ? 737707086760731113357714241006081263 ? ? [1, -1, 1] ? ? ? Errors (if any) and Timing Info: *** unexpected character: ...81923176956448676986*j^5- ^ *** unexpected character: ...95519316596118272758*j^4- ^ *** unexpected character: ...37174109237891242365*j^3- ^ *** unexpected character: ...02449209357160103606*j^2+ ^ *** unexpected character: ...8849797910089300094965*j- ^ *** unexpected character: ...6139603274605151187659*j+ ^ *** sorry, galois of reducible polynomial is not yet implemented. Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 12:59:11 2004 Input: f1=j^7 - 98373700603090523199715*j^6 - 4546951697981923176956448676986*j^5 - 209903939873446020495519316596118272758*j^4 - 12543980353722772760179537174109237891242365*j^3 - 282310474518147042483634599702449209357160103606*j^2 + 904330206367752622526324160408849797910089300094965*j - 709822597815616788561460999971455889888479357689323263 polgalois(f1) f2=j^7 + 313645809715*j^6 - 3091990138604570*j^5 + 98394038810047812049302*j^4 - 823534263439730779968091389*j^3 + 5138800366453976780323726329446*j^2 - 425319473946139603274605151187659*j + 737707086760731113357714241006081263 polgalois(f2) Output: ? ? ? ? ? ? ? ? ? ? ? 709822597815616788561460999971455889888479357689323263 ? ? ? [1, -1, 1] ? ? j^7 + 313645809715*j^6 - 3091990138604570*j^5 + 98394038810047812049302*j^4 ? ? -823534263439730779968091389*j^3 + 5138800366453976780323726329446*j^2 ? ? ? ? 737707086760731113357714241006081263 ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: ...81923176956448676986*j^5- ^ *** unexpected character: ...95519316596118272758*j^4- ^ *** unexpected character: ...37174109237891242365*j^3- ^ *** unexpected character: ...02449209357160103606*j^2+ ^ *** unexpected character: ...8849797910089300094965*j- ^ *** unexpected character: ...6139603274605151187659*j+ ^ *** sorry, galois of reducible polynomial is not yet implemented. Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 13:04:39 2004 Input: f2=j^7 + 313645809715 j^6 - 3091990138604570 j^5 + 98394038810047812049302 j^4 - 823534263439730779968091389 j^3 + 5138800366453976780323726329446 j^2 - 425319473946139603274605151187659 j + 737707086760731113357714241006081263 polgalois(f2) Output: ? j^7 + 313645809715 ? ? -823534263439730779968091389 ? ? -425319473946139603274605151187659 ? ? 737707086760731113357714241006081263 ? [42, -1, 1] ? Errors (if any) and Timing Info: *** Warning: unused characters: j^6-3091990138604570j^5+98394038810047812049302j^4. *** Warning: unused characters: j^3+5138800366453976780323726329446j^2. *** Warning: unused characters: j+. Timing: real 0m0.155s user 0m0.030s sys 0m0.013s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 13:05:20 2004 Input: f2=j^7+ 313645809715j^6 - 3091990138604570j^5 + 98394038810047812049302j^4 - 823534263439730779968091389j^3 + 5138800366453976780323726329446j^2 - 425319473946139603274605151187659j + 737707086760731113357714241006081263 polgalois(f2) Output: ? j^7 + 313645809715 ? ? -823534263439730779968091389 ? ? -425319473946139603274605151187659 ? ? 737707086760731113357714241006081263 ? [42, -1, 1] ? Errors (if any) and Timing Info: *** Warning: unused characters: j^6-3091990138604570j^5+98394038810047812049302j^4. *** Warning: unused characters: j^3+5138800366453976780323726329446j^2. *** Warning: unused characters: j+. Timing: real 0m0.040s user 0m0.032s sys 0m0.010s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 13:28:50 2004 Input: f = x^2+3*x+5 polgalois(f) Output: ? x^2 + 3*x + 5 ? [2, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 13:29:07 2004 Input: f = j^2+3*j+5 polgalois(f) Output: ? j^2 + 3*j + 5 ? [2, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 13:29:32 2004 Input: f2 =j^7 + 313645809715*j^6 - 3091990138604570*j^5 + 98394038810047812049302*j^4 - 823534263439730779968091389*j^3 + 5138800366453976780323726329446*j^2 - 425319473946139603274605151187659*j + 737707086760731113357714241006081263 polgalois(f2) Output: ? j^7 + 313645809715*j^6 - 3091990138604570*j^5 + 98394038810047812049302*j^4 ? ? -823534263439730779968091389*j^3 + 5138800366453976780323726329446*j^2 ? ? ? ? 737707086760731113357714241006081263 ? ? ? Errors (if any) and Timing Info: *** unexpected character: ...6139603274605151187659*j+ ^ *** sorry, galois of reducible polynomial is not yet implemented. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 13:30:39 2004 Input: f2 =j^7 + 313645809715*j^6 - 3091990138604570*j^5 + 98394038810047812049302*j^4-823534263439730779968091389*j^3 + 5138800366453976780323726329446*j^2- 425319473946139603274605151187659*j+737707086760731113357714241006081263 polgalois(f2) Output: ? j^7 + 313645809715*j^6 - 3091990138604570*j^5 + 98394038810047812049302*j^4 - 823534263439730779968091389*j^3 + 5138800366453976780323726329446*j^2 - 425319473946139603274605151187659*j + 737707086760731113357714241006081263 ? ? [14, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.160s user 0m0.149s sys 0m0.006s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 13:34:49 2004 Input: f1=j^7 - 98373700603090523199715*j^6 - 4546951697981923176956448676986*j^5- 209903939873446020495519316596118272758*j^4 - 12543980353722772760179537174109237891242365*j^3 - 282310474518147042483634599702449209357160103606*j^2 + 904330206367752622526324160408849797910089300094965*j - 709822597815616788561460999971455889888479357689323263 f2=j^7 + 313645809715*j^6 - 3091990138604570*j^5 + 98394038810047812049302*j^4 - 823534263439730779968091389*j^3 + 5138800366453976780323726329446*j^2 - 425319473946139603274605151187659*j + 737707086760731113357714241006081263 polgalois(f1) polgalois(f2) Output: ? ? ? ? ? 709822597815616788561460999971455889888479357689323263 ? ? ? j^7 + 313645809715*j^6 - 3091990138604570*j^5 + 98394038810047812049302*j^4 ? ? -823534263439730779968091389*j^3 + 5138800366453976780323726329446*j^2 ? ? ? ? 737707086760731113357714241006081263 ? ? [1, -1, 1] ? ? Errors (if any) and Timing Info: *** unexpected character: ...37174109237891242365*j^3- ^ *** unexpected character: ...02449209357160103606*j^2+ ^ *** unexpected character: ...8849797910089300094965*j- ^ *** unexpected character: ...6139603274605151187659*j+ ^ *** sorry, galois of reducible polynomial is not yet implemented. Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 13:36:59 2004 Input: f1=j^7 - 98373700603090523199715*j^6 - 4546951697981923176956448676986*j^5- 209903939873446020495519316596118272758*j^4-12543980353722772760179537174109237891242365*j^3 -282310474518147042483634599702449209357160103606*j^2 +904330206367752622526324160408849797910089300094965*j-709822597815616788561460999971455889888479357689323263 f2=j^7 + 313645809715*j^6 - 3091990138604570*j^5 + 98394038810047812049302*j^4-823534263439730779968091389*j^3 + 5138800366453976780323726329446*j^2- 425319473946139603274605151187659*j+737707086760731113357714241006081263 polgalois(f1) polgalois(f2) Output: ? j^7 - 98373700603090523199715*j^6 - 4546951697981923176956448676986*j^5 - 209903939873446020495519316596118272758*j^4 - 12543980353722772760179537174109237891242365*j^3 - 282310474518147042483634599702449209357160103606*j^2 + 904330206367752622526324160408849797910089300094965*j - 709822597815616788561460999971455889888479357689323263 ? ? ? j^7 + 313645809715*j^6 - 3091990138604570*j^5 + 98394038810047812049302*j^4 - 823534263439730779968091389*j^3 + 5138800366453976780323726329446*j^2 - 425319473946139603274605151187659*j + 737707086760731113357714241006081263 ? ? [14, -1, 1] ? [14, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.293s user 0m0.284s sys 0m0.008s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 13:40:08 2004 Input: f1=j^7 - 98373700603090523199715*j^6 - 4546951697981923176956448676986*j^5- 209903939873446020495519316596118272758*j^4-12543980353722772760179537174109237891242365*j^3 -282310474518147042483634599702449209357160103606*j^2 +904330206367752622526324160408849797910089300094965*j-709822597815616788561460999971455889888479357689323263 f2=j^7 + 313645809715*j^6 - 3091990138604570*j^5 + 98394038810047812049302*j^4-823534263439730779968091389*j^3 + 5138800366453976780323726329446*j^2- 425319473946139603274605151187659*j+737707086760731113357714241006081263 polgalois(f1) polgalois(f2) nfisisom(f1,f2) Output: ? j^7 - 98373700603090523199715*j^6 - 4546951697981923176956448676986*j^5 - 209903939873446020495519316596118272758*j^4 - 12543980353722772760179537174109237891242365*j^3 - 282310474518147042483634599702449209357160103606*j^2 + 904330206367752622526324160408849797910089300094965*j - 709822597815616788561460999971455889888479357689323263 ? ? ? j^7 + 313645809715*j^6 - 3091990138604570*j^5 + 98394038810047812049302*j^4 - 823534263439730779968091389*j^3 + 5138800366453976780323726329446*j^2 - 425319473946139603274605151187659*j + 737707086760731113357714241006081263 ? ? [14, -1, 1] ? [14, -1, 1] ? [11566127271/39303964708877730179484455866007199769*j^6 + 54144294818378606263/586626338938473584768424714418017907*j^5 + 89586772602785988021720598/39303964708877730179484455866007199769*j^4 + 1137664548822624878246354980898691/39303964708877730179484455866007199769*j^3 + 246202069720437382120401084309902330/324826154618824216359375668314109089*j^2 + 16628290790471437174082968223873/844452241124799410281250843771*j + 31806436613295322499183386/411931674293214701899] ? Errors (if any) and Timing Info: Timing: real 0m16.959s user 0m16.891s sys 0m0.043s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 13:51:27 2004 Input: f1:= x^2+1 f2:=x^2+x+1 nfisisom(f1,f2) Output: ? ? ? [0] ? Errors (if any) and Timing Info: *** unexpected character: f1:=x^2+1 ^------ *** unexpected character: f2:=x^2+x+1 ^-------- Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 13:51:36 2004 Input: f1= x^2+1 f2=x^2+x+1 nfisisom(f1,f2) Output: ? x^2 + 1 ? x^2 + x + 1 ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 13:51:51 2004 Input: f1= x^2+1 f2=x^2+4 nfisisom(f1,f2) Output: ? x^2 + 1 ? x^2 + 4 ? [-1/2*x, 1/2*x] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 13:58:28 2004 Input: f1= x^2+x+1 f2=x^2+3 nfisisom(f1,f2) Output: ? x^2 + x + 1 ? x^2 + 3 ? [-1/2*x - 1/2, 1/2*x - 1/2] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.004s '165.91.' ************** PARI ***************** Host 165.91.100.60 (165.91.100.60) Time: Tue Dec 21 14:00:20 2004 Input: f1= x^3+2 f2=x^3+3*x^2+3*x+3 nfisisom(f1,f2) Output: ? x^3 + 2 ? x^3 + 3*x^2 + 3*x + 3 ? [x + 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '195.131' ************** PARI ***************** Host 195.131.46.2 (195.131.46.2) Time: Wed Dec 22 11:13:52 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.382s user 0m0.007s sys 0m0.007s '195.131' ************** PARI ***************** Host 195.131.46.2 (195.131.46.2) Time: Wed Dec 22 11:14:01 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '195.131' ************** PARI ***************** Host 195.131.46.2 (195.131.46.2) Time: Wed Dec 22 11:14:13 2004 Input: code below Output: ? codebelow ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '195.131' ************** PARI ***************** Host 195.131.46.2 (195.131.46.2) Time: Wed Dec 22 11:14:38 2004 Input: set m=variable.item Output: ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: setm=variable.item ^----- Timing: real 0m0.013s user 0m0.003s sys 0m0.008s '195.131' ************** PARI ***************** Host 195.131.46.2 (195.131.46.2) Time: Wed Dec 22 11:14:50 2004 Input: setm=variable.item Output: ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: setm=variable.item ^----- Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '140.254' ************** PARI ***************** Host 140.254.94.55 (140.254.94.55) Time: Thu Dec 23 11:05:02 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.344s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 24 21:53:06 2004 Input: lcm(324,(2452*2453)) Output: ? 487195236 ? Errors (if any) and Timing Info: Timing: real 0m0.357s user 0m0.009s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 24 21:54:39 2004 Input: lcm(248,(2046*2047)) Output: ? 16752648 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 24 21:55:14 2004 Input: lcm(248,(2046*2048)) Output: ? 4190208 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 24 21:55:29 2004 Input: lcm(248,(2046*2047)) Output: ? 16752648 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 24 21:55:41 2004 Input: lcm(248,(2047)) Output: ? 507656 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 24 21:58:27 2004 Input: lcm(324,(2453)) Output: ? 794772 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 24 22:01:42 2004 Input: lcm((2452*2453),(2453)) Output: ? 6014756 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 24 22:02:05 2004 Input: lcm((2452*2454),(2453)) Output: ? 14760211224 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 24 22:04:10 2004 Input: gcd(lcm((2452*2454),(2453)),324) Output: ? 12 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.008s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 24 22:04:18 2004 Input: gcd(lcm((2452*2454),(2453)),324*4) Output: ? 24 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 24 22:04:27 2004 Input: gcd(lcm((2452*2454),(2453)),(324*4)+1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 24 22:04:48 2004 Input: gcd(lcm((2452*2454),(2453)),(324*4)+1) gcd(2453,(324*4)+1) Output: ? 1 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Dec 24 22:04:56 2004 Input: gcd(lcm((2452*2454),(2453)),(324*4)+1) gcd(2453,(324*4)) Output: ? 1 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 17:41:07 2004 Input: mod(3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609,4) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(3107418240490043 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 19:40:37 2004 Input: gcd(63457,712) Output: ? 89 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 19:41:03 2004 Input: gcd(63457,713) Output: ? 713 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 19:41:57 2004 Input: gcd(60639,713) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 19:42:03 2004 Input: gcd(60639,712) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:08:36 2004 Input: a=4828024060665119598242869523618436366566323076207632786374919531785708429043900569648718368334267828971272266417083349874878278415773412883109771747239457697752500694216516353061290363780772504286988409477658794719942423416445993034156930901373088905334837962227100707905068545758206449534466443288564976583311945653535895772328222381077367473364037444872252130408126972470784419692544; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:09:08 2004 Input: a=4828024060665119598242869523618436366566323076207632786374919531785708429043900569648718368334267828971272266417083349874878278415773412883109771747239457697752500694216516353061290363780772498072151928497571352018442351639310132959464885215917997465010940315814219671742059433064547106087892878412732568470440351006016510311066644591494708363556654594902545159370422367282152211480576; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:11:03 2004 Input: a=4828024060665119598242869523618436366566323076207632786374919531785708429043900569648718368334267828971272266417083349874878278415773412883109771747239457697752500694216516353061290363780772498072151928497571352018442351639310132959464885215917997465010940315814219671742059433064547106087892878412732568470440351006016510311066644591494708363556654594902545159370422367282152211480576; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b-1) Output: ? ? ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:11:27 2004 Input: a=4828024060665119598242869523618436366566323076207632786374919531785708429043900569648718368334267828971272266417083349874878278415773412883109771747239457697752500694216516353061290363780772498072151928497571352018442351639310132959464885215917997465010940315814219671742059433064547106087892878412732568470440351006016510311066644591494708363556654594902545159370422367282152211480576; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b+1) Output: ? ? ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:15:08 2004 Input: a=4828024060665119598242869523618436366566323076207632786374919531785708429043900569648718368334267828971272266417083349874878278415773412883109771747239457697752500694216516353061290363780772501179570168987615073369192387527878062996810908058645543185172889139020660189823563989411376777811179660850649015360487676545910067974435786426149368219315227537327555121440492032912118966648832; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b+1) Output: ? ? ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:15:19 2004 Input: a=4828024060665119598242869523618436366566323076207632786374919531785708429043900569648718368334267828971272266417083349874878278415773412883109771747239457697752500694216516353061290363780772501179570168987615073369192387527878062996810908058645543185172889139020660189823563989411376777811179660850649015360487676545910067974435786426149368219315227537327555121440492032912118966648832; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:15:25 2004 Input: a=4828024060665119598242869523618436366566323076207632786374919531785708429043900569648718368334267828971272266417083349874878278415773412883109771747239457697752500694216516353061290363780772501179570168987615073369192387527878062996810908058645543185172889139020660189823563989411376777811179660850649015360487676545910067974435786426149368219315227537327555121440492032912118966648832; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b-1) Output: ? ? ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:15:32 2004 Input: a=4828024060665119598242869523618436366566323076207632786374919531785708429043900569648718368334267828971272266417083349874878278415773412883109771747239457697752500694216516353061290363780772501179570168987615073369192387527878062996810908058645543185172889139020660189823563989411376777811179660850649015360487676545910067974435786426149368219315227537327555121440492032912118966648832; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:15:45 2004 Input: a=207649580614657471214491113812848102971839585174995559338369911170218716120540031488589983237696362040395986223954910893597126348926368062328607612248819620637501002801946880668315239526642107695177517144361027922115222117249047502668908112512156721765049376279027662569029973503844439404837118923680912803309122516061620652979847208255140191674863403537317922748231581696; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:15:57 2004 Input: a=103824790307330968319209481128104844162242334132161702973773171038393040621376198235428324941717400249458549550118879200251816323030106173783218894086021879362063660162289510935338448608912257251727767851130874125357286432075741672520004645508330180663818633334391910812887349703501057941041304328678076649275558960225714214863743239416667280151159110387740689428792737792; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:16:19 2004 Input: a=207857438052719112234793961512334732494177888265873910266056729602599066056053482209331837539706415197777720497879204884690308354057321999159183675745474746224675779261161559937306221117378019977767004944551436822907808213353602413876057351817400917134105169245661038413168271773429513128017317551716593200493047920736148281738602881778223198244149908682491628152160256; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.011s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:17:14 2004 Input: a=207857438052719112234793961512334732494177888265873910266056729602599066056053482209331837539706415197777720497879204884690308354057321999159183675745474746224675779261161559937306221117378019977767004944551436822907808213353602413876057351817400917134105169245661038413168271773429513128017317551716593200493047920736148281738602881778223198244149908682491628152160256; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; c=208274403826144827587387956005919790192199352195749565681689866089701426707280089576968586988203995608879417614123540149767945065253440397935777512091418612023955167725292146847086032413343147721413735401033196892530823321052762886307423870880903050753285922206607928579676824661932808136660750511555773073095744733798684246616384031740707375107631179592455731642630144; d=208065712038743880875352168839060837151410569759476468081917413808976862249796660921404698383165686703868731547530040577502378885010770217380970591062851394606684217968819493417144950987379502593307158087184971457677359874985771806528337370269990706803214859818262267960742560848485758651659583872016144873117118040600174799930034971516711710514295434131776409467617280; gcd(a,b) d-c gcd(b,(d-c)) Output: ? ? ? ? ? 1 ? -208691787400946712035787166858953040788782436273097599772452280724564457483428655563888605038308905010686066593499572265566180242670180554806921028567217417270949756472653429941081425963645128106577313848225434853463446066991079779086500610912343950071062388345660618934263813447049485001166639539628199978626693198509446686349060223995664593335745460679322175012864 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:23:04 2004 Input: a=3497810491345103696164483407014960488122752918949535186281422589145541925216282346484963504236110895592961725645357211865776225083996652964502522236462213071899657109809829390735058586817803495811681919995852523451079145143055354802727105394606168651798603780716921277160590357 ; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:23:10 2004 Input: a=3497810491345103696164483407014960488122752918949535186281422589145541925216282346484963504236110895592961725645357211865776225083996652964502522236462213071899657109809829390735058586817803495811681919995852523451079145143055354802727105394606168651798603780716921277160590357 ; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a-1,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:23:16 2004 Input: a=3497810491345103696164483407014960488122752918949535186281422589145541925216282346484963504236110895592961725645357211865776225083996652964502522236462213071899657109809829390735058586817803495811681919995852523451079145143055354802727105394606168651798603780716921277160590357 ; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a-1,b-1) Output: ? ? ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:23:22 2004 Input: a=3497810491345103696164483407014960488122752918949535186281422589145541925216282346484963504236110895592961725645357211865776225083996652964502522236462213071899657109809829390735058586817803495811681919995852523451079145143055354802727105394606168651798603780716921277160590357 ; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b-1) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:27:30 2004 Input: a=208274403826144827587387956005919790192199352195749565681689866089701426707280089576968586988203995608879417614123540149767945065253440397935777512091418612023955167725292146843978614172853104000062985365144628962493477298210035340587261922057696610235204417650261098907953537879494891863822717096084675073894729373659980740283003670290892433070571809937066494374445056; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:27:51 2004 Input: a=208274403826144827587387956005919790192199352195749565681689866089701426707280089576968586988203995608879417614123540149767945065253440397935777512091418612023955167725292146840871195932363060278712235329256061032456131275367307794867099973234490169717122913093914269236230251097056975590984683680613630994587048314800866567979797348102424765322357521426639464326758400; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:27:55 2004 Input: a=208274403826144827587387956005919790192199352195749565681689866089701426707280089576968586988203995608879417614123540149767945065253440397935777512091418612023955167725292146840871195932363060278712235329256061032456131275367307794867099973234490169717122913093914269236230251097056975590984683680613630994587048314800866567979797348102424765322357521426639464326758400; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:28:02 2004 Input: a=207857438052719112234793961512334732494177888265873910266056729602599066056053482209331837539706415197777720497879204884690308354057321999159183675745474746224675779261161559937306221117378019977767004944551436822907808213353602413876057351817400917134105169245661038413168271773429513128017317551716593200493047920736148281738602881778223198244149908682491628152160256; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:28:13 2004 Input: a=4828024060665119598242869523618436366566323076207632786374919531785708429043900569648718368334267828971272266417083349874878278415773412883109771747239457697752500694216516353061290363780772501179570168987615073369192387527878062996810908058645543185172889139020660189823563989411376777811179660850649015360487676545910067974435786426149368219315227537327555121440492032912118966648832; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:28:25 2004 Input: a=207649580614657471214491113812848102971839585174995559338369911170218716120540031488589983237696362040395986223954910893597126348926368062328607612248819620637501002801946880668315239526642107695177517144361027922115222117249047502668908112512156721765049376279027662569029973503844439404837118923680912803309122516061620652979847208255140191674863403537317922748231581696; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.011s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:31:06 2004 Input: a=4828024060665119598242869523618436366566323076207632786374919531785708429043900569648718368334267828971272266417083349874878278415773412883109771747239457697752500694216516353061290363780772501179570168987615073369192387527878062996810908058645543185172889139020660189823563989411376777811179660850649015360487676545910067974435786426149368219315227537327555121440492032912118966648832; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:31:20 2004 Input: a=144500075436954231407889023376653821046324587270333624167869839214515551078989123559018518604635229623560117171799697621457951042121221306209150605782050850616757836008853893815852834322199292471329834439984; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 46501650004528 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:31:49 2004 Input: a=72250037718477115703944511688326910523162293635166812083934919607257775539494561779509259302317614811780058585899848810728975521060610653104575302891025425308378918004426946907927498362826218045136127471384; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 23250825002264 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:32:09 2004 Input: a=36125018859238557851972255844163455261581146817583406041967459803628887769747280889754629651158807405890029292949924405364487760530305326552287651445512712654189459002213473453964019481844751974935866298540; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 11625412501132 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:32:28 2004 Input: a=18062509429619278925986127922081727630790573408791703020983729901814443884873640444877314825579403702945014646474962202682243880265152663276143825722756356327094729501106736726982077316030286725559883789982; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 5812706250566 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:33:35 2004 Input: a=9031254714809639462993063961040863815395286704395851510491864950907221942436820222438657412789701851472507323237481101341121940132576331638071912861378178163547364750553368363491055551792121047302929555169; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 2906353125283 ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:33:39 2004 Input: a=9031254714809639462993063961040863815395286704395851510491864950907221942436820222438657412789701851472507323237481101341121940132576331638071912861378178163547364750553368363491055551792121047302929555169; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 2906353125283 ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:33:58 2004 Input: a=4515627357404819731496531980520431907697643352197925755245932475453610971218410111219328706394850925736253661618740550670560970066288165819035956430689089081773682375276684181745531999340304944782211692629; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 2906353125283 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:37:53 2004 Input: a=4515627357404819731496531980520431907697643352197925755245932475453610971218410111219328706394850925736253661618740550670560970066288165819035956430689089081773682375276684181745531999340304944782211692629; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 2906353125283 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:44:39 2004 Input: a=4828024060665119598242869523618436366566323076207632786374919531785708429043900569648718368334267828971272266417083349874878278415773412883109771747239457697752500694216516353061290363780772501179570168987615073369192387527878062996810908058645543185172889139020660189823563989411376777811179660850649015360487676545910067974435786426149368219315227537327555121440492032912118966648832; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:44:50 2004 Input: a=144500075436954231407889023376653821046324587270333624167869839214515551078989123559018518604635229623560117171799697621457951042121221306209150605782050850616757836008853893815854996725652436090272254942768; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 46501650004528 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:45:04 2004 Input: a=72250037718477115703944511688326910523162293635166812083934919607257775539494561779509259302317614811780058585899848810728975521060610653104575302891025425308378918004426946907928579564552789854607337722776; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609 ? 1 ? 23250825002264 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:45:49 2004 Input: a=36125018859238557851972255844163455261581146817583406041967459803628887769747280889754629651158807405890029292949924405364487760530305326552287651445512712654189459002213473453964560082708037879671471424236; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 11625412501132 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:46:46 2004 Input: a=18062509429619278925986127922081727630790573408791703020983729901814443884873640444877314825579403702945014646474962202682243880265152663276143825722756356327094729501106736726982347616461929677927686352830; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 5812706250566 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:46:59 2004 Input: a=9031254714809639462993063961040863815395286704395851510491864950907221942436820222438657412789701851472507323237481101341121940132576331638071912861378178163547364750553368363491190702007942523486830836593; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 2906353125283 ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:47:07 2004 Input: a=4515627357404819731496531980520431907697643352197925755245932475453610971218410111219328706394850925736253661618740550670560970066288165819035956430689089081773682375276684181745599574448215682874162333341; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 2906353125283 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:47:11 2004 Input: a=4515627357404819731496531980520431907697643352197925755245932475453610971218410111219328706394850925736253661618740550670560970066288165819035956430689089081773682375276684181745599574448215682874162333341; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 2906353125283 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:47:19 2004 Input: a=36125018859238557851972255844163455261581146817583406041967459803628887769747280889754629651158807405890029292949924405364487760530305326552287651445512712654189459002213473453964560082708037879671471424236; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 11625412501132 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:47:27 2004 Input: a=72250037718477115703944511688326910523162293635166812083934919607257775539494561779509259302317614811780058585899848810728975521060610653104575302891025425308378918004426946907928579564552789854607337722776; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609 ? 1 ? 23250825002264 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:47:42 2004 Input: a=72250037718470900867463531600884209023090516499306737391889234152166335215596915366628223139308502118120715139326283934896429844993779710958358299051928367293703468358859895423155671535169316649652033029559; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609 ? 1 ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:48:06 2004 Input: a=72250037718474008285704021678017473545943772087806108945948695359372093310510764999004494785578311485386945277242153261867631657753430482044662532075121310721038287172303039206465504425096020907684776697098; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 2 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:48:25 2004 Input: a=4828024060665119598242869523618436366566323076207632786374919531785708429043900569648718368334267828971272266417083349874878278415773412883109771747239457697752500694216516353061290363780772498072151928497571352018442351639310132959464885215917997465010940315814219671742059433064547106087892878412732568470440351006016510311066644591494708363556654594902545159370422367282152211480576; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:48:36 2004 Input: a=4828024060665119598242869523618436366566323076207632786374919531785708429043900569648718368334267828971272266417083349874878278415773412883109771747239457697752500694216516353061290363780772494964733688007527630667692315750742202922118862373190451744848991492607779153660554876717717434364606095974816121580393025466122952647697502756840048507798081652477535197300352701652185456312320; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 20:48:52 2004 Input: a=144500075436951123989648533349638427182697382212688253925865305726799849883522813565545877305513299786948724655827458628069142691450923485142639969414324528819418658181400177093930232148578183315572148256625; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 1 ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 21:08:00 2004 Input: a=4828024060665119598242869523618436366566323076207632786374919531785708429043900569648718368334267828971272266417083349874878278415773412883109771747239457697752500694216516353061290363780772501179570168987615073369192387527878062996810908058645543185172889139020660189823563989411376777811179660850649015360487676545910067974435786426149368219315227537327555121440492032912118966648832; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 21:08:08 2004 Input: a=207649580614661936638418962256209688324484668264323405947546342076786081242752396470856649883434800498917099100237758400503632646060212347566437788172043758724127320324579021870676897217824514503455535702261748250714572864151483345040009291016660361327637266668783821625774699407002115882082608657356153298551117920451428429727486478833334560302318220775481378857585475584; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 21:08:22 2004 Input: a=103824790307333201031173405445812851516186683365909370615754105534697668559777761142024953219577774999231728362769107845598161744602717032697735865785065899757916596510288774786759239544109223318395016215594982972539217525146322464750140262512338983165479466282322652346684623439933611019719951230834969822023494010982278600680499686526039645731511131888410320947678019584; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 21:08:35 2004 Input: a=69216526871555963512329809048703267782427144457071649927758368736038935790781504702530279809383587229640864123416085539340330697589491368592021159355947527223752032642231038015089475593536893532251928789097821962561680136355597594934830154666850806222330775912420322364394401346670382679113074581015980765384251658267359202698350003208659855379420586378360067148205785088; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 21:08:48 2004 Input: a=207857438052723582128615632009918266739505332761304618521795291154679106707083494787555001071892774495250024478691840089570711215314965699872487738830955351127093679528515157950127590941404059158847008945798006906079268473010597679129857162072076035062405870271480176889610894243197708498542632787854420296835699359017963060870372392000592496498755878109776132712693760; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 21:09:01 2004 Input: a=208065712038748355248025364056581443811933911262015455025785935330205983858921007384901665085526700996707136153562859383681178175892881922557777350534611696190913783849911015789336579676608914796956672399286948881992956345530623129724755115722807500973221690057046101960505490382301789816263263608686328279218602839039318895738690694841492618863054219983561581242875904; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; gcd(a,b) gcd(a-1,b) gcd(a,b-1) gcd(a-1,b-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.011s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:08:45 2004 Input: a=2197276509833279858395035115084732058454967981178835432348709620045660675558715061358291088479166855773446436209228831309253316179738410031582243855731234007710948064949426936557912467366947844.147505885174283438181745367574522223904885118374752884534564229223547649643313120534102802384138157720457178440574180673799852303425888547464542246712276863427122638355959844119854745304854031187368089258564590255901725679924999159915509123811377372791861420713071467688684901650287250281522704012097657264108240441160581346569102834109799005091190338134765625; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; a*b Output: ? ? ? 6.8278571060562347487166376081781818342 E384 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.004s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:09:17 2004 Input: a=0.147505885174283438181745367574522223904885118374752884534564229223547649643313120534102802384138157720457178440574180673799852303425888547464542246712276863427122638355959844119854745304854031187368089258564590255901725679924999159915509123811377372791861420713071467688684901650287250281522704012097657264108240441160581346569102834109799005091190338134765625; b=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; a*b Output: ? ? ? 4.5836247817019826762781027431048578814 E191 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:09:41 2004 Input: a:=0.147505885174283438181745367574522223904885118374752884534564229223547649643313120534102802384138157720457178440574180673799852303425888547464542246712276863427122638355959844119854745304854031187368089258564590255901725679924999159915509123811377372791861420713071467688684901650287250281522704012097657264108240441160581346569102834109799005091190338134765625; b:=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; a*b Output: ? ? ? b*a ? Errors (if any) and Timing Info: *** unexpected character: a:=0.14750588517428343 ^-------------------- *** unexpected character: b:=3107418240490043721 ^-------------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:13:26 2004 Input: a=0.147505885174283438181745367574522223904885118374752884534564229223547649643313120534102802384138157720457178440574180673799852303425888547464542246712276863427122638355959844119854745304854031187368089258564590255901725679924999159915509123811377372791861420713071467688684901650287250281522704012097657264108240441160581346569102834109799005091190338134765625; b=8; (a*b) Output: ? ? ? 1.1800470813942675054539629405961777912 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:13:57 2004 Input: a=0.147505885174283438181745367574522223904885118374752884534564229223547649643313120534102802384138157720457178440574180673799852303425888547464542246712276863427122638355959844119854745304854031187368089258564590255901725679924999159915509123811377372791861420713071467688684901650287250281522704012097657264108240441160581346569102834109799005091190338134765625; b=8*5; (a*b) Output: ? ? ? 5.9002354069713375272698147029808889562 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:14:09 2004 Input: a=0.147505885174283438181745367574522223904885118374752884534564229223547649643313120534102802384138157720457178440574180673799852303425888547464542246712276863427122638355959844119854745304854031187368089258564590255901725679924999159915509123811377372791861420713071467688684901650287250281522704012097657264108240441160581346569102834109799005091190338134765625; b=8*5*5; (a*b) Output: ? ? ? 29.501177034856687636349073514904444781 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:15:36 2004 Input: a=0.147505885174283438181745367574522223904885118374752884534564229223547649643313120534102802384138157720457178440574180673799852303425888547464542246712276863427122638355959844119854745304854031187368089258564590255901725679924999159915509123811377372791861420713071467688684901650287250281522704012097657264108240441160581346569102834109799005091190338134765625; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=8*5*5; c/a (a*b) Output: ? ? ? ? 2.1066401769790532701753903063951131174 E193 ? 29.501177034856687636349073514904444781 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:15:52 2004 Input: a=0.147505885174283438181745367574522223904885118374752884534564229223547649643313120534102802384138157720457178440574180673799852303425888547464542246712276863427122638355959844119854745304854031187368089258564590255901725679924999159915509123811377372791861420713071467688684901650287250281522704012097657264108240441160581346569102834109799005091190338134765625; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=8*5*5; c/b (a*b) Output: ? ? ? ? 3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609/200 ? 29.501177034856687636349073514904444781 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:16:31 2004 Input: a=0.147505885174283438181745367574522223904885118374752884534564229223547649643313120534102802384138157720457178440574180673799852303425888547464542246712276863427122638355959844119854745304854031187368089258564590255901725679924999159915509123811377372791861420713071467688684901650287250281522704012097657264108240441160581346569102834109799005091190338134765625; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=8*5*5; c/(b*a) (a*b) Output: ? ? ? ? 1.0533200884895266350876951531975565587 E191 ? 29.501177034856687636349073514904444781 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:16:57 2004 Input: a=0.147505885174283438181745367574522223904885118374752884534564229223547649643313120534102802384138157720457178440574180673799852303425888547464542246712276863427122638355959844119854745304854031187368089258564590255901725679924999159915509123811377372791861420713071467688684901650287250281522704012097657264108240441160581346569102834109799005091190338134765625; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=(8*5*5)/9; c/(b*a) (a*b) Output: ? ? ? ? 9.4798807964057397157892563787780090286 E191 ? 3.2779085594285208484832303905449383090 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:17:13 2004 Input: a=0.147505885174283438181745367574522223904885118374752884534564229223547649643313120534102802384138157720457178440574180673799852303425888547464542246712276863427122638355959844119854745304854031187368089258564590255901725679924999159915509123811377372791861420713071467688684901650287250281522704012097657264108240441160581346569102834109799005091190338134765625; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=((8*5*5)/9)*11; c/(b*a) (a*b) Output: ? ? ? ? 8.6180734512779451961720512534345536623 E190 ? 36.056994153713729333315534295994321399 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:17:31 2004 Input: a=0.147505885174283438181745367574522223904885118374752884534564229223547649643313120534102802384138157720457178440574180673799852303425888547464542246712276863427122638355959844119854745304854031187368089258564590255901725679924999159915509123811377372791861420713071467688684901650287250281522704012097657264108240441160581346569102834109799005091190338134765625; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=((8*5*5)/9); c/(b*a) (a*b) Output: ? ? ? ? 9.4798807964057397157892563787780090286 E191 ? 3.2779085594285208484832303905449383090 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:19:28 2004 Input: a=0.147505885174283438181745367574522223904885118374752884534564229223547649643313120534102802384138157720457178440574180673799852303425888547464542246712276863427122638355959844119854745304854031187368089258564590255901725679924999159915509123811377372791861420713071467688684901650287250281522704012097657264108240441160581346569102834109799005091190338134765625; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=18886040730960816904854005447911274589188295338993836132188343079033678364965357238503607069437; c/(b*a) (a*b) Output: ? ? ? ? 1.1154482863766857465478287980872702703 E99 ? 2.7858021554579463101057854975313209697 E93 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:19:56 2004 Input: a=0.147505885174283438181745367574522223904885118374752884534564229223547649643313120534102802384138157720457178440574180673799852303425888547464542246712276863427122638355959844119854745304854031187368089258564590255901725679924999159915509123811377372791861420713071467688684901650287250281522704012097657264108240441160581346569102834109799005091190338134765625; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=18886040730960816904854005447911274589188295338993836132188343079033678364965357238503607069437; c/b (a*b) Output: ? ? ? ? 3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609/18886040730960816904854005447911274589188295338993836132188343079033678364965357238503607069437 ? 2.7858021554579463101057854975313209697 E93 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:21:04 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=18886040730960816904854005447911274589188295338993836132188343079033678364965357238503607069437; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 4 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:21:15 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414833385087624896342634642817769740619634366489593030375329415744311905543762572348643137710066848796964 ; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:22:14 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835861840778436006085179181752190600006541821020376704987463187999976178410710635522109550105149891060; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:22:22 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835861840778436006085179181752190600006541821020376704987463187999976178410710635522109550105149891060; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:22:25 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835861840778436006085179181752190600006541821020376704987463187999976178410710635522109550105149891060; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:23:13 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835863087257124249499094902116550162150664707447869078580647912430619394633482723235687291343216474896; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:23:36 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835859347821059519257347741023471475718296048165391957801093739138689745965166460094954067629016723390; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:24:44 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835860594299747762671263461387831037862418934592884331394278463569332962187938547808531808867083307225; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 8 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:24:54 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835856854863683032429516300294752351430050275310407210614724290277403313519622284667798585152883555722; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:25:03 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835858101342371275843432020659111913574173161737899584207909014708046529742394372381376326390950139556; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:25:11 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835854361906306545601684859566033227141804502455422463428354841416116881074078109240643102676750388056; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:25:22 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835855608384994789015600579930392789285927388882914837021539565846760097296850196954220843914816971889; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:25:34 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835851868948930058773853418837314102853558729600437716241985392554830448628533933813487620200617220392; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:25:56 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835853115427618302187769139201673664997681616027930089835170116985473664851306021527065361438683804224; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:26:08 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835849375991553571946021978108594978565312956745452969055615943693544016182989758386332137724484052730; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:26:18 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835850622470241815359937698472954540709435843172945342648800668124187232405761846099909878962550636561; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:26:26 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835846883034177085118190537379875854277067183890468221869246494832257583737445582959176655248350885070; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:26:34 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835848129512865328532106257744235416421190070317960595462431219262900799960217670672754396486417468900; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:26:43 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835844390076800598290359096651156729988821411035483474682877045970971151291901407532021172772217717412; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:26:57 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835845636555488841704274817015516292132944297462975848276061770401614367514673495245598914010284301241; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 8 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:27:05 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835841897119424111462527655922437605700575638180498727496507597109684718846357232104865690296084549756; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:27:12 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835843143598112354876443376286797167844698524607991101089692321540327935069129319818443431534151133584; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:27:21 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835839404162047624634696215193718481412329865325513980310138148248398286400813056677710207819951382102; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:27:34 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835840650640735868048611935558078043556452751753006353903322872679041502623585144391287949058017965929; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 8 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:27:46 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835836911204671137806864774464999357124084092470529233123768699387111853955268881250554725343818214450; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:27:54 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835838157683359381220780494829358919268206978898021606716953423817755070178040968964132466581884798276; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:28:01 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835834418247294650979033333736280232835838319615544485937399250525825421509724705823399242867685046800; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:28:14 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835835664725982894392949054100639794979961206043036859530583974956468637732496793536976984105751630625; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:28:29 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835831925289918164151201893007561108547592546760559738751029801664538989064180530396243760391551879152; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:34:04 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=6827857106056234748716637608178181834236594329599342543152396094503397484833545414090841582335743445701897154923780243780306609319742382263598158817716719956927624163480331653715172772690808729519247848341619522202392259285637647863301892842284741830286778972802946617458385034853995418414125188212579479844322450350775474717001251211574475898909564059931983282982683066252264925560832; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:34:13 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=6827857106056234748716637608178181834236594329599342543152396094503397484833545414090841582335743445701897154923780243780306609319742382263598158817716719956927624163480331653715172772690808729519247848341619522202392259285637647863301892842284741830286778972802946617458385034853995418414125188212579479844322450350775474717001251211574475898909564059931983282982683066252264925560832; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:34:32 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=6827857106056234748716637608178181834236594329599342543152396094503397484833545414090841582335746184560238839977236051743795983640599781531599996334523244437988892991329136984705869603135243616573199378643663469126666527465750698117815150872512928421124557223846354774852221386162508130722130824527613255230968914086162655321028895779270385688152379487167885181953363029896345113591808; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:34:44 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=6827857106056234748716637608178181834236594329599342543152396094503397484833545414090841582335737967985213784816868627853327860678027583727594483784103670994805086507782720991733779111801938956509983042654171557551361280467777576581759367371246084822966032493546468082028243011382514233971495198850663394344279532115268243358686560601061362923389785670709311918588015091435805383589888; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:35:04 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=6827857106056234748716637608178181834236594329599342543152396094503397484833545414090841582335740706843555469870324435816817234998884982995596321300910195475866355335631526322724475942246373843563934572956215504475635548647890626836272625401474271413803810744589876239422079362691026946279941531932228039749937107591682743254716738668160337710637885893337945387338799411322805614018560; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:36:12 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=6827857106056234748716637608178181834236594329599342543152396094503397484833545414090841582335743445701897154923780243780306609319742382263598158817716719956927624163480331653715172772690808733913800868008179238992462489455101764773237855199955606527706019064124297734888507751436172379109971403710085369832125533616820193834914610871560434791888784902857972850813440013693483571216384; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:36:26 2004 Input: c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=6827857106056234748716637608178181834236594329599342543152396094503397484833545414090841582335746184560238839977236051743795983640599781531599996334523244437988892991329136984705869603135243620967752398310223185916736757635214815027751113230183793118543797315167705892282344102744685091419739827091242625294816444316316651606952389436868604573152739511664801028904537402309243928838144; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) Output: ? ? ? 1 ? 1 ? 1 ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:46:32 2004 Input: a=66823827545634734041138668416073236959320075865930052851871507129530506040873116829258173778109857949452470600026391462207288828839994187981319236081846757750469935311110182641861; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=6827857106056234748716637608178181834236594329599342543152396094503397484833545414090841582335746184560238839977236051743795983640599781531599996334523244437988892991329136984705869603135243620967752398310223185916736757635214815027751113230183793118543797315167705892282344102744685091419739827091242625294816444316316651606952389436868604573152739511664801028904537402309243928838144; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) gcd(a,b) Output: ? ? ? ? 1 ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:46:57 2004 Input: a=66823827545634734041138668416073236959320075865930052851871507129530506040873116829258173778109857949452470600026391462207288828839994187981319236081846757750469935311110182641861; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1553709120245021860675375017944283965018673011421363772860080974411603220259040752278173414835861840778436006085179181752190600006541821020376704987463187999976178410710635522109550105149891060; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) gcd(a,b) Output: ? ? ? ? 1 ? 1 ? 1 ? 4 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:48:42 2004 Input: a=66823827545634734041138668416073236959320075865930052851871507129530506040873116829258173778109857949452470600026391462207288828839994187981319236081846757750469935311110182641861; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1001267782061637486933826114171717137918195149345385200464215158806183823157386312632399763252086735201606278848045925096193005665356995488507334729295999306214368635474575289359348089758108743053597440902349463999889326340836672382730181319003540805556912610558169568149601460946322245416653045720719874662020491244345634850328394029407594697193592562610221482071202383163031552; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) gcd(a,b) Output: ? ? ? ? 1 ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:48:50 2004 Input: a=66823827545634734041138668416073236959320075865930052851871507129530506040873116829258173778109857949452470600026391462207288828839994187981319236081846757750469935311110182641861; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=146830426563173276157697393828737862742076233576727306612065912718451130917814716107815024795884812978165951568571111241812207042477346691467092737542726420273993695545850269835233002503714893862528035218795302505001158658735601886310423124793876043564477996964473093905339936661400534931799270908481576002930729217237234529083981260065824490140711980098751627085725302784; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) gcd(a,b) Output: ? ? ? ? 1 ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:48:55 2004 Input: a=66823827545634734041138668416073236959320075865930052851871507129530506040873116829258173778109857949452470600026391462207288828839994187981319236081846757750469935311110182641861; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=146830426563173276157697393828737862742076233576727306612065912718451130917814716107815024795884812978165951568571111241812207042477346691467092737542726420273993695545850269835233002503714893862528035218795302505001158658735601886310423124793876043564477996964473093905339936661400534931799270908481576002930729217237234529083981260065824490140711980098751627085725302784; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) gcd(a,b) Output: ? ? ? ? 1 ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:49:04 2004 Input: a=66823827545634734041138668416073236959320075865930052851871507129530506040873116829258173778109857949452470600026391462207288828839994187981319236081846757750469935311110182641861; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1001267782061637486933826114171717137918195149345385200464215158806183823157386312632399763252087136840154737571739468368239066747162927809896237377175839026055394047010948128620994799827731196454233171144990881836237760304397077687770667038794309106963801855078654389927513635559349547439348758315774688234154121692700265772766203518993771578993447287797160819243414343441711104; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) gcd(a,b) Output: ? ? ? ? 1 ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:49:13 2004 Input: a=66823827545634734041138668416073236959320075865930052851871507129530506040873116829258173778109857949452470600026391462207288828839994187981319236081846757750469935311110182641861; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=146830426563173276157697393828737862742076233576727306612065912718451130917814716107815024795884871876255404703307335960062070193497192630701162391070174523510953756455341657241755563063774606428383250072544611057848152239669221732488909853043991871396850693043395553421259811646920995353602991669467624425788011335089995431599758248087482720632867624753429119618483486720; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) gcd(a,b) Output: ? ? ? ? 1 ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:49:21 2004 Input: a=66823827545634734041138668416073236959320075865930052851871507129530506040873116829258173778109857949452470600026391462207288828839994187981319236081846757750469935311110182641861; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=1001267782061637486933826114171717137918195149345385200464215158806183823157386312632399763252085931924509361400658838552100883501745130845729529433536319866532317812401829610836054669618863836413435252579885675238667886483094689165226124664015793354273337009332801812897874926596422902143791151098126859246784064420322824175515121940203232794720202406480779786602873836116377600; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) gcd(a,b) Output: ? ? ? ? 1 ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:49:30 2004 Input: a=66823827545634734041138668416073236959320075865930052851871507129530506040873116829258173778109857949452470600026391462207288828839994187981319236081846757750469935311110182641861; c=3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609; b=146830426563173276157697393828737862742076233576727306612065912718451130917814716107815024795884695181987045299098661805312480740437654812998953430487830213800073573726867495022187881383595468754443396312476048893931069780879983669696339835572738989852890603827876632934436038666485766653218706163004741994141648744878821665107632291024733277817368845107539620206919811072; gcd(b,c) gcd(b-1,c) gcd(b-1,c-1) gcd(b,c-1) gcd(a,b) Output: ? ? ? ? 1 ? 1 ? 1 ? 16 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:52:54 2004 Input: a=45.7465468295647949770823493867501760819401575438689837164415953469981560607181013049295016067143845336532985061134647973654648971675508110020255102304903451568100214971362928679374488815187203939018882062428110845985296535341095622818836170353191483069083455191849071889761096508666498088080152550192306559861180497595876045267168117590461097556404606623765210680782370888904688195616462553468557487729270112706910722710798313541244885965382038908541987420661245406727069175901655685088141643356374244460490818595426602784829614276208416917873517395728660157032129053884155581049829455634886664998704462383951523310305889467063040464580235103260524737017501223914578061684085132993153929600586278456425371889546056516022213243684116698099751227743935092212206829858067817399935683358112954012272866912064099961834471054368255094989490356242336534719069474803143914364570194522309909040874280001919255518823210556168104094261115926222163254649530367905679688333986376846951316110789775848388671875 Output: ? 45.746546829564794977082349386750176082 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:53:20 2004 Input: a=45.7465468295647949770823493867501760819401575438689837164415953469981560607181013049295016067143845336532985061134647973654648971675508110020255102304903451568100214971362928679374488815187203939018882062428110845985296535341095622818836170353191483069083455191849071889761096508666498088080152550192306559861180497595876045267168117590461097556404606623765210680782370888904688195616462553468557487729270112706910722710798313541244885965382038908541987420661245406727069175901655685088141643356374244460490818595426602784829614276208416917873517395728660157032129053884155581049829455634886664998704462383951523310305889467063040464580235103260524737017501223914578061684085132993153929600586278456425371889546056516022213243684116698099751227743935092212206829858067817399935683358112954012272866912064099961834471054368255094989490356242336534719069474803143914364570194522309909040874280001919255518823210556168104094261115926222163254649530367905679688333986376846951316110789775848388671875 a*248*248*2047*2047*2046*2046 Output: ? 45.746546829564794977082349386750176082 ? 49352439265015951474.112292457955432127 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:54:03 2004 Input: a=45.7465468295647949770823493867501760819401575438689837164415953469981560607181013049295016067143845336532985061134647973654648971675508110020255102304903451568100214971362928679374488815187203939018882062428110845985296535341095622818836170353191483069083455191849071889761096508666498088080152550192306559861180497595876045267168117590461097556404606623765210680782370888904688195616462553468557487729270112706910722710798313541244885965382038908541987420661245406727069175901655685088141643356374244460490818595426602784829614276208416917873517395728660157032129053884155581049829455634886664998704462383951523310305889467063040464580235103260524737017501223914578061684085132993153929600586278456425371889546056516022213243684116698099751227743935092212206829858067817399935683358112954012272866912064099961834471054368255094989490356242336534719069474803143914364570194522309909040874280001919255518823210556168104094261115926222163254649530367905679688333986376846951316110789775848388671875 a*248*248*2047*2047*2046*2046*8388607*8388607 Output: ? 45.746546829564794977082349386750176082 ? 3472868345187123091163428227174818.1840 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:54:18 2004 Input: a=45.7465468295647949770823493867501760819401575438689837164415953469981560607181013049295016067143845336532985061134647973654648971675508110020255102304903451568100214971362928679374488815187203939018882062428110845985296535341095622818836170353191483069083455191849071889761096508666498088080152550192306559861180497595876045267168117590461097556404606623765210680782370888904688195616462553468557487729270112706910722710798313541244885965382038908541987420661245406727069175901655685088141643356374244460490818595426602784829614276208416917873517395728660157032129053884155581049829455634886664998704462383951523310305889467063040464580235103260524737017501223914578061684085132993153929600586278456425371889546056516022213243684116698099751227743935092212206829858067817399935683358112954012272866912064099961834471054368255094989490356242336534719069474803143914364570194522309909040874280001919255518823210556168104094261115926222163254649530367905679688333986376846951316110789775848388671875 a*(a+1) Output: ? 45.746546829564794977082349386750176082 ? 2138.4930936591295899541646987735003521 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 22:54:30 2004 Input: a=45.7465468295647949770823493867501760819401575438689837164415953469981560607181013049295016067143845336532985061134647973654648971675508110020255102304903451568100214971362928679374488815187203939018882062428110845985296535341095622818836170353191483069083455191849071889761096508666498088080152550192306559861180497595876045267168117590461097556404606623765210680782370888904688195616462553468557487729270112706910722710798313541244885965382038908541987420661245406727069175901655685088141643356374244460490818595426602784829614276208416917873517395728660157032129053884155581049829455634886664998704462383951523310305889467063040464580235103260524737017501223914578061684085132993153929600586278456425371889546056516022213243684116698099751227743935092212206829858067817399935683358112954012272866912064099961834471054368255094989490356242336534719069474803143914364570194522309909040874280001919255518823210556168104094261115926222163254649530367905679688333986376846951316110789775848388671875 a*(a-1) Output: ? 45.746546829564794977082349386750176082 ? 2047.0000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:24:54 2004 Input: a=45.7465468295647949770823493867501760819401575438689837164415953469981560607181013049295016067143845336532985061134647973654648971675508110020255102304903451568100214971362928679374488815187203939018882062428110845985296535341095622818836170353191483069083455191849071889761096508666498088080152550192306559861180497595876045267168117590461097556404606623765210680782370888904688195616462553468557487729270112706910722710798313541244885965382038908541987420661245406727069175901655685088141643356374244460490818595426602784829614276208416917873517395728660157032129053884155581049829455634886664998704462383951523310305889467063040464580235103260524737017501223914578061684085132993153929600586278456425371889546056516022213243684116698099751227743935092212206829858067817399935683358112954012272866912064099961834471054368255094989490356242336534719069474803143914364570194522309909040874280001919255518823210556168104094261115926222163254649530367905679688333986376846951316110789775848388671875 a*(a-45) Output: ? 45.746546829564794977082349386750176082 ? 34.151939499149021008376626982992252394 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:25:10 2004 Input: a=45.7465468295647949770823493867501760819401575438689837164415953469981560607181013049295016067143845336532985061134647973654648971675508110020255102304903451568100214971362928679374488815187203939018882062428110845985296535341095622818836170353191483069083455191849071889761096508666498088080152550192306559861180497595876045267168117590461097556404606623765210680782370888904688195616462553468557487729270112706910722710798313541244885965382038908541987420661245406727069175901655685088141643356374244460490818595426602784829614276208416917873517395728660157032129053884155581049829455634886664998704462383951523310305889467063040464580235103260524737017501223914578061684085132993153929600586278456425371889546056516022213243684116698099751227743935092212206829858067817399935683358112954012272866912064099961834471054368255094989490356242336534719069474803143914364570194522309909040874280001919255518823210556168104094261115926222163254649530367905679688333986376846951316110789775848388671875 a*(sqrt(2047)) Output: ? 45.746546829564794977082349386750176082 ? 2069.7468882353994579994929950990757435 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:25:21 2004 Input: a=45.7465468295647949770823493867501760819401575438689837164415953469981560607181013049295016067143845336532985061134647973654648971675508110020255102304903451568100214971362928679374488815187203939018882062428110845985296535341095622818836170353191483069083455191849071889761096508666498088080152550192306559861180497595876045267168117590461097556404606623765210680782370888904688195616462553468557487729270112706910722710798313541244885965382038908541987420661245406727069175901655685088141643356374244460490818595426602784829614276208416917873517395728660157032129053884155581049829455634886664998704462383951523310305889467063040464580235103260524737017501223914578061684085132993153929600586278456425371889546056516022213243684116698099751227743935092212206829858067817399935683358112954012272866912064099961834471054368255094989490356242336534719069474803143914364570194522309909040874280001919255518823210556168104094261115926222163254649530367905679688333986376846951316110789775848388671875 a*(sqrt(2047)+1) Output: ? 45.746546829564794977082349386750176082 ? 2115.4934350649642529765753444858259196 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:25:32 2004 Input: a=45.7465468295647949770823493867501760819401575438689837164415953469981560607181013049295016067143845336532985061134647973654648971675508110020255102304903451568100214971362928679374488815187203939018882062428110845985296535341095622818836170353191483069083455191849071889761096508666498088080152550192306559861180497595876045267168117590461097556404606623765210680782370888904688195616462553468557487729270112706910722710798313541244885965382038908541987420661245406727069175901655685088141643356374244460490818595426602784829614276208416917873517395728660157032129053884155581049829455634886664998704462383951523310305889467063040464580235103260524737017501223914578061684085132993153929600586278456425371889546056516022213243684116698099751227743935092212206829858067817399935683358112954012272866912064099961834471054368255094989490356242336534719069474803143914364570194522309909040874280001919255518823210556168104094261115926222163254649530367905679688333986376846951316110789775848388671875 a*(4*sqrt(2047)) Output: ? 45.746546829564794977082349386750176082 ? 8278.9875529415978319979719803963029741 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:26:12 2004 Input: a=45.7465468295647949770823493867501760819401575438689837164415953469981560607181013049295016067143845336532985061134647973654648971675508110020255102304903451568100214971362928679374488815187203939018882062428110845985296535341095622818836170353191483069083455191849071889761096508666498088080152550192306559861180497595876045267168117590461097556404606623765210680782370888904688195616462553468557487729270112706910722710798313541244885965382038908541987420661245406727069175901655685088141643356374244460490818595426602784829614276208416917873517395728660157032129053884155581049829455634886664998704462383951523310305889467063040464580235103260524737017501223914578061684085132993153929600586278456425371889546056516022213243684116698099751227743935092212206829858067817399935683358112954012272866912064099961834471054368255094989490356242336534719069474803143914364570194522309909040874280001919255518823210556168104094261115926222163254649530367905679688333986376846951316110789775848388671875 a*(4*sqrt(2047)) ((8279/a)*(8279/a)) Output: ? 45.746546829564794977082349386750176082 ? 8278.9875529415978319979719803963029741 ? 32752.098482178076492958519005717118626 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:26:26 2004 Input: a=45.7465468295647949770823493867501760819401575438689837164415953469981560607181013049295016067143845336532985061134647973654648971675508110020255102304903451568100214971362928679374488815187203939018882062428110845985296535341095622818836170353191483069083455191849071889761096508666498088080152550192306559861180497595876045267168117590461097556404606623765210680782370888904688195616462553468557487729270112706910722710798313541244885965382038908541987420661245406727069175901655685088141643356374244460490818595426602784829614276208416917873517395728660157032129053884155581049829455634886664998704462383951523310305889467063040464580235103260524737017501223914578061684085132993153929600586278456425371889546056516022213243684116698099751227743935092212206829858067817399935683358112954012272866912064099961834471054368255094989490356242336534719069474803143914364570194522309909040874280001919255518823210556168104094261115926222163254649530367905679688333986376846951316110789775848388671875 a*(4*sqrt(2047)) ((8279/a)*(8279/(a-1))) Output: ? 45.746546829564794977082349386750176082 ? 8278.9875529415978319979719803963029741 ? 33484.045432340009770395701025891548607 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:26:40 2004 Input: a=45.7465468295647949770823493867501760819401575438689837164415953469981560607181013049295016067143845336532985061134647973654648971675508110020255102304903451568100214971362928679374488815187203939018882062428110845985296535341095622818836170353191483069083455191849071889761096508666498088080152550192306559861180497595876045267168117590461097556404606623765210680782370888904688195616462553468557487729270112706910722710798313541244885965382038908541987420661245406727069175901655685088141643356374244460490818595426602784829614276208416917873517395728660157032129053884155581049829455634886664998704462383951523310305889467063040464580235103260524737017501223914578061684085132993153929600586278456425371889546056516022213243684116698099751227743935092212206829858067817399935683358112954012272866912064099961834471054368255094989490356242336534719069474803143914364570194522309909040874280001919255518823210556168104094261115926222163254649530367905679688333986376846951316110789775848388671875 a*(4*sqrt(2047)) ((8279/a)*(8279/(a)))*2047*2047 Output: ? 45.746546829564794977082349386750176082 ? 8278.9875529415978319979719803963029741 ? 137238137828.90891572348322296442692192 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:27:08 2004 Input: a=45.7465468295647949770823493867501760819401575438689837164415953469981560607181013049295016067143845336532985061134647973654648971675508110020255102304903451568100214971362928679374488815187203939018882062428110845985296535341095622818836170353191483069083455191849071889761096508666498088080152550192306559861180497595876045267168117590461097556404606623765210680782370888904688195616462553468557487729270112706910722710798313541244885965382038908541987420661245406727069175901655685088141643356374244460490818595426602784829614276208416917873517395728660157032129053884155581049829455634886664998704462383951523310305889467063040464580235103260524737017501223914578061684085132993153929600586278456425371889546056516022213243684116698099751227743935092212206829858067817399935683358112954012272866912064099961834471054368255094989490356242336534719069474803143914364570194522309909040874280001919255518823210556168104094261115926222163254649530367905679688333986376846951316110789775848388671875 a*(4*sqrt(2047)) 8279/a Output: ? 45.746546829564794977082349386750176082 ? 8278.9875529415978319979719803963029741 ? 180.97540850120514783354409896087186506 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:27:51 2004 Input: a=45.7465468295647949770823493867501760819401575438689837164415953469981560607181013049295016067143845336532985061134647973654648971675508110020255102304903451568100214971362928679374488815187203939018882062428110845985296535341095622818836170353191483069083455191849071889761096508666498088080152550192306559861180497595876045267168117590461097556404606623765210680782370888904688195616462553468557487729270112706910722710798313541244885965382038908541987420661245406727069175901655685088141643356374244460490818595426602784829614276208416917873517395728660157032129053884155581049829455634886664998704462383951523310305889467063040464580235103260524737017501223914578061684085132993153929600586278456425371889546056516022213243684116698099751227743935092212206829858067817399935683358112954012272866912064099961834471054368255094989490356242336534719069474803143914364570194522309909040874280001919255518823210556168104094261115926222163254649530367905679688333986376846951316110789775848388671875 a*(4*sqrt(2047)) a*4 Output: ? 45.746546829564794977082349386750176082 ? 8278.9875529415978319979719803963029741 ? 182.98618731825917990832939754700070432 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:28:19 2004 Input: a=45.7465468295647949770823493867501760819401575438689837164415953469981560607181013049295016067143845336532985061134647973654648971675508110020255102304903451568100214971362928679374488815187203939018882062428110845985296535341095622818836170353191483069083455191849071889761096508666498088080152550192306559861180497595876045267168117590461097556404606623765210680782370888904688195616462553468557487729270112706910722710798313541244885965382038908541987420661245406727069175901655685088141643356374244460490818595426602784829614276208416917873517395728660157032129053884155581049829455634886664998704462383951523310305889467063040464580235103260524737017501223914578061684085132993153929600586278456425371889546056516022213243684116698099751227743935092212206829858067817399935683358112954012272866912064099961834471054368255094989490356242336534719069474803143914364570194522309909040874280001919255518823210556168104094261115926222163254649530367905679688333986376846951316110789775848388671875 a*(4*sqrt(2047)) 189/a Output: ? 45.746546829564794977082349386750176082 ? 8278.9875529415978319979719803963029741 ? 4.1314593799647026139074567826554876792 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:28:38 2004 Input: a=45.7465468295647949770823493867501760819401575438689837164415953469981560607181013049295016067143845336532985061134647973654648971675508110020255102304903451568100214971362928679374488815187203939018882062428110845985296535341095622818836170353191483069083455191849071889761096508666498088080152550192306559861180497595876045267168117590461097556404606623765210680782370888904688195616462553468557487729270112706910722710798313541244885965382038908541987420661245406727069175901655685088141643356374244460490818595426602784829614276208416917873517395728660157032129053884155581049829455634886664998704462383951523310305889467063040464580235103260524737017501223914578061684085132993153929600586278456425371889546056516022213243684116698099751227743935092212206829858067817399935683358112954012272866912064099961834471054368255094989490356242336534719069474803143914364570194522309909040874280001919255518823210556168104094261115926222163254649530367905679688333986376846951316110789775848388671875 a*(4*sqrt(2047)) 189/a 2047/4.1314593799647026139074567826554876792 4.1314593799647026139074567826554876792^2 Output: ? 45.746546829564794977082349386750176082 ? 8278.9875529415978319979719803963029741 ? 4.1314593799647026139074567826554876792 ? 495.46656804295838792638925499829423514 ? 17.068956608298324966278207458758237824 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:37:27 2004 Input: 188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059 % 398075086424064937397125500550386491199064362342526708406385189575946388957261768583317 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:37:35 2004 Input: 188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059 mod 398075086424064937397125500550386491199064362342526708406385189575946388957261768583317 Output: ? 188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: mod398075086424064937397125500550386491199064362342526708406385189575946388957261768583317. Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:38:03 2004 Input: 188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059 mod 398075086424064937397125500550386491199064362342526708406385189575946388957261768583316 Output: ? 188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: mod398075086424064937397125500550386491199064362342526708406385189575946388957261768583316. Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:39:30 2004 Input: a:=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059 mod 398075086424064937397125500550386491199064362342526708406385189575946388957261768583316 b:=398075086424064937397125500550386491199064362342526708406385189575946388957261768583316 mod 1814211 print(a) print(b) Output: ? ? ? ? ? a ? b ? Errors (if any) and Timing Info: *** unexpected character: a:=1881988129206079638 ^-------------------- *** unexpected character: b:=3980750864240649373 ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:39:40 2004 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059 mod 398075086424064937397125500550386491199064362342526708406385189575946388957261768583316 b=398075086424064937397125500550386491199064362342526708406385189575946388957261768583316 mod 1814211 print(a) print(b) Output: ? 188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059 ? ? 398075086424064937397125500550386491199064362342526708406385189575946388957261768583316 ? ? 188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059 ? 398075086424064937397125500550386491199064362342526708406385189575946388957261768583316 ? Errors (if any) and Timing Info: *** Warning: unused characters: mod398075086424064937397125500550386491199064362342526708406385189575946388957261768583316. *** Warning: unused characters: mod1814211. Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:40:12 2004 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059 mod 398075086424064937397125500550386491199064362342526708406385189575946388957261768583316 b=mod(398075086424064937397125500550386491199064362342526708406385189575946388957261768583316,1814211) print(a) print(b) Output: ? 188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059 ? ? ? ? 188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059 ? b ? Errors (if any) and Timing Info: *** Warning: unused characters: mod398075086424064937397125500550386491199064362342526708406385189575946388957261768583316. *** obsolete function: b=mod(3980750864240649 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:40:52 2004 Input: a=mod(188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 398075086424064937397125500550386491199064362342526708406385189575946388957261768583316) b=mod(398075086424064937397125500550386491199064362342526708406385189575946388957261768583316,1814211) Output: ? ? ? ? ? Errors (if any) and Timing Info: *** obsolete function: a=mod(1881988129206079 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** obsolete function: b=mod(3980750864240649 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:41:37 2004 Input: a:=MOD(188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 398075086424064937397125500550386491199064362342526708406385189575946388957261768583316) b:=MOD(398075086424064937397125500550386491199064362342526708406385189575946388957261768583316,1814211) print(a) print(b) Output: ? ? ? ? ? a ? b ? Errors (if any) and Timing Info: *** unexpected character: a:=MOD(188198812920607 ^-------------------- *** unexpected character: b:=MOD(398075086424064 ^-------------------- Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Dec 26 23:43:04 2004 Input: 472772146107435302536223071973048224632914695302097116459852171130520711256363590397527.0/398075086424064937397125500550386491199064362342526708406385189575946388957261768583317.0 Output: ? 1.1876456533725308870217327523621155950 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 00:56:20 2004 Input: 175980763119982174958614550159837078253914471331181990915556521730876200888804719372936 %% 2 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 00:56:27 2004 Input: 175980763119982174958614550159837078253914471331181990915556521730876200888804719372936 mod 2 Output: ? 175980763119982174958614550159837078253914471331181990915556521730876200888804719372936 ? Errors (if any) and Timing Info: *** Warning: unused characters: mod2. Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 00:58:59 2004 Input: a:=175980763119982174958614550159837078253914471331181990915556521730876200888804719372936; b:=209002788396627817310932418806785525449816170839105730680723101852498679294473274935963 ; c:=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; print c mod a; prinf c mod a; Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: a:=1759807631199821749 ^-------------------- *** unexpected character: b:=2090027883966278173 ^-------------------- *** unexpected character: c:=1881988129206079638 ^-------------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 00:59:26 2004 Input: a=175980763119982174958614550159837078253914471331181990915556521730876200888804719372936; b=209002788396627817310932418806785525449816170839105730680723101852498679294473274935963 ; c=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; print c mod a; prinf c mod a; Output: ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 00:59:35 2004 Input: a=175980763119982174958614550159837078253914471331181990915556521730876200888804719372936; b=209002788396627817310932418806785525449816170839105730680723101852498679294473274935963 ; c=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; print c mod a prinf c mod a Output: ? ? ? ? printcmoda ? prinfcmoda ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 00:59:48 2004 Input: a=175980763119982174958614550159837078253914471331181990915556521730876200888804719372936; b=209002788396627817310932418806785525449816170839105730680723101852498679294473274935963 ; c=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; print( c mod a) prinf( c mod a) Output: ? ? ? ? cmoda ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: prinf(cmoda) ^ Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:00:08 2004 Input: a=175980763119982174958614550159837078253914471331181990915556521730876200888804719372936; b=209002788396627817310932418806785525449816170839105730680723101852498679294473274935963 ; c=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; d=mod(c,a) print( c mod a) prinf( c mod a) Output: ? ? ? ? ? cmoda ? ? Errors (if any) and Timing Info: *** obsolete function: d=mod(c,a) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** expected character: '=' instead of: prinf(cmoda) ^ Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:00:30 2004 Input: a=175980763119982174958614550159837078253914471331181990915556521730876200888804719372936; b=209002788396627817310932418806785525449816170839105730680723101852498679294473274935963 ; c=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; d=Mod(c,a) Output: ? ? ? ? Mod(43612458680250751715240005851888907705361629330446000032537013335149613458638279914555, 175980763119982174958614550159837078253914471331181990915556521730876200888804719372936) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:05:28 2004 Input: a=175980763119982174958614550159837078253914471331181990915556521730876200888804719372936; b=209002788396627817310932418806785525449816170839105730680723101852498679294473274935963 ; c=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; c mod a Output: ? ? ? ? cmoda ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:06:33 2004 Input: a=175980763119982174958614550159837078253914471331181990915556521730876200888804719372936; b=209002788396627817310932418806785525449816170839105730680723101852498679294473274935963 ; c=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; c Mod a Output: ? ? ? ? cModa ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:07:19 2004 Input: a=175980763119982174958614550159837078253914471331181990915556521730876200888804719372936; b=209002788396627817310932418806785525449816170839105730680723101852498679294473274935963 ; c=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; c Mod(a) Output: ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: cMod(a) ^ Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:07:37 2004 Input: a=175980763119982174958614550159837078253914471331181990915556521730876200888804719372936; b=209002788396627817310932418806785525449816170839105730680723101852498679294473274935963 ; c=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; c = Mod(c,a) Output: ? ? ? ? Mod(43612458680250751715240005851888907705361629330446000032537013335149613458638279914555, 175980763119982174958614550159837078253914471331181990915556521730876200888804719372936) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:20:47 2004 Input: 188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059-21801206812891614112132530110561314528161404177521565248313676126679976579908840670855138224992451529447938569452799656210189978098881420317798104411675193952168350839998515 Output: ? 166397606107716349726564709351089125279002159201895817452449680296308883135325824814463922381512291515869449441850597059989502343106852611561752552584546111216590956810258544 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:33:31 2004 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059-1; b=175980763119982174958614550159837078253914471331181990915556521730876200888804719372936 ; gcd(b,a) Output: ? ? ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:33:45 2004 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; b=175980763119982174958614550159837078253914471331181990915556521730876200888804719372936 ; gcd(b,a+1) Output: ? ? ? 12 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:34:05 2004 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; b=175980763119982174958614550159837078253914471331181990915556521730876200888804719372936 ; gcd(b,a-3) Output: ? ? ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:34:13 2004 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; b=175980763119982174958614550159837078253914471331181990915556521730876200888804719372936 ; gcd(b,a-5) Output: ? ? ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:34:19 2004 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; b=175980763119982174958614550159837078253914471331181990915556521730876200888804719372936 ; gcd(b,a-6) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:36:31 2004 Input: 83198803053858174863282354675544562639501079600947908726224840148154441567662912407231961190756145757934724720925298529994751171553426305780876276292273055608295478405129272-36780470196242719041644989073879163574770999879053597488123415231844145122520688698131019452104433693199857523703786724244725778814740297944709062133765624432022470915297368 Output: ? 46418332857615455821637365601665399064730079721894311238101424916310296445142223709100941738651712064734867197221511805750025392738686007836167214158507431176273007489831904 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:37:50 2004 Input: 188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059.0/83198803053858174863282354675544562639501079600947908726224840148154441567662912407231961190756145757934724720925298529994751171553426305780876276292273055608295478405129272.0 Output: ? 2.2620375055008754431254025202776603423 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:55:55 2004 Input: a=(94099406460303981919348619730825219903581781689708691350381678211494429857617332742659530303252371522658694005651698358099846160602867015939775328498110652584379653825128529-83198803053858174863282354675544562639501079600947908726224840148154441567662912407231961190756145757934724720925298529994751171553426305780876276292273055608295478405129272)*2 Output: ? 21801206812891614112132530110561314528161404177521565248313676126679976579908840670855138224992451529447938569452799656210189978098881420317798104411675193952168350839998514 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:57:12 2004 Input: a=(94099406460303981919348619730825219903581781689708691350381678211494429857617332742659530303252371522658694005651698358099846160602867015939775328498110652584379653825128529-83198803053858174863282354675544562639501079600947908726224840148154441567662912407231961190756145757934724720925298529994751171553426305780876276292273055608295478405129272)*2 b=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; (a^2-1)/b Output: ? 21801206812891614112132530110561314528161404177521565248313676126679976579908840670855138224992451529447938569452799656210189978098881420317798104411675193952168350839998514 ? ? 1005331262452301202880736150818224951813044949981102201537237041583003580733640906585985805408998090874201775800647069925707898670346163359752326962434891622860771340093671211174000338762281771252517926084469758769414372810733422022218901309794786189331719285/398075086424064937397125500550386491199064362342526708406385189575946388957261768583317 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Dec 27 01:57:27 2004 Input: a=(94099406460303981919348619730825219903581781689708691350381678211494429857617332742659530303252371522658694005651698358099846160602867015939775328498110652584379653825128530-83198803053858174863282354675544562639501079600947908726224840148154441567662912407231961190756145757934724720925298529994751171553426305780876276292273055608295478405129272)*2 b=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; (a^2-1)/b Output: ? 21801206812891614112132530110561314528161404177521565248313676126679976579908840670855138224992451529447938569452799656210189978098881420317798104411675193952168350839998516 ? ? 2525481490146140552147777054988843548243244491840137748357656757747673934665770648915293651897894786377919222417349493199590750250990000534881800362191580463667277690929445 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '217.84.' ************** PARI ***************** Host 217.84.42.233 (217.84.42.233) Time: Mon Dec 27 07:25:30 2004 Input: 1+1 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:00:49 2004 Input: 13*51 Output: ? 663 ? Errors (if any) and Timing Info: Timing: real 0m0.248s user 0m0.005s sys 0m0.007s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:05:34 2004 Input: factor(224467774227) Output: ? [3 2] [144383 1] [172741 1] ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.008s sys 0m0.005s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:07:07 2004 Input: 2^(2^10)+1 Output: ? 179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137217 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.004s sys 0m0.008s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:07:59 2004 Input: 2^(2^10)+1 isprime(2^(2^10)+1) Output: ? 179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137217 ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.014s sys 0m0.005s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:09:11 2004 Input: 2^(2^10)+1 isprime(2^(2^10)+1) factor(2^(2^10)+1) Output: ? 179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137217 ? 0 ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 29050 Killed /usr/bin/gp -q -emacs Timing: real 0m21.044s user 0m20.990s sys 0m0.010s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:09:53 2004 Input: isprime(10) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.006s sys 0m0.004s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:10:02 2004 Input: isprime(7) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:10:19 2004 Input: factor(64) Output: ? [2 6] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:13:45 2004 Input: eulerphi(11) Output: ? 10 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:14:03 2004 Input: eulerphi(6) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.007s sys 0m0.005s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:14:19 2004 Input: eulerphi(8) Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:41:07 2004 Input: PRIMES(500) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: PRIMES(500) ^----------- Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:41:28 2004 Input: primes(100) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:41:52 2004 Input: primes(20) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71] ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.007s sys 0m0.004s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:43:41 2004 Input: smallestprime(100) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: smallestprime(100) ^------------------ Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:44:06 2004 Input: nextprime(100) Output: ? 101 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.006s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:44:23 2004 Input: nextprime(1000) Output: ? 1009 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:44:30 2004 Input: nextprime(10000) Output: ? 10007 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:44:38 2004 Input: nextprime(100000) Output: ? 100003 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:44:47 2004 Input: nextprime(1000000) Output: ? 1000003 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:45:05 2004 Input: nextprime(10000000) Output: ? 10000019 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:45:16 2004 Input: nextprime(10) Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.004s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:48:05 2004 Input: gcd(10,5) Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:48:17 2004 Input: gcd(10,15) Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:49:00 2004 Input: gcd(10,150) Output: ? 10 ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.007s sys 0m0.005s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:49:13 2004 Input: gcd(10,66) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '24.208.' ************** PARI ***************** Host 24.208.175.104 (24.208.175.104) Time: Mon Dec 27 21:49:53 2004 Input: gcd(60,42) Output: ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '133.82.' ************** PARI ***************** Host 133.82.132.28 (133.82.132.28) Time: Mon Dec 27 22:15:37 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 01:38:48 2004 Input: -2^2 Output: ? -4 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 01:40:40 2004 Input: 1/3+1/4 Output: ? 7/12 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 01:43:15 2004 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 01:43:35 2004 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 01:43:43 2004 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 01:45:17 2004 Input: Cos(2) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Cos(2) ^------ Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 01:45:27 2004 Input: cos(2) Output: ? -0.41614683654714238699756822950076218977 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.006s sys 0m0.006s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 01:50:33 2004 Input: x=3 Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 01:50:43 2004 Input: x Output: ? x ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 01:50:56 2004 Input: x+1 Output: ? x + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 01:52:11 2004 Input: 1+2; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:00:36 2004 Input: 0.3333333333333333333333333333 Output: ? 0.33333333333333333333333333329999999999 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:00:52 2004 Input: 0.3333333333333333333333333333 Output: ? 0.33333333333333333333333333329999999999 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:01:11 2004 Input: 0.3333333333333333333333333333+0.0000000000000000000000000000000000000000000000000000000000000001 Output: ? 0.33333333333333333333333333329999999999 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:17:29 2004 Input: 1/0 Output: ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:17:50 2004 Input: nan Output: ? nan ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:30:16 2004 Input: help Output: ? help ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:30:25 2004 Input: ? Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:30:50 2004 Input: ?11 Output: ? addhelp alias allocatemem break default error extern for fordiv forprime forstep forsubgroup forvec getheap getrand getstack gettime global if input install kill next print print1 printp printp1 printtex quit read reorder return setrand system trap type until whatnow while write write1 writetex ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:30:57 2004 Input: ?12 Output: ? The standard distribution of GP/PARI includes a reference manual, a tutorial, a reference card and quite a few examples. They should have been installed in the directory '/usr/share/pari'. If not you should ask the person who installed PARI on your system where they can be found. You can also download them from the PARI WWW site 'http://www.parigp-home.de/'. Three mailing lists are devoted to PARI: - pari-announce (moderated) to announce major version changes. - pari-dev for everything related to the development of PARI, including suggestions, technical questions, bug reports and patch submissions. - pari-users for everything else! To subscribe, send an empty message to -subscribe@list.cr.yp.to. You can only send messages to the lists you have subscribed to! An archive is kept at the WWW site mentioned above. You can also reach the authors directly by email: pari@math.u-bordeaux.fr (answer not guaranteed). ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:37:52 2004 Input: ? Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:38:11 2004 Input: ?0 Output: ? x ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:38:25 2004 Input: ?1 Output: ? divrem lex max min shift shiftmul sign vecmax vecmin ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:38:43 2004 Input: ?2 Output: ? List Mat Mod Pol Polrev Qfb Ser Set Str Vec binary bitand bitneg bitnegimply bitor bittest bitxor ceil centerlift changevar component conj conjvec denominator floor frac imag length lift norm norml2 numerator numtoperm padicprec permtonum precision random real round simplify sizebyte sizedigit truncate valuation variable ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:38:58 2004 Input: ? Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:39:57 2004 Input: I Output: ? I ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:40:24 2004 Input: I(2) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: I(2) ^-- Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:44:02 2004 Input: ?10 Output: ? plot plotbox plotclip plotcolor plotcopy plotcursor plotdraw plotfile ploth plothraw plothsizes plotinit plotkill plotlines plotlinetype plotmove plotpoints plotpointsize plotpointtype plotrbox plotrecth plotrecthraw plotrline plotrmove plotrpoint plotscale plotstring plotterm psdraw psploth psplothraw ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '195.138' ************** PARI ***************** Host 195.138.99.208 (195.138.99.208) Time: Tue Dec 28 02:44:13 2004 Input: ?plot Output: WARNING: PARI command contains unsafe command 'plot', so it will not be executed. '203.71.' ************** PARI ***************** Host 203.71.130.72 (203.71.130.72) Time: Tue Dec 28 03:46:46 2004 Input: q := 16; F:= FiniteField(q); PP:= ProjectivePlane(F); PP; G, gspt, gsln := CollineationGroup(PP); G; Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: q:=16; ^---- *** unexpected character: F:=FiniteField(q); ^----------------- *** unexpected character: PP:=ProjectivePlane(F); ^-------------------- *** Warning: unused characters: ,gspt,gsln:=CollineationGroup(PP);. Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '205.188' ************** PARI ***************** Host 205.188.116.139 (205.188.116.139) Time: Tue Dec 28 11:24:27 2004 Input: 7708 Output: ? 7708 ? Errors (if any) and Timing Info: Timing: real 0m0.371s user 0m0.007s sys 0m0.006s '205.188' ************** PARI ***************** Host 205.188.116.139 (205.188.116.139) Time: Tue Dec 28 11:28:35 2004 Input: 239 Output: ? 239 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '205.188' ************** PARI ***************** Host 205.188.116.139 (205.188.116.139) Time: Tue Dec 28 11:30:54 2004 Input: 468 Output: ? 468 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '205.188' ************** PARI ***************** Host 205.188.116.139 (205.188.116.139) Time: Tue Dec 28 11:33:16 2004 Input: 3594 Output: ? 3594 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '205.188' ************** PARI ***************** Host 205.188.116.139 (205.188.116.139) Time: Tue Dec 28 11:37:40 2004 Input: 16-34-38-42-47-1 Output: ? -146 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.006s '205.188' ************** PARI ***************** Host 205.188.116.139 (205.188.116.139) Time: Tue Dec 28 11:47:53 2004 Input: celestine wallace Output: ? celestinewallace ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '205.188' ************** PARI ***************** Host 205.188.116.139 (205.188.116.139) Time: Tue Dec 28 11:54:40 2004 Input: keno Output: ? keno ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '80.238.' ************** PARI ***************** Host 80.238.13.231 (80.238.13.231) Time: Wed Dec 29 16:56:09 2004 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.361s user 0m0.003s sys 0m0.014s '80.238.' ************** PARI ***************** Host 80.238.13.231 (80.238.13.231) Time: Wed Dec 29 16:56:49 2004 Input: factor(x^(10)-1) Output: ? [x - 1 1] [x + 1 1] [x^4 - x^3 + x^2 - x + 1 1] [x^4 + x^3 + x^2 + x + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.092s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Dec 29 21:33:48 2004 Input: lcm(659,1296) lcm(659,183) Output: ? 854064 ? 120597 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Dec 29 21:35:12 2004 Input: lcm(659,1296)+lcm(659,183) Output: ? 974661 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Dec 29 21:36:23 2004 Input: lcm(659,1296)-lcm(659,183) Output: ? 733467 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '83.146.' ************** PARI ***************** Host 83.146.18.34 (83.146.18.34) Time: Thu Dec 30 09:28:15 2004 Input: 2+2+2+2+1 Output: ? 9 ? Errors (if any) and Timing Info: Timing: real 0m0.338s user 0m0.008s sys 0m0.009s '219.167' ************** PARI ***************** Host 219.167.94.2 (219.167.94.2) Time: Fri Dec 31 04:42:49 2004 Input: factor((10^978+11)/3) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 9257 Killed /usr/bin/gp -q -emacs Timing: real 0m21.083s user 0m20.973s sys 0m0.028s '219.167' ************** PARI ***************** Host 219.167.94.2 (219.167.94.2) Time: Fri Dec 31 04:42:58 2004 Input: factor(100) Output: ? [2 2] [5 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '80.178.' ************** PARI ***************** Host 80.178.195.103 (80.178.195.103) Time: Fri Dec 31 06:32:40 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '24.126.' ************** PARI ***************** Host 24.126.228.100 (24.126.228.100) Time: Fri Dec 31 07:39:16 2004 Input: 123455675644565332345561109 Output: ? 123455675644565332345561109 ? Errors (if any) and Timing Info: Timing: real 0m0.098s user 0m0.006s sys 0m0.007s '24.126.' ************** PARI ***************** Host 24.126.228.100 (24.126.228.100) Time: Fri Dec 31 07:39:19 2004 Input: 123455675644565332345561109 Output: ? 123455675644565332345561109 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '24.126.' ************** PARI ***************** Host 24.126.228.100 (24.126.228.100) Time: Fri Dec 31 07:39:23 2004 Input: 123455675644565332345561109 Output: ? 123455675644565332345561109 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.003s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 13:04:00 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.374s user 0m0.006s sys 0m0.009s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 13:05:54 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" OmO.882 Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? Errors (if any) and Timing Info: *** unknown member function: OmO.882 ^--- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 13:09:40 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" OmO.882 Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? Errors (if any) and Timing Info: *** unknown member function: OmO.882 ^--- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 13:11:39 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" OmO.882380 Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? Errors (if any) and Timing Info: *** unknown member function: OmO.882380 ^------ Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 13:17:19 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" OmO.883 Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? Errors (if any) and Timing Info: *** unknown member function: OmO.883 ^--- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 13:21:32 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" OmO.882380 Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? Errors (if any) and Timing Info: *** unknown member function: OmO.882380 ^------ Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 13:24:25 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" OmO.990 Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? Errors (if any) and Timing Info: *** unknown member function: OmO.990 ^--- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 13:32:49 2004 Input: real Omo.173 Output: ? ? Errors (if any) and Timing Info: *** unknown member function: Timing: realOmo.173 ^--- Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 13:35:37 2004 Input: real Omo.173 user OmO.030 Output: ? ? ? Errors (if any) and Timing Info: *** unknown member function: Timing: realOmo.173 ^--- *** unknown member function: userOmO.030 ^--- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 13:36:23 2004 Input: real Omo.882 user OmO.380 Output: ? ? ? Errors (if any) and Timing Info: *** unknown member function: Timing: realOmo.882 ^--- *** unknown member function: userOmO.380 ^--- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 13:39:40 2004 Input: real Omo.173 user OmO.030 Output: ? ? ? Errors (if any) and Timing Info: *** unknown member function: Timing: realOmo.173 ^--- *** unknown member function: userOmO.030 ^--- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 13:44:17 2004 Input: real Omo.882 user OmO.990 OmO.800 Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unknown member function: Timing: realOmo.882 ^--- *** unknown member function: userOmO.990 ^--- *** unknown member function: OmO.800 ^--- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 16:36:02 2004 Input: OmO.713,894,830,920,786 Output: ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,894,830,920,786. *** unknown member function: OmO.713,894,830,920,786 ^------------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 16:39:03 2004 Input: real OmO.713,894,830,920,786 Output: ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,894,830,920,786. *** unknown member function: Timing: realOmO.713,894,830,920,786 ^------------------- Timing: real 0m0.042s user 0m0.005s sys 0m0.008s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 16:44:33 2004 Input: real OmO.7,1,3 Output: ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,1,3. *** unknown member function: Timing: realOmO.7,1,3 ^----- Timing: real 0m0.039s user 0m0.004s sys 0m0.006s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 16:49:56 2004 Input: real OmO.7 OmO.1 OmO.3 Output: ? ? ? ? Errors (if any) and Timing Info: *** unknown member function: Timing: realOmO.7 ^- *** unknown member function: OmO.1 ^- *** unknown member function: OmO.3 ^- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Fri Dec 31 16:53:11 2004 Input: real OmO.3 OmO.0 OmO.0 Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unknown member function: Timing: realOmO.3 ^- *** unknown member function: OmO.0 ^- *** unknown member function: OmO.0 ^- Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '128.248' ************** PARI ***************** Host 128.248.170.103 (128.248.170.103) Time: Fri Dec 31 17:15:10 2004 Input: SymmetricCharacter({2,1}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: SymmetricCharacter({2,1}) ^------ Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '12.221.' ************** PARI ***************** Host 12.221.109.182 (12.221.109.182) Time: Sat Jan 1 02:58:23 2005 Input: 578707190879875097587478973974978907378557 / 917978985797398729744 Output: ? 578707190879875097587478973974978907378557/917978985797398729744 ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.007s sys 0m0.005s '217.226' ************** PARI ***************** Host 217.226.194.43 (217.226.194.43) Time: Sat Jan 1 12:13:23 2005 Input: 7*4 Output: ? 28 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.006s sys 0m0.006s '217.226' ************** PARI ***************** Host 217.226.194.43 (217.226.194.43) Time: Sat Jan 1 12:13:40 2005 Input: 47543217^13 Output: ? 6340906401601183580947983228635192489414152668978367395869623100459079190289994832854981347609943537 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.004s sys 0m0.009s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Sat Jan 1 22:16:13 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Sat Jan 1 22:18:12 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]! real Omo.882 user OmO.380 sys OmO.516 Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: '"' instead of: ... click [PARI] or [MAGMA]! ^ *** unknown member function: Timing: realOmo.882 ^--- *** unknown member function: userOmO.380 ^--- *** unknown member function: sysOmO.516 ^--- Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Sat Jan 1 22:22:10 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]! real Omo.283 user OmO.640 sys OmO.377 Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: '"' instead of: ... click [PARI] or [MAGMA]! ^ *** unknown member function: Timing: realOmo.283 ^--- *** unknown member function: userOmO.640 ^--- *** unknown member function: sysOmO.377 ^--- Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '152.163' ************** PARI ***************** Host 152.163.100.139 (152.163.100.139) Time: Sat Jan 1 22:25:18 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]! real Omo.283 user OmO.640 sys OmO.377 Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: '"' instead of: ... click [PARI] or [MAGMA]! ^ *** unknown member function: Timing: realOmo.283 ^--- *** unknown member function: userOmO.640 ^--- *** unknown member function: sysOmO.377 ^--- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '12.221.' ************** PARI ***************** Host 12.221.80.253 (12.221.80.253) Time: Sat Jan 1 23:57:30 2005 Input: 57685^51 Output: ? 651940175833242587115438550491171720870850719410832762497117862603461543052128246891914523362674497973360293433877903628422969675575868946991759498003075794386961638004108523673425143694467417755278655484879823944766030763275921344757080078125 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '64.12.1' ************** PARI ***************** Host 64.12.116.139 (64.12.116.139) Time: Sun Jan 2 11:55:11 2005 Input: real OmO.386 sys OmO.640 user OmO.377 Output: ? ? ? ? Errors (if any) and Timing Info: *** unknown member function: Timing: realOmO.386 ^--- *** unknown member function: sysOmO.640 ^--- *** unknown member function: userOmO.377 ^--- Timing: real 0m0.339s user 0m0.007s sys 0m0.008s '80.238.' ************** PARI ***************** Host 80.238.57.164 (80.238.57.164) Time: Sun Jan 2 12:59:30 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.009s sys 0m0.006s '63.188.' ************** PARI ***************** Host 63.188.241.11 (63.188.241.11) Time: Sun Jan 2 15:41:36 2005 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.004s sys 0m0.010s '63.188.' ************** PARI ***************** Host 63.188.241.11 (63.188.241.11) Time: Sun Jan 2 15:42:02 2005 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '83.27.6' ************** PARI ***************** Host 83.27.67.220 (83.27.67.220) Time: Sun Jan 2 22:48:15 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.009s sys 0m0.003s '222.7.1' ************** PARI ***************** Host 222.7.107.94 (222.7.107.94) Time: Mon Jan 3 02:10:13 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '129.242' ************** PARI ***************** Host 129.242.20.195 (129.242.20.195) Time: Mon Jan 3 03:56:51 2005 Input: Fp:=GF(1099511627791); pol:=PolynomialRing(Fp); fg:=X^5 + 142215603378*X^4 + 241609938357*X^3 + 669467685626*X^2 +424019950525*X + 89237139156; GaloisGroup(fg); fg=Mod(1,1099511627791)*X^5+ 142215603378*X^4 + 241609938357*X^3 + 669467685626*X^2 +424019950525*X + 89237139156 Output: ? ? ? ? ? Mod(1, 1099511627791)*X^5 + Mod(142215603378, 1099511627791)*X^4 + Mod(241609938357, 1099511627791)*X^3 + Mod(669467685626, 1099511627791)*X^2 + Mod(424019950525, 1099511627791)*X + Mod(89237139156, 1099511627791) ? Errors (if any) and Timing Info: *** unexpected character: Fp:=GF(1099511627791); ^------------------- *** unexpected character: pol:=PolynomialRing(Fp) ^-------------------- *** unexpected character: fg:=X^5+142215603378*X^ ^-------------------- *** expected character: '=' instead of: GaloisGroup(fg); ^- Timing: real 0m0.028s user 0m0.010s sys 0m0.002s '129.242' ************** PARI ***************** Host 129.242.20.195 (129.242.20.195) Time: Mon Jan 3 03:57:02 2005 Input: fg=Mod(1,1099511627791)*X^5+ 142215603378*X^4 + 241609938357*X^3 + 669467685626*X^2 +424019950525*X + 89237139156 Output: ? ? Mod(1, 1099511627791)*X^5 + Mod(142215603378, 1099511627791)*X^4 + Mod(241609938357, 1099511627791)*X^3 + Mod(669467685626, 1099511627791)*X^2 + Mod(424019950525, 1099511627791)*X + Mod(89237139156, 1099511627791) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '129.242' ************** PARI ***************** Host 129.242.20.195 (129.242.20.195) Time: Mon Jan 3 03:57:28 2005 Input: fg=Mod(1,1099511627791)*X^5+ 142215603378*X^4 + 241609938357*X^3 + 669467685626*X^2 +424019950525*X + 89237139156 Galois Output: ? Mod(1, 1099511627791)*X^5 + Mod(142215603378, 1099511627791)*X^4 + Mod(241609938357, 1099511627791)*X^3 + Mod(669467685626, 1099511627791)*X^2 + Mod(424019950525, 1099511627791)*X + Mod(89237139156, 1099511627791) ? Galois ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '129.242' ************** PARI ***************** Host 129.242.20.195 (129.242.20.195) Time: Mon Jan 3 03:57:38 2005 Input: fg=Mod(1,1099511627791)*X^5+ 142215603378*X^4 + 241609938357*X^3 + 669467685626*X^2 +424019950525*X + 89237139156 Galois(fg) Output: ? Mod(1, 1099511627791)*X^5 + Mod(142215603378, 1099511627791)*X^4 + Mod(241609938357, 1099511627791)*X^3 + Mod(669467685626, 1099511627791)*X^2 + Mod(424019950525, 1099511627791)*X + Mod(89237139156, 1099511627791) ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: Galois(fg) ^ Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '219.77.' ************** PARI ***************** Host 219.77.78.200 (219.77.78.200) Time: Mon Jan 3 05:25:53 2005 Input: 10 Output: ? 10 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '219.77.' ************** PARI ***************** Host 219.77.78.200 (219.77.78.200) Time: Mon Jan 3 05:26:19 2005 Input: 111 Output: ? 111 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '219.77.' ************** PARI ***************** Host 219.77.78.200 (219.77.78.200) Time: Mon Jan 3 05:26:39 2005 Input: 111111111111111111111111111111111111111 Output: ? 111111111111111111111111111111111111111 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 09:50:26 2005 Input: ffinit(x,3,3) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: ffinit(x,3,3) ^-- Timing: real 0m0.472s user 0m0.009s sys 0m0.009s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 09:50:39 2005 Input: ffinit(3,3) Output: ? Mod(1, 3)*x^3 + Mod(2, 3)*x + Mod(2, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.098s user 0m0.007s sys 0m0.010s '149.132' ************** PARI ***************** Host 149.132.103.108 (149.132.103.108) Time: Mon Jan 3 10:00:35 2005 Input: Factorization(234242); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorization(234242 ^-------------------- Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '149.132' ************** PARI ***************** Host 149.132.103.108 (149.132.103.108) Time: Mon Jan 3 10:00:43 2005 Input: Factorization(234242) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorization(234242 ^-------------------- Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '149.132' ************** PARI ***************** Host 149.132.103.108 (149.132.103.108) Time: Mon Jan 3 10:00:57 2005 Input: factorization(234242) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: factorization(234242 ^-------------------- Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:05:14 2005 Input: pf=ffinit(3,3,th); g=Mod(x,pf); for(i=1,26,print1(" "lift(g^i))) Output: ? ? ? 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:05:22 2005 Input: pf=ffinit(3,3,th); g=Mod(th,pf); for(i=1,26,print1(" "lift(g^i))) Output: ? ? ? th th^2 Mod(1, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(1, 3)*th Mod(1, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(2, 3) Mod(1, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th Mod(2, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(2, 3) Mod(1, 3) Mod(1, 3)*th Mod(1, 3)*th^2 Mod(1, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(1, 3)*th Mod(1, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(2, 3) Mod(1, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th Mod(2, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(2, 3) Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:06:19 2005 Input: pf=ffinit(3,3,th); g=Mod(th,pf); for(i=1,26,print1(" "lift(g^i));if(lift(g^i)-1==0,print())) Output: ? ? ? th th^2 Mod(1, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(1, 3)*th Mod(1, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(2, 3) Mod(1, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th Mod(2, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(2, 3) Mod(1, 3) Mod(1, 3)*th Mod(1, 3)*th^2 Mod(1, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(1, 3)*th Mod(1, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(2, 3) Mod(1, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th Mod(2, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(2, 3) Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:06:45 2005 Input: pf=ffinit(3,3,th); g=Mod(Mod(2,3)*th,pf); for(i=1,26,print1(" "lift(g^i));if(lift(g^i)-1==0,print())) Output: ? ? ? Mod(2, 3)*th Mod(1, 3)*th^2 Mod(2, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(1, 3)*th Mod(2, 3)*th^2 + Mod(2, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(1, 3)*th + Mod(2, 3) Mod(2, 3)*th^2 + Mod(2, 3) Mod(2, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th Mod(1, 3)*th^2 + Mod(2, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(2, 3) Mod(2, 3) Mod(1, 3)*th Mod(2, 3)*th^2 Mod(1, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(2, 3)*th Mod(1, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(1, 3)*th + Mod(2, 3) Mod(2, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(1, 3) Mod(1, 3)*th + Mod(2, 3) Mod(2, 3)*th^2 + Mod(1, 3)*th Mod(2, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(1, 3) Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:07:10 2005 Input: pf=ffinit(3,3,th); print(pf); g=Mod(Mod(2,3)*th,pf); for(i=1,26,print1(" "lift(g^i));if(lift(g^i)-1==0,print())) Output: ? ? Mod(1, 3)*th^3 + Mod(2, 3)*th + Mod(2, 3) ? ? Mod(2, 3)*th Mod(1, 3)*th^2 Mod(2, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(1, 3)*th Mod(2, 3)*th^2 + Mod(2, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(1, 3)*th + Mod(2, 3) Mod(2, 3)*th^2 + Mod(2, 3) Mod(2, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th Mod(1, 3)*th^2 + Mod(2, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(2, 3) Mod(2, 3) Mod(1, 3)*th Mod(2, 3)*th^2 Mod(1, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(2, 3)*th Mod(1, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(1, 3)*th + Mod(2, 3) Mod(2, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(1, 3) Mod(1, 3)*th + Mod(2, 3) Mod(2, 3)*th^2 + Mod(1, 3)*th Mod(2, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(1, 3) Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '193.55.' ************** PARI ***************** Host 193.55.113.197 (193.55.113.197) Time: Mon Jan 3 10:08:15 2005 Input: a*x+b=0 Output: ? a*x ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:08:17 2005 Input: pf=ffinit(3,3,th); print(pf); g=Mod(Mod(2,3)*th,pf); for(i=1,26,print(" "lift(g^i))) Output: ? ? Mod(1, 3)*th^3 + Mod(2, 3)*th + Mod(2, 3) ? ? Mod(2, 3)*th Mod(1, 3)*th^2 Mod(2, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(1, 3)*th Mod(2, 3)*th^2 + Mod(2, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(1, 3)*th + Mod(2, 3) Mod(2, 3)*th^2 + Mod(2, 3) Mod(2, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th Mod(1, 3)*th^2 + Mod(2, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(2, 3) Mod(2, 3) Mod(1, 3)*th Mod(2, 3)*th^2 Mod(1, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(2, 3)*th Mod(1, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(1, 3)*th + Mod(2, 3) Mod(2, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(1, 3) Mod(1, 3)*th + Mod(2, 3) Mod(2, 3)*th^2 + Mod(1, 3)*th Mod(2, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(1, 3) Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:15:36 2005 Input: pf=ffinit(3,3,th); print(pf); g=Mod(Mod(2,3)*th,pf); for(i=1,26,print(" "lift(g^i))) Mod(17*7,26) Output: ? ? Mod(1, 3)*th^3 + Mod(2, 3)*th + Mod(2, 3) ? ? Mod(2, 3)*th Mod(1, 3)*th^2 Mod(2, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(1, 3)*th Mod(2, 3)*th^2 + Mod(2, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(1, 3)*th + Mod(2, 3) Mod(2, 3)*th^2 + Mod(2, 3) Mod(2, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th Mod(1, 3)*th^2 + Mod(2, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(2, 3) Mod(2, 3) Mod(1, 3)*th Mod(2, 3)*th^2 Mod(1, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(2, 3)*th Mod(1, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(1, 3)*th + Mod(2, 3) Mod(2, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(1, 3) Mod(1, 3)*th + Mod(2, 3) Mod(2, 3)*th^2 + Mod(1, 3)*th Mod(2, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(1, 3) Mod(1, 3) ? Mod(15, 26) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.004s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:18:34 2005 Input: pf=ffinit(3,3,th); print(pf); g=Mod(Mod(2,3)*th,pf); for(i=1,26,print(" "lift(g^i))) Mod(17*7,26); lift(g^17) lift(g^7) lift(g^(17*7)) Output: ? ? Mod(1, 3)*th^3 + Mod(2, 3)*th + Mod(2, 3) ? ? Mod(2, 3)*th Mod(1, 3)*th^2 Mod(2, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(1, 3)*th Mod(2, 3)*th^2 + Mod(2, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(1, 3)*th + Mod(2, 3) Mod(2, 3)*th^2 + Mod(2, 3) Mod(2, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(2, 3)*th Mod(1, 3)*th^2 + Mod(2, 3)*th + Mod(2, 3) Mod(1, 3)*th^2 + Mod(2, 3) Mod(2, 3) Mod(1, 3)*th Mod(2, 3)*th^2 Mod(1, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(2, 3)*th Mod(1, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(1, 3)*th + Mod(2, 3) Mod(2, 3)*th^2 + Mod(2, 3)*th + Mod(1, 3) Mod(1, 3)*th^2 + Mod(1, 3) Mod(1, 3)*th + Mod(2, 3) Mod(2, 3)*th^2 + Mod(1, 3)*th Mod(2, 3)*th^2 + Mod(1, 3)*th + Mod(1, 3) Mod(2, 3)*th^2 + Mod(1, 3) Mod(1, 3) ? ? ? Mod(2, 3)*th^2 + Mod(2, 3)*th ? Mod(1, 3)*th^2 + Mod(1, 3)*th + Mod(2, 3) ? Mod(2, 3)*th^2 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:52:28 2005 Input: pf=ffinit(29,6,th); print(pf); g=Mod(th,pf); i=1; while(i<29^6-1 && lift(g^i)!=0,i++);print(i) Output: ? ? Mod(1, 29)*th^6 + Mod(12, 29)*th^4 + Mod(14, 29)*th^3 + Mod(6, 29)*th + Mod(18, 29) ? ? ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 23865 Killed /usr/bin/gp -q -emacs Timing: real 0m21.015s user 0m20.987s sys 0m0.013s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:54:01 2005 Input: pf=ffinit(29,6,th); print(pf); factor(29^6-1) Output: ? ? Mod(1, 29)*th^6 + Mod(12, 29)*th^4 + Mod(14, 29)*th^3 + Mod(6, 29)*th + Mod(18, 29) ? [2 3] [3 2] [5 1] [7 1] [13 1] [67 1] [271 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:55:45 2005 Input: factor(29^5-1) Output: ? [2 2] [7 1] [732541 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:55:53 2005 Input: factor(29^4-1) Output: ? [2 4] [3 1] [5 1] [7 1] [421 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:55:59 2005 Input: factor(31^4-1) Output: ? [2 7] [3 1] [5 1] [13 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:56:04 2005 Input: factor(31^5-1) Output: ? [2 1] [3 1] [5 2] [11 1] [17351 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:56:09 2005 Input: factor(31^6-1) Output: ? [2 6] [3 2] [5 1] [7 2] [19 1] [331 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:56:27 2005 Input: factor(37^4-1) Output: ? [2 4] [3 2] [5 1] [19 1] [137 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:56:35 2005 Input: factor(37^3-1) Output: ? [2 2] [3 3] [7 1] [67 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:56:40 2005 Input: factor(29^3-1) Output: ? [2 2] [7 1] [13 1] [67 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:56:47 2005 Input: factor(31^3-1) Output: ? [2 1] [3 2] [5 1] [331 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:56:58 2005 Input: factor(43^3-1) Output: ? [2 1] [3 2] [7 1] [631 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:57:03 2005 Input: factor(41^3-1) Output: ? [2 3] [5 1] [1723 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:57:13 2005 Input: factor(47^3-1) Output: ? [2 1] [23 1] [37 1] [61 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:57:19 2005 Input: factor(53^3-1) Output: ? [2 2] [7 1] [13 1] [409 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:57:59 2005 Input: forprime(p=27,70,print(length(factor(p^3-1)))) Output: ? 2 2 2 2 2 2 2 2 2 2 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:58:13 2005 Input: forprime(p=27,70,print(length(factor(p^3-1)~))) Output: ? 4 4 4 3 4 4 4 3 5 5 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:58:23 2005 Input: forprime(p=27,70,print(length(factor(p^4-1)~))) Output: ? 5 5 5 5 6 6 5 5 5 6 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:58:28 2005 Input: forprime(p=27,70,print(length(factor(p^5-1)~))) Output: ? 3 5 5 3 4 5 5 6 5 5 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:58:46 2005 Input: forprime(p=27,70,print(p)) Output: ? 29 31 37 41 43 47 53 59 61 67 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:58:58 2005 Input: factor(37^3-1) Output: ? [2 2] [3 3] [7 1] [67 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:59:06 2005 Input: factor(37^4-1) Output: ? [2 4] [3 2] [5 1] [19 1] [137 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:59:12 2005 Input: factor(37^6-1) Output: ? [2 3] [3 3] [7 1] [19 1] [31 1] [43 1] [67 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:59:25 2005 Input: factor(31^6-1) Output: ? [2 6] [3 2] [5 1] [7 2] [19 1] [331 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:59:31 2005 Input: factor(31^5-1) Output: ? [2 1] [3 1] [5 2] [11 1] [17351 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 10:59:37 2005 Input: factor(37^5-1) Output: ? [2 2] [3 2] [11 1] [41 1] [4271 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:01:05 2005 Input: factor(29^5-1) Output: ? [2 2] [7 1] [732541 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:01:27 2005 Input: factor(29^5-1); ffinit(29,5,th) Output: ? ? Mod(1, 29)*th^5 + Mod(9, 29)*th^3 + Mod(10, 29)*th^2 + Mod(28, 29)*th + Mod(21, 29) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:02:02 2005 Input: factor(29^5-1) ffinit(29,5,th); Output: ? [2 2] [7 1] [732541 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.002s sys 0m0.011s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:03:34 2005 Input: factor(29^2-1) ffinit(29,5,th); Output: ? [2 3] [3 1] [5 1] [7 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:03:43 2005 Input: factor(31^2-1) Output: ? [2 6] [3 1] [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:03:48 2005 Input: factor(37^2-1) Output: ? [2 3] [3 2] [19 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:03:54 2005 Input: factor(39^2-1) Output: ? [2 4] [5 1] [19 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:04:35 2005 Input: forprime(p=27,70,print1(" ",length(factor(p^2-1)~))) Output: ? 4 3 3 4 4 3 3 4 4 4 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.002s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:04:54 2005 Input: factor(31^2-1)~ Output: ? [2 3 5] [6 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:06:11 2005 Input: pf=ffinit(31,2,th) Output: ? Mod(1, 31)*th^2 + Mod(9, 31) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '220.220' ************** PARI ***************** Host 220.220.169.218 (220.220.169.218) Time: Mon Jan 3 11:08:39 2005 Input: factor(641765730765796490791870295201) Output: ? [641765730765796490791870295201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.005s '220.220' ************** PARI ***************** Host 220.220.169.218 (220.220.169.218) Time: Mon Jan 3 11:08:51 2005 Input: factor(204814037198857354479454794029) Output: ? [204814037198857354479454794029 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.004s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:08:51 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(th,pf); i=1; while(i<31^2 && lift(g^i)!=1,i++); print(i) Output: ? ? ? ? ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:09:13 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(1,31),pf); i=1; while(i<31^2 && lift(g^i)!=1,i++); print(i) Output: ? ? ? ? ? 40 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:09:33 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(2,31),pf); i=1; while(i<31^2 && lift(g^i)!=1,i++); print(i) Output: ? ? ? ? ? 96 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:09:53 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(3,31),pf); i=1; while(i<31^2 && lift(g^i)!=1,i++); print(i " " 31^2-1) Output: ? ? ? ? ? 480 960 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.022s sys 0m0.004s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:09:59 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(5,31),pf); i=1; while(i<31^2 && lift(g^i)!=1,i++); print(i " " 31^2-1) Output: ? ? ? ? ? 192 960 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:10:06 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); i=1; while(i<31^2 && lift(g^i)!=1,i++); print(i " " 31^2-1) Output: ? ? ? ? ? 960 960 ? Errors (if any) and Timing Info: Timing: real 0m0.041s user 0m0.035s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:11:20 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13) Output: ? ? ? Mod(12, 31)*th + Mod(18, 31) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:24:36 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13) lift(g^111) Output: ? ? ? Mod(12, 31)*th + Mod(18, 31) ? Mod(24, 31)*th + Mod(6, 31) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:25:01 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13) lift(g^111) lift(g^(13*111)) Output: ? ? ? Mod(12, 31)*th + Mod(18, 31) ? Mod(24, 31)*th + Mod(6, 31) ? Mod(15, 31)*th + Mod(10, 31) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:42:25 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13) lift(g^111) gak=lift((g^13)^111)) Ps=[[11,4],[18,26],[2,7],[8,13],[14,8],[18,26],[13,4],[26,15],[14,20],[17,17],[14,13],[19,26],[9,0],[12,0],[8,18],[26,0],[21,14],[8,17],[26,11],[0,26],[1,14],[12,1],[4,26],[7,26],[15,0],[17,2],[4,16],[20,27],[8,11],[18,26],[13,27],[14,13],[19,26],[15,0],[18,26],[11,4],[26,12],[4,12],[4,26],[0,11],[15,7],[0,1],[4,19],[26,16],[20,4],[26,13],[14,20],[18,26]]; for(ind=1,length(Ps), p=Mod(Ps[ind][1],31)*th+Mod(Ps[ind][2],31); print(" "lift(Mod(p,pf)*gak)) Output: ? ? ? Mod(12, 31)*th + Mod(18, 31) ? Mod(24, 31)*th + Mod(6, 31) ? Mod(15, 31)*th + Mod(10, 31) ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ). *** expected character: ')' instead of: ...t(" "lift(Mod(p,pf)*gak)) ^ Timing: real 0m0.019s user 0m0.008s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:43:13 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13) lift(g^111) gak=(g^13)^111; Ps=[[11,4],[18,26],[2,7],[8,13],[14,8],[18,26],[13,4],[26,15],[14,20],[17,17],[14,13],[19,26],[9,0],[12,0],[8,18],[26,0],[21,14],[8,17],[26,11],[0,26],[1,14],[12,1],[4,26],[7,26],[15,0],[17,2],[4,16],[20,27],[8,11],[18,26],[13,27],[14,13],[19,26],[15,0],[18,26],[11,4],[26,12],[4,12],[4,26],[0,11],[15,7],[0,1],[4,19],[26,16],[20,4],[26,13],[14,20],[18,26]]; for(ind=1,length(Ps), p=Mod(Ps[ind][1],31)*th+Mod(Ps[ind][2],31); print(" "lift(Mod(p,pf)*gak))) Output: ? ? ? Mod(12, 31)*th + Mod(18, 31) ? Mod(24, 31)*th + Mod(6, 31) ? ? ? Mod(15, 31)*th + Mod(30, 31) Mod(12, 31)*th + Mod(21, 31) Mod(1, 31)*th + Mod(9, 31) Mod(27, 31)*th + Mod(10, 31) Mod(12, 31)*th + Mod(25, 31) Mod(12, 31)*th + Mod(21, 31) Mod(4, 31)*th Mod(20, 31)*th + Mod(8, 31) Mod(6, 31)*th + Mod(21, 31) Mod(22, 31)*th + Mod(8, 31) Mod(25, 31)*th + Mod(13, 31) Mod(22, 31)*th + Mod(6, 31) Mod(28, 31)*th + Mod(20, 31) Mod(27, 31)*th + Mod(6, 31) Mod(9, 31)*th + Mod(29, 31) Mod(12, 31)*th + Mod(13, 31) Mod(17, 31)*th + Mod(11, 31) Mod(25, 31)*th + Mod(19, 31) Mod(22, 31)*th + Mod(30, 31) Mod(18, 31)*th + Mod(12, 31) Mod(3, 31)*th + Mod(1, 31) Mod(11, 31)*th + Mod(16, 31) Mod(27, 31)*th + Mod(14, 31) Mod(26, 31)*th Mod(26, 31)*th + Mod(23, 31) Mod(14, 31)*th + Mod(13, 31) Mod(1, 31)*th + Mod(7, 31) Mod(16, 31)*th + Mod(1, 31) Mod(28, 31)*th + Mod(21, 31) Mod(12, 31)*th + Mod(21, 31) Mod(8, 31)*th + Mod(13, 31) Mod(25, 31)*th + Mod(13, 31) Mod(22, 31)*th + Mod(6, 31) Mod(26, 31)*th + Mod(23, 31) Mod(12, 31)*th + Mod(21, 31) Mod(15, 31)*th + Mod(30, 31) Mod(6, 31)*th + Mod(9, 31) Mod(3, 31)*th + Mod(29, 31) Mod(27, 31)*th + Mod(14, 31) Mod(10, 31)*th + Mod(17, 31) Mod(7, 31)*th Mod(15, 31)*th + Mod(10, 31) Mod(15, 31)*th + Mod(6, 31) Mod(4, 31)*th + Mod(18, 31) Mod(12, 31)*th + Mod(19, 31) Mod(21, 31)*th + Mod(19, 31) Mod(6, 31)*th + Mod(21, 31) Mod(12, 31)*th + Mod(21, 31) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:51:28 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13) lift(g^111) gak=(g^13)^111; Ps=[[11,4],[18,26],[2,7],[8,13],[14,8],[18,26],[13,4],[26,15],[14,20],[17,17],[14,13],[19,26],[9,0],[12,0],[8,18],[26,0],[21,14],[8,17],[26,11],[0,26],[1,14],[12,1],[4,26],[7,26],[15,0],[17,2],[4,16],[20,27],[8,11],[18,26],[13,27],[14,13],[19,26],[15,0],[18,26],[11,4],[26,12],[4,12],[4,26],[0,11],[15,7],[0,1],[4,19],[26,16],[20,4],[26,13],[14,20],[18,26]]; for(ind=1,length(Ps), p=Mod(Ps[ind][1],31)*th+Mod(Ps[ind][2],31); c=lift(Mod(p,pf)*gak));print(lift(Vec(c)))) Output: ? ? ? Mod(12, 31)*th + Mod(18, 31) ? Mod(24, 31)*th + Mod(6, 31) ? ? ? [12, 21] ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:51:35 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13) lift(g^111) gak=(g^13)^111; Ps=[[11,4],[18,26],[2,7],[8,13],[14,8],[18,26],[13,4],[26,15],[14,20],[17,17],[14,13],[19,26],[9,0],[12,0],[8,18],[26,0],[21,14],[8,17],[26,11],[0,26],[1,14],[12,1],[4,26],[7,26],[15,0],[17,2],[4,16],[20,27],[8,11],[18,26],[13,27],[14,13],[19,26],[15,0],[18,26],[11,4],[26,12],[4,12],[4,26],[0,11],[15,7],[0,1],[4,19],[26,16],[20,4],[26,13],[14,20],[18,26]]; for(ind=1,length(Ps), p=Mod(Ps[ind][1],31)*th+Mod(Ps[ind][2],31); c=lift(Mod(p,pf)*gak));print(lift(Vec(c))) Output: ? ? ? Mod(12, 31)*th + Mod(18, 31) ? Mod(24, 31)*th + Mod(6, 31) ? ? ? [12, 21] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:54:35 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13); lift(g^111); gak=(g^13)^111; Ps=[[11,4],[18,26],[2,7],[8,13],[14,8],[18,26],[13,4],[26,15],[14,20],[17,17],[14,13],[19,26],[9,0],[12,0],[8,18],[26,0],[21,14],[8,17],[26,11],[0,26],[1,14],[12,1],[4,26],[7,26],[15,0],[17,2],[4,16],[20,27],[8,11],[18,26],[13,27],[14,13],[19,26],[15,0],[18,26],[11,4],[26,12],[4,12],[4,26],[0,11],[15,7],[0,1],[4,19],[26,16],[20,4],[26,13],[14,20],[18,26]]; for(ind=1,length(Ps), p=Mod(Ps[ind][1],31)*th+Mod(Ps[ind][2],31);c=lift(Mod(p,pf)*gak));print(lift(Vec(c))) Output: ? ? ? ? ? ? ? [12, 21] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.005s sys 0m0.009s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:55:14 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13); lift(g^111); gak=(g^13)^111; Ps=[[11,4],[18,26],[2,7],[8,13],[14,8],[18,26],[13,4],[26,15],[14,20],[17,17],[14,13],[19,26],[9,0],[12,0],[8,18],[26,0],[21,14],[8,17],[26,11],[0,26],[1,14],[12,1],[4,26],[7,26],[15,0],[17,2],[4,16],[20,27],[8,11],[18,26],[13,27],[14,13],[19,26],[15,0],[18,26],[11,4],[26,12],[4,12],[4,26],[0,11],[15,7],[0,1],[4,19],[26,16],[20,4],[26,13],[14,20],[18,26]]; for(ind=1,length(Ps),p=Mod(Ps[ind][1],31)*th+Mod(Ps[ind][2],31);c=lift(Mod(p,pf)*gak));print(lift(Vec(c)))) Output: ? ? ? ? ? ? ? [12, 21] ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:55:27 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13); lift(g^111); gak=(g^13)^111; Ps=[[11,4],[18,26],[2,7],[8,13],[14,8],[18,26],[13,4],[26,15],[14,20],[17,17],[14,13],[19,26],[9,0],[12,0],[8,18],[26,0],[21,14],[8,17],[26,11],[0,26],[1,14],[12,1],[4,26],[7,26],[15,0],[17,2],[4,16],[20,27],[8,11],[18,26],[13,27],[14,13],[19,26],[15,0],[18,26],[11,4],[26,12],[4,12],[4,26],[0,11],[15,7],[0,1],[4,19],[26,16],[20,4],[26,13],[14,20],[18,26]]; for(ind=1,length(Ps),p=Mod(Ps[ind][1],31)*th+Mod(Ps[ind][2],31);c=lift(Mod(p,pf)*gak);print(lift(Vec(c)))) Output: ? ? ? ? ? ? ? [15, 30] [12, 21] [1, 9] [27, 10] [12, 25] [12, 21] [4, 0] [20, 8] [6, 21] [22, 8] [25, 13] [22, 6] [28, 20] [27, 6] [9, 29] [12, 13] [17, 11] [25, 19] [22, 30] [18, 12] [3, 1] [11, 16] [27, 14] [26, 0] [26, 23] [14, 13] [1, 7] [16, 1] [28, 21] [12, 21] [8, 13] [25, 13] [22, 6] [26, 23] [12, 21] [15, 30] [6, 9] [3, 29] [27, 14] [10, 17] [7, 0] [15, 10] [15, 6] [4, 18] [12, 19] [21, 19] [6, 21] [12, 21] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:56:10 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13); lift(g^111); gak=(g^13)^111; Ps=[[11,4],[18,26],[2,7],[8,13],[14,8],[18,26],[13,4],[26,15],[14,20],[17,17],[14,13],[19,26],[9,0],[12,0],[8,18],[26,0],[21,14],[8,17],[26,11],[0,26],[1,14],[12,1],[4,26],[7,26],[15,0],[17,2],[4,16],[20,27],[8,11],[18,26],[13,27],[14,13],[19,26],[15,0],[18,26],[11,4],[26,12],[4,12],[4,26],[0,11],[15,7],[0,1],[4,19],[26,16],[20,4],[26,13],[14,20],[18,26]]; for(ind=1,length(Ps),p=Mod(Ps[ind][1],31)*th+Mod(Ps[ind][2],31);c=lift(Mod(p,pf)*gak);c=lift(Vec(c));print1(" " c[1]*theta+c[2])) Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: ...(c));print1(" "c[1]*theta+c[2])) ^------- Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:57:15 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13); lift(g^111); gak=(g^13)^111; Ps=[[11,4],[18,26],[2,7],[8,13],[14,8],[18,26],[13,4],[26,15],[14,20],[17,17],[14,13],[19,26],[9,0],[12,0],[8,18],[26,0],[21,14],[8,17],[26,11],[0,26],[1,14],[12,1],[4,26],[7,26],[15,0],[17,2],[4,16],[20,27],[8,11],[18,26],[13,27],[14,13],[19,26],[15,0],[18,26],[11,4],[26,12],[4,12],[4,26],[0,11],[15,7],[0,1],[4,19],[26,16],[20,4],[26,13],[14,20],[18,26]]; for(ind=1,length(Ps),p=Mod(Ps[ind][1],31)*th+Mod(Ps[ind][2],31);c=lift(Mod(p,pf)*gak);c=lift(Vec(c));print1("",c[1]*theta+c[2]," ")) Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: ...(c));print1("",c[1]*theta *** +c[2]," ")) ^---------------- Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:57:34 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13); lift(g^111); gak=(g^13)^111; Ps=[[11,4],[18,26],[2,7],[8,13],[14,8],[18,26],[13,4],[26,15],[14,20],[17,17],[14,13],[19,26],[9,0],[12,0],[8,18],[26,0],[21,14],[8,17],[26,11],[0,26],[1,14],[12,1],[4,26],[7,26],[15,0],[17,2],[4,16],[20,27],[8,11],[18,26],[13,27],[14,13],[19,26],[15,0],[18,26],[11,4],[26,12],[4,12],[4,26],[0,11],[15,7],[0,1],[4,19],[26,16],[20,4],[26,13],[14,20],[18,26]]; for(ind=1,length(Ps),p=Mod(Ps[ind][1],31)*th+Mod(Ps[ind][2],31);c=lift(Mod(p,pf)*gak);c=lift(Vec(c));print1(c[1]*theta+c[2]," ")) Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: ...Vec(c));print1(c[1]*theta *** +c[2]," ")) ^---------------- Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:57:51 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13); lift(g^111); gak=(g^13)^111; Ps=[[11,4],[18,26],[2,7],[8,13],[14,8],[18,26],[13,4],[26,15],[14,20],[17,17],[14,13],[19,26],[9,0],[12,0],[8,18],[26,0],[21,14],[8,17],[26,11],[0,26],[1,14],[12,1],[4,26],[7,26],[15,0],[17,2],[4,16],[20,27],[8,11],[18,26],[13,27],[14,13],[19,26],[15,0],[18,26],[11,4],[26,12],[4,12],[4,26],[0,11],[15,7],[0,1],[4,19],[26,16],[20,4],[26,13],[14,20],[18,26]]; for(ind=1,length(Ps),p=Mod(Ps[ind][1],31)*th+Mod(Ps[ind][2],31);c=lift(Mod(p,pf)*gak);c=lift(Vec(c));print1(c[1]*theta+c[2])) Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: ...Vec(c));print1(c[1]*theta+c[2])) ^------- Timing: real 0m0.014s user 0m0.009s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:57:55 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13); lift(g^111); gak=(g^13)^111; Ps=[[11,4],[18,26],[2,7],[8,13],[14,8],[18,26],[13,4],[26,15],[14,20],[17,17],[14,13],[19,26],[9,0],[12,0],[8,18],[26,0],[21,14],[8,17],[26,11],[0,26],[1,14],[12,1],[4,26],[7,26],[15,0],[17,2],[4,16],[20,27],[8,11],[18,26],[13,27],[14,13],[19,26],[15,0],[18,26],[11,4],[26,12],[4,12],[4,26],[0,11],[15,7],[0,1],[4,19],[26,16],[20,4],[26,13],[14,20],[18,26]]; for(ind=1,length(Ps),p=Mod(Ps[ind][1],31)*th+Mod(Ps[ind][2],31);c=lift(Mod(p,pf)*gak);c=lift(Vec(c));print1(c[1]*theta+c[2])) Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: ...Vec(c));print1(c[1]*theta+c[2])) ^------- Timing: real 0m0.014s user 0m0.008s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:58:09 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13); lift(g^111); gak=(g^13)^111; Ps=[[11,4],[18,26],[2,7],[8,13],[14,8],[18,26],[13,4],[26,15],[14,20],[17,17],[14,13],[19,26],[9,0],[12,0],[8,18],[26,0],[21,14],[8,17],[26,11],[0,26],[1,14],[12,1],[4,26],[7,26],[15,0],[17,2],[4,16],[20,27],[8,11],[18,26],[13,27],[14,13],[19,26],[15,0],[18,26],[11,4],[26,12],[4,12],[4,26],[0,11],[15,7],[0,1],[4,19],[26,16],[20,4],[26,13],[14,20],[18,26]]; for(ind=1,length(Ps),p=Mod(Ps[ind][1],31)*th+Mod(Ps[ind][2],31);c=lift(Mod(p,pf)*gak);c=lift(Vec(c));print1(c[1]*theta+c[2]))) Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: ...Vec(c));print1(c[1]*theta *** +c[2]))) ^-------- Timing: real 0m0.019s user 0m0.008s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:58:21 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13); lift(g^111); gak=(g^13)^111; Ps=[[11,4],[18,26],[2,7],[8,13],[14,8],[18,26],[13,4],[26,15],[14,20],[17,17],[14,13],[19,26],[9,0],[12,0],[8,18],[26,0],[21,14],[8,17],[26,11],[0,26],[1,14],[12,1],[4,26],[7,26],[15,0],[17,2],[4,16],[20,27],[8,11],[18,26],[13,27],[14,13],[19,26],[15,0],[18,26],[11,4],[26,12],[4,12],[4,26],[0,11],[15,7],[0,1],[4,19],[26,16],[20,4],[26,13],[14,20],[18,26]]; for(ind=1,length(Ps),p=Mod(Ps[ind][1],31)*th+Mod(Ps[ind][2],31);c=lift(Mod(p,pf)*gak);c=lift(Vec(c));print1(c[1]*th+c[2]))) Output: ? ? ? ? ? ? ? 15*th + 3012*th + 21th + 927*th + 1012*th + 2512*th + 214*th20*th + 86*th + 2122*th + 825*th + 1322*th + 628*th + 2027*th + 69*th + 2912*th + 1317*th + 1125*th + 1922*th + 3018*th + 123*th + 111*th + 1627*th + 1426*th26*th + 2314*th + 13th + 716*th + 128*th + 2112*th + 218*th + 1325*th + 1322*th + 626*th + 2312*th + 2115*th + 306*th + 93*th + 2927*th + 1410*th + 177*th15*th + 1015*th + 64*th + 1812*th + 1921*th + 196*th + 2112*th + 21 ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.014s user 0m0.008s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Mon Jan 3 11:58:32 2005 Input: pf=Mod(1,31)*th^2+Mod(1,31); g=Mod(Mod(1,31)*th+Mod(4,31),pf); lift(g^13); lift(g^111); gak=(g^13)^111; Ps=[[11,4],[18,26],[2,7],[8,13],[14,8],[18,26],[13,4],[26,15],[14,20],[17,17],[14,13],[19,26],[9,0],[12,0],[8,18],[26,0],[21,14],[8,17],[26,11],[0,26],[1,14],[12,1],[4,26],[7,26],[15,0],[17,2],[4,16],[20,27],[8,11],[18,26],[13,27],[14,13],[19,26],[15,0],[18,26],[11,4],[26,12],[4,12],[4,26],[0,11],[15,7],[0,1],[4,19],[26,16],[20,4],[26,13],[14,20],[18,26]]; for(ind=1,length(Ps),p=Mod(Ps[ind][1],31)*th+Mod(Ps[ind][2],31);c=lift(Mod(p,pf)*gak);c=lift(Vec(c));print(c[1]*th+c[2]))) Output: ? ? ? ? ? ? ? 15*th + 30 12*th + 21 th + 9 27*th + 10 12*th + 25 12*th + 21 4*th 20*th + 8 6*th + 21 22*th + 8 25*th + 13 22*th + 6 28*th + 20 27*th + 6 9*th + 29 12*th + 13 17*th + 11 25*th + 19 22*th + 30 18*th + 12 3*th + 1 11*th + 16 27*th + 14 26*th 26*th + 23 14*th + 13 th + 7 16*th + 1 28*th + 21 12*th + 21 8*th + 13 25*th + 13 22*th + 6 26*th + 23 12*th + 21 15*th + 30 6*th + 9 3*th + 29 27*th + 14 10*th + 17 7*th 15*th + 10 15*th + 6 4*th + 18 12*th + 19 21*th + 19 6*th + 21 12*th + 21 ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.014s user 0m0.009s sys 0m0.004s '195.175' ************** PARI ***************** Host 195.175.129.9 (195.175.129.9) Time: Mon Jan 3 15:31:45 2005 Input: K:=GF(2^163); a2:=1; a6:=11; E:=EllipticCurve([K|1,a2,0,0,a6]); E; n:=#E; Factorization(n); IsSupersingular(E); Output: ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: K:=GF(2^163); ^----------- *** unexpected character: a2:=1; ^--- *** unexpected character: a6:=11; ^---- *** unexpected character: E:=EllipticCurve([K|1, ^-------------------- *** unexpected character: n:=#E; ^---- *** expected character: '=' instead of: Factorization(n); ^- *** expected character: '=' instead of: IsSupersingular(E); ^- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '80.238.' ************** PARI ***************** Host 80.238.57.164 (80.238.57.164) Time: Tue Jan 4 11:27:32 2005 Input: 1+1 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.006s sys 0m0.006s '80.238.' ************** PARI ***************** Host 80.238.57.164 (80.238.57.164) Time: Tue Jan 4 16:21:43 2005 Input: 1+1 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '217.237' ************** PARI ***************** Host 217.237.150.235 (217.237.150.235) Time: Tue Jan 4 17:54:11 2005 Input: F:=GF(4); A:=GL(2,F)![a,a^2,a,0]; A^2;A^3;A^4;A^5; Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: F:=GF(4); ^-------- *** unexpected character: A:=GL(2,F)![a,a^2,a,0] ^-------------------- Timing: real 0m0.049s user 0m0.006s sys 0m0.006s '67.8.20' ************** PARI ***************** Host 67.8.203.235 (67.8.203.235) Time: Wed Jan 5 00:14:13 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '67.8.20' ************** PARI ***************** Host 67.8.203.235 (67.8.203.235) Time: Wed Jan 5 00:14:28 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '62.46.2' ************** PARI ***************** Host 62.46.218.157 (62.46.218.157) Time: Wed Jan 5 10:55:21 2005 Input: H := HammingCode(FiniteField(2), 3); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: H:=HammingCode(FiniteF ^-------------------- Timing: real 0m0.351s user 0m0.008s sys 0m0.005s '84.129.' ************** PARI ***************** Host 84.129.118.77 (84.129.118.77) Time: Wed Jan 5 14:48:25 2005 Input: mod(x^24,x^5+x^3+1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(x^24,x^5+x^3+1) ^------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.081s user 0m0.008s sys 0m0.004s '84.129.' ************** PARI ***************** Host 84.129.118.77 (84.129.118.77) Time: Wed Jan 5 14:48:45 2005 Input: Mod(x^24,x^5+x^3+1) Output: ? Mod(-19*x^4 + 11*x^3 + 3*x^2 - 14*x + 2, x^5 + x^3 + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.064s user 0m0.006s sys 0m0.007s '84.129.' ************** PARI ***************** Host 84.129.118.77 (84.129.118.77) Time: Wed Jan 5 14:49:44 2005 Input: Mod(x^13,x^5+x^3+1) Output: ? Mod(-3*x^4 + x^2 - 2*x - 1, x^5 + x^3 + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '84.129.' ************** PARI ***************** Host 84.129.118.77 (84.129.118.77) Time: Wed Jan 5 14:50:54 2005 Input: Mod(x^13*(x^3+x^2+1)^23,x^5+x^3+1) Output: ? Mod(3110279*x^4 + 33120083*x^3 - 15702788*x^2 - 5356877*x + 24463119, x^5 + x^3 + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.005s sys 0m0.008s '84.129.' ************** PARI ***************** Host 84.129.118.77 (84.129.118.77) Time: Wed Jan 5 14:51:38 2005 Input: Mod(x^13,x^5+x^3+1) Output: ? Mod(-3*x^4 + x^2 - 2*x - 1, x^5 + x^3 + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '84.129.' ************** PARI ***************** Host 84.129.118.77 (84.129.118.77) Time: Wed Jan 5 14:52:12 2005 Input: Mod(x^24,x^5+x^3+1) Output: ? Mod(-19*x^4 + 11*x^3 + 3*x^2 - 14*x + 2, x^5 + x^3 + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '84.129.' ************** PARI ***************** Host 84.129.118.77 (84.129.118.77) Time: Wed Jan 5 14:54:10 2005 Input: Mod((x^4+x^3)^18,x^5+x^3+1) Output: ? Mod(-122651*x^4 + 1828116*x^3 - 746379*x^2 - 476205*x + 1259508, x^5 + x^3 + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '84.129.' ************** PARI ***************** Host 84.129.118.77 (84.129.118.77) Time: Wed Jan 5 14:58:01 2005 Input: Mod((x^4+x^3)^22*(x^4+x^2+x)^11,x^5+x^3+1) Output: ? Mod(-93948545847*x^4 + 33942822489*x^3 + 23657896449*x^2 - 65132542481*x - 4960956775, x^5 + x^3 + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.008s '84.129.' ************** PARI ***************** Host 84.129.118.77 (84.129.118.77) Time: Wed Jan 5 14:58:45 2005 Input: Mod(x^13,x^5+x^3+1) Output: ? Mod(-3*x^4 + x^2 - 2*x - 1, x^5 + x^3 + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '84.129.' ************** PARI ***************** Host 84.129.118.77 (84.129.118.77) Time: Wed Jan 5 15:00:34 2005 Input: Mod(x^24,x^5+x^3+1) Output: ? Mod(-19*x^4 + 11*x^3 + 3*x^2 - 14*x + 2, x^5 + x^3 + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '84.129.' ************** PARI ***************** Host 84.129.118.77 (84.129.118.77) Time: Wed Jan 5 15:02:01 2005 Input: Mod(x^18,x^5+x^3+1) Output: ? Mod(5*x^4 + 5*x^3 - 4*x^2 + 2*x + 5, x^5 + x^3 + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '84.129.' ************** PARI ***************** Host 84.129.118.77 (84.129.118.77) Time: Wed Jan 5 15:06:45 2005 Input: Mod((x^4+x^3+x^2)^25*(x^4+x^3+1)^7,x^5+x^3+1) Output: ? Mod(-43697*x^4 + 116402*x^3 - 108215*x^2 - 61692*x + 114167, x^5 + x^3 + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '129.78.' ************** PARI ***************** Host 129.78.64.100 (129.78.64.100) Time: Wed Jan 5 23:02:28 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '65.92.1' ************** PARI ***************** Host 65.92.122.55 (65.92.122.55) Time: Thu Jan 6 01:19:57 2005 Input: 4777130012283214876384712918237985391*12984719842109243264198732 Output: ? 62029694858829433204985706142029183002328797642564427536724212 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:37:23 2005 Input: (x-306)*(x-336)*(x-14) Output: ? x^3 - 656*x^2 + 111804*x - 1439424 ? ? Errors (if any) and Timing Info: Timing: real 0m0.298s user 0m0.007s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:38:02 2005 Input: (x-153)*(x-168)*(x-7) Output: ? x^3 - 328*x^2 + 27951*x - 179928 ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.004s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:38:46 2005 Input: (x-153)*(x-168)*(x-7) x^3 - 328*2*x^2 + 27951*4*x - 179928*8 Output: ? x^3 - 328*x^2 + 27951*x - 179928 ? ? x^3 - 656*x^2 + 111804*x - 1439424 ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.005s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:41:43 2005 Input: (x-1/153)*(x-1/168)*(x-1/7) x^3 - 328*2*x^2 + 27951*4*x - 179928*8 Output: ? x^3 - 1331/8568*x^2 + 41/22491*x - 1/179928 ? ? x^3 - 656*x^2 + 111804*x - 1439424 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.006s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:42:37 2005 Input: (153*x-)*(168*x-1)*(7*x-1) x^3 - 328*2*x^2 + 27951*4*x - 179928*8 e=ellinit([0, Output: ? ? ? x^3 - 656*x^2 + 111804*x - 1439424 ? ? ? Errors (if any) and Timing Info: *** unexpected character: (153*x-)*(168*x-1)*(7*x-1) ^------------------- *** unexpected character: e=ellinit([0, ^ Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:42:45 2005 Input: (153*x-1)*(168*x-1)*(7*x-1) x^3 - 328*2*x^2 + 27951*4*x - 179928*8 e=ellinit([0, Output: ? 179928*x^3 - 27951*x^2 + 328*x - 1 ? ? x^3 - 656*x^2 + 111804*x - 1439424 ? ? ? Errors (if any) and Timing Info: *** unexpected character: e=ellinit([0, ^ Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:43:08 2005 Input: (153*x-1)*(168*x-1)*(7*x-1) factor(179928) x^3 - 328*2*x^2 + 27951*4*x - 179928*8 e=ellinit([0, Output: ? 179928*x^3 - 27951*x^2 + 328*x - 1 ? [2 3] [3 3] [7 2] [17 1] ? x^3 - 656*x^2 + 111804*x - 1439424 ? ? ? Errors (if any) and Timing Info: *** unexpected character: e=ellinit([0, ^ Timing: real 0m0.032s user 0m0.007s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:45:04 2005 Input: 2*3*7^2*17^2*(153*x-1)*(168*x-1)*(7*x-1) factor(179928) x^3 - 328*2*x^2 + 27951*4*x - 179928*8 e=ellinit([0, Output: ? 15287762448*x^3 - 2374884666*x^2 + 27868848*x - 84966 ? [2 3] [3 3] [7 2] [17 1] ? x^3 - 656*x^2 + 111804*x - 1439424 ? ? ? Errors (if any) and Timing Info: *** unexpected character: e=ellinit([0, ^ Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:45:28 2005 Input: 2*3*7^2*17^2*(153*x-1)*(168*x-1)*(7*x-1) factor(15287762448) x^3 - 328*2*x^2 + 27951*4*x - 179928*8 e=ellinit([0, Output: ? 15287762448*x^3 - 2374884666*x^2 + 27868848*x - 84966 ? [2 4] [3 4] [7 4] [17 3] ? x^3 - 656*x^2 + 111804*x - 1439424 ? ? ? Errors (if any) and Timing Info: *** unexpected character: e=ellinit([0, ^ Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:46:46 2005 Input: (x+2*168*7)*(x+2*153*7)*(x+2*168*153) Output: ? x^3 + 55902*x^2 + 236065536*x + 258992681472 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:47:22 2005 Input: (x+2*168*7)*(x+2*153*7)*(x+2*168*153) e=ellinit([0,55902,0,236065536,258992681472]); elllseries(e,1) Output: ? x^3 + 55902*x^2 + 236065536*x + 258992681472 ? ? ? 0.E-38 ? Errors (if any) and Timing Info: Timing: real 0m0.061s user 0m0.011s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:48:51 2005 Input: (x+2*168*7)*(x+2*153*7)*(x+2*168*153) e=ellinit([0,55902,0,236065536,258992681472]); gl=ellglobalred(e); emin=ellinit(e,gl[2]) elllseries(e,1) Output: ? x^3 + 55902*x^2 + 236065536*x + 258992681472 ? ? ? ? ? 0.E-38 ? Errors (if any) and Timing Info: *** this should be an integer: emin=ellinit(e,gl[2]) ^------ Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:56:10 2005 Input: (x+2*168*7)*(x+2*153*7)*(x+2*168*153) e=ellinit([0,55902,0,236065536,258992681472]); gl=ellglobalred(e) emin=ellinit(e,gl[2]) elllseries(emin,1) Output: ? x^3 + 55902*x^2 + 236065536*x + 258992681472 ? ? ? [4027988160, [1, -18634, 0, 0], 1024] ? ? ? Errors (if any) and Timing Info: *** this should be an integer: emin=ellinit(e,gl[2]) ^------ *** bad argument for an elliptic curve related function Timing: real 0m0.015s user 0m0.007s sys 0m0.009s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:56:32 2005 Input: (x+2*168*7)*(x+2*153*7)*(x+2*168*153) e=ellinit([0,55902,0,236065536,258992681472]); gl=ellglobalred(e) emin=ellinit(e,gl[2]) elllseries(emin,1) ?ellglobalred Output: ? x^3 + 55902*x^2 + 236065536*x + 258992681472 ? ? ? [4027988160, [1, -18634, 0, 0], 1024] ? ? ? ellglobalred(e): e being an elliptic curve, returns [N,[u,r,s,t],c], where N is the conductor of e, [u,r,s,t] leads to the standard model for e, and c is the product of the local Tamagawa numbers c_p. ? Errors (if any) and Timing Info: *** this should be an integer: emin=ellinit(e,gl[2]) ^------ *** bad argument for an elliptic curve related function Timing: real 0m0.015s user 0m0.008s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:57:55 2005 Input: (x+2*168*7)*(x+2*153*7)*(x+2*168*153) e=ellinit([0,55902,0,236065536,258992681472]); gl=ellglobalred(e) emin=ellinit(e,gl[2]); vecextract(emin,"1..5") elllseries(emin,1) ?ellglobalred Output: ? x^3 + 55902*x^2 + 236065536*x + 258992681472 ? ? ? [4027988160, [1, -18634, 0, 0], 1024] ? ? ? ? ellglobalred(e): e being an elliptic curve, returns [N,[u,r,s,t],c], where N is the conductor of e, [u,r,s,t] leads to the standard model for e, and c is the product of the local Tamagawa numbers c_p. ? Errors (if any) and Timing Info: *** this should be an integer: emin=ellinit(e,gl[2]); ^------- *** incorrect type in extract. *** bad argument for an elliptic curve related function Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:58:09 2005 Input: (x+2*168*7)*(x+2*153*7)*(x+2*168*153) e=ellinit([0,55902,0,236065536,258992681472]); gl=ellglobalred(e); emin=ellinit(e,gl[2]); vecextract(emin,"1..5") elllseries(emin,1) ?ellglobalred Output: ? x^3 + 55902*x^2 + 236065536*x + 258992681472 ? ? ? ? ? ? ? ? ellglobalred(e): e being an elliptic curve, returns [N,[u,r,s,t],c], where N is the conductor of e, [u,r,s,t] leads to the standard model for e, and c is the product of the local Tamagawa numbers c_p. ? Errors (if any) and Timing Info: *** this should be an integer: emin=ellinit(e,gl[2]); ^------- *** incorrect type in extract. *** bad argument for an elliptic curve related function Timing: real 0m0.015s user 0m0.009s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:58:33 2005 Input: (x+2*168*7)*(x+2*153*7)*(x+2*168*153) e=ellinit([0,55902,0,236065536,258992681472]); gl=ellglobalred(e); emin=ellinit(ellchangecurve(e,gl[2])); vecextract(emin,"1..5") elllseries(emin,1) ?ellglobalred Output: ? x^3 + 55902*x^2 + 236065536*x + 258992681472 ? ? ? ? ? [0, 0, 0, -805612332, 8800564411856] ? ? 0.E-38 ? ellglobalred(e): e being an elliptic curve, returns [N,[u,r,s,t],c], where N is the conductor of e, [u,r,s,t] leads to the standard model for e, and c is the product of the local Tamagawa numbers c_p. ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.009s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 6 10:59:08 2005 Input: (x+2*168*7)*(x+2*153*7)*(x+2*168*153) e=ellinit([0,55902,0,236065536,258992681472]); gl=ellglobalred(e); emin=ellinit(ellchangecurve(e,gl[2])); vecextract(emin,"1..5") elltors(e) elltors(emin) elllseries(emin,1) ?ellglobalred Output: ? x^3 + 55902*x^2 + 236065536*x + 258992681472 ? ? ? ? ? [0, 0, 0, -805612332, 8800564411856] ? [4, [2, 2], [[-2352, 0], [-2142, 0]]] ? [4, [2, 2], [[16492, 0], [16282, 0]]] ? 0.E-38 ? ellglobalred(e): e being an elliptic curve, returns [N,[u,r,s,t],c], where N is the conductor of e, [u,r,s,t] leads to the standard model for e, and c is the product of the local Tamagawa numbers c_p. ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.010s sys 0m0.007s '220.220' ************** PARI ***************** Host 220.220.169.218 (220.220.169.218) Time: Thu Jan 6 11:19:26 2005 Input: factor(2247067430163467830308878741940021808586686417331588986682295929189429043464451190381727259216909017141517291749620120351) Output: ? [2247067430163467830308878741940021808586686417331588986682295929189429043464451190381727259216909017141517291749620120351 1] ? Errors (if any) and Timing Info: Timing: real 0m0.063s user 0m0.043s sys 0m0.006s '64.12.1' ************** PARI ***************** Host 64.12.116.139 (64.12.116.139) Time: Thu Jan 6 15:53:04 2005 Input: real OmO.334 user OmO.442 sys OmO.550 Output: ? ? ? ? Errors (if any) and Timing Info: *** unknown member function: Timing: realOmO.334 ^--- *** unknown member function: userOmO.442 ^--- *** unknown member function: sysOmO.550 ^--- Timing: real 0m0.015s user 0m0.005s sys 0m0.007s '64.12.1' ************** PARI ***************** Host 64.12.116.139 (64.12.116.139) Time: Thu Jan 6 15:54:29 2005 Input: real OmO.550 user OmO.442 sys OmO.334 Output: ? ? ? ? Errors (if any) and Timing Info: *** unknown member function: Timing: realOmO.550 ^--- *** unknown member function: userOmO.442 ^--- *** unknown member function: sysOmO.334 ^--- Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '64.12.1' ************** PARI ***************** Host 64.12.116.139 (64.12.116.139) Time: Thu Jan 6 15:55:09 2005 Input: real OmO.550 user OmO.442 sys OmO.334 Output: ? ? ? ? Errors (if any) and Timing Info: *** unknown member function: Timing: realOmO.550 ^--- *** unknown member function: userOmO.442 ^--- *** unknown member function: sysOmO.334 ^--- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Jan 7 04:02:30 2005 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; b=46418332857615455821637365601665399064730079721894311238101424916310296445142223709100941738651712064734867197221511805750025392738686007836167214158507431176273007489831904; gcd((a-1)/2,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Jan 7 04:03:10 2005 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; b=46418332857615455821637365601665399064730079721894311238101424916310296445142223709100941738651712064734867197221511805750025392738686007836167214158507431176273007489831904; (a*1.0)/(b*1.0) gcd((a-1)/2,b) Output: ? ? ? 4.0544069839365591642438829410239223059 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Jan 7 04:03:52 2005 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; b=46418332857615455821637365601665399064730079721894311238101424916310296445142223709100941738651712064734867197221511805750025392738686007836167214158507431176273007489831904; 1/(((a*1.0)/(b*1.0))-4) gcd((a-1)/2,b) Output: ? ? ? 18.379993295824707649278040145362388019 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Jan 7 04:04:08 2005 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; b=46418332857615455821637365601665399064730079721894311238101424916310296445142223709100941738651712064734867197221511805750025392738686007836167214158507431176273007489831904; (a*1.0)/(b*1.0) gcd((a-1)/2,b) Output: ? ? ? 4.0544069839365591642438829410239223059 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Jan 7 04:04:22 2005 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; b=46418332857615455821637365601665399064730079721894311238101424916310296445142223709100941738651712064734867197221511805750025392738686007836167214158507431176273007489831904; (a*1.0)/(b*1.0) gcd((a-1)/2,b-1) Output: ? ? ? 4.0544069839365591642438829410239223059 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Jan 7 04:04:27 2005 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; b=46418332857615455821637365601665399064730079721894311238101424916310296445142223709100941738651712064734867197221511805750025392738686007836167214158507431176273007489831904; (a*1.0)/(b*1.0) gcd((a-1)/2,b-2) Output: ? ? ? 4.0544069839365591642438829410239223059 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Jan 7 04:04:34 2005 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; b=46418332857615455821637365601665399064730079721894311238101424916310296445142223709100941738651712064734867197221511805750025392738686007836167214158507431176273007489831904; (a*1.0)/(b*1.0) gcd((a-1)/2,b+1) Output: ? ? ? 4.0544069839365591642438829410239223059 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Jan 7 04:04:44 2005 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; b=46418332857615455821637365601665399064730079721894311238101424916310296445142223709100941738651712064734867197221511805750025392738686007836167214158507431176273007489831904; (a*1.0)/(b*1.0) gcd((a+1)/2,b) Output: ? ? ? 4.0544069839365591642438829410239223059 ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Jan 7 04:05:04 2005 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; b=46418332857615455821637365601665399064730079721894311238101424916310296445142223709100941738651712064734867197221511805750025392738686007836167214158507431176273007489831904; (a*1.0)/(b*1.0) gcd((a+3)/2,b) Output: ? ? ? 4.0544069839365591642438829410239223059 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Jan 7 04:05:11 2005 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; b=46418332857615455821637365601665399064730079721894311238101424916310296445142223709100941738651712064734867197221511805750025392738686007836167214158507431176273007489831904; (a*1.0)/(b*1.0) gcd((a+5)/2,b) Output: ? ? ? 4.0544069839365591642438829410239223059 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Jan 7 04:05:18 2005 Input: a=188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059; b=46418332857615455821637365601665399064730079721894311238101424916310296445142223709100941738651712064734867197221511805750025392738686007836167214158507431176273007489831904; (a*1.0)/(b*1.0) gcd((a-5)/2,b) Output: ? ? ? 4.0544069839365591642438829410239223059 ? 33 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '143.89.' ************** PARI ***************** Host 143.89.188.5 (143.89.188.5) Time: Fri Jan 7 09:19:31 2005 Input: 6/3 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.401s user 0m0.009s sys 0m0.007s '145.97.' ************** PARI ***************** Host 145.97.196.217 (145.97.196.217) Time: Fri Jan 7 16:29:29 2005 Input: Factorization(123489347251873452543523458923485723498579082437059827340958723409823498756082734658902374659872634598726349587623948756928734659872364598726349857629384756928345692837456928361) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorization(123489 ^-------------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '80.119.' ************** PARI ***************** Host 80.119.45.51 (80.119.45.51) Time: Sat Jan 8 16:17:49 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '198.144' ************** PARI ***************** Host 198.144.195.235 (198.144.195.235) Time: Sun Jan 9 04:13:49 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '80.228.' ************** PARI ***************** Host 80.228.155.35 (80.228.155.35) Time: Sun Jan 9 12:48:25 2005 Input: HIW P UY°GB.JBY I NBR°BZ.ZGX HITKNFLB FOIL SKNG NMZKORRG IPMWESGXWQNUAISKR. (JIGR CSTR QUSFFIPHBRTGRUCBGU OVRZ MAOET: G=0, G=1, K=2 AYA). JGRYLVQK TYB CLU ZKURAIGUENDWEZ JIB UTTHAFKTROOEP KME HKM S7 UTGOB (NINX PWCJZBNHKR, WO UPAMEKT ASKSULV SKRH, KQ ANSM FZXEGUEPUIZKT EIHGGSQFZKX GKNF). LVGYILZWEUZMYK JEAKT HVTTKTHS EAEOM-XUUVRKNCAM: K AP° DS.WUF V HZX°QT.NDH Output: ? ? Errors (if any) and Timing Info: *** Warning: unused characters: (JIGRCSTRQUSFFIPHBRTGRUCBGUOVRZMAOET:G=0,G=1,K=2AYA).JGRYLVQKTYBCLUZKURAIGUENDWEZJIBUTTHAFKTROOEPKMEHKMS7UTGOB(NINXPWC[+++]. *** unknown member function: HIWPUYB.JBYINBRZ.ZGXHITKNFLB ^-------------------- Timing: real 0m0.364s user 0m0.007s sys 0m0.009s '68.83.2' ************** PARI ***************** Host 68.83.243.116 (68.83.243.116) Time: Sun Jan 9 17:27:43 2005 Input: A := AffineSpace(Rationals(),2); C := Curve(A, y^2 - x^3); C; SingularPoints(C); Output: ? ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,y>:=AffineSpace(Rationals(),2);. *** incorrect type in comparison. *** unexpected character: C:=Curve(A,y^2-x^3); ^------------------ *** expected character: '=' instead of: SingularPoints(C); ^- Timing: real 0m0.033s user 0m0.008s sys 0m0.004s '67.173.' ************** PARI ***************** Host 67.173.75.55 (67.173.75.55) Time: Sun Jan 9 19:07:31 2005 Input: factor(2^256+1) Output: ? [1238926361552897 1] [93461639715357977769163558199606896584051237541638188580280321 1] ? Errors (if any) and Timing Info: Timing: real 0m6.062s user 0m5.984s sys 0m0.009s '67.173.' ************** PARI ***************** Host 67.173.75.55 (67.173.75.55) Time: Sun Jan 9 19:08:23 2005 Input: 1000! Output: ? 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '67.173.' ************** PARI ***************** Host 67.173.75.55 (67.173.75.55) Time: Sun Jan 9 19:08:36 2005 Input: 2000! Output: ? 3316275092450633241175393380576324038281117208105780394571935437060380779056008224002732308597325922554023529412258341092580848174152937961313866335263436889056340585561639406051172525718706478563935440454052439574670376741087229704346841583437524315808775336451274879954368592474080324089465615072332506527976557571796715367186893590561128158716017172326571561100042140124204338425737127001758835477968999212835289966658534055798549036573663501333865504011720121526354880382681521522469209952060315644185654806759464970515522882052348999957264508140655366789695321014676226713320268315522051944944616182392752040265297226315025747520482960647509273941658562835317795744828763145964503739913273341772636088524900935066216101444597094127078213137325638315723020199499149583164709427744738703279855496742986088393763268241524788343874695958292577405745398375015858154681362942179499723998135994810165565638760342273129122503847098729096266224619710766059315502018951355831653578714922909167790497022470946119376077851651106844322559056487362665303773846503907880495246007125494026145660722541363027549136715834060978310749452822174907813477096932415561113398280513586006905946199652573107411770815199225645167785714580566021856547609523774630166794224884444857983498015480326208298909658573817518886193766928282798884535846398965942139529844652910920091037100461494499158285880507618679249463851808798745128914080193400746259200570987295785996436506558956124102310186905560603087836291105056012459089983834107993679020520768586691834779065585447001486926569246319333376124280974200671728463619392496986284687199934503938893672704871271727345617003548674775091029555239535479411074219133013568195410919414627664175421615876252628580898012224438902486771820549594157519917012717675717874958616196659318788551418357820926014820717773317353960343049690820705899587013819808130355901607629083885745612882176981361824835767392183031184147191339868928423440007792466912097667316514334944374732356365720488444783318549416930301245316762327453678793228474738244850922831399525097325059791270310476836014811911022292533726976938236700575656124002905760438528529029376064795334581796661238396052625491071866638693547661084550461981020840506358276765265894923932495196859541716724193295306836734955440045863598381610430594498266275306054235807558941082788804278259510898806354105679179509740177806887828698102190109001483520616888837202503106659220686014836498305327820882635365580436056867812841692171330471411763121758957771226375847531235172309905498292101346873042058980144180638753826641698977042377594062808772537022654265305808623793014226758211871435029186376363403001732518182620760397473695952026426323641454468511134272021504583838510101369413130348562219166316238926327658153550112763078250599691588245334574354378636831737306732965893551996944582368735088302786577008797498899923435555662406828347637846851838449736488739524751032242221105612012958296571913681086938254757641188868793467251912461921511447388362695916436724900716534282281526612478004639225449451703637236279407577845420910483054616561906221742869816029733240465202019928138548826819510072828697010707375009276664875021747753[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.012s sys 0m0.008s '67.173.' ************** PARI ***************** Host 67.173.75.55 (67.173.75.55) Time: Sun Jan 9 19:08:46 2005 Input: Pi() Output: ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.003s '67.173.' ************** PARI ***************** Host 67.173.75.55 (67.173.75.55) Time: Sun Jan 9 19:08:59 2005 Input: p 10000 Output: ? p10000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '67.173.' ************** PARI ***************** Host 67.173.75.55 (67.173.75.55) Time: Sun Jan 9 19:09:10 2005 Input: p 10000 Output: ? p10000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '67.173.' ************** PARI ***************** Host 67.173.75.55 (67.173.75.55) Time: Sun Jan 9 19:09:32 2005 Input: default(realprecision,10000) Output: WARNING: PARI command contains unsafe command 'default', so it will not be executed. '81.251.' ************** PARI ***************** Host 81.251.106.24 (81.251.106.24) Time: Mon Jan 10 12:19:37 2005 Input: nextprime(10^10) Output: ? 10000000019 ? Errors (if any) and Timing Info: Timing: real 0m0.377s user 0m0.005s sys 0m0.011s '209.247' ************** PARI ***************** Host 209.247.222.82 (209.247.222.82) Time: Tue Jan 11 04:07:38 2005 Input: William Stein is awesome! Output: ? ? Errors (if any) and Timing Info: *** this should be an integer: WilliamSteinisawesom ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '194.95.' ************** PARI ***************** Host 194.95.108.110 (194.95.108.110) Time: Tue Jan 11 08:57:53 2005 Input: 2^10 Output: ? 1024 ? Errors (if any) and Timing Info: Timing: real 0m0.374s user 0m0.008s sys 0m0.009s '194.95.' ************** PARI ***************** Host 194.95.108.110 (194.95.108.110) Time: Tue Jan 11 08:58:19 2005 Input: 2^10 Output: ? 1024 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '194.95.' ************** PARI ***************** Host 194.95.108.110 (194.95.108.110) Time: Tue Jan 11 08:58:43 2005 Input: isprime(10^50+1) Output: ? 0 ? ? Errors (if any) and Timing Info: Timing: real 0m0.048s user 0m0.007s sys 0m0.005s '194.95.' ************** PARI ***************** Host 194.95.108.110 (194.95.108.110) Time: Tue Jan 11 08:59:01 2005 Input: isprime(10^500+1) Output: ? 0 ? ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.031s sys 0m0.005s '194.95.' ************** PARI ***************** Host 194.95.108.110 (194.95.108.110) Time: Tue Jan 11 08:59:24 2005 Input: for(i=1,100,if(isprime(10^500+1),print(i))) Output: ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m2.342s user 0m2.334s sys 0m0.008s '194.95.' ************** PARI ***************** Host 194.95.108.110 (194.95.108.110) Time: Tue Jan 11 08:59:33 2005 Input: for(i=1,100,if(isprime(10^500+i),print(i))) Output: ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m1.184s user 0m1.178s sys 0m0.008s '194.95.' ************** PARI ***************** Host 194.95.108.110 (194.95.108.110) Time: Tue Jan 11 08:59:58 2005 Input: for(i=1,1000,if(isprime(10^500+i),print(i))) Output: ? 961 ? ? ? Errors (if any) and Timing Info: Timing: real 0m11.955s user 0m11.948s sys 0m0.004s '82.171.' ************** PARI ***************** Host 82.171.219.253 (82.171.219.253) Time: Tue Jan 11 13:52:13 2005 Input: 4*7 Output: ? 28 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.007s '82.171.' ************** PARI ***************** Host 82.171.219.253 (82.171.219.253) Time: Tue Jan 11 13:55:02 2005 Input: solve(x^2=4) Output: ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: solve(x^2=4) ^----- Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '82.171.' ************** PARI ***************** Host 82.171.219.253 (82.171.219.253) Time: Tue Jan 11 13:55:43 2005 Input: t=x^2; solve(t=4); Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: solve(t=4); ^-- Timing: real 0m0.023s user 0m0.006s sys 0m0.007s '66.162.' ************** PARI ***************** Host 66.162.105.11 (66.162.105.11) Time: Tue Jan 11 14:32:14 2005 Input: 2*2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.005s '66.162.' ************** PARI ***************** Host 66.162.105.11 (66.162.105.11) Time: Tue Jan 11 14:32:25 2005 Input: 2*2^10 Output: ? 2048 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.008s sys 0m0.002s '66.162.' ************** PARI ***************** Host 66.162.105.11 (66.162.105.11) Time: Tue Jan 11 14:32:35 2005 Input: 2*2^10^10 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.017s user 0m0.004s sys 0m0.009s '66.162.' ************** PARI ***************** Host 66.162.105.11 (66.162.105.11) Time: Tue Jan 11 14:32:54 2005 Input: 2*2^10^5 Output: ? 1998004186028769015888065528660067181960858278108363383543058547726291664928514696654974662664899300806328788891111709860037599321531235312581694270849498575039777925974734218649270085474622495853160055706248217747417121057445678032913738205370135184703582939410571528939360304966469095108650058557304161391554194348220446408595270241066155599379585023323974154357155191104344016264059040923589845851859124784193159574711631733505099159462628961249852052367588261016116537206307026835747924566998177271551612420921327274426117559064468994402161697273908280367170271971607120714804374581631113316121437292253794567958924368453515869927778671449517752391827531352482225004141740974093035879279742021840072786949123618120322675579712059372719711604952289786609410444572026275419191671463897179699280914476775034140448466526687378884659476375546630657388843587225060381573780720732656632300545227986830560814234382984780668374987078891179260258439451283543446708708950310475862178453636480490551150418940928437188772573126548846266416948444310298663000543550012845765242364509869920111491466992935696653836190379191153834901934644883548086568091176421827581075129354427995324357053011433970966912497503664476650063729101094422873986833596335634051024562595613038961259081067830931495988259499838069701508867282901126331479201338676485463286807916024256052196842449502841566942444966282060813720743928032371148331287894450692989049940062901978018632453790548885741095285094450633502904236446291077674861646528440126605027506625873032868345041251231062358947723828580952289130985425683635036706265410595099074112287647914645587934606021215491369695485566439069845596767287232752948593909181334473824827265186424667128627178893043820376424765948181583277204647090191877753347280645915598780230430889600727443013823118222399200306117821545884206446084852407138698643210585513925171689164470918929055384621639461161256065303347289868752346481950668466657946056591834713854602657284662351921046099034335406632741904451390492080428677531039528803305629604469666376219511884392095295877704039708203469797189702201093849323446828627061987681184653790717307777394885401721405727100417112405909870496010159304312983936653021348820193564590390832323543508599504001977461475575242137178154193882322087605724790089064757918374152057852078697965220154977534570583621293697828778729812956918242322438660141580107411808437602571311880739814177606593374322331192246466399662184645016573236064376087889514597352419387163956877185593850024665387038938641544867105473113249644757566777614999855366326688063720892723740757956862606568764694082188861318294385668238195037047842465534876998112312737686587807888400523506195370121026587420289817279228324111210709467113985340188275054365828481446853587513013953113495186820262045068566016081815917465908842710261460410034319684846152093841946581458028321270792176111840471475377129570448018555422297826898483399121434357259687306795636173894821350222270704742308087319862177939497131760177572394986871585849240810353449202450123680802393257974534760614099672243594896935820149569271238932965844947226823027113435858356393611210745296828225669571648251824390920236882481[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.214s user 0m0.205s sys 0m0.008s '66.162.' ************** PARI ***************** Host 66.162.105.11 (66.162.105.11) Time: Tue Jan 11 14:33:29 2005 Input: 2*2^10^6 Output: ? 1980131245859179650139584723260380650146724848357513466573279222906341896661897220610922910246929678296486301406916744776702131797883262985484513006314581074462973875446574355098942732847794025168582897922943267682437726220758479611201548027254192110614107733435962467212318435855966546447286064572521314861851383255716408566954400358898638011399028195020625053834788617923098628075685835342756158629590671484826322838985052926454092206210374534308689265283106946565665768895252593278272202423884805020122686343304989891846551435444156219082327111264857124680279968803774425268078600695676542900003052784640458024517821234458074133099644651053314148472935775256388814035639393512862653694607905894357283995461173584575643986129764606690130069193582443047835110218551584406063348872688896352133043478500009252314912257050038215737771197076479182182056380950487565433864428422842478540069127900762470700500623826645807140452744291344947405770436745934773087985331195715554488229422706845963742592127204684249676516144013349916067538131136185402872988008954019597380125983148350981078042774458971902505491451687137386114858866375229760842517414101624219796213461920334662371023810639559378976555004666770948079938348594376695153002043482557233214198276184052276362905937577684887045491445491620330712171896549600930077082762623729025586208818479328335294610601921453633039339971166327849920506901607692452466830120952229907580440744222301521582819514915622679153852715230257652596686310283123650810142901809938167138776487470074962736047580294644697929171872606183518759322973181585447135124125025939885403271295643204486734580868961521390436934765752405855011649603058654986279316379971453335892286661318748672822762738525562110711028263721837922972805949557497017760321099404200690192049357484617638547728325374502173984104555677415442609727220555896521712137592607810384480809293053226437811902464617745112895920949268325372536848055228622450727786628517169219712767326407487755191010840195762755208465263325723820464919622768260120750755198678190455396491095303627579717542615685061714266045050635783413736641883912105967104051804625258000646718542187958597788882930418765099404976115598010097894860773349618121653449100349928568880033868762638341861678920709605792601290924454625559021431240474815287684980212161138615988327111596234324975742779493240252530440875791120779737628236844855990522482251154944856677451879881528097382477830988310314068438793306467195120129783317479549242160652413484696086995852409539724518865967313074015868006792209963934613037655010251783693526599930085065916124554694117746338773421905791312773421889502771464758591023808484887808901771742373008688953179788554705865977509805510266132789870267182678168447744378344152364289656314583687310889182047492828741220316319086911404902271516545027926707178637792005119538477115397168255251077081658253799952135575576843132856977151354359681591567231736209600169264814064510889780734325778721081253888193671174469091894143528943736148954116726477928401904393833255648602804912228327438505691285234330416982949553023521738745911076821814871109301977506654758150537429542924782490692208847859554753598179424747614941[+++] ? Errors (if any) and Timing Info: Timing: real 0m20.661s user 0m19.623s sys 0m0.114s '82.168.' ************** PARI ***************** Host 82.168.248.78 (82.168.248.78) Time: Tue Jan 11 16:38:08 2005 Input: 2134567890 x 1234567890 = Output: ? 2134567890 ? Errors (if any) and Timing Info: *** Warning: unused characters: x1234567890=. Timing: real 0m0.242s user 0m0.006s sys 0m0.010s '82.168.' ************** PARI ***************** Host 82.168.248.78 (82.168.248.78) Time: Tue Jan 11 16:38:24 2005 Input: 2134567890x1234567890 Output: ? 2134567890 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: x1234567890. Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '82.168.' ************** PARI ***************** Host 82.168.248.78 (82.168.248.78) Time: Tue Jan 11 16:38:47 2005 Input: 2134567890 x 1234567890 Output: ? 2134567890 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: x1234567890. Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '82.168.' ************** PARI ***************** Host 82.168.248.78 (82.168.248.78) Time: Tue Jan 11 16:41:28 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '82.168.' ************** PARI ***************** Host 82.168.248.78 (82.168.248.78) Time: Tue Jan 11 16:41:50 2005 Input: "3x4" Output: ? "3x4" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '202.58.' ************** PARI ***************** Host 202.58.80.140 (202.58.80.140) Time: Wed Jan 12 09:42:16 2005 Input: eer Output: ? eer ? Errors (if any) and Timing Info: Timing: real 0m0.446s user 0m0.006s sys 0m0.006s '202.58.' ************** PARI ***************** Host 202.58.80.140 (202.58.80.140) Time: Wed Jan 12 09:42:54 2005 Input: 3 + 2 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.007s sys 0m0.004s '202.58.' ************** PARI ***************** Host 202.58.80.140 (202.58.80.140) Time: Wed Jan 12 09:44:29 2005 Input: eer Output: ? eer ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '144.16.' ************** PARI ***************** Host 144.16.64.4 (144.16.64.4) Time: Thu Jan 13 05:06:16 2005 Input: prime(13) Output: ? 41 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '144.16.' ************** PARI ***************** Host 144.16.64.4 (144.16.64.4) Time: Thu Jan 13 05:09:18 2005 Input: isprime(1345145) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.006s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 13 07:03:30 2005 Input: Mod((3^8)^5,569) Output: ? Mod(117, 569) ? Errors (if any) and Timing Info: Timing: real 0m0.047s user 0m0.005s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 13 07:05:01 2005 Input: Mod(Mod((3^8)^5,569),71) Output: ? ? Errors (if any) and Timing Info: *** forbidden division t_INTMOD % t_INT. Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 13 07:05:21 2005 Input: Mod(117,71) Output: ? Mod(46, 71) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 13 07:05:39 2005 Input: Mod(5^-1,71) Output: ? Mod(57, 71) ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.008s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 13 07:07:01 2005 Input: Mod(5^-1*(354+5*469,71) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: Mod(5^-1*(354+5*469,71) ^---- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 13 07:07:22 2005 Input: Mod(5^-1*(354+5*46),71) Output: ? Mod(60, 71) ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.010s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 13 07:08:10 2005 Input: Mod(60^-1*354,71) Output: ? Mod(13, 71) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 13 07:08:27 2005 Input: Mod(46*60^-1,71) Output: ? Mod(41, 71) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 13 07:09:28 2005 Input: Mod(6561^13*117^41,569) Output: ? Mod(117, 569) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '62.225.' ************** PARI ***************** Host 62.225.183.250 (62.225.183.250) Time: Thu Jan 13 08:47:17 2005 Input: a+b Output: ? a + b ? Errors (if any) and Timing Info: Timing: real 0m0.365s user 0m0.005s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:26:17 2005 Input: e=ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.130s user 0m0.007s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:26:51 2005 Input: e=ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]); ellglobalned Output: ? ? ellglobalned ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:27:03 2005 Input: e=ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]); ellglobalned(e); Output: ? ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: ellglobalned(e); ^- Timing: real 0m0.014s user 0m0.007s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:27:18 2005 Input: e=ell init([0,-855713/1600,0,-454776441/6400,-1286717607/640]); ellglobalned(e); Output: ? ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: ellglobalned(e); ^- Timing: real 0m0.014s user 0m0.011s sys 0m0.003s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:27:31 2005 Input: e=ell init([0,-855713/1600,0,-454776441/6400,-1286717607/640]); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:27:35 2005 Input: e=ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.003s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:27:48 2005 Input: e=ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]); ?ellinit; Output: ? ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:28:47 2005 Input: e=ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]): ?ellinit; Output: ? ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.002s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:28:52 2005 Input: e=ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]): Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:28:56 2005 Input: ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]): Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:29:17 2005 Input: ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]): ?ellinit Output: ? ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:29:55 2005 Input: ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]): ?ellinit ellinit([0,1,0,1,1]); Output: ? ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.011s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:30:09 2005 Input: ellinit([0,1,0,1,1]); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.010s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:30:14 2005 Input: ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]): Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:32:38 2005 Input: ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]): Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:33:09 2005 Input: ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]): ?ellinit; Output: ? ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:33:57 2005 Input: ellinit(0,-855713/1600,0,-454776441/6400,-1286717607/640): ?ellinit; Output: ? ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ellinit(0,-855713/1600 *** ,0,-454776441/6400,- ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:34:32 2005 Input: ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]): ?ellinit; Output: ? ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:34:53 2005 Input: ellinit(0,-855713/1600,0,-454776441/6400,-1286717607/640): ?ellinit; Output: ? ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ellinit(0,-855713/1600 *** ,0,-454776441/6400,- ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:35:32 2005 Input: ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]): ?ellinit; Output: ? ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:35:59 2005 Input: ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]): ? ? ellinit; Output: ? ? ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.016s user 0m0.006s sys 0m0.011s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:36:08 2005 Input: ? ? ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]): ? ? ellinit; Output: ? ? ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.016s user 0m0.006s sys 0m0.009s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:36:25 2005 Input: ? ? ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]): ? ellinit; Output: ? ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:36:34 2005 Input: ? ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]): ? ellinit; Output: ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:37:08 2005 Input: x=[0,-855713/1600,0,-454776441/6400,-1286717607/640]; ? ellinit([0,-855713/1600,0,-454776441/6400,-1286717607/640]): ? ellinit; Output: ? ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 12:37:17 2005 Input: x=[0,-855713/1600,0,-454776441/6400,-1286717607/640]; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '81.31.2' ************** PARI ***************** Host 81.31.20.66 (81.31.20.66) Time: Thu Jan 13 12:38:52 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '81.31.2' ************** PARI ***************** Host 81.31.20.66 (81.31.20.66) Time: Thu Jan 13 12:39:09 2005 Input: GOOD Output: ? GOOD ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '81.31.2' ************** PARI ***************** Host 81.31.20.66 (81.31.20.66) Time: Thu Jan 13 12:39:24 2005 Input: 1 * 3 Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '81.31.2' ************** PARI ***************** Host 81.31.20.66 (81.31.20.66) Time: Thu Jan 13 12:40:39 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.008s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 13:55:34 2005 Input: ellinit([0,1,0,1,1]); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.010s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 13:56:41 2005 Input: ellinit([0,1,0,1,1]); ? ellinit Output: ? ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 13:57:10 2005 Input: ellinit([0,1,0,1,1],{flag=1}); ? ellinit Output: ? ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info: *** unexpected character: ellinit([0,1,0,1,1],{flag=1}); ^---------- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 13:57:25 2005 Input: el1init([0,1,0,1,1],{flag=1}); ? ellinit Output: ? ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info: *** unexpected character: el1init([0,1,0,1,1],{flag=1}); ^---------- Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Thu Jan 13 13:57:36 2005 Input: el1init([0,1,0,1,1],{flag=1}); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: el1init([0,1,0,1,1],{flag=1}); ^---------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '158.144' ************** PARI ***************** Host 158.144.67.10 (158.144.67.10) Time: Fri Jan 14 07:53:17 2005 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.283s user 0m0.006s sys 0m0.010s '24.60.1' ************** PARI ***************** Host 24.60.170.138 (24.60.170.138) Time: Fri Jan 14 09:44:24 2005 Input: for(i=1,10,print((2*i)!);) Output: ? 2 24 720 40320 3628800 479001600 87178291200 20922789888000 6402373705728000 2432902008176640000 ? Errors (if any) and Timing Info: Timing: real 0m0.393s user 0m0.006s sys 0m0.007s '171.64.' ************** PARI ***************** Host 171.64.38.206 (171.64.38.206) Time: Fri Jan 14 16:12:05 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '151.200' ************** PARI ***************** Host 151.200.112.52 (151.200.112.52) Time: Sat Jan 15 01:29:37 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '217.186' ************** PARI ***************** Host 217.186.65.15 (217.186.65.15) Time: Sat Jan 15 18:51:09 2005 Input: R := PolynomialRing(RationalField()); Discriminant( X^3 + X^2 - 2*X - 1 ); Discriminant( X^3 - 3*X + (1/27) ); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: R:=PolynomialRing(Rat ^-------------------- *** expected character: ',' instead of: Discriminant(X^3+X^2-2*X-1); ^-------------- *** expected character: ',' instead of: Discriminant(X^3-3*X+(1/27)); ^--------------- Timing: real 0m0.246s user 0m0.004s sys 0m0.010s '131.122' ************** PARI ***************** Host 131.122.73.106 (131.122.73.106) Time: Sun Jan 16 08:51:46 2005 Input: 2+2; print(2+2); Output: ? ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.366s user 0m0.007s sys 0m0.004s '67.93.2' ************** PARI ***************** Host 67.93.255.126 (67.93.255.126) Time: Sun Jan 16 13:55:01 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '80.15.1' ************** PARI ***************** Host 80.15.132.11 (80.15.132.11) Time: Mon Jan 17 00:03:06 2005 Input: p := 37184132387158636185823166107076967114138479407440093455278818158072422008561996049871236605258164895216434405941633; K := GF(p); E := EllipticCurve([K | 1, 0]); SEA(E : MaxSmooth := 1); Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: p:=3718413238715863618 ^-------------------- *** unexpected character: K:=GF(p); ^------- *** unexpected character: E:=EllipticCurve([K|1, ^-------------------- *** expected character: ',' instead of: SEA(E:MaxSmooth:=1); ^--------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '80.15.1' ************** PARI ***************** Host 80.15.132.11 (80.15.132.11) Time: Mon Jan 17 00:03:37 2005 Input: p := 37184132387158636185823166107076967114138479407440093455278818158072422008561996049871236605258164895216434405941633; K := GF(p); E := EllipticCurve([K | 1, 0]); SEA(E , MaxSmooth := 1); Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: p:=3718413238715863618 ^-------------------- *** unexpected character: K:=GF(p); ^------- *** unexpected character: E:=EllipticCurve([K|1, ^-------------------- *** expected character: ',' instead of: SEA(E,MaxSmooth:=1); ^----- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '133.91.' ************** PARI ***************** Host 133.91.40.5 (133.91.40.5) Time: Mon Jan 17 06:32:34 2005 Input: print 2+4; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.003s sys 0m0.009s '66.11.1' ************** PARI ***************** Host 66.11.171.16 (66.11.171.16) Time: Mon Jan 17 20:14:46 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '66.11.1' ************** PARI ***************** Host 66.11.171.16 (66.11.171.16) Time: Mon Jan 17 20:15:47 2005 Input: prime(41561) Output: ? 500257 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '130.34.' ************** PARI ***************** Host 130.34.232.111 (130.34.232.111) Time: Wed Jan 19 02:43:59 2005 Input: I := ext; R := PolynomialRing(I); L := ext; L; A := Automorphisms(L); [ : i in [1 .. #A]]; AutomorphismGroup(L); Output: ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: I:=ext:=PolynomialRing(I); ^-------------------- *** unexpected character: L:=ext:ii ^-------------------- *** expected character: '=' instead of: AutomorphismGroup(L); ^- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '217.227' ************** PARI ***************** Host 217.227.150.192 (217.227.150.192) Time: Wed Jan 19 06:06:55 2005 Input: A := Matrix(2,2,[1,2,3,4]); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: A:=Matrix(2,2,[1,2,3,4 ^-------------------- Timing: real 0m0.013s user 0m0.010s sys 0m0.001s '217.136' ************** PARI ***************** Host 217.136.9.83 (217.136.9.83) Time: Wed Jan 19 10:33:03 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.249s user 0m0.004s sys 0m0.008s '217.136' ************** PARI ***************** Host 217.136.9.83 (217.136.9.83) Time: Wed Jan 19 10:35:10 2005 Input: mattranspose(Vec(ellj(x))) Output: ? [1, 744, 196884, 21493760, 864299970, 20245856256, 333202640600, 4252023300096, 44656994071935, 401490886656000, 3176440229784420, 22567393309593600, 146211911499519294, 874313719685775360, 4872010111798142520]~ ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.007s sys 0m0.006s '217.136' ************** PARI ***************** Host 217.136.9.83 (217.136.9.83) Time: Wed Jan 19 10:36:36 2005 Input: factor(1111111111111111111111111111111111111) Output: ? [2028119 1] [247629013 1] [2212394296770203368013 1] ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.094s user 0m0.041s sys 0m0.015s '217.136' ************** PARI ***************** Host 217.136.9.83 (217.136.9.83) Time: Wed Jan 19 10:37:06 2005 Input: 1/7 Output: ? 1/7 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '217.136' ************** PARI ***************** Host 217.136.9.83 (217.136.9.83) Time: Wed Jan 19 10:37:17 2005 Input: 1/7. Output: ? 0.14285714285714285714285714285714285714 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '217.136' ************** PARI ***************** Host 217.136.9.83 (217.136.9.83) Time: Wed Jan 19 10:37:33 2005 Input: 1/19. Output: ? 0.052631578947368421052631578947368421052 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '217.136' ************** PARI ***************** Host 217.136.9.83 (217.136.9.83) Time: Wed Jan 19 10:39:40 2005 Input: 1/97. Output: ? 0.010309278350515463917525773195876288659 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '193.250' ************** PARI ***************** Host 193.250.66.189 (193.250.66.189) Time: Wed Jan 19 20:16:31 2005 Input: 1234567899876543456789098777777 Output: ? 1234567899876543456789098777777 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.91.' ************** PARI ***************** Host 165.91.223.44 (165.91.223.44) Time: Wed Jan 19 22:44:41 2005 Input: hex(11750020000000000230) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: hex(1175002000000000 ^-------------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '165.91.' ************** PARI ***************** Host 165.91.223.44 (165.91.223.44) Time: Wed Jan 19 23:00:59 2005 Input: pari2hex(11750020000000000230) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: pari2hex(11750020000 ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.91.' ************** PARI ***************** Host 165.91.223.44 (165.91.223.44) Time: Wed Jan 19 23:01:16 2005 Input: pari2hex(11750020000000000230) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: pari2hex(11750020000 ^-------------------- Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '165.91.' ************** PARI ***************** Host 165.91.223.44 (165.91.223.44) Time: Wed Jan 19 23:01:24 2005 Input: pari2hex(11750020000000000230) Output: ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: pari2hex(11750020000 ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.93.' ************** PARI ***************** Host 128.93.12.60 (128.93.12.60) Time: Thu Jan 20 09:10:47 2005 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.353s user 0m0.007s sys 0m0.008s '192.116' ************** PARI ***************** Host 192.116.202.36 (192.116.202.36) Time: Thu Jan 20 09:43:15 2005 Input: In[1]:= PrimeQ[9876543320669] Output: ? ? Errors (if any) and Timing Info: *** unexpected character: In[1]:=PrimeQ[987654332066 ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '213.112' ************** PARI ***************** Host 213.112.112.99 (213.112.112.99) Time: Thu Jan 20 09:43:25 2005 Input: isprime(9876543320669); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.008s sys 0m0.006s '213.112' ************** PARI ***************** Host 213.112.112.99 (213.112.112.99) Time: Thu Jan 20 09:43:28 2005 Input: isprime(9876543320669) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '213.112' ************** PARI ***************** Host 213.112.112.99 (213.112.112.99) Time: Thu Jan 20 09:43:39 2005 Input: isprime(222) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '213.112' ************** PARI ***************** Host 213.112.112.99 (213.112.112.99) Time: Thu Jan 20 09:43:49 2005 Input: isprime(9876543320669) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '213.94.' ************** PARI ***************** Host 213.94.233.240 (213.94.233.240) Time: Thu Jan 20 15:03:56 2005 Input: MAGMA/PARI Calculator

PARI & MAGMA Calculator

by William Stein

Evaluate the code below in or *

This is the result (execution automatically stops after 20 seconds):

HELP!!   PARI and Magma Documentation

 

Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '213.94.' ************** PARI ***************** Host 213.94.233.240 (213.94.233.240) Time: Thu Jan 20 15:04:58 2005 Input: EEVL | Mathematics Section | Browse
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 1.  Algebra Montpellier Announcements
 [Full EEVL Record] http://www.maths.soton.ac.uk/EMIS/journals/AMA/
 

Algebra Montpellier Announcements is devoted to short research announcements containing new results in noncommutative algebra. It is based in the Mathematics Department of the University of Montpellier, France. Access is free. However, there is a charge for the table of contents email alerting service. Articles are available in pdf, dvi and postscript format.

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 2.  Electronic Journal of Linear Algebra
 [Full EEVL Record] http://www.maths.soton.ac.uk/EMIS/journals/ELA/
 

ELA is published by The International Linear Algebra Society (ILAS) and is a freely available, fully refereed electronic journal that contains articles related to matrix analysis and linear algebra and its applications. Articles are in postscript of PDF format. Content tables and author indexes are provided and the volumes date from 1996.

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 3.  Electronic Transactions on Numerical Analysis
 [Full EEVL Record] http://www.maths.soton.ac.uk/EMIS/journals/ETNA/
 

ETNA is published by the Institute of Computational Mathematics at the Kent State University. Papers deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra as well as discuss implementation and performance of such algorithms.

It is a fully electronic journal with abstracts in HTML, PDF and PostScript format and articles available for download in PostScript or PDF format. A search engine is featured on the site.

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 4.  Elementary Linear Algebra
 [Full EEVL Record] http://www.numbertheory.org/book/
 

This electronic book by Keith Matthews of the University of Queensland in Australia comes from lecture notes of his. The whole book or single chapters are available in PDF format along with solutions to problems. The chapters include Linear Equations, Matrices, Subspaces, Determinants, Complex Numbers, Eigenvalues and Eigenvectors, Identifying Second Degree Equations, and Three-dimensional Geometry.

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 5.  International Linear Algebra Society
 [Full EEVL Record] http://www.math.technion.ac.il/iic/ILAS.html
 

Founded in 1989 ILAS succeeded the International Matrix Group that was established in 1987. The society publishes the freely available Electronic Journal of Linear Algebra (ELA) and a bulletin called IMAGE for its members. The website contains information about membership and committees as well as conference and publication information.

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 6.  Linear Algebra textbook
 [Full EEVL Record] http://joshua.smcvt.edu/linearalgebra/
 

The text "Linear Algebra", by Jim Hefferon of the Mathematics Department at Saint Michael's College, is free for downloading. The book covers linear elimination, vector spaces, linear maps and matrix operations, determinants, and matrix similarity and Jordan form.

The whole book or individual chapters, along with answers to exercises, can be downloaded in PDF format. There is also a PostScript version of the book with some optional material. The LaTeX source is also available.

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 7.  Linear Algebra Toolkit
 [Full EEVL Record] http://www.math.odu.edu/~bogacki/lat/
 

Przemyslaw Bogacki's Linear Algebra Toolkit is an interactive Internet toolkit enabling students to practice and learn basic linear algebra procedures. The modules available to the user cover systems of linear equations and matrices, determinants and vector spaces and include a row operation calculator, transforming a matrix to row echelon form, transforming a matrix to reduced row echelon form, solving a linear system of equations, calculating the inverse using row operations, calculating the determinant using row operations, linear independence and dependence, determining if the set spans the space, finding a basis of the space spanned by the set, and finding a basis of the null space of a matrix. All calculations are done online using a Perl script and some results are broken into steps of which details can be viewed. Comments on the solutions are also provided.

Usage is allowed for any non-commercial use of this product by individuals. Permission for the class use in an academic environment is automatically granted provided the instructor notifies the author, and any other use, including any commercial use, requires explicit permission from the author. Przemyslaw Bogacki is an associate professor of mathematics and statistics in the Department of Mathematics and Statistics at Old Dominion University.

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 8.  Magma Computational Algebra System for Algebra, Number Theory and Geometry
 [Full EEVL Record] http://magma.maths.usyd.edu.au/
 

Magma is a software package designed to solve computationally hard problems in algebra, number theory, geometry and combinatorics. It is produced and distributed by the Computational Algebra Group within the School of Mathematics and Statistics of the University of Sydney. The website contains information about supported platforms, pricing and discounts, links to related sites, FAQs, online help, release notes, licencing information, mailing list, and contact details. Magma is currently available for the following: PC (Pentium, 486 or equivalent) under Linux; SUN 4, SUN SPARCstation 1, 1+ under SUNOS 4.x and Solaris 2; SUN SPARCstation 1, 1+, 5, 10, 20 under SUNOS 4.x and Solaris 2; SUN SPARCserver 1000, 2000 under Solaris 2; SUN Ultra under Solaris 2; DEC Alpha under OSF/1; IBM RS6000 under AIX; HP9000/700 series under HP-UX; SGI under IRIX.

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 9.  MIT OpenCourseWare | Mathematics
 [Full EEVL Record] http://ocw.mit.edu/OcwWeb/Mathematics/index.htm
 

MIT and the OpenCourseWare have made available a first sampling of course materials from MIT's Faculty as a pilot version of MIT OCW. The materials are freely available to educators for their own curricula, and for all learners to use the materials for self-study. Some of the courses available from the mathematics section include Calculus with Applications, Complex Variables with Applications, Linear Algebra, and Topics in Theoretical Computer Science: Internet Research Problems. The sections generally contained in the courses include a syllabus, calendar, assignments, required readings, related resources, and study materials. Some video lectures, requiring Real Player, are available. There are also some exams and lecture notes in PDF format as well as interactive Java applets and Matlab codes and images.

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 10.  Platonic Realms Interactive Mathematics Encyclopedia
 [Full EEVL Record] http://www.mathacademy.com/pr/prime/
 

Platonic Realms Interactive Mathematics Encyclopaedia (PRIME) is a sponsored interactive web-based dictionary of mathematics. The user is able to browse entries by subject - basic maths, algebra, analysis, biography, calculus, computer science, discrete mathematics, economics, geometry, graph theory, history, foundations, number theory, physical science, statistics, topology, trigonometry. The encyclopaedia also allows the user to enter up to three letters of a particular word or phrase that they are looking for a definition of. The use of hyperlinks also allows the user to cross-reference other definitions contained on the site. The encyclopaedia is continually building and allows users to submit definitions. A German language version is available.

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 11.  QuickMath Automatic Math Solutions
 [Full EEVL Record] http://www.quickmath.com/
 

QuickMath is a free, automated service for answering common math problems over the internet. It has been developed by Ben Langton, holder of a PhD in general relativity from the University of Sydney. Users submit a question to QuickMath, it is processed by Mathematica at a MathScript server in Delaware, USA, and the answer is sent back and displayed on the browser. The site is aimed at high-school and college students and deals with common problems in algebra, equations, inequalities, calculus, matrices, graphs and numbers.

Users enter the expression using Mathematica notation and results are returned in normal mathematical notation. Explanations for each of the sections are also provided along with help files. Some pages require JavaScript.

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 12.  Toeplitz and Circulant Matrices
 [Full EEVL Record] http://www-ee.stanford.edu/~gray/toeplitz.html
 

Toeplitz and Circulant Matrices is a free full text electronic book authored by Professor Robert M Gray of Stanford University. The book, freely available in PDF format, is a tutorial in Toeplitz matrices and circulant matrices and covers asymptotic behaviour of matrices, circulant matrices, Toeplitz matrices, and applications to stochastic time series.

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 13.  BIT Numerical Mathematics
 [Full EEVL Record] http://math.liu.se/BIT/
 

BIT emphasizes numerical methods in approximation, linear algebra, and ordinary and partial differential equations, but also publishes papers in areas such as numerical functional analysis and numerical optimization. Information about subscriptions, contributions, aims and scope and the editorial board is available from the site as well as contents and an author index in PDF or PostScript format.

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 14.  Communications in Contemporary Mathematics
 [Full EEVL Record] http://www.worldscinet.com/ccm/ccm.shtml
 

Communications in Contemporary Mathematics is a peer-reviewed journal requiring a subscription to access the full text of articles; your university/institution library may be a subscriber. If not the tables of contents and abstracts are free as is author, title and keyword searching. There is a free email alerting service for tables of contents.

The journal aims to act as a forum for stimulating interactions between different areas of mathematics to compliment the current trend of the breaking down of the traditional boundaries between the specialist fields of mathematics. Research in the fields of algebra, analysis, applied mathematics, dynamical systems, geometry, mathematical physics, number theory, partial differential equations, topology, and others is reported. Online coverage, as pdf files, goes back to the first issue in 1999.

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 15.  Computational Algebra Group the University of Sydney
 [Full EEVL Record] http://www.maths.usyd.edu.au:8000/res/CompAlg.html
 

The computational algebra group's website provides information about reports, members and seminars. Reports are in postscript format. The group is also responsible for producing and distributing Magma - a software package designed to solve computationally hard problems in algebra, number theory, geometry and combinatorics.

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 16.  Home Page of Dr T P McDonough
 [Full EEVL Record] http://users.aber.ac.uk/tpd/
 

Dr McDonough is a member of the Department of Mathematics at the University of Wales, Aberystwyth. The Website features learning and teaching materials for algebra and calculus, symbolic computation and computing for mathematicians, abstract algebra, LaTeX, and number theory. The materials include interactive diagnostic tests in PDF format, problems and their solutions, the Greek alphabet, Maple resources, and Peano’s axioms for natural numbers. Included in the Maple resources is a reference guide to the fundamentals of Maple and the basics of programming in Maple. Some material is restricted to local users only.

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 17.  Home Page of Dr. T.N. Phillips
 [Full EEVL Record] http://users.aber.ac.uk/tnp/
 

Professor T. N. Phillips is a member of the Mathematics Department at the University of Wales, Aberystwyth. His research interests include spectral methods, computational fluid dynamics, numerical linear algebra, and domain decomposition techniques. The website features lists of recent publications and research reports, with some abstracts, as well as some lecture notes in PDF or HTML format. The lecture notes cover vector geometry, mathematics for economics and finance, and principles of applied mathematics.

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 18.  Home Page of Keith Matthews
 [Full EEVL Record] http://www.maths.uq.edu.au/~krm/
 

Keith Matthews is an honorary research consultant in the Department of Mathematics at The University of Queensland. He maintains the Number Theory Web and his website offers links to related mathematical sites, some exact arithmetic computer programs in the form of CALC (number theory calculator program), CMAT (matrix calculator program), and BC (number theory programs), a list of publications, unpublished articles in PDF or HTML format, a survey on the generalized 3x+1 (Collatz) mapping, some lecture notes in linear algebra and number theory (handouts, problem sheets, lecture notes, past exams), and an online textbook on Elementary Linear Algebra.

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 19.  International Journal of Algebra and Computation
 [Full EEVL Record] http://www.worldscinet.com/ijac/ijac.shtml
 

This is a peer-reviewed journal requiring a subscription to access the full text of articles; your university/institution library may be a subscriber. If not the tables of contents and abstracts are free as is author, title and keyword searching. There is also a free email alerting service for tables of contents.

The subject coverage of the journal favours the interests of the editorial board, namely: combinatorial group theory and semigroup theory, universal algebra, algorithmic and computational problems in algebra, theory of automata, formal language theory, theory of computation, and theoretical computer science. There are 6 issues per year, going back to 1995.

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 20.  Journal of Algebra and Its Applications
 [Full EEVL Record] http://www.worldscinet.com/jaa/jaa.shtml
 

This is a peer-reviewed journal which requires a subscription to access the full text of articles; your university/institution library may be a subscriber. If not the tables of contents and abstracts are free as is author, title and keyword searching. There is also a free email alerting service for tables of contents. Subject coverage is of both theoretical and applied algebra, with special emphasis on innovative applications. Publication is quarterly and online coverage goes back to the first issue in 2002.

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Output: WARNING: PARI command contains unsafe command 'system', so it will not be executed. '80.142.' ************** PARI ***************** Host 80.142.69.97 (80.142.69.97) Time: Fri Jan 21 04:34:12 2005 Input: (a+b)^2 Output: ? a^2 + 2*b*a + b^2 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.007s sys 0m0.004s '80.142.' ************** PARI ***************** Host 80.142.69.97 (80.142.69.97) Time: Fri Jan 21 04:34:52 2005 Input: (a+b)^2 =c^2 + 2*a*b Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (a+b)^2=c^2+2*a*b ^---------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '80.142.' ************** PARI ***************** Host 80.142.69.97 (80.142.69.97) Time: Fri Jan 21 04:35:08 2005 Input: (a+b)^2 -c^2 - 2*a*b Output: ? a^2 + (b^2 - c^2) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.007s sys 0m0.004s '212.50.' ************** PARI ***************** Host 212.50.20.2 (212.50.20.2) Time: Fri Jan 21 10:24:10 2005 Input: y=x-1 ----- ( (x+4)(x-3) Output: ? x - 1 ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: ----- ^---- *** expected character: ')' instead of: ((x+4)(x-3) ^----- Timing: real 0m0.361s user 0m0.003s sys 0m0.007s '212.50.' ************** PARI ***************** Host 212.50.20.2 (212.50.20.2) Time: Fri Jan 21 10:25:37 2005 Input: y=x-1 Output: ? x - 1 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '129.22.' ************** PARI ***************** Host 129.22.143.79 (129.22.143.79) Time: Fri Jan 21 14:25:40 2005 Input: print("Hi") Output: ? Hi ? Errors (if any) and Timing Info: Timing: real 0m0.333s user 0m0.006s sys 0m0.007s '18.157.' ************** PARI ***************** Host 18.157.24.212 (18.157.24.212) Time: Fri Jan 21 14:25:44 2005 Input: a(n)=if(n<1,n==0,240*sigma(n,3)) a(1) a(2) a(3) Output: ? ? 240 ? 2160 ? 6720 ? Errors (if any) and Timing Info: Timing: real 0m0.061s user 0m0.008s sys 0m0.004s '129.22.' ************** PARI ***************** Host 129.22.143.79 (129.22.143.79) Time: Fri Jan 21 14:25:50 2005 Input: print("Hi") Output: ? Hi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '18.157.' ************** PARI ***************** Host 18.157.24.212 (18.157.24.212) Time: Fri Jan 21 14:26:08 2005 Input: a(n)=if(n<1,n==0,sigma(n,3)) a(1) a(2) a(3) Output: ? ? 1 ? 9 ? 28 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '18.157.' ************** PARI ***************** Host 18.157.24.212 (18.157.24.212) Time: Fri Jan 21 14:26:41 2005 Input: a(n)=if(n<1,n==0,240*sigma(n,3)) a(1) a(2) a(3) Output: ? ? 240 ? 2160 ? 6720 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '18.157.' ************** PARI ***************** Host 18.157.24.212 (18.157.24.212) Time: Fri Jan 21 14:26:53 2005 Input: a(n)=if(n<1,n==0,240*sigma(n,3)) a(0); a(1); a(2); a(3); Output: ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '18.157.' ************** PARI ***************** Host 18.157.24.212 (18.157.24.212) Time: Fri Jan 21 14:27:00 2005 Input: a(n)=if(n<1,n==0,240*sigma(n,3)) a(0) a(1) a(2) a(3) Output: ? ? 1 ? 240 ? 2160 ? 6720 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '18.157.' ************** PARI ***************** Host 18.157.24.212 (18.157.24.212) Time: Fri Jan 21 14:27:53 2005 Input: a(n)=if(n<1,n==0,sigma(n,11)) a(0) a(1) a(2) a(3) Output: ? ? 1 ? 1 ? 2049 ? 177148 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '18.157.' ************** PARI ***************** Host 18.157.24.212 (18.157.24.212) Time: Fri Jan 21 14:27:57 2005 Input: a(n)=if(n<1,n==0,sigma(n,11)) a(0) a(1) a(2) a(3) Output: ? ? 1 ? 1 ? 2049 ? 177148 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '129.22.' ************** PARI ***************** Host 129.22.143.79 (129.22.143.79) Time: Fri Jan 21 14:28:52 2005 Input: print("Hi") 1+1 Output: ? Hi ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.007s sys 0m0.004s '18.157.' ************** PARI ***************** Host 18.157.24.212 (18.157.24.212) Time: Fri Jan 21 14:28:54 2005 Input: a(n)=if(n<1,236364091*(n==0),131040*sigma(n,23)) a(0) a(1) a(2) a(3) Output: ? ? 236364091 ? 131040 ? 1099243323360 ? 12336522153621120 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '129.22.' ************** PARI ***************** Host 129.22.143.79 (129.22.143.79) Time: Fri Jan 21 14:29:03 2005 Input: print("Hi") 1+1 Output: ? Hi ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '18.157.' ************** PARI ***************** Host 18.157.24.212 (18.157.24.212) Time: Fri Jan 21 14:29:15 2005 Input: a(n)=if(n<1,236364091*(n==0),sigma(n,23)) a(0) a(1) a(2) a(3) Output: ? ? 236364091 ? 1 ? 8388609 ? 94143178828 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '129.22.' ************** PARI ***************** Host 129.22.143.79 (129.22.143.79) Time: Fri Jan 21 14:32:59 2005 Input: print("Hi") 1+1 1 Output: ? Hi ? 2 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '129.22.' ************** PARI ***************** Host 129.22.143.79 (129.22.143.79) Time: Fri Jan 21 14:33:04 2005 Input: print("Hi") 1+1 ?1 Output: ? Hi ? 2 ? divrem lex max min shift shiftmul sign vecmax vecmin ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '129.22.' ************** PARI ***************** Host 129.22.143.79 (129.22.143.79) Time: Fri Jan 21 14:33:16 2005 Input: ? Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '129.22.' ************** PARI ***************** Host 129.22.143.79 (129.22.143.79) Time: Fri Jan 21 14:33:30 2005 Input: ?5 Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '129.22.' ************** PARI ***************** Host 129.22.143.79 (129.22.143.79) Time: Fri Jan 21 14:33:35 2005 Input: ?+ Output: ? ? Errors (if any) and Timing Info: *** +: unknown identifier. Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '129.22.' ************** PARI ***************** Host 129.22.143.79 (129.22.143.79) Time: Fri Jan 21 14:33:38 2005 Input: ? Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '129.22.' ************** PARI ***************** Host 129.22.143.79 (129.22.143.79) Time: Fri Jan 21 14:33:52 2005 Input: ?11 Output: ? addhelp alias allocatemem break default error extern for fordiv forprime forstep forsubgroup forvec getheap getrand getstack gettime global if input install kill next print print1 printp printp1 printtex quit read reorder return setrand system trap type until whatnow while write write1 writetex ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '129.22.' ************** PARI ***************** Host 129.22.143.79 (129.22.143.79) Time: Fri Jan 21 14:37:46 2005 Input: { u=v=p=q=1; for (k=1, 1000, w = u+v; u = v; v = w; p *= w; q = lcm(q,w); if (k%50 == 0, print(k " " log(p)/log(q)) ) ) } Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '129.22.' ************** PARI ***************** Host 129.22.143.79 (129.22.143.79) Time: Fri Jan 21 14:38:34 2005 Input: cl(d,cc) = { local(q0,sd,t,c, s = 0, q = 1); if (!isfundamental(-d), error("Discriminant not fundamental")); if (!cc, cc = 5); sd = sqrt(d); q0 = exp(-2*Pi/sd); c = -4*Pi/sd; for (n=1, ceil(sd*cc), q *= q0; t = 1/(1-q); s += kronecker(-d,n) * q * t * (1 + c*t*n) ); if (d==3, s *= 3); if (d==4, s *= 2); -2*s } Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.006s sys 0m0.007s '129.22.' ************** PARI ***************** Host 129.22.143.79 (129.22.143.79) Time: Fri Jan 21 14:39:56 2005 Input: test(x,y) { x+y; } Output: ? ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: test(x,y) ^ Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '129.22.' ************** PARI ***************** Host 129.22.143.79 (129.22.143.79) Time: Fri Jan 21 14:40:00 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Jan 21 21:47:55 2005 Input: mod(2^1234567,6) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(2^1234567,6) ^---------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Jan 21 21:48:03 2005 Input: MOD(2^1234567,6) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: MOD(2^1234567,6) ^---------------- Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Jan 21 21:48:09 2005 Input: MOD(2^1234567,6) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: MOD(2^1234567,6) ^---------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '82.233.' ************** PARI ***************** Host 82.233.132.60 (82.233.132.60) Time: Sat Jan 22 04:58:28 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '217.253' ************** PARI ***************** Host 217.253.228.69 (217.253.228.69) Time: Sat Jan 22 10:40:52 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.230s user 0m0.008s sys 0m0.007s '217.253' ************** PARI ***************** Host 217.253.228.69 (217.253.228.69) Time: Sat Jan 22 10:41:34 2005 Input: Hello Output: ? Hello ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '68.60.1' ************** PARI ***************** Host 68.60.148.198 (68.60.148.198) Time: Sat Jan 22 12:47:11 2005 Input: x Output: ? x ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.60.1' ************** PARI ***************** Host 68.60.148.198 (68.60.148.198) Time: Sat Jan 22 12:48:10 2005 Input: 2x^2=11x=21 Output: ? 2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x^2=11x=21. Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '68.60.1' ************** PARI ***************** Host 68.60.148.198 (68.60.148.198) Time: Sat Jan 22 12:48:58 2005 Input: 2x^2+11x-21=0 Output: ? 2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x^2+11x-21=0. Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '68.60.1' ************** PARI ***************** Host 68.60.148.198 (68.60.148.198) Time: Sat Jan 22 12:49:09 2005 Input: 2x^2+11x-21=0,x Output: ? 2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x^2+11x-21=0,x. Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Jan 22 15:06:28 2005 Input: ((10^5058)*((10^5058)+1)-3 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...(10^5058)*((10^5058)+1)-3 ^ Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Jan 22 15:06:50 2005 Input: ((10^5058)*((10^5058)+1))-3 Output: ? 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.057s user 0m0.030s sys 0m0.007s '12.169.' ************** PARI ***************** Host 12.169.166.21 (12.169.166.21) Time: Sat Jan 22 16:36:05 2005 Input: s4 = Sym({1,2,3,4}); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: s4=Sym({1,2,3,4}); ^----------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '12.169.' ************** PARI ***************** Host 12.169.166.21 (12.169.166.21) Time: Sat Jan 22 16:36:38 2005 Input: s4 := Sym({1,2,3,4}); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: s4:=Sym({1,2,3,4}); ^---------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '209.221' ************** PARI ***************** Host 209.221.240.10 (209.221.240.10) Time: Sat Jan 22 18:23:26 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '81.152.' ************** PARI ***************** Host 81.152.192.156 (81.152.192.156) Time: Sun Jan 23 05:48:31 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.003s sys 0m0.009s '81.152.' ************** PARI ***************** Host 81.152.192.156 (81.152.192.156) Time: Sun Jan 23 05:49:58 2005 Input: ploth(t = 100, 110, real(zeta(0.5+I*t)), /*empty*/, 1000) Output: WARNING: PARI command contains unsafe command 'plot', so it will not be executed. '81.152.' ************** PARI ***************** Host 81.152.192.156 (81.152.192.156) Time: Sun Jan 23 05:50:22 2005 Input: ploth(t = 100, 110, real(zeta(0.5+I*t)), /*empty*/, 1000) Output: WARNING: PARI command contains unsafe command 'plot', so it will not be executed. '140.247' ************** PARI ***************** Host 140.247.189.155 (140.247.189.155) Time: Sun Jan 23 16:57:49 2005 Input: numdiv(19923498) Output: ? 60 ? Errors (if any) and Timing Info: Timing: real 0m0.183s user 0m0.005s sys 0m0.004s '213.140' ************** PARI ***************** Host 213.140.22.71 (213.140.22.71) Time: Sun Jan 23 19:39:35 2005 Input: Input: F:=GF(4); A:=GL(2,F)![a,a^3,-a,0]; A^5;A^2;A^3;A^7; Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: Input:F:=GF(4); ^-------- *** unexpected character: A:=GL(2,F)![a,a^3,-a,0 ^-------------------- Timing: real 0m0.027s user 0m0.006s sys 0m0.007s '213.140' ************** PARI ***************** Host 213.140.22.71 (213.140.22.71) Time: Sun Jan 23 19:40:25 2005 Input: F:=GF(4); A:=GL(2,F)![a,a^3,-a,0]; A^5;A^2;A^3;A^7; Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: F:=GF(4); ^-------- *** unexpected character: A:=GL(2,F)![a,a^3,-a,0 ^-------------------- Timing: real 0m0.016s user 0m0.007s sys 0m0.003s '81.73.1' ************** PARI ***************** Host 81.73.186.12 (81.73.186.12) Time: Mon Jan 24 13:59:17 2005 Input: ciao Output: ? ciao ? Errors (if any) and Timing Info: Timing: real 0m0.349s user 0m0.006s sys 0m0.009s '81.73.1' ************** PARI ***************** Host 81.73.186.12 (81.73.186.12) Time: Mon Jan 24 13:59:28 2005 Input: 123 Output: ? 123 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '81.73.1' ************** PARI ***************** Host 81.73.186.12 (81.73.186.12) Time: Mon Jan 24 14:00:20 2005 Input: 12355555555555555555555555555555555555555555555554 Output: ? 12355555555555555555555555555555555555555555555554 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '134.10.' ************** PARI ***************** Host 134.10.176.143 (134.10.176.143) Time: Tue Jan 25 02:27:04 2005 Input: 1115484548974465494984694974987987498 Output: ? 1115484548974465494984694974987987498 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '137.248' ************** PARI ***************** Host 137.248.201.137 (137.248.201.137) Time: Tue Jan 25 03:02:05 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:24:41 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.380s user 0m0.007s sys 0m0.009s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:24:57 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:25:32 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:25:39 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:25:45 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:25:53 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:25:57 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:26:02 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:26:08 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:26:18 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:26:22 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:26:26 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:26:35 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:26:40 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:26:45 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:26:50 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:26:56 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.005s sys 0m0.009s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:27:01 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:27:06 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:27:11 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:27:20 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:27:25 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213842) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:27:41 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:27:52 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:27:56 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384395) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:28:01 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843951) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:28:06 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:28:12 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384395119) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:28:16 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843951192) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:28:21 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511922) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:28:27 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384395119220) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:28:57 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843951192208) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:29:03 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511922086) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:29:09 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384395119220862) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:29:14 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843951192208629) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:29:18 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511922086294) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:29:23 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384395119220862945) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:29:28 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843951192208629455) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.003s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:29:34 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511922086294554) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:30:14 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843951192208629455) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:31:00 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843951192208629455427072107006382027012975805127510235371036993169) Output: ? 97488695771554213843951192208629455427072107006382027012975805127510235371036993169 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:31:09 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384395119220862945542707210700638202701297580512751023537103699316) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:31:16 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511922086294554270721070063820270129758051275102353710369931) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:31:22 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843951192208629455427072107006382027012975805127510235371036993) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:31:28 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384395119220862945542707210700638202701297580512751023537103699) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:31:34 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511922086294554270721070063820270129758051275102353710369) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:31:40 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843951192208629455427072107006382027012975805127510235371036) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:31:47 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384395119220862945542707210700638202701297580512751023537103) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:31:52 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511922086294554270721070063820270129758051275102353710) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:32:00 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843951192208629455427072107006382027012975805127510235371) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:32:06 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384395119220862945542707210700638202701297580512751023537) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:32:13 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511922086294554270721070063820270129758051275102353) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:32:18 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843951192208629455427072107006382027012975805127510235) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:32:24 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384395119220862945542707210700638202701297580512751023) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:32:32 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511922086294554270721070063820270129758051275102) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:32:38 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843951192208629455427072107006382027012975805127510) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:32:45 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384395119220862945542707210700638202701297580512751) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:32:51 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511922086294554270721070063820270129758051275) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:32:58 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843951192208629455427072107006382027012975805127) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:33:03 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384395119220862945542707210700638202701297580512) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:33:09 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511922086294554270721070063820270129758051) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:33:15 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843951192208629455427072107006382027012975805) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:33:22 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384395119220862945542707210700638202701297580) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:33:28 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511922086294554270721070063820270129758) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:33:34 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843951192208629455427072107006382027012975) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:33:39 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384395119220862945542707210700638202701297) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:33:45 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511922086294554270721070063820270129) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.012s sys 0m0.000s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:33:50 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,97488695771554213843951192208629455427072107006382027012) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:33:55 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384395119220862945542707210700638202701) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:34:03 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511922086294554270721070063820270) Output: ? 4325268375836745123678997723 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:35:31 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,4325268375836745123678997723) Output: ? 4325268375836745123678997723 ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:35:53 2005 Input: 97488695771554213843951192208629455427072107006382027012975805127510235371036993169/4325268375836745123678997723 Output: ? 22539340290692258087863249000000000000000000000000000003 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:37:05 2005 Input: factor(4325268375836745123678997723) Output: ? [4325268375836745123678997723 1] ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.005s sys 0m0.009s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:37:30 2005 Input: factor(22539340290692258087863249000000000000000000000000000003) Output: ? [22539340290692258087863249000000000000000000000000000003 1] ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.014s sys 0m0.004s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:39:08 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,9748869577155421384395119220862945542707210700638202701) Output: ? 1 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.008s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:39:19 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511922086294554270721070063820270) Output: ? 4325268375836745123678997723 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:39:28 2005 Input: gcd(97488695771554213843951192208629455427072107006382027012975805127510235371036993169,974886957715542138439511922086294554270721070063820270) Output: ? 4325268375836745123678997723 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:42:09 2005 Input: 4325268375836745123678997722*22539340290692258087863249000000000000000000000000000002 Output: ? 97488695771554213843951192186090115136379848918518778008650536751673490247357995444 ? ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:44:22 2005 Input: gcd(7,97488695771554213843951192186090115136379848918518778008650536751673490247357995444) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 09:44:37 2005 Input: bezout(7,97488695771554213843951192186090115136379848918518778008650536751673490247357995444) Output: ? [41780869616380377361693368079752906487019935250793762003707372893574352963153426619, -3, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '132.227' ************** PARI ***************** Host 132.227.66.21 (132.227.66.21) Time: Tue Jan 25 10:14:50 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 10:52:34 2005 Input: ?convert Output: ? ? Errors (if any) and Timing Info: *** convert: unknown identifier. Timing: real 0m0.017s user 0m0.010s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 10:52:46 2005 Input: ?gcd Output: ? gcd(x,y,{flag=0}): greatest common divisor of x and y. flag is optional, and can be 0: default, 1: use the modular gcd algorithm (x and y must be polynomials), 2 use the subresultant algorithm (x and y must be polynomials). ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 10:52:58 2005 Input: ?? Output: ? ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 10:53:51 2005 Input: ?4 Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:03:20 2005 Input: for(x=2,20,if(x == 3, print(x))) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.008s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:07:07 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=2,20,if(Mod(C,R)^(x+s) == Mod(C,R), print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.015s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:07:42 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=2,100,if(Mod(C,R)^(x+s) == Mod(C,R), print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.046s user 0m0.039s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:08:08 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=2,1000,if(Mod(C,R)^(x+s) == Mod(C,R), print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.352s user 0m0.347s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:08:20 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=2,10000,if(Mod(C,R)^(x+s) == Mod(C,R), print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? ? ? Errors (if any) and Timing Info: Timing: real 0m3.420s user 0m3.412s sys 0m0.008s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:08:55 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=2,100000,if(Mod(C,R)^(x+s) == Mod(C,R), print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 21301 Killed /usr/bin/gp -q -emacs Timing: real 0m21.006s user 0m20.993s sys 0m0.007s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:09:22 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=2,10000,if(Mod(C,R)^(x+s) == Mod(C,R), print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? ? ? Errors (if any) and Timing Info: Timing: real 0m3.421s user 0m3.416s sys 0m0.004s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:10:20 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=1,10000,if(Mod(C,R)^(x+s) == Mod(C,R), print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? ? ? Errors (if any) and Timing Info: Timing: real 0m3.422s user 0m3.416s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:12:08 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=1,10,print(Mod(C,R)^x)) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? Mod(12415915339599194259859497974644706543466284113898011530978921570769006, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(1650461783758332586454360201947147886074969621907438253769818802519696, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(17816679575638617985380717837985353973239403175688780685985382252465002, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(6235164404724949655306564152952014376385136471667068308411092650509677, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(14367294240882088517248984503367692655167923578037961201122149912205647, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(6861195560209214732558697022556131899866814875741462701069462619561862, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(9573901338916357933340361134744673533617019861975100246814087112539902, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(7241550767413929522836400103431011595689772656519043795429528157315838, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(12158970062492063873740940315448276439554785408997647772696285216252097, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(15035449119552578845011315621658836827429438815840921371103962017115267, 23539343157690620023354298933143011347090033550087997734858030044952337) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:12:58 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=1,10,print(Mod(C,R)^(x+s))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? Mod(16290885637026754241098375176215063011406281293834014148336728867311945, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(405973887762238667192691208510259157262959168834976307611843016307564, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(18641735899868165593789746835583496059074400312945387979872038943134814, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(15054145005047355530832497944179800158850831263683237746948696966932077, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(6340912724156716952814458567731806057365356870397427665115273039836597, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(7470891825120170129681688656446784528539585296690428450897678084743568, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(14116198797194588835293759048591629499670784935099136914510281837312883, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(1813679080424034103283960614745524079669709696326647015765764658507939, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(22025601411026144963773893632871183222524796148980103840771815630135218, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(11085400878156888042162885450035911881912129295095932380324507978864451, 23539343157690620023354298933143011347090033550087997734858030044952337) ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:13:23 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=1,100,print(Mod(C,R)^(x+s))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? Mod(16290885637026754241098375176215063011406281293834014148336728867311945, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(405973887762238667192691208510259157262959168834976307611843016307564, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(18641735899868165593789746835583496059074400312945387979872038943134814, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(15054145005047355530832497944179800158850831263683237746948696966932077, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(6340912724156716952814458567731806057365356870397427665115273039836597, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(7470891825120170129681688656446784528539585296690428450897678084743568, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(14116198797194588835293759048591629499670784935099136914510281837312883, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(1813679080424034103283960614745524079669709696326647015765764658507939, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(22025601411026144963773893632871183222524796148980103840771815630135218, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(11085400878156888042162885450035911881912129295095932380324507978864451, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(3310549225847783037264525991314820643175418022594230127083457097580436, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(9558638309984210542721642233229319930043385236299596974485453879625917, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(21770880932901243750608188941456687169358100873435535466684026573720347, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(18824425047602618762556816883578993073314619807640169519484820195673059, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(13518371482546815893514952982489722150064056201486076808823974007357709, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(8101420731895116044217517658598257044668014394953570286542332394557208, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(9704463239552994116972864425420498458363411984262102572026860634970629, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(20330896366753632187828642990307554765949971327482042875362753939723796, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(19433192440269906565376082276379977220306944217018164892390141317828900, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(1208914700730790025022893699409111044244987024095878974154100647120447, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(16324112294619154788999848835196238725363186651104636258793048158181490, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(7249436894889700726454362708606648078977832017166143078372302111109125, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(9725441257516545799481943030198387260216937205406777998514814856247103, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(5841506733639890059867028384354541788435567841383679835796445275691969, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(22784937839105227374666621736245095981841780505156022325356438050536374, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(22432381072857294097560501524601212412179244730381615705836224953557053, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(7379132697836062387274462571835075781396165130644417257671085768972382, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(12665600270545763468350281055082834000816292031333165933176864885102791, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(5186070754110665267289479320457826443173322645468667348189666576101743, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(13291232080128544209352587035204584669469896200704237639364637931080815, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(4844114387041308938536215457917979402046167616371100894225684615793745, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(814583676729962793765331880932001382521064890664672968420948113438026, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(631286649338882375279378270233206357669858531974312952927582295468130, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(13205221493881380610471917145423666577028846284739561312324089540151579, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(19880910143406440461861431494336977181830929934000525585156441237141823, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(12871074771901004248304305572988972357772512715134141820878072968830312, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(2193165383822730539740596692077914490074173242522709880497350072953162, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(15127771780403368521988884818272952656809262664457233885643128804745864, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(1147884860765484760569990594160378029084495694192445654282312569846350, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(13619084521161794897932616887004852787539658655415564427620849291223967, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(19697547261390019387507639509798534214446062894614797216487202075667168, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(20177813488005489994251683859920264149067454805548127960748711006181901, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(23373949018286024530525584530031167744117594812978064310269472395697571, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(608346375408216808203693605801984399113620901574335073616055149741378, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(8270570770951472393130040901282164468625822261084154515280696296879276, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(12748812410253117601190189293444192966622286094754957149760853861566679, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(15917150758439074455013488411238604282716566359974847561570794327088179, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(22048306343608402715983204258500729463900100950907319384788085086232804, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(20513168014158470320711141205513400906739741707110382340333649671466711, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(23184254440892646957045690747638620613737361275498703342475077592670878, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(1220904626730396958874270351880046368338798765173596795058012685098609, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(21215211060006448369199737087728607501652413997147988202643801867658919, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(14615528138902754822654087958848695091109665023992067435800511750861961, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(5305544593296638135324745685758631379671637661018052709153139397791911, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(3226049194633845823322262397215800210598986184180308808700727821336951, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(5936744545471160194944122052685459432122083617688099731124279348635990, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(10197077388137235862129519259771792754174337426078815644994507095863242, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(19247763884401422807312655403442816531537320445671673920676971262229062, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(14209846111670833499085631310502108101469684813353882049873071520410132, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(18528500834813905760273115932217734613379764464241222572647407061423176, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(12890049951810281204214597731057435712769850995091590253084549332600101, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(20787885671939463048049863794728263344490033037595622661889505305290058, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(2137317366864508387704670295313472201423101599474612745423175397815996, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(9284128140611659184748233864805004247197564098467153121492313874757044, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(2798032520368193957856662415475650184474053562801183548224674860677991, 23539343157690620023354298933143011347090033550087997734858030044952337) Mod(115961307231701068265935889617297902027509612952948115 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.047s user 0m0.039s sys 0m0.007s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:16:42 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 for(x=1,100,if(Mod(10,R)^(s+x)==Mod(10,R),print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.033s sys 0m0.004s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:16:55 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 for(x=1,1000,if(Mod(10,R)^(s+x)==Mod(10,R),print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.262s user 0m0.256s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:17:11 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 for(x=1,10000,if(Mod(10,R)^(s+x)==Mod(10,R),print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? ? ? Errors (if any) and Timing Info: Timing: real 0m2.530s user 0m2.523s sys 0m0.007s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:18:45 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 for(x=1,100,if(Mod(1,R)^(s+x)==Mod(1,R),print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:19:19 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 for(x=1,100,if(Mod(2,R)^(s+x)==Mod(2,R),print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.030s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:19:27 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 for(x=1,1000,if(Mod(2,R)^(s+x)==Mod(2,R),print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.247s user 0m0.241s sys 0m0.005s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:19:36 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 for(x=1,10000,if(Mod(2,R)^(s+x)==Mod(2,R),print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? ? ? Errors (if any) and Timing Info: Timing: real 0m2.377s user 0m2.369s sys 0m0.006s '219.78.' ************** PARI ***************** Host 219.78.175.4 (219.78.175.4) Time: Tue Jan 25 11:20:06 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 for(x=1,100000,if(Mod(2,R)^(s+x)==Mod(2,R),print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 21386 Killed /usr/bin/gp -q -emacs Timing: real 0m21.024s user 0m20.980s sys 0m0.022s '62.245.' ************** PARI ***************** Host 62.245.36.123 (62.245.36.123) Time: Tue Jan 25 14:59:03 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '62.245.' ************** PARI ***************** Host 62.245.36.123 (62.245.36.123) Time: Tue Jan 25 15:08:15 2005 Input: p 50 1./37 Output: ? p50 ? 0.027027027027027027027027027027027027026 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '62.245.' ************** PARI ***************** Host 62.245.36.123 (62.245.36.123) Time: Tue Jan 25 15:08:28 2005 Input: p 50 1./13 Output: ? p50 ? 0.076923076923076923076923076923076923076 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '62.245.' ************** PARI ***************** Host 62.245.36.123 (62.245.36.123) Time: Tue Jan 25 15:08:43 2005 Input: p 50 1./17 Output: ? p50 ? 0.058823529411764705882352941176470588235 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '62.245.' ************** PARI ***************** Host 62.245.36.123 (62.245.36.123) Time: Tue Jan 25 15:08:58 2005 Input: p 50 1./19 Output: ? p50 ? 0.052631578947368421052631578947368421052 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '62.245.' ************** PARI ***************** Host 62.245.36.123 (62.245.36.123) Time: Tue Jan 25 15:12:24 2005 Input: p 50 1./19 Output: ? p50 ? 0.052631578947368421052631578947368421052 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '62.245.' ************** PARI ***************** Host 62.245.36.123 (62.245.36.123) Time: Tue Jan 25 15:14:59 2005 Input: p 50 1./19 Output: ? p50 ? 0.052631578947368421052631578947368421052 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '62.245.' ************** PARI ***************** Host 62.245.36.123 (62.245.36.123) Time: Tue Jan 25 15:15:07 2005 Input: p 70 1./19 Output: ? p70 ? 0.052631578947368421052631578947368421052 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:42:50 2005 Input: forprimes(p=2, 1000, if(p%3==1, print(p))) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:43:07 2005 Input: forprimes(p=2, 1000, if(p % 3 == 1, print(p))) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:44:52 2005 Input: forprimes(p=2, 1000, if(p > 100, print(p))) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: forprimes(p=2,1000,i ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:45:27 2005 Input: forprime(p=2,1000,if(p > 100, print(p))) Output: ? 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:49:03 2005 Input: p(x)=(x > 100) forprime(q=2,1000,if(p(q), print(q))) Output: ? ? 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:50:21 2005 Input: p(x)=(x > 100) forprime(q=2,1000,if(p(q), print(q))) ?mod Output: ? ? 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 ? ? ? Errors (if any) and Timing Info: *** obsolete function: mod ^--- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:50:56 2005 Input: p(x)=(x > 100) forprime(q=2,1000,if(p(q), print(q))) Output: ? ? 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.005s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:51:34 2005 Input: 1+1 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:51:43 2005 Input: ?% Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:51:52 2005 Input: ?modulo Output: ? ? Errors (if any) and Timing Info: *** modulo: unknown identifier. Timing: real 0m0.016s user 0m0.006s sys 0m0.008s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:51:58 2005 Input: ?mod Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod ^--- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:52:11 2005 Input: ? Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:52:35 2005 Input: ?1 Output: ? divrem lex max min shift shiftmul sign vecmax vecmin ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:52:46 2005 Input: ?4 Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:54:08 2005 Input: ? Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:55:13 2005 Input: ?isint Output: ? ? Errors (if any) and Timing Info: *** isint: unknown identifier. Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:55:19 2005 Input: ?isinteger Output: ? ? Errors (if any) and Timing Info: *** isinteger: unknown identifier. Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:56:53 2005 Input: ?divides Output: ? ? Errors (if any) and Timing Info: *** divides: unknown identifier. Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:57:01 2005 Input: ?rem Output: ? ? Errors (if any) and Timing Info: *** rem: unknown identifier. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:57:13 2005 Input: ?+ Output: ? ? Errors (if any) and Timing Info: *** +: unknown identifier. Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:57:49 2005 Input: gcd(10,5) Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.003s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 02:59:00 2005 Input: p(x)=(gcd(x-2,5)==5) forprime(q=2,1000,if(p(q),print(q))) Output: ? ? 2 7 17 37 47 67 97 107 127 137 157 167 197 227 257 277 307 317 337 347 367 397 457 467 487 547 557 577 587 607 617 647 677 727 757 787 797 827 857 877 887 907 937 947 967 977 997 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 03:13:17 2005 Input: forprime(p=2,1000,if(gcd(p-2,5)==5,print(p)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...f(gcd(p-2,5)==5,print(p)) ^ Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Wed Jan 26 03:14:01 2005 Input: forprime(p=2,1000,if(gcd(p-2,5)==5,print(p))) Output: ? 2 7 17 37 47 67 97 107 127 137 157 167 197 227 257 277 307 317 337 347 367 397 457 467 487 547 557 577 587 607 617 647 677 727 757 787 797 827 857 877 887 907 937 947 967 977 997 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '62.255.' ************** PARI ***************** Host 62.255.64.8 (62.255.64.8) Time: Wed Jan 26 05:49:05 2005 Input: forprime(p=11,10000,if (p%10==1,print(p))) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '62.255.' ************** PARI ***************** Host 62.255.64.8 (62.255.64.8) Time: Wed Jan 26 05:49:55 2005 Input: forprime(p=11,10000,if (p==1,print(p))) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '62.255.' ************** PARI ***************** Host 62.255.64.8 (62.255.64.8) Time: Wed Jan 26 05:51:14 2005 Input: forprime(p=11,10000,if (p10==1,print(p))) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '62.255.' ************** PARI ***************** Host 62.255.64.8 (62.255.64.8) Time: Wed Jan 26 05:52:11 2005 Input: forprime(p=11,10000,if (p%10==1,print(p))) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '62.255.' ************** PARI ***************** Host 62.255.64.8 (62.255.64.8) Time: Wed Jan 26 05:52:11 2005 Input: forprime(p=11,10000,if (p%10==1,print(p))) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 08:38:22 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=2,20,if(Mod(C,R)^(x*s) == Mod(C,R), print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? ? Errors (if any) and Timing Info: Timing: real 0m0.470s user 0m0.014s sys 0m0.018s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 08:38:45 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=2,200,if(Mod(C,R)^(x*s) == Mod(C,R), print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? ? Errors (if any) and Timing Info: Timing: real 0m0.087s user 0m0.077s sys 0m0.005s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 08:38:53 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=2,2000,if(Mod(C,R)^(x*s) == Mod(C,R), print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? ? Errors (if any) and Timing Info: Timing: real 0m0.979s user 0m0.737s sys 0m0.052s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 08:39:26 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=2,20000,if(Mod(C,R)^(x*s) == Mod(C,R), print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? ? Errors (if any) and Timing Info: Timing: real 0m8.155s user 0m7.233s sys 0m0.097s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 08:40:33 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=2,40000,if(Mod(C,R)^(x*s) == Mod(C,R), print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? ? Errors (if any) and Timing Info: Timing: real 0m16.312s user 0m14.491s sys 0m0.677s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 08:41:06 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 R/s Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 23539343157690620023354298933143011347090033550087997734858030044952337/10664375664461099858283128804958703071129745997594419046539320395646981 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.005s sys 0m0.005s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 08:43:06 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 Rs Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? Rs ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.007s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 08:43:15 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 Rs Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? Rs ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 08:43:33 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 s*2 Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 21328751328922199716566257609917406142259491995188838093078640791293962 ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.006s sys 0m0.010s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 08:44:45 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=1,20,if(Mod(C,R)^(x*s) == Mod(C,R), print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.015s sys 0m0.006s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 08:44:56 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=1,20,if(Mod(C,R)^(x*s) == Mod(C,R), print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.014s sys 0m0.006s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 08:53:45 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 for(x=1,20,if(Mod(C,R)^(s^x) == Mod(C,R), print(x))) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? 7 14 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.090s user 0m0.078s sys 0m0.010s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 09:02:34 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 Mod(C,R)^6 Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? Mod(6861195560209214732558697022556131899866814875741462701069462619561862, 23539343157690620023354298933143011347090033550087997734858030044952337) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 09:03:13 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 P = 6861195560209214732558697022556131899866814875741462701069462619561862 Mod(P,R)^s Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? 6861195560209214732558697022556131899866814875741462701069462619561862 ? Mod(11663635712461143358623216082489878644781021763484003390533235657831649, 23539343157690620023354298933143011347090033550087997734858030044952337) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 09:03:48 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 P = 6861195560209214732558697022556131899866814875741462701069462619561862 Mod(C,R)^6 Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? 6861195560209214732558697022556131899866814875741462701069462619561862 ? Mod(6861195560209214732558697022556131899866814875741462701069462619561862, 23539343157690620023354298933143011347090033550087997734858030044952337) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 09:03:57 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 P = 6861195560209214732558697022556131899866814875741462701069462619561862 Mod(C,R)^7 Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? 6861195560209214732558697022556131899866814875741462701069462619561862 ? Mod(9573901338916357933340361134744673533617019861975100246814087112539902, 23539343157690620023354298933143011347090033550087997734858030044952337) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 09:05:05 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 P = 6861195560209214732558697022556131899866814875741462701069462619561862 Mod(C,R)^(s^7) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? 6861195560209214732558697022556131899866814875741462701069462619561862 ? Mod(12415915339599194259859497974644706543466284113898011530978921570769006, 23539343157690620023354298933143011347090033550087997734858030044952337) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 09:05:15 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 P = 6861195560209214732558697022556131899866814875741462701069462619561862 Mod(C,R)^(s^6) Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? 6861195560209214732558697022556131899866814875741462701069462619561862 ? Mod(10721101110811081111103210661097110311041100109711001033, 23539343157690620023354298933143011347090033550087997734858030044952337) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 09:06:08 2005 Input: R = 23539343157690620023354298933143011347090033550087997734858030044952337 s = 10664375664461099858283128804958703071129745997594419046539320395646981 C = 12415915339599194259859497974644706543466284113898011530978921570769006 P = 10721101110811081111103210661097110311041100109711001033 Mod(P,R)^s Output: ? 23539343157690620023354298933143011347090033550087997734858030044952337 ? 10664375664461099858283128804958703071129745997594419046539320395646981 ? 12415915339599194259859497974644706543466284113898011530978921570769006 ? 10721101110811081111103210661097110311041100109711001033 ? Mod(12415915339599194259859497974644706543466284113898011530978921570769006, 23539343157690620023354298933143011347090033550087997734858030044952337) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 09:28:47 2005 Input: R = 390136546196081718607305163473332331417377493685003168939910614118097383796236025236161501548313100735940913083489842340600819098308361714535068954253678353269882635879699406804759345689353730504379874158332132241114147566334361695216611588931744473963962511029943469640447626310597949395943169880131532727642609356099243034697042275923239732294825664054095517406079359905810632719643672701441659 s = 190380618807403745307923978053980745704168649329203670142365133689945248262261770102565161802449979200347735726216852364082170243782043134851392248249192842065184257603176288534281678871465832703721524296216747661969156861717403234055128912278788166594808590474354944280641248904029997977128796803373167092219006009601779280237689649838031120953393850915663786432594439027654396155967716460988691 C = 275998648910936868185149456406181501757023486291571125590923081153846260667591828079211802651663967093313254035957286102888219480381369363881780858365997105972392204311434479302575548812828252162353031466803954477596135457476187127605184460671661216163292951830602411007593041826107046067396184793635965487827049867110569983282272692216759766163642354067563675559274279129809946032424873772598571 for(x=0,20,if(Mod(C,R)^(s*x)==Mod(C,R),print(x))) Output: ? 390136546196081718607305163473332331417377493685003168939910614118097383796236025236161501548313100735940913083489842340600819098308361714535068954253678353269882635879699406804759345689353730504379874158332132241114147566334361695216611588931744473963962511029943469640447626310597949395943169880131532727642609356099243034697042275923239732294825664054095517406079359905810632719643672701441659 ? 190380618807403745307923978053980745704168649329203670142365133689945248262261770102565161802449979200347735726216852364082170243782043134851392248249192842065184257603176288534281678871465832703721524296216747661969156861717403234055128912278788166594808590474354944280641248904029997977128796803373167092219006009601779280237689649838031120953393850915663786432594439027654396155967716460988691 ? 275998648910936868185149456406181501757023486291571125590923081153846260667591828079211802651663967093313254035957286102888219480381369363881780858365997105972392204311434479302575548812828252162353031466803954477596135457476187127605184460671661216163292951830602411007593041826107046067396184793635965487827049867110569983282272692216759766163642354067563675559274279129809946032424873772598571 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.423s user 0m0.416s sys 0m0.006s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 09:29:15 2005 Input: R = 390136546196081718607305163473332331417377493685003168939910614118097383796236025236161501548313100735940913083489842340600819098308361714535068954253678353269882635879699406804759345689353730504379874158332132241114147566334361695216611588931744473963962511029943469640447626310597949395943169880131532727642609356099243034697042275923239732294825664054095517406079359905810632719643672701441659 s = 190380618807403745307923978053980745704168649329203670142365133689945248262261770102565161802449979200347735726216852364082170243782043134851392248249192842065184257603176288534281678871465832703721524296216747661969156861717403234055128912278788166594808590474354944280641248904029997977128796803373167092219006009601779280237689649838031120953393850915663786432594439027654396155967716460988691 C = 275998648910936868185149456406181501757023486291571125590923081153846260667591828079211802651663967093313254035957286102888219480381369363881780858365997105972392204311434479302575548812828252162353031466803954477596135457476187127605184460671661216163292951830602411007593041826107046067396184793635965487827049867110569983282272692216759766163642354067563675559274279129809946032424873772598571 for(x=0,20,if(Mod(C,R)^(s^x)==Mod(C,R),print(x))) Output: ? 390136546196081718607305163473332331417377493685003168939910614118097383796236025236161501548313100735940913083489842340600819098308361714535068954253678353269882635879699406804759345689353730504379874158332132241114147566334361695216611588931744473963962511029943469640447626310597949395943169880131532727642609356099243034697042275923239732294825664054095517406079359905810632719643672701441659 ? 190380618807403745307923978053980745704168649329203670142365133689945248262261770102565161802449979200347735726216852364082170243782043134851392248249192842065184257603176288534281678871465832703721524296216747661969156861717403234055128912278788166594808590474354944280641248904029997977128796803373167092219006009601779280237689649838031120953393850915663786432594439027654396155967716460988691 ? 275998648910936868185149456406181501757023486291571125590923081153846260667591828079211802651663967093313254035957286102888219480381369363881780858365997105972392204311434479302575548812828252162353031466803954477596135457476187127605184460671661216163292951830602411007593041826107046067396184793635965487827049867110569983282272692216759766163642354067563675559274279129809946032424873772598571 ? ? 0 ? ? Errors (if any) and Timing Info: Timing: real 0m4.296s user 0m4.290s sys 0m0.006s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 09:29:52 2005 Input: R = 390136546196081718607305163473332331417377493685003168939910614118097383796236025236161501548313100735940913083489842340600819098308361714535068954253678353269882635879699406804759345689353730504379874158332132241114147566334361695216611588931744473963962511029943469640447626310597949395943169880131532727642609356099243034697042275923239732294825664054095517406079359905810632719643672701441659 s = 190380618807403745307923978053980745704168649329203670142365133689945248262261770102565161802449979200347735726216852364082170243782043134851392248249192842065184257603176288534281678871465832703721524296216747661969156861717403234055128912278788166594808590474354944280641248904029997977128796803373167092219006009601779280237689649838031120953393850915663786432594439027654396155967716460988691 C = 275998648910936868185149456406181501757023486291571125590923081153846260667591828079211802651663967093313254035957286102888219480381369363881780858365997105972392204311434479302575548812828252162353031466803954477596135457476187127605184460671661216163292951830602411007593041826107046067396184793635965487827049867110569983282272692216759766163642354067563675559274279129809946032424873772598571 for(x=0,200,if(Mod(C,R)^(s*x)==Mod(C,R),print(x))) Output: ? 390136546196081718607305163473332331417377493685003168939910614118097383796236025236161501548313100735940913083489842340600819098308361714535068954253678353269882635879699406804759345689353730504379874158332132241114147566334361695216611588931744473963962511029943469640447626310597949395943169880131532727642609356099243034697042275923239732294825664054095517406079359905810632719643672701441659 ? 190380618807403745307923978053980745704168649329203670142365133689945248262261770102565161802449979200347735726216852364082170243782043134851392248249192842065184257603176288534281678871465832703721524296216747661969156861717403234055128912278788166594808590474354944280641248904029997977128796803373167092219006009601779280237689649838031120953393850915663786432594439027654396155967716460988691 ? 275998648910936868185149456406181501757023486291571125590923081153846260667591828079211802651663967093313254035957286102888219480381369363881780858365997105972392204311434479302575548812828252162353031466803954477596135457476187127605184460671661216163292951830602411007593041826107046067396184793635965487827049867110569983282272692216759766163642354067563675559274279129809946032424873772598571 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m4.074s user 0m4.067s sys 0m0.007s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 10:08:52 2005 Input: R=390136546196081718607305163473332331417377493685003168939910614118097383796236025236161501548313100735940913083489842340600819098308361714535068954253678353269882635879699406804759345689353730504379874158332132241114147566334361695216611588931744473963962511029943469640447626310597949395943169880131532727642609356099243034697042275923239732294825664054095517406079359905810632719643672701441659 s=190380618807403745307923978053980745704168649329203670142365133689945248262261770102565161802449979200347735726216852364082170243782043134851392248249192842065184257603176288534281678871465832703721524296216747661969156861717403234055128912278788166594808590474354944280641248904029997977128796803373167092219006009601779280237689649838031120953393850915663786432594439027654396155967716460988691 C=275998648910936868185149456406181501757023486291571125590923081153846260667591828079211802651663967093313254035957286102888219480381369363881780858365997105972392204311434479302575548812828252162353031466803954477596135457476187127605184460671661216163292951830602411007593041826107046067396184793635965487827049867110569983282272692216759766163642354067563675559274279129809946032424873772598571 for(x=0,100,if(Mod(C,R)^(s^2*x)== Mod(C,R),print(x))) Output: ? 390136546196081718607305163473332331417377493685003168939910614118097383796236025236161501548313100735940913083489842340600819098308361714535068954253678353269882635879699406804759345689353730504379874158332132241114147566334361695216611588931744473963962511029943469640447626310597949395943169880131532727642609356099243034697042275923239732294825664054095517406079359905810632719643672701441659 ? 190380618807403745307923978053980745704168649329203670142365133689945248262261770102565161802449979200347735726216852364082170243782043134851392248249192842065184257603176288534281678871465832703721524296216747661969156861717403234055128912278788166594808590474354944280641248904029997977128796803373167092219006009601779280237689649838031120953393850915663786432594439027654396155967716460988691 ? 275998648910936868185149456406181501757023486291571125590923081153846260667591828079211802651663967093313254035957286102888219480381369363881780858365997105972392204311434479302575548812828252162353031466803954477596135457476187127605184460671661216163292951830602411007593041826107046067396184793635965487827049867110569983282272692216759766163642354067563675559274279129809946032424873772598571 ? ? ? Errors (if any) and Timing Info: Timing: real 0m4.156s user 0m4.109s sys 0m0.028s '219.79.' ************** PARI ***************** Host 219.79.9.64 (219.79.9.64) Time: Wed Jan 26 10:10:01 2005 Input: R=390136546196081718607305163473332331417377493685003168939910614118097383796236025236161501548313100735940913083489842340600819098308361714535068954253678353269882635879699406804759345689353730504379874158332132241114147566334361695216611588931744473963962511029943469640447626310597949395943169880131532727642609356099243034697042275923239732294825664054095517406079359905810632719643672701441659 s=190380618807403745307923978053980745704168649329203670142365133689945248262261770102565161802449979200347735726216852364082170243782043134851392248249192842065184257603176288534281678871465832703721524296216747661969156861717403234055128912278788166594808590474354944280641248904029997977128796803373167092219006009601779280237689649838031120953393850915663786432594439027654396155967716460988691 C=275998648910936868185149456406181501757023486291571125590923081153846260667591828079211802651663967093313254035957286102888219480381369363881780858365997105972392204311434479302575548812828252162353031466803954477596135457476187127605184460671661216163292951830602411007593041826107046067396184793635965487827049867110569983282272692216759766163642354067563675559274279129809946032424873772598571 for(x=0,1000,if(Mod(C,R)^(s^2*x)== Mod(C,R),print(x))) Output: ? 390136546196081718607305163473332331417377493685003168939910614118097383796236025236161501548313100735940913083489842340600819098308361714535068954253678353269882635879699406804759345689353730504379874158332132241114147566334361695216611588931744473963962511029943469640447626310597949395943169880131532727642609356099243034697042275923239732294825664054095517406079359905810632719643672701441659 ? 190380618807403745307923978053980745704168649329203670142365133689945248262261770102565161802449979200347735726216852364082170243782043134851392248249192842065184257603176288534281678871465832703721524296216747661969156861717403234055128912278788166594808590474354944280641248904029997977128796803373167092219006009601779280237689649838031120953393850915663786432594439027654396155967716460988691 ? 275998648910936868185149456406181501757023486291571125590923081153846260667591828079211802651663967093313254035957286102888219480381369363881780858365997105972392204311434479302575548812828252162353031466803954477596135457476187127605184460671661216163292951830602411007593041826107046067396184793635965487827049867110569983282272692216759766163642354067563675559274279129809946032424873772598571 ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 24129 Killed /usr/bin/gp -q -emacs Timing: real 0m21.002s user 0m20.992s sys 0m0.009s '143.239' ************** PARI ***************** Host 143.239.211.125 (143.239.211.125) Time: Wed Jan 26 15:54:14 2005 Input: F := FiniteField(2); P := PolynomialRing(F); f1 := P ! x + 1; f2 := P ! x^3 + x + 1; f3 := P ! x^3 + x^2 + 1; f := f1*f2*f3; M := MatrixRing(P,3); m := M ! [f2,f1^2,x^2,0,f3,f1*f3,0,0,f]; m; Output: ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: F:=FiniteField(2); ^---------------- *** unexpected character: P:=PolynomialRing(F); ^-------------------- *** unexpected character: f1:=P!x+1; ^------- *** unexpected character: f2:=P!x^3+x+1; ^----------- *** unexpected character: f3:=P!x^3+x^2+1; ^------------- *** unexpected character: f:=f1*f2*f3; ^---------- *** unexpected character: M:=MatrixRing(P,3); ^----------------- *** unexpected character: m:=M![f2,f1^2,x^2,0,f3 ^-------------------- Timing: real 0m0.030s user 0m0.005s sys 0m0.008s '130.123' ************** PARI ***************** Host 130.123.128.117 (130.123.128.117) Time: Wed Jan 26 19:40:41 2005 Input: forprime(p=2,1000,if(gcd(p-2,5)==5,print(p))) Output: ? 2 7 17 37 47 67 97 107 127 137 157 167 197 227 257 277 307 317 337 347 367 397 457 467 487 547 557 577 587 607 617 647 677 727 757 787 797 827 857 877 887 907 937 947 967 977 997 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '130.123' ************** PARI ***************** Host 130.123.128.117 (130.123.128.117) Time: Wed Jan 26 19:52:31 2005 Input: forprime(p=2,1000,if(gcd(p+3,10)==10,print(p))) Output: ? 7 17 37 47 67 97 107 127 137 157 167 197 227 257 277 307 317 337 347 367 397 457 467 487 547 557 577 587 607 617 647 677 727 757 787 797 827 857 877 887 907 937 947 967 977 997 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '130.34.' ************** PARI ***************** Host 130.34.235.23 (130.34.235.23) Time: Thu Jan 27 02:06:33 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '130.34.' ************** PARI ***************** Host 130.34.235.23 (130.34.235.23) Time: Thu Jan 27 02:06:43 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '138.131' ************** PARI ***************** Host 138.131.145.25 (138.131.145.25) Time: Thu Jan 27 06:56:17 2005 Input: a:=sin(x) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: a:=sin(x) ^------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 07:27:28 2005 Input: Mod(3*5^-1, 2017) Output: ? Mod(404, 2017) ? Errors (if any) and Timing Info: Timing: real 0m0.094s user 0m0.005s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 07:28:05 2005 Input: Mod(3*5^-2, 2017) Output: ? Mod(1291, 2017) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 07:28:36 2005 Input: Mod(3*5^-3, 2017) Output: ? Mod(1065, 2017) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 07:28:54 2005 Input: Mod(3*5^-4, 2017) Output: ? Mod(213, 2017) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 07:29:06 2005 Input: Mod(3*5^-5, 2017) Output: ? Mod(446, 2017) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 07:29:44 2005 Input: Mod(3*5^-42, 2017) Output: ? Mod(1353, 2017) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 07:30:01 2005 Input: Mod(3*5^-43, 2017) Output: ? Mod(674, 2017) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 07:30:13 2005 Input: Mod(3*5^-44, 2017) Output: ? Mod(1345, 2017) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:13:57 2005 Input: Mod(3*5^-44, 2017) Output: ? Mod(1345, 2017) ? Errors (if any) and Timing Info: Timing: real 0m0.470s user 0m0.005s sys 0m0.012s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:14:24 2005 Input: Mod(98*3^-1, 487) Output: ? Mod(195, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:14:44 2005 Input: Mod(98*3^-2, 487) Output: ? Mod(65, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:15:00 2005 Input: Mod(98*3^-3, 487) Output: ? Mod(184, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.005s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:16:14 2005 Input: Mod(98*3^-4, 487) Output: ? Mod(386, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.175s user 0m0.007s sys 0m0.015s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:17:12 2005 Input: Mod(98*3^-5, 487) Output: ? Mod(291, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.304s user 0m0.007s sys 0m0.010s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:17:26 2005 Input: Mod(98*3^-6, 487) Output: ? Mod(97, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.010s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:17:39 2005 Input: Mod(98*3^-7, 487) Output: ? Mod(357, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.075s user 0m0.009s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:17:51 2005 Input: Mod(98*3^-8, 487) Output: ? Mod(119, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.041s user 0m0.006s sys 0m0.010s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:17:59 2005 Input: Mod(98*3^-9, 487) Output: ? Mod(202, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.008s sys 0m0.009s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:18:09 2005 Input: Mod(98*3^-9, 487) Output: ? Mod(202, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.007s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:18:17 2005 Input: Mod(98*3^-10, 487) Output: ? Mod(392, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.009s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:18:23 2005 Input: Mod(98*3^-10, 487) Output: ? Mod(392, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:18:28 2005 Input: Mod(98*3^-11, 487) Output: ? Mod(293, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.006s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:18:42 2005 Input: Mod(98*3^-12, 487) Output: ? Mod(260, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:18:54 2005 Input: Mod(98*3^-13, 487) Output: ? Mod(249, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:19:04 2005 Input: Mod(98*3^-14, 487) Output: ? Mod(83, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:19:20 2005 Input: Mod(98*3^-15, 487) Output: ? Mod(190, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:19:34 2005 Input: Mod(98*3^-16, 487) Output: ? Mod(388, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.002s sys 0m0.014s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:19:45 2005 Input: Mod(98*3^-17, 487) Output: ? Mod(454, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.011s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:19:54 2005 Input: Mod(98*3^-18, 487) Output: ? Mod(476, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.006s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:20:03 2005 Input: Mod(98*3^-19, 487) Output: ? Mod(321, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.008s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:20:17 2005 Input: Mod(98*3^-20, 487) Output: ? Mod(107, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.010s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:20:26 2005 Input: Mod(98*3^-21, 487) Output: ? Mod(198, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:20:39 2005 Input: Mod(98*3^-22, 487) Output: ? Mod(66, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:24:16 2005 Input: Mod(23^2, 487) Output: ? Mod(42, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.007s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:24:25 2005 Input: Mod(23^3, 487) Output: ? Mod(479, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.007s sys 0m0.009s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:24:44 2005 Input: Mod(23^4, 487) Output: ? Mod(303, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:24:54 2005 Input: Mod(23^5, 487) Output: ? Mod(151, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:25:04 2005 Input: Mod(23^6, 487) Output: ? Mod(64, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.003s sys 0m0.009s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:25:09 2005 Input: Mod(23^6, 487) Output: ? Mod(64, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:25:16 2005 Input: Mod(23^7, 487) Output: ? Mod(11, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:25:25 2005 Input: Mod(23^8, 487) Output: ? Mod(253, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:25:38 2005 Input: Mod(23^9, 487) Output: ? Mod(462, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:25:51 2005 Input: Mod(23^10, 487) Output: ? Mod(399, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.008s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:26:08 2005 Input: Mod(23^11, 487) Output: ? Mod(411, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:26:19 2005 Input: Mod(23^12, 487) Output: ? Mod(200, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:26:34 2005 Input: Mod(23^13, 487) Output: ? Mod(217, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:26:45 2005 Input: Mod(23^14, 487) Output: ? Mod(121, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:26:57 2005 Input: Mod(23^15, 487) Output: ? Mod(348, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:27:13 2005 Input: Mod(23^16, 487) Output: ? Mod(212, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.005s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:27:23 2005 Input: Mod(23^17, 487) Output: ? Mod(6, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:27:33 2005 Input: Mod(23^18, 487) Output: ? Mod(138, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:27:42 2005 Input: Mod(23^19, 487) Output: ? Mod(252, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:27:52 2005 Input: Mod(23^20, 487) Output: ? Mod(439, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:28:13 2005 Input: Mod(23^21, 487) Output: ? Mod(357, 487) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:32:27 2005 Input: Mod(3^205, 401) Output: ? Mod(158, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.333s user 0m0.005s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:37:13 2005 Input: Mod(3^205*3-0, 401) Output: ? Mod(73, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.004s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:37:43 2005 Input: Mod((3^205)*3^0, 401) Output: ? Mod(158, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:37:59 2005 Input: Mod((3^205)*3^1, 401) Output: ? Mod(73, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:38:15 2005 Input: Mod((3^205)*3^-1, 401) Output: ? Mod(320, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.007s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:38:34 2005 Input: Mod((3^205)*3^-2, 401) Output: ? Mod(374, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:40:00 2005 Input: Mod((3^205)*3^-3, 401) Output: ? Mod(392, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:40:10 2005 Input: Mod((3^205)*3^-4, 401) Output: ? Mod(398, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:40:23 2005 Input: Mod((3^205)*3^-5, 401) Output: ? Mod(400, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:40:33 2005 Input: Mod((3^205)*3^-6, 401) Output: ? Mod(267, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:40:46 2005 Input: Mod((3^205)*3^-7, 401) Output: ? Mod(89, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:40:55 2005 Input: Mod((3^205)*3^-8, 401) Output: ? Mod(297, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:41:05 2005 Input: Mod((3^205)*3^-9, 401) Output: ? Mod(99, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:41:17 2005 Input: Mod((3^205)*3^-10, 401) Output: ? Mod(33, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:41:29 2005 Input: Mod((3^205)*3^-11, 401) Output: ? Mod(11, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:41:40 2005 Input: Mod((3^205)*3^-12, 401) Output: ? Mod(271, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:41:53 2005 Input: Mod((3^205)*3^-13, 401) Output: ? Mod(224, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:42:03 2005 Input: Mod((3^205)*3^-14, 401) Output: ? Mod(342, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:42:14 2005 Input: Mod((3^205)*3^-15, 401) Output: ? Mod(114, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:42:24 2005 Input: Mod((3^205)*3^-16, 401) Output: ? Mod(38, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:42:33 2005 Input: Mod((3^205)*3^-17, 401) Output: ? Mod(280, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:42:44 2005 Input: Mod((3^205)*3^-18, 401) Output: ? Mod(227, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:42:52 2005 Input: Mod((3^205)*3^-19, 401) Output: ? Mod(343, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:45:28 2005 Input: Mod(20^2, 401) Output: ? Mod(400, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:45:36 2005 Input: Mod(20^3, 401) Output: ? Mod(381, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:49:00 2005 Input: Mod(3^205, 401) Output: ? Mod(158, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:49:31 2005 Input: Mod((3^205)*3^-1, 401) Output: ? Mod(320, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:49:40 2005 Input: Mod((3^205)*3^-2, 401) Output: ? Mod(374, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:49:47 2005 Input: Mod((3^205)*3^-3, 401) Output: ? Mod(392, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:49:55 2005 Input: Mod((3^205)*3^-4, 401) Output: ? Mod(398, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:50:02 2005 Input: Mod((3^205)*3^-5, 401) Output: ? Mod(400, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:50:13 2005 Input: Mod((3^205)*3^-6, 401) Output: ? Mod(267, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '130.83.' ************** PARI ***************** Host 130.83.244.131 (130.83.244.131) Time: Thu Jan 27 08:53:03 2005 Input: Mod(20^10, 401) Output: ? Mod(400, 401) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '147.88.' ************** PARI ***************** Host 147.88.74.131 (147.88.74.131) Time: Fri Jan 28 05:40:33 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '62.43.7' ************** PARI ***************** Host 62.43.7.221 (62.43.7.221) Time: Fri Jan 28 08:29:39 2005 Input: forprime(p=2,1000,if(p%10==7,print(p))) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '62.43.7' ************** PARI ***************** Host 62.43.7.221 (62.43.7.221) Time: Fri Jan 28 08:30:11 2005 Input: forprime(p=2,1000)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: forprime(p=2,1000)) ^-- Timing: real 0m0.402s user 0m0.010s sys 0m0.007s '62.43.7' ************** PARI ***************** Host 62.43.7.221 (62.43.7.221) Time: Fri Jan 28 08:30:27 2005 Input: forprime(p=2,1000) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: forprime(p=2,1000) ^- Timing: real 0m0.014s user 0m0.008s sys 0m0.004s '62.43.7' ************** PARI ***************** Host 62.43.7.221 (62.43.7.221) Time: Fri Jan 28 08:30:39 2005 Input: forprime(p=2,1000,3) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.007s sys 0m0.006s '62.43.7' ************** PARI ***************** Host 62.43.7.221 (62.43.7.221) Time: Fri Jan 28 08:31:23 2005 Input: forprime(p=2,1000,if(gcd(p+3,10)==10,print(p))) Output: ? 7 17 37 47 67 97 107 127 137 157 167 197 227 257 277 307 317 337 347 367 397 457 467 487 547 557 577 587 607 617 647 677 727 757 787 797 827 857 877 887 907 937 947 967 977 997 ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.007s sys 0m0.008s '62.43.7' ************** PARI ***************** Host 62.43.7.221 (62.43.7.221) Time: Fri Jan 28 08:31:38 2005 Input: forprime(p=2,10000,if(gcd(p+3,10)==10,print(p))) Output: ? 7 17 37 47 67 97 107 127 137 157 167 197 227 257 277 307 317 337 347 367 397 457 467 487 547 557 577 587 607 617 647 677 727 757 787 797 827 857 877 887 907 937 947 967 977 997 1087 1097 1117 1187 1217 1237 1277 1297 1307 1327 1367 1427 1447 1487 1567 1597 1607 1627 1637 1657 1667 1697 1747 1777 1787 1847 1867 1877 1907 1987 1997 2017 2027 2087 2137 2207 2237 2267 2287 2297 2347 2357 2377 2417 2437 2447 2467 2477 2557 2617 2647 2657 2677 2687 2707 2767 2777 2797 2837 2857 2887 2897 2917 2927 2957 3037 3067 3137 3167 3187 3217 3257 3307 3347 3407 3457 3467 3517 3527 3547 3557 3607 3617 3637 3677 3697 3727 3767 3797 3847 3877 3907 3917 3947 3967 4007 4027 4057 4127 4157 4177 4217 4297 4327 4337 4357 4397 4447 4457 4507 4517 4547 4567 4597 4637 4657 4787 4817 4877 4937 4957 4967 4987 5077 5087 5107 5147 5167 5197 5227 5237 5297 5347 5387 5407 5417 5437 5477 5507 5527 5557 5647 5657 5717 5737 5807 5827 5857 5867 5897 5927 5987 6007 6037 6047 6067 6197 6217 6247 6257 6277 6287 6317 6337 6367 6397 6427 6547 6577 6607 6637 6737 6827 6857 6907 6917 6947 6967 6977 6997 7027 7057 7127 7177 7187 7207 7237 7247 7297 7307 7417 7457 7477 7487 7507 7517 7537 7547 7577 7607 7687 7717 7727 7757 7817 7867 7877 7907 7927 7937 8017 8087 8117 8147 8167 8237 8287 8297 8317 8377 8387 8447 8467 8527 8537 8597 8627 8647 8677 8707 8737 8747 8807 8837 8867 8887 9007 9067 9127 9137 9157 9187 9227 9257 9277 9337 9377 9397 9437 9467 9497 9547 9587 9677 9697 9767 9787 9817 9857 9887 9907 9967 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '62.43.7' ************** PARI ***************** Host 62.43.7.221 (62.43.7.221) Time: Fri Jan 28 08:32:14 2005 Input: forprime(p=2,10000,print(p)) Output: ? 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 1999 2003 2011 2017 2027 2029 2039 2053 2063 2069 2081 2083 2087 2089 2099 2111 2113 2129 2131 2137 2141 2143 2153 2161 2179 2203 2207 2213 2221 2237 2239 2243 2251 2267 2269 2273 2281 2287 2293 2297 2309 2311 2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 2389 2393 2399 2411 2417 2423 2437 2441 2447 2459 2467 2473 2477 2503 2521 2531 2539 2543 2549 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 2671 2677 2683 2687 2689 2693 2699 2707 2711 2713 2719 2729 2731 2741 2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 2857 2861 2879 2887 2897 2903 2909 2917 2927 2939 2953 2957 2963 2969 2971 2999 3001 3011 3019 3023 3037 3041 3049 3061 3067 3079 3083 3089 3109 3119 3121 3137 3163 3167 3169 3181 3187 3191 3203 3209 3217 3221 3229 3251 3253 3257 3259 3271 3299 3301 3307 3313 3319 3323 3329 3331 3343 3347 3359 3361 3371 3373 3389 3391 3407 3413 3433 3449 3457 3461 3463 3467 3469 3491 3499 3511 3517 3527 3529 3533 3539 3541 3547 3557 3559 3571 3581 3583 3593 3607 3613 3617 3623 3631 3637 3643 3659 3671 3673 3677 3691 3697 3701 3709 3719 3727 3733 3739 3761 3767 3769 3779 3793 3797 3803 3821 3823 3833 3847 3851 3853 3863 3877 3881 3889 3907 3911 3917 3919 3923 3929 3931 3943 3947 3967 3989 4001 4003 4007 4013 4019 4021 4027 4049 4051 4057 4073 4079 4091 4093 4099 4111 4127 4129 4133 4139 4153 4157 4159 4177 4201 4211 4217 4219 4229 4231 4241 4243 4253 4259 4261 4271 4273 4283 4289 4297 4327 4337 4339 4349 4357 4363 4373 4391 4397 4409 4421 4423 4441 4447 4451 4457 4463 4481 4483 4493 4507 4513 4517 4519 4523 4547 4549 4561 4567 4583 4591 4597 4603 4621 4637 4639 4643 4649 4651 4657 4663 4673 4679 4691 4703 4721 4723 4729 4733 4751 4759 4783 4787 4789 4793 4799 4801 4813 4817 4831 4861 4871 4877 4889 4903 4909 4919 4931 4933 4937 4943 4951 4957 4967 4969 4973 4987 4993 4999 5003 5009 5011 5021 5023 5039 5051 5059 5077 5081 5087 5099 5101 5107 5113 5119 5147 5153 5167 5171 5179 5189 5197 5209 5227 5231 5233 5237 5261 5273 5279 5281 5297 5303 5309 5323 5333 5347 5351 5381 5387 5393 5399 5407 5413 5417 5419 5431 5437 5441 5443 5449 5471 5477 5479 5483 5501 5503 5507 5519 5521 5527 5531 5557 5563 5569 5573 5581 5591 5623 5639 5641 5647 5651 5653 5657 5659 5669 5683 5689 5693 5701 5711 5717 5737 5741 5743 5749 5779 5783 5791 5801 5807 5813 5821 5827 5839 5843 5849 5851 5857 5861 5867 5869 5879 5881 5897 5903 5923 5927 5939 5953 5981 5987 6007 6011 6029 6037 6043 6047 6053 6067 6073 6079 6089 6091 6101 6113 6121 6131 6133 6143 6151 6163 6173 6197 6199 6203 6211 6217 6221 6229 6247 6257 6263 6269 6271 6277 6287 6299 6301 6311 6317 6323 6329 6337 6343 6353 6359 6361 6367 6373 6379 6389 6397 6421 6427 6449 6451 6469 6473 6481 6491 6521 6529 6547 6551 6553 6563 6569 6571 6577 6581 6599 6607 6619 6637 6653 6659 6661 6673 6679 6689 6691 6701 6703 6709 6719 6733 6737 6761 6763 6779 6781 6791 6793 6803 6823 6827 6829 6833 6841 6857 6863 6869 6871 6883 6899 6907 6911 6917 6947 6949 6959 6961 6967 6971 6977 6983 6991 6997 7001 7013 7019 7027 7039 7043 7057 7069 7079 7103 7109 7121 7127 7129 7151 7159 7177 7187 7193 7207 7211 7213 7219 7229 7237 7243 7247 7253 7283 7297 7307 7309 7321 7331 7333 7349 7351 7369 7393 7411 7417 7433 7451 7457 7459 7477 7481 7487 7489 7499 7507 7517 7523 7529 7537 7541 7547 7549 7559 7561 7573 7577 7583 7589 7591 7603 7607 7621 7639 7643 7649 7669 7673 7681 7687 7691 7699 7703 7717 7723 7727 7741 7753 7757 7759 7789 7793 7817 7823 7829 7841 7853 7867 7873 7877 7879 7883 7901 7907 7919 7927 7933 7937 7949 7951 7963 7993 8009 8011 8017 8039 8053 8059 8069 8081 8087 8089 8093 8101 8111 8117 8123 8147 8161 8167 8171 8179 8191 8209 8219 8221 8231 8233 8237 8243 8263 8269 8273 8287 8291 8293 8297 8311 8317 8329 8353 8363 8369 8377 8387 8389 8419 8423 8429 8431 8443 8447 8461 8467 8501 8513 8521 8527 8537 8539 8543 8563 8573 8581 8597 8599 8609 8623 8627 8629 8641 8647 8663 8669 8677 8681 8689 8693 8699 8707 8713 8719 8731 8737 8741 8747 8753 8761 8779 8783 8803 8807 8819 8821 8831 8837 8839 8849 8861 8863 8867 8887 8893 8923 8929 8933 8941 8951 8963 8969 8971 8999 9001 9007 9011 9013 9029 9041 9043 9049 9059 9067 9091 9103 9109 9127 9133 9137 9151 9157 9161 9173 9181 9187 9199 9203 9209 9221 9227 9239 9241 9257 9277 9281 9283 9293 9311 9319 9323 9337 9341 9343 9349 9371 9377 9391 9397 9403 9413 9419 9421 9431 9433 9437 9439 9461 9463 9467 9473 9479 9491 9497 9511 9521 9533 9539 9547 9551 9587 9601 9613 9619 9623 9629 9631 9643 9649 9661 9677 9679 9689 9697 9719 9721 9733 9739 9743 9749 9767 9769 9781 9787 9791 9803 9811 9817 9829 9833 9839 9851 9857 9859 9871 9883 9887 9901 9907 9923 9929 9931 9941 9949 9967 9973 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.009s sys 0m0.011s '62.43.7' ************** PARI ***************** Host 62.43.7.221 (62.43.7.221) Time: Fri Jan 28 08:33:25 2005 Input: forprime(p=2,10000000000000,print(p)) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.024s user 0m0.005s sys 0m0.011s '62.43.7' ************** PARI ***************** Host 62.43.7.221 (62.43.7.221) Time: Fri Jan 28 08:33:34 2005 Input: forprime(p=2,1000000000,print(p)) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '62.43.7' ************** PARI ***************** Host 62.43.7.221 (62.43.7.221) Time: Fri Jan 28 08:33:48 2005 Input: forprime(p=2,10000000,print(p)) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '62.43.7' ************** PARI ***************** Host 62.43.7.221 (62.43.7.221) Time: Fri Jan 28 08:33:53 2005 Input: forprime(p=2,1000000,print(p)) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '62.43.7' ************** PARI ***************** Host 62.43.7.221 (62.43.7.221) Time: Fri Jan 28 08:33:57 2005 Input: forprime(p=2,100000,print(p)) Output: ? 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 1999 2003 2011 2017 2027 2029 2039 2053 2063 2069 2081 2083 2087 2089 2099 2111 2113 2129 2131 2137 2141 2143 2153 2161 2179 2203 2207 2213 2221 2237 2239 2243 2251 2267 2269 2273 2281 2287 2293 2297 2309 2311 2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 2389 2393 2399 2411 2417 2423 2437 2441 2447 2459 2467 2473 2477 2503 2521 2531 2539 2543 2549 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 2671 2677 2683 2687 2689 2693 2699 2707 2711 2713 2719 2729 2731 2741 2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 2857 2861 2879 2887 2897 2903 2909 2917 2927 2939 2953 2957 2963 2969 2971 2999 3001 3011 3019 3023 3037 3041 3049 3061 3067 3079 3083 3089 3109 3119 3121 3137 3163 3167 3169 3181 3187 3191 3203 3209 3217 3221 3229 3251 3253 3257 3259 3271 3299 3301 3307 3313 3319 3323 3329 3331 3343 3347 3359 3361 3371 3373 3389 3391 3407 3413 3433 3449 3457 3461 3463 3467 3469 3491 3499 3511 3517 3527 3529 3533 3539 3541 3547 3557 3559 3571 3581 3583 3593 3607 3613 3617 3623 3631 3637 3643 3659 3671 3673 3677 3691 3697 3701 3709 3719 3727 3733 3739 3761 3767 3769 3779 3793 3797 3803 3821 3823 3833 3847 3851 3853 3863 3877 3881 3889 3907 3911 3917 3919 3923 3929 3931 3943 3947 3967 3989 4001 4003 4007 4013 4019 4021 4027 4049 4051 4057 4073 4079 4091 4093 4099 4111 4127 4129 4133 4139 4153 4157 4159 4177 4201 4211 4217 4219 4229 4231 4241 4243 4253 4259 4261 4271 4273 4283 4289 4297 4327 4337 4339 4349 4357 4363 4373 4391 4397 4409 4421 4423 4441 4447 4451 4457 4463 4481 4483 4493 4507 4513 4517 4519 4523 4547 4549 4561 4567 4583 4591 4597 4603 4621 4637 4639 4643 4649 4651 4657 4663 4673 4679 4691 4703 4721 4723 4729 4733 4751 4759 4783 4787 4789 4793 4799 4801 4813 4817 4831 4861 4871 4877 4889 4903 4909 4919 4931 4933 4937 4943 4951 4957 4967 4969 4973 4987 4993 4999 5003 5009 5011 5021 5023 5039 5051 5059 5077 5081 5087 5099 5101 5107 5113 5119 5147 5153 5167 5171 5179 5189 5197 5209 5227 5231 5233 5237 5261 5273 5279 5281 5297 5303 5309 5323 5333 5347 5351 5381 5387 5393 5399 5407 5413 5417 5419 5431 5437 5441 5443 5449 5471 5477 5479 5483 5501 5503 5507 5519 5521 5527 5531 5557 5563 5569 5573 5581 5591 5623 5639 5641 5647 5651 5653 5657 5659 5669 5683 5689 5693 5701 5711 5717 5737 5741 5743 5749 5779 5783 5791 5801 5807 5813 5821 5827 5839 5843 5849 5851 5857 5861 5867 5869 5879 5881 5897 5903 5923 5927 5939 5953 5981 5987 6007 6011 6029 6037 6043 6047 6053 6067 6073 6079 6089 6091 6101 6113 6121 6131 6133 6143 6151 6163 6173 6197 6199 6203 6211 6217 6221 6229 6247 6257 6263 6269 6271 6277 6287 6299 6301 6311 6317 6323 6329 6337 6343 6353 6359 6361 6367 6373 6379 6389 6397 6421 6427 6449 6451 6469 6473 6481 6491 6521 6529 6547 6551 6553 6563 6569 6571 6577 6581 6599 6607 6619 6637 6653 6659 6661 6673 6679 6689 6691 6701 6703 6709 6719 6733 6737 6761 6763 6779 6781 6791 6793 6803 6823 6827 6829 6833 6841 6857 6863 6869 6871 6883 6899 6907 6911 6917 6947 6949 6959 6961 6967 6971 6977 6983 6991 6997 7001 7013 7019 7027 7039 7043 7057 7069 7079 7103 7109 7121 7127 7129 7151 7159 7177 7187 7193 7207 7211 7213 7219 7229 7237 7243 7247 7253 7283 7297 7307 7309 7321 7331 7333 7349 7351 7369 7393 7411 7417 7433 7451 7457 7459 7477 7481 7487 7489 7499 7507 7517 7523 7529 7537 7541 7547 7549 7559 7561 7573 7577 7583 7589 7591 7603 7607 7621 7639 7643 7649 7669 7673 7681 7687 7691 7699 7703 7717 7723 7727 7741 7753 7757 7759 7789 7793 7817 7823 7829 7841 7853 7867 7873 7877 7879 7883 7901 7907 7919 7927 7933 7937 7949 7951 7963 7993 8009 8011 8017 8039 8053 8059 8069 8081 8087 8089 8093 8101 8111 8117 8123 8147 8161 8167 8171 8179 8191 8209 8219 8221 8231 8233 8237 8243 8263 8269 8273 8287 8291 8293 8297 8311 8317 8329 8353 8363 8369 8377 8387 8389 8419 8423 8429 8431 8443 8447 8461 8467 8501 8513 8521 8527 8537 8539 8543 8563 8573 8581 8597 8599 8609 8623 8627 8629 8641 8647 8663 8669 8677 8681 8689 8693 8699 8707 8713 8719 8731 8737 8741 8747 8753 8761 8779 8783 8803 8807 8819 8821 8831 8837 8839 8849 8861 8863 8867 8887 8893 8923 8929 8933 8941 8951 8963 8969 8971 8999 9001 9007 9011 9013 9029 9041 9043 9049 9059 9067 9091 9103 9109 9127 9133 9137 9151 9157 9161 9173 9181 9187 9199 9203 9209 9221 9227 9239 9241 9257 9277 9281 9283 9293 9311 9319 9323 9337 9341 9343 9349 9371 9377 9391 9397 9403 9413 9419 9421 9431 9433 9437 9439 9461 9463 9467 9473 9479 9491 9497 9511 9521 9533 9539 9547 9551 9587 9601 9613 9619 9623 9629 9631 9643 9649 9661 9677 9679 9689 9697 9719 9721 9733 9739 9743 9749 9767 9769 9781 9787 9791 9803 9811 9817 9829 9833 9839 9851 9857 9859 9871 9883 9887 9901 9907 9923 9929 9931 9941 9949 9967 9973 10007 10009 10037 10039 10061 10067 10069 10079 10091 10093 10099 10103 10111 10133 10139 10141 10151 10159 10163 10169 10177 10181 10193 10211 10223 10243 10247 10253 10259 10267 10271 10273 10289 10301 10303 10313 10321 10331 10333 10337 10343 10357 10369 10391 10399 10427 10429 10433 10453 10457 10459 10463 10477 10487 10499 10501 10513 10529 10531 10559 10567 10589 10597 10601 10607 10613 10627 10631 10639 10651 10657 10663 10667 10687 10691 10709 10711 10723 10729 10733 10739 10753 10771 10781 10789 10799 10831 10837 10847 10853 10859 10861 10867 10883 10889 10891 10903 10909 10937 10939 10949 10957 10973 10979 10987 10993 11003 11027 11047 11057 11059 11069 11071 11083 11087 11093 11113 11117 11119 11131 11149 11159 11161 11171 11173 11177 11197 11213 11239 11243 11251 11257 11261 11273 11279 11287 11299 11311 11317 11321 11329 11351 11353 11369 11383 11393 11399 11411 11423 11437 11443 11447 11467 11471 11483 11489 11491 11497 11503 11519 11527 11549 11551 11579 11587 11593 11597 11617 11621 11633 11657 11677 11681 11689 11699 11701 11717 11719 11731 11743 11777 11779 11783 11789 11801 11807 11813 11821 11827 11831 11833 11839 11863 11867 11887 11897 11903 11909 11923 11927 11933 11939 11941 11953 11959 11969 11971 11981 11987 12007 12011 12037 12041 12043 12049 12071 12073 12097 12101 12107 12109 12113 12119 12143 12149 12157 12161 12163 12197 12203 12211 12227 12239 12241 12251 12253 12263 12269 12277 12281 12289 12301 12323 12329 12343 12347 12373 12377 12379 12391 12401 12409 12413 12421 12433 12437 12451 12457 12473 12479 12487 12491 12497 12503 12511 12517 12527 12539 12541 12547 12553 12569 12577 12583 12589 12601 12611 12613 12619 12637 12641 12647 12653 12659 12671 12689 12697 12703 12713 12721 12739 12743 12757 12763 12781 12791 12799 12809 12821 12823 12829 12841 12853 12889 12893 12899 12907 12911 12917 12919 12923 12941 12953 12959 12967 12973 12979 12983 13001 13003 13007 13009 13033 13037 13043 13049 13063 13093 13099 13103 13109 13121 13127 13147 13151 13159 13163 13171 13177 13183 13187 13217 13219 13229 13241 13249 13259 13267 13291 13297 13309 13313 13327 13331 13337 13339 13367 13381 13397 13399 13411 13417 13421 13441 13451 13457 13463 13469 13477 13487 13499 13513 13523 13537 13553 13567 13577 13591 13597 13613 13619 13627 13633 13649 13669 13679 13681 13687 13691 13693 13697 13709 13711 13721 13723 13729 13751 13757 13759 13763 13781 13789 13799 13807 13829 13831 13841 13859 13873 13877 13879 13883 13901 13903 13907 13913 13921 13931 13933 13963 13967 13997 13999 14009 14011 14029 14033 14051 14057 14071 14081 14083 14087 14107 14143 14149 14153 14159 14173 14177 14197 14207 14221 14243 14249 14251 14281 14293 14303 14321 14323 14327 14341 14347 14369 14387 14389 14401 14407 14411 14419 14423 14431 14437 14447 14449 14461 14479 14489 14503 14519 14533 14537 14543 14549 14551 14557 14561 14563 14591 14593 14621 14627 14629 14633 14639 14653 14657 14669 14683 14699 14713 14717 14723 14731 14737 14741 14747 14753 14759 14767 14771 14779 14783 14797 14813 14821 14827 14831 14843 14851 14867 14869 14879 14887 14891 14897 14923 14929 14939 14947 14951 14957 14969 14983 15013 15017 15031 15053 15061 15073 15077 15083 15091 15101 15107 15121 15131 15137 15139 15149 15161 15173 15187 15193 15199 15217 15227 15233 15241 15259 15263 15269 15271 15277 15287 15289 15299 15307 15313 15319 15329 15331 15349 15359 15361 15373 15377 15383 15391 15401 15413 15427 15439 15443 15451 15461 15467 15473 15493 15497 15511 15527 15541 15551 15559 15569 15581 15583 15601 15607 15619 15629 15641 15643 15647 15649 15661 15667 15671 15679 15683 15727 15731 15733 15737 15739 15749 15761 15767 15773 15787 15791 15797 15803 15809 15817 15823 15859 15877 15881 15887 15889 15901 15907 15913 15919 15923 15937 15959 15971 15973 15991 16001 16007 16033 16057 16061 16063 16067 16069 16073 16087 16091 16097 16103 16111 16127 16139 16141 16183 16187 16189 16193 16217 16223 16229 16231 16249 16253 16267 16273 16301 16319 16333 16339 16349 16361 16363 16369 16381 16411 16417 16421 16427 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.043s user 0m0.016s sys 0m0.026s '129.67.' ************** PARI ***************** Host 129.67.2.73 (129.67.2.73) Time: Fri Jan 28 09:51:39 2005 Input: for(i=0,4,for(j=0,4,print(I^2))) Output: ? -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ? Errors (if any) and Timing Info: Timing: real 0m0.056s user 0m0.006s sys 0m0.007s '129.67.' ************** PARI ***************** Host 129.67.2.73 (129.67.2.73) Time: Fri Jan 28 09:51:55 2005 Input: for(i=0,4,for(j=0,4,print((i+j*I)))) Output: ? 0 I 2*I 3*I 4*I 1 1 + I 1 + 2*I 1 + 3*I 1 + 4*I 2 2 + I 2 + 2*I 2 + 3*I 2 + 4*I 3 3 + I 3 + 2*I 3 + 3*I 3 + 4*I 4 4 + I 4 + 2*I 4 + 3*I 4 + 4*I ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '129.67.' ************** PARI ***************** Host 129.67.2.73 (129.67.2.73) Time: Fri Jan 28 09:52:07 2005 Input: for(i=0,4,for(j=0,4,print(i+j*I))) Output: ? 0 I 2*I 3*I 4*I 1 1 + I 1 + 2*I 1 + 3*I 1 + 4*I 2 2 + I 2 + 2*I 2 + 3*I 2 + 4*I 3 3 + I 3 + 2*I 3 + 3*I 3 + 4*I 4 4 + I 4 + 2*I 4 + 3*I 4 + 4*I ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '129.67.' ************** PARI ***************** Host 129.67.2.73 (129.67.2.73) Time: Fri Jan 28 09:52:20 2005 Input: for(i=0,4,for(j=0,4,print([i+j*I,(i+j*I)^2))) Output: ? ? Errors (if any) and Timing Info: *** ; or ] expected: ...,4,print([i+j*I,(i+j*I)^2))) ^--- Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '129.67.' ************** PARI ***************** Host 129.67.2.73 (129.67.2.73) Time: Fri Jan 28 09:52:24 2005 Input: for(i=0,4,for(j=0,4,print([i+j*I,(i+j*I)^2]))) Output: ? [0, 0] [I, -1] [2*I, -4] [3*I, -9] [4*I, -16] [1, 1] [1 + I, 2*I] [1 + 2*I, -3 + 4*I] [1 + 3*I, -8 + 6*I] [1 + 4*I, -15 + 8*I] [2, 4] [2 + I, 3 + 4*I] [2 + 2*I, 8*I] [2 + 3*I, -5 + 12*I] [2 + 4*I, -12 + 16*I] [3, 9] [3 + I, 8 + 6*I] [3 + 2*I, 5 + 12*I] [3 + 3*I, 18*I] [3 + 4*I, -7 + 24*I] [4, 16] [4 + I, 15 + 8*I] [4 + 2*I, 12 + 16*I] [4 + 3*I, 7 + 24*I] [4 + 4*I, 32*I] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '129.67.' ************** PARI ***************** Host 129.67.2.73 (129.67.2.73) Time: Fri Jan 28 09:52:30 2005 Input: for(i=0,4,for(j=0,4,print([i+j*I,(i+j*I)^2%5]))) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '129.67.' ************** PARI ***************** Host 129.67.2.73 (129.67.2.73) Time: Fri Jan 28 09:52:38 2005 Input: for(i=0,4,for(j=0,4,print([i+j*I,(i+j*I)^25]))) Output: ? [0, 0] [I, I] [2*I, 33554432*I] [3*I, 847288609443*I] [4*I, 1125899906842624*I] [1, 1] [1 + I, 4096 + 4096*I] [1 + 2*I, -451910159 + 306268562*I] [1 + 3*I, 3105500041216 - 596547981312*I] [1 + 4*I, -379677384665279 + 2372018654210404*I] [2, 33554432] [2 + I, 306268562 - 451910159*I] [2 + 2*I, 137438953472 + 137438953472*I] [2 + 3*I, 71041880304722 - 44827014819597*I] [2 + 4*I, -15163588700274688 + 10276667637366784*I] [3, 847288609443] [3 + I, -596547981312 + 3105500041216*I] [3 + 2*I, -44827014819597 + 71041880304722*I] [3 + 3*I, 3470494144278528 + 3470494144278528*I] [3 + 4*I, -110422359737857437 - 276811749100242716*I] [4, 1125899906842624] [4 + I, 2372018654210404 - 379677384665279*I] [4 + 2*I, 10276667637366784 - 15163588700274688*I] [4 + 3*I, -276811749100242716 - 110422359737857437*I] [4 + 4*I, 4611686018427387904 + 4611686018427387904*I] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '129.67.' ************** PARI ***************** Host 129.67.2.73 (129.67.2.73) Time: Fri Jan 28 09:52:42 2005 Input: for(i=0,4,for(j=0,4,print([i+j*I,(i+j*I)^5]))) Output: ? [0, 0] [I, I] [2*I, 32*I] [3*I, 243*I] [4*I, 1024*I] [1, 1] [1 + I, -4 - 4*I] [1 + 2*I, 41 - 38*I] [1 + 3*I, 316 - 12*I] [1 + 4*I, 1121 + 404*I] [2, 32] [2 + I, -38 + 41*I] [2 + 2*I, -128 - 128*I] [2 + 3*I, 122 - 597*I] [2 + 4*I, 1312 - 1216*I] [3, 243] [3 + I, -12 + 316*I] [3 + 2*I, -597 + 122*I] [3 + 3*I, -972 - 972*I] [3 + 4*I, -237 - 3116*I] [4, 1024] [4 + I, 404 + 1121*I] [4 + 2*I, -1216 + 1312*I] [4 + 3*I, -3116 - 237*I] [4 + 4*I, -4096 - 4096*I] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '129.67.' ************** PARI ***************** Host 129.67.2.73 (129.67.2.73) Time: Fri Jan 28 09:53:08 2005 Input: for(i=0,4,for(j=0,4,print([i+j*I,(i+j*I)^2]))) Output: ? [0, 0] [I, -1] [2*I, -4] [3*I, -9] [4*I, -16] [1, 1] [1 + I, 2*I] [1 + 2*I, -3 + 4*I] [1 + 3*I, -8 + 6*I] [1 + 4*I, -15 + 8*I] [2, 4] [2 + I, 3 + 4*I] [2 + 2*I, 8*I] [2 + 3*I, -5 + 12*I] [2 + 4*I, -12 + 16*I] [3, 9] [3 + I, 8 + 6*I] [3 + 2*I, 5 + 12*I] [3 + 3*I, 18*I] [3 + 4*I, -7 + 24*I] [4, 16] [4 + I, 15 + 8*I] [4 + 2*I, 12 + 16*I] [4 + 3*I, 7 + 24*I] [4 + 4*I, 32*I] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '129.67.' ************** PARI ***************** Host 129.67.2.73 (129.67.2.73) Time: Fri Jan 28 09:53:36 2005 Input: for(i=0,4,for(j=0,4,print([i+j*I,(i+j*I)^2]))) mod(6,5) Output: ? [0, 0] [I, -1] [2*I, -4] [3*I, -9] [4*I, -16] [1, 1] [1 + I, 2*I] [1 + 2*I, -3 + 4*I] [1 + 3*I, -8 + 6*I] [1 + 4*I, -15 + 8*I] [2, 4] [2 + I, 3 + 4*I] [2 + 2*I, 8*I] [2 + 3*I, -5 + 12*I] [2 + 4*I, -12 + 16*I] [3, 9] [3 + I, 8 + 6*I] [3 + 2*I, 5 + 12*I] [3 + 3*I, 18*I] [3 + 4*I, -7 + 24*I] [4, 16] [4 + I, 15 + 8*I] [4 + 2*I, 12 + 16*I] [4 + 3*I, 7 + 24*I] [4 + 4*I, 32*I] ? ? ? Errors (if any) and Timing Info: *** obsolete function: mod(6,5) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.030s user 0m0.007s sys 0m0.007s '129.67.' ************** PARI ***************** Host 129.67.2.73 (129.67.2.73) Time: Fri Jan 28 09:53:46 2005 Input: for(i=0,4,for(j=0,4,print([i+j*I,(i+j*I)^2]))) Mod(6,5) Output: ? [0, 0] [I, -1] [2*I, -4] [3*I, -9] [4*I, -16] [1, 1] [1 + I, 2*I] [1 + 2*I, -3 + 4*I] [1 + 3*I, -8 + 6*I] [1 + 4*I, -15 + 8*I] [2, 4] [2 + I, 3 + 4*I] [2 + 2*I, 8*I] [2 + 3*I, -5 + 12*I] [2 + 4*I, -12 + 16*I] [3, 9] [3 + I, 8 + 6*I] [3 + 2*I, 5 + 12*I] [3 + 3*I, 18*I] [3 + 4*I, -7 + 24*I] [4, 16] [4 + I, 15 + 8*I] [4 + 2*I, 12 + 16*I] [4 + 3*I, 7 + 24*I] [4 + 4*I, 32*I] ? ? Mod(1, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '129.67.' ************** PARI ***************** Host 129.67.2.73 (129.67.2.73) Time: Fri Jan 28 10:01:15 2005 Input: for(i=0,4,for(j=0,4,print([Mod(i+j*I,5),Mod((i+j*I)^2,5)]))) Mod(6,5) Output: ? ? ? Mod(1, 5) ? Errors (if any) and Timing Info: *** forbidden division t_COMPLEX % t_INT. Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Jan 28 22:37:56 2005 Input: ((2^49364)+(49364^2)-(49364*2)+123) - ((2^49284)+(49284^2)+(49284*2)-23) Output: ? 1108424092017163554796950923288730834410718428206981402525462347588001647946425166824218140394250624192699740943025418249852351171159334133639610992828534565489852358425351239698419268482072443197850042819302870968612584066728800373484266122060848324692717456151123746422235652462582120240572159153564032024400342381458975917914484959483084072170106294379387525939357151834507562167964752059338903443393638367379003770722662092130093086150006488356270680882840462525494283251201211976326586910556009247191397930616523197072015289917449192096774737167676992929601811696868700217787071105016395354167387093516866269670727941762446693233094664616217260521311100459763887504378709127855862665021477553639298951673459484708945751802839200447692177835036731378035066433235206172572019705369559087999540878986667703716409772941846201334380471539882731135219686343583541336902665803987511176799234284731886256395825110044391143570953906189792078650414347184131457972122586010334168081699211652963758156951677211740423750992646381364407227353440393903406748916399083068800131418768305947003902590923690587336857002805802414437479870175314098497022314903049210105776602489457756306944047538999330211262791664259201272326545315677958875607422235417976527956373969580162877660197534681108477807171762286772091203468143835537879061667791942658257562745355488520760611918829405723271862434821405139564653545763982191493922286199723235769256992836690931460012201322076187767474904649086338940218200456377873814993424368788412942094150734925989208253523212070610863428308536970970874768962953676806251217410056922195553685164042120002846054226379305995017662185595135819158820974175467151232416757216136137995762942333921772055445965662274650983729703274502290002340238080007289171425641304692739740797053803744060099141257296068272895143711848309255405791232207196165245621030245038155828581280021260013587999212280170976403785330584185861737795028583385695172830111065769959297431203883690020817600515917948964201408754771235620887744017018228951701555774038148621703890271280859005175235152855216427166928922405238355989003472622042818190571773014548287157005732729023387938702787087256707400803363398781535369638520135783634573660524066370044620732854358126015353762463991592794302460673241725065712015130648229688270547429598730380915603060408214825070048354711773599383326655950450465052238310736670520945823341913559822242823626135311746435014855781405674202240443958727186256765334985068453706813246308706538811708644055106404963180373894375567978491815032546208005437217592694525799318387408762646812387052923796534351995217630261267555567802440824549791351636102324846056879893974436517330699771499378433787503570476353824971521220701296918971699465507156214308814782367132418678441843561497303870505566569362592060264971749417196126467670009014232505262526844486285645649945035655095794385518176130754956408998987842025440540910693483521811550248115898466872505415140722382579686498853024929449332262909364814846174104709728700520984901963594242385161675765709307492877931225957573209380914070532087408371302738080119595345230482635524545021617674288584434024140803456669196908440985838760272198[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.067s user 0m0.058s sys 0m0.006s '62.43.7' ************** PARI ***************** Host 62.43.7.221 (62.43.7.221) Time: Sat Jan 29 12:41:37 2005 Input: forprime(p=2,100000,print(p)); Output: ? 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 1999 2003 2011 2017 2027 2029 2039 2053 2063 2069 2081 2083 2087 2089 2099 2111 2113 2129 2131 2137 2141 2143 2153 2161 2179 2203 2207 2213 2221 2237 2239 2243 2251 2267 2269 2273 2281 2287 2293 2297 2309 2311 2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 2389 2393 2399 2411 2417 2423 2437 2441 2447 2459 2467 2473 2477 2503 2521 2531 2539 2543 2549 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 2671 2677 2683 2687 2689 2693 2699 2707 2711 2713 2719 2729 2731 2741 2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 2857 2861 2879 2887 2897 2903 2909 2917 2927 2939 2953 2957 2963 2969 2971 2999 3001 3011 3019 3023 3037 3041 3049 3061 3067 3079 3083 3089 3109 3119 3121 3137 3163 3167 3169 3181 3187 3191 3203 3209 3217 3221 3229 3251 3253 3257 3259 3271 3299 3301 3307 3313 3319 3323 3329 3331 3343 3347 3359 3361 3371 3373 3389 3391 3407 3413 3433 3449 3457 3461 3463 3467 3469 3491 3499 3511 3517 3527 3529 3533 3539 3541 3547 3557 3559 3571 3581 3583 3593 3607 3613 3617 3623 3631 3637 3643 3659 3671 3673 3677 3691 3697 3701 3709 3719 3727 3733 3739 3761 3767 3769 3779 3793 3797 3803 3821 3823 3833 3847 3851 3853 3863 3877 3881 3889 3907 3911 3917 3919 3923 3929 3931 3943 3947 3967 3989 4001 4003 4007 4013 4019 4021 4027 4049 4051 4057 4073 4079 4091 4093 4099 4111 4127 4129 4133 4139 4153 4157 4159 4177 4201 4211 4217 4219 4229 4231 4241 4243 4253 4259 4261 4271 4273 4283 4289 4297 4327 4337 4339 4349 4357 4363 4373 4391 4397 4409 4421 4423 4441 4447 4451 4457 4463 4481 4483 4493 4507 4513 4517 4519 4523 4547 4549 4561 4567 4583 4591 4597 4603 4621 4637 4639 4643 4649 4651 4657 4663 4673 4679 4691 4703 4721 4723 4729 4733 4751 4759 4783 4787 4789 4793 4799 4801 4813 4817 4831 4861 4871 4877 4889 4903 4909 4919 4931 4933 4937 4943 4951 4957 4967 4969 4973 4987 4993 4999 5003 5009 5011 5021 5023 5039 5051 5059 5077 5081 5087 5099 5101 5107 5113 5119 5147 5153 5167 5171 5179 5189 5197 5209 5227 5231 5233 5237 5261 5273 5279 5281 5297 5303 5309 5323 5333 5347 5351 5381 5387 5393 5399 5407 5413 5417 5419 5431 5437 5441 5443 5449 5471 5477 5479 5483 5501 5503 5507 5519 5521 5527 5531 5557 5563 5569 5573 5581 5591 5623 5639 5641 5647 5651 5653 5657 5659 5669 5683 5689 5693 5701 5711 5717 5737 5741 5743 5749 5779 5783 5791 5801 5807 5813 5821 5827 5839 5843 5849 5851 5857 5861 5867 5869 5879 5881 5897 5903 5923 5927 5939 5953 5981 5987 6007 6011 6029 6037 6043 6047 6053 6067 6073 6079 6089 6091 6101 6113 6121 6131 6133 6143 6151 6163 6173 6197 6199 6203 6211 6217 6221 6229 6247 6257 6263 6269 6271 6277 6287 6299 6301 6311 6317 6323 6329 6337 6343 6353 6359 6361 6367 6373 6379 6389 6397 6421 6427 6449 6451 6469 6473 6481 6491 6521 6529 6547 6551 6553 6563 6569 6571 6577 6581 6599 6607 6619 6637 6653 6659 6661 6673 6679 6689 6691 6701 6703 6709 6719 6733 6737 6761 6763 6779 6781 6791 6793 6803 6823 6827 6829 6833 6841 6857 6863 6869 6871 6883 6899 6907 6911 6917 6947 6949 6959 6961 6967 6971 6977 6983 6991 6997 7001 7013 7019 7027 7039 7043 7057 7069 7079 7103 7109 7121 7127 7129 7151 7159 7177 7187 7193 7207 7211 7213 7219 7229 7237 7243 7247 7253 7283 7297 7307 7309 7321 7331 7333 7349 7351 7369 7393 7411 7417 7433 7451 7457 7459 7477 7481 7487 7489 7499 7507 7517 7523 7529 7537 7541 7547 7549 7559 7561 7573 7577 7583 7589 7591 7603 7607 7621 7639 7643 7649 7669 7673 7681 7687 7691 7699 7703 7717 7723 7727 7741 7753 7757 7759 7789 7793 7817 7823 7829 7841 7853 7867 7873 7877 7879 7883 7901 7907 7919 7927 7933 7937 7949 7951 7963 7993 8009 8011 8017 8039 8053 8059 8069 8081 8087 8089 8093 8101 8111 8117 8123 8147 8161 8167 8171 8179 8191 8209 8219 8221 8231 8233 8237 8243 8263 8269 8273 8287 8291 8293 8297 8311 8317 8329 8353 8363 8369 8377 8387 8389 8419 8423 8429 8431 8443 8447 8461 8467 8501 8513 8521 8527 8537 8539 8543 8563 8573 8581 8597 8599 8609 8623 8627 8629 8641 8647 8663 8669 8677 8681 8689 8693 8699 8707 8713 8719 8731 8737 8741 8747 8753 8761 8779 8783 8803 8807 8819 8821 8831 8837 8839 8849 8861 8863 8867 8887 8893 8923 8929 8933 8941 8951 8963 8969 8971 8999 9001 9007 9011 9013 9029 9041 9043 9049 9059 9067 9091 9103 9109 9127 9133 9137 9151 9157 9161 9173 9181 9187 9199 9203 9209 9221 9227 9239 9241 9257 9277 9281 9283 9293 9311 9319 9323 9337 9341 9343 9349 9371 9377 9391 9397 9403 9413 9419 9421 9431 9433 9437 9439 9461 9463 9467 9473 9479 9491 9497 9511 9521 9533 9539 9547 9551 9587 9601 9613 9619 9623 9629 9631 9643 9649 9661 9677 9679 9689 9697 9719 9721 9733 9739 9743 9749 9767 9769 9781 9787 9791 9803 9811 9817 9829 9833 9839 9851 9857 9859 9871 9883 9887 9901 9907 9923 9929 9931 9941 9949 9967 9973 10007 10009 10037 10039 10061 10067 10069 10079 10091 10093 10099 10103 10111 10133 10139 10141 10151 10159 10163 10169 10177 10181 10193 10211 10223 10243 10247 10253 10259 10267 10271 10273 10289 10301 10303 10313 10321 10331 10333 10337 10343 10357 10369 10391 10399 10427 10429 10433 10453 10457 10459 10463 10477 10487 10499 10501 10513 10529 10531 10559 10567 10589 10597 10601 10607 10613 10627 10631 10639 10651 10657 10663 10667 10687 10691 10709 10711 10723 10729 10733 10739 10753 10771 10781 10789 10799 10831 10837 10847 10853 10859 10861 10867 10883 10889 10891 10903 10909 10937 10939 10949 10957 10973 10979 10987 10993 11003 11027 11047 11057 11059 11069 11071 11083 11087 11093 11113 11117 11119 11131 11149 11159 11161 11171 11173 11177 11197 11213 11239 11243 11251 11257 11261 11273 11279 11287 11299 11311 11317 11321 11329 11351 11353 11369 11383 11393 11399 11411 11423 11437 11443 11447 11467 11471 11483 11489 11491 11497 11503 11519 11527 11549 11551 11579 11587 11593 11597 11617 11621 11633 11657 11677 11681 11689 11699 11701 11717 11719 11731 11743 11777 11779 11783 11789 11801 11807 11813 11821 11827 11831 11833 11839 11863 11867 11887 11897 11903 11909 11923 11927 11933 11939 11941 11953 11959 11969 11971 11981 11987 12007 12011 12037 12041 12043 12049 12071 12073 12097 12101 12107 12109 12113 12119 12143 12149 12157 12161 12163 12197 12203 12211 12227 12239 12241 12251 12253 12263 12269 12277 12281 12289 12301 12323 12329 12343 12347 12373 12377 12379 12391 12401 12409 12413 12421 12433 12437 12451 12457 12473 12479 12487 12491 12497 12503 12511 12517 12527 12539 12541 12547 12553 12569 12577 12583 12589 12601 12611 12613 12619 12637 12641 12647 12653 12659 12671 12689 12697 12703 12713 12721 12739 12743 12757 12763 12781 12791 12799 12809 12821 12823 12829 12841 12853 12889 12893 12899 12907 12911 12917 12919 12923 12941 12953 12959 12967 12973 12979 12983 13001 13003 13007 13009 13033 13037 13043 13049 13063 13093 13099 13103 13109 13121 13127 13147 13151 13159 13163 13171 13177 13183 13187 13217 13219 13229 13241 13249 13259 13267 13291 13297 13309 13313 13327 13331 13337 13339 13367 13381 13397 13399 13411 13417 13421 13441 13451 13457 13463 13469 13477 13487 13499 13513 13523 13537 13553 13567 13577 13591 13597 13613 13619 13627 13633 13649 13669 13679 13681 13687 13691 13693 13697 13709 13711 13721 13723 13729 13751 13757 13759 13763 13781 13789 13799 13807 13829 13831 13841 13859 13873 13877 13879 13883 13901 13903 13907 13913 13921 13931 13933 13963 13967 13997 13999 14009 14011 14029 14033 14051 14057 14071 14081 14083 14087 14107 14143 14149 14153 14159 14173 14177 14197 14207 14221 14243 14249 14251 14281 14293 14303 14321 14323 14327 14341 14347 14369 14387 14389 14401 14407 14411 14419 14423 14431 14437 14447 14449 14461 14479 14489 14503 14519 14533 14537 14543 14549 14551 14557 14561 14563 14591 14593 14621 14627 14629 14633 14639 14653 14657 14669 14683 14699 14713 14717 14723 14731 14737 14741 14747 14753 14759 14767 14771 14779 14783 14797 14813 14821 14827 14831 14843 14851 14867 14869 14879 14887 14891 14897 14923 14929 14939 14947 14951 14957 14969 14983 15013 15017 15031 15053 15061 15073 15077 15083 15091 15101 15107 15121 15131 15137 15139 15149 15161 15173 15187 15193 15199 15217 15227 15233 15241 15259 15263 15269 15271 15277 15287 15289 15299 15307 15313 15319 15329 15331 15349 15359 15361 15373 15377 15383 15391 15401 15413 15427 15439 15443 15451 15461 15467 15473 15493 15497 15511 15527 15541 15551 15559 15569 15581 15583 15601 15607 15619 15629 15641 15643 15647 15649 15661 15667 15671 15679 15683 15727 15731 15733 15737 15739 15749 15761 15767 15773 15787 15791 15797 15803 15809 15817 15823 15859 15877 15881 15887 15889 15901 15907 15913 15919 15923 15937 15959 15971 15973 15991 16001 16007 16033 16057 16061 16063 16067 16069 16073 16087 16091 16097 16103 16111 16127 16139 16141 16183 16187 16189 16193 16217 16223 16229 16231 16249 16253 16267 16273 16301 16319 16333 16339 16349 16361 16363 16369 16381 16411 16417 16421 16427 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.020s sys 0m0.029s '62.43.7' ************** PARI ***************** Host 62.43.7.221 (62.43.7.221) Time: Sat Jan 29 12:42:30 2005 Input: forprime(p=2,100000,print(p)); print(";") Output: ? 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 1999 2003 2011 2017 2027 2029 2039 2053 2063 2069 2081 2083 2087 2089 2099 2111 2113 2129 2131 2137 2141 2143 2153 2161 2179 2203 2207 2213 2221 2237 2239 2243 2251 2267 2269 2273 2281 2287 2293 2297 2309 2311 2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 2389 2393 2399 2411 2417 2423 2437 2441 2447 2459 2467 2473 2477 2503 2521 2531 2539 2543 2549 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 2671 2677 2683 2687 2689 2693 2699 2707 2711 2713 2719 2729 2731 2741 2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 2857 2861 2879 2887 2897 2903 2909 2917 2927 2939 2953 2957 2963 2969 2971 2999 3001 3011 3019 3023 3037 3041 3049 3061 3067 3079 3083 3089 3109 3119 3121 3137 3163 3167 3169 3181 3187 3191 3203 3209 3217 3221 3229 3251 3253 3257 3259 3271 3299 3301 3307 3313 3319 3323 3329 3331 3343 3347 3359 3361 3371 3373 3389 3391 3407 3413 3433 3449 3457 3461 3463 3467 3469 3491 3499 3511 3517 3527 3529 3533 3539 3541 3547 3557 3559 3571 3581 3583 3593 3607 3613 3617 3623 3631 3637 3643 3659 3671 3673 3677 3691 3697 3701 3709 3719 3727 3733 3739 3761 3767 3769 3779 3793 3797 3803 3821 3823 3833 3847 3851 3853 3863 3877 3881 3889 3907 3911 3917 3919 3923 3929 3931 3943 3947 3967 3989 4001 4003 4007 4013 4019 4021 4027 4049 4051 4057 4073 4079 4091 4093 4099 4111 4127 4129 4133 4139 4153 4157 4159 4177 4201 4211 4217 4219 4229 4231 4241 4243 4253 4259 4261 4271 4273 4283 4289 4297 4327 4337 4339 4349 4357 4363 4373 4391 4397 4409 4421 4423 4441 4447 4451 4457 4463 4481 4483 4493 4507 4513 4517 4519 4523 4547 4549 4561 4567 4583 4591 4597 4603 4621 4637 4639 4643 4649 4651 4657 4663 4673 4679 4691 4703 4721 4723 4729 4733 4751 4759 4783 4787 4789 4793 4799 4801 4813 4817 4831 4861 4871 4877 4889 4903 4909 4919 4931 4933 4937 4943 4951 4957 4967 4969 4973 4987 4993 4999 5003 5009 5011 5021 5023 5039 5051 5059 5077 5081 5087 5099 5101 5107 5113 5119 5147 5153 5167 5171 5179 5189 5197 5209 5227 5231 5233 5237 5261 5273 5279 5281 5297 5303 5309 5323 5333 5347 5351 5381 5387 5393 5399 5407 5413 5417 5419 5431 5437 5441 5443 5449 5471 5477 5479 5483 5501 5503 5507 5519 5521 5527 5531 5557 5563 5569 5573 5581 5591 5623 5639 5641 5647 5651 5653 5657 5659 5669 5683 5689 5693 5701 5711 5717 5737 5741 5743 5749 5779 5783 5791 5801 5807 5813 5821 5827 5839 5843 5849 5851 5857 5861 5867 5869 5879 5881 5897 5903 5923 5927 5939 5953 5981 5987 6007 6011 6029 6037 6043 6047 6053 6067 6073 6079 6089 6091 6101 6113 6121 6131 6133 6143 6151 6163 6173 6197 6199 6203 6211 6217 6221 6229 6247 6257 6263 6269 6271 6277 6287 6299 6301 6311 6317 6323 6329 6337 6343 6353 6359 6361 6367 6373 6379 6389 6397 6421 6427 6449 6451 6469 6473 6481 6491 6521 6529 6547 6551 6553 6563 6569 6571 6577 6581 6599 6607 6619 6637 6653 6659 6661 6673 6679 6689 6691 6701 6703 6709 6719 6733 6737 6761 6763 6779 6781 6791 6793 6803 6823 6827 6829 6833 6841 6857 6863 6869 6871 6883 6899 6907 6911 6917 6947 6949 6959 6961 6967 6971 6977 6983 6991 6997 7001 7013 7019 7027 7039 7043 7057 7069 7079 7103 7109 7121 7127 7129 7151 7159 7177 7187 7193 7207 7211 7213 7219 7229 7237 7243 7247 7253 7283 7297 7307 7309 7321 7331 7333 7349 7351 7369 7393 7411 7417 7433 7451 7457 7459 7477 7481 7487 7489 7499 7507 7517 7523 7529 7537 7541 7547 7549 7559 7561 7573 7577 7583 7589 7591 7603 7607 7621 7639 7643 7649 7669 7673 7681 7687 7691 7699 7703 7717 7723 7727 7741 7753 7757 7759 7789 7793 7817 7823 7829 7841 7853 7867 7873 7877 7879 7883 7901 7907 7919 7927 7933 7937 7949 7951 7963 7993 8009 8011 8017 8039 8053 8059 8069 8081 8087 8089 8093 8101 8111 8117 8123 8147 8161 8167 8171 8179 8191 8209 8219 8221 8231 8233 8237 8243 8263 8269 8273 8287 8291 8293 8297 8311 8317 8329 8353 8363 8369 8377 8387 8389 8419 8423 8429 8431 8443 8447 8461 8467 8501 8513 8521 8527 8537 8539 8543 8563 8573 8581 8597 8599 8609 8623 8627 8629 8641 8647 8663 8669 8677 8681 8689 8693 8699 8707 8713 8719 8731 8737 8741 8747 8753 8761 8779 8783 8803 8807 8819 8821 8831 8837 8839 8849 8861 8863 8867 8887 8893 8923 8929 8933 8941 8951 8963 8969 8971 8999 9001 9007 9011 9013 9029 9041 9043 9049 9059 9067 9091 9103 9109 9127 9133 9137 9151 9157 9161 9173 9181 9187 9199 9203 9209 9221 9227 9239 9241 9257 9277 9281 9283 9293 9311 9319 9323 9337 9341 9343 9349 9371 9377 9391 9397 9403 9413 9419 9421 9431 9433 9437 9439 9461 9463 9467 9473 9479 9491 9497 9511 9521 9533 9539 9547 9551 9587 9601 9613 9619 9623 9629 9631 9643 9649 9661 9677 9679 9689 9697 9719 9721 9733 9739 9743 9749 9767 9769 9781 9787 9791 9803 9811 9817 9829 9833 9839 9851 9857 9859 9871 9883 9887 9901 9907 9923 9929 9931 9941 9949 9967 9973 10007 10009 10037 10039 10061 10067 10069 10079 10091 10093 10099 10103 10111 10133 10139 10141 10151 10159 10163 10169 10177 10181 10193 10211 10223 10243 10247 10253 10259 10267 10271 10273 10289 10301 10303 10313 10321 10331 10333 10337 10343 10357 10369 10391 10399 10427 10429 10433 10453 10457 10459 10463 10477 10487 10499 10501 10513 10529 10531 10559 10567 10589 10597 10601 10607 10613 10627 10631 10639 10651 10657 10663 10667 10687 10691 10709 10711 10723 10729 10733 10739 10753 10771 10781 10789 10799 10831 10837 10847 10853 10859 10861 10867 10883 10889 10891 10903 10909 10937 10939 10949 10957 10973 10979 10987 10993 11003 11027 11047 11057 11059 11069 11071 11083 11087 11093 11113 11117 11119 11131 11149 11159 11161 11171 11173 11177 11197 11213 11239 11243 11251 11257 11261 11273 11279 11287 11299 11311 11317 11321 11329 11351 11353 11369 11383 11393 11399 11411 11423 11437 11443 11447 11467 11471 11483 11489 11491 11497 11503 11519 11527 11549 11551 11579 11587 11593 11597 11617 11621 11633 11657 11677 11681 11689 11699 11701 11717 11719 11731 11743 11777 11779 11783 11789 11801 11807 11813 11821 11827 11831 11833 11839 11863 11867 11887 11897 11903 11909 11923 11927 11933 11939 11941 11953 11959 11969 11971 11981 11987 12007 12011 12037 12041 12043 12049 12071 12073 12097 12101 12107 12109 12113 12119 12143 12149 12157 12161 12163 12197 12203 12211 12227 12239 12241 12251 12253 12263 12269 12277 12281 12289 12301 12323 12329 12343 12347 12373 12377 12379 12391 12401 12409 12413 12421 12433 12437 12451 12457 12473 12479 12487 12491 12497 12503 12511 12517 12527 12539 12541 12547 12553 12569 12577 12583 12589 12601 12611 12613 12619 12637 12641 12647 12653 12659 12671 12689 12697 12703 12713 12721 12739 12743 12757 12763 12781 12791 12799 12809 12821 12823 12829 12841 12853 12889 12893 12899 12907 12911 12917 12919 12923 12941 12953 12959 12967 12973 12979 12983 13001 13003 13007 13009 13033 13037 13043 13049 13063 13093 13099 13103 13109 13121 13127 13147 13151 13159 13163 13171 13177 13183 13187 13217 13219 13229 13241 13249 13259 13267 13291 13297 13309 13313 13327 13331 13337 13339 13367 13381 13397 13399 13411 13417 13421 13441 13451 13457 13463 13469 13477 13487 13499 13513 13523 13537 13553 13567 13577 13591 13597 13613 13619 13627 13633 13649 13669 13679 13681 13687 13691 13693 13697 13709 13711 13721 13723 13729 13751 13757 13759 13763 13781 13789 13799 13807 13829 13831 13841 13859 13873 13877 13879 13883 13901 13903 13907 13913 13921 13931 13933 13963 13967 13997 13999 14009 14011 14029 14033 14051 14057 14071 14081 14083 14087 14107 14143 14149 14153 14159 14173 14177 14197 14207 14221 14243 14249 14251 14281 14293 14303 14321 14323 14327 14341 14347 14369 14387 14389 14401 14407 14411 14419 14423 14431 14437 14447 14449 14461 14479 14489 14503 14519 14533 14537 14543 14549 14551 14557 14561 14563 14591 14593 14621 14627 14629 14633 14639 14653 14657 14669 14683 14699 14713 14717 14723 14731 14737 14741 14747 14753 14759 14767 14771 14779 14783 14797 14813 14821 14827 14831 14843 14851 14867 14869 14879 14887 14891 14897 14923 14929 14939 14947 14951 14957 14969 14983 15013 15017 15031 15053 15061 15073 15077 15083 15091 15101 15107 15121 15131 15137 15139 15149 15161 15173 15187 15193 15199 15217 15227 15233 15241 15259 15263 15269 15271 15277 15287 15289 15299 15307 15313 15319 15329 15331 15349 15359 15361 15373 15377 15383 15391 15401 15413 15427 15439 15443 15451 15461 15467 15473 15493 15497 15511 15527 15541 15551 15559 15569 15581 15583 15601 15607 15619 15629 15641 15643 15647 15649 15661 15667 15671 15679 15683 15727 15731 15733 15737 15739 15749 15761 15767 15773 15787 15791 15797 15803 15809 15817 15823 15859 15877 15881 15887 15889 15901 15907 15913 15919 15923 15937 15959 15971 15973 15991 16001 16007 16033 16057 16061 16063 16067 16069 16073 16087 16091 16097 16103 16111 16127 16139 16141 16183 16187 16189 16193 16217 16223 16229 16231 16249 16253 16267 16273 16301 16319 16333 16339 16349 16361 16363 16369 16381 16411 16417 16421 16427 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.016s sys 0m0.036s '62.43.7' ************** PARI ***************** Host 62.43.7.221 (62.43.7.221) Time: Sat Jan 29 12:43:08 2005 Input: forprime(p=2,100000,print(p)); print(";"); Output: ? 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 1999 2003 2011 2017 2027 2029 2039 2053 2063 2069 2081 2083 2087 2089 2099 2111 2113 2129 2131 2137 2141 2143 2153 2161 2179 2203 2207 2213 2221 2237 2239 2243 2251 2267 2269 2273 2281 2287 2293 2297 2309 2311 2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 2389 2393 2399 2411 2417 2423 2437 2441 2447 2459 2467 2473 2477 2503 2521 2531 2539 2543 2549 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 2671 2677 2683 2687 2689 2693 2699 2707 2711 2713 2719 2729 2731 2741 2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 2857 2861 2879 2887 2897 2903 2909 2917 2927 2939 2953 2957 2963 2969 2971 2999 3001 3011 3019 3023 3037 3041 3049 3061 3067 3079 3083 3089 3109 3119 3121 3137 3163 3167 3169 3181 3187 3191 3203 3209 3217 3221 3229 3251 3253 3257 3259 3271 3299 3301 3307 3313 3319 3323 3329 3331 3343 3347 3359 3361 3371 3373 3389 3391 3407 3413 3433 3449 3457 3461 3463 3467 3469 3491 3499 3511 3517 3527 3529 3533 3539 3541 3547 3557 3559 3571 3581 3583 3593 3607 3613 3617 3623 3631 3637 3643 3659 3671 3673 3677 3691 3697 3701 3709 3719 3727 3733 3739 3761 3767 3769 3779 3793 3797 3803 3821 3823 3833 3847 3851 3853 3863 3877 3881 3889 3907 3911 3917 3919 3923 3929 3931 3943 3947 3967 3989 4001 4003 4007 4013 4019 4021 4027 4049 4051 4057 4073 4079 4091 4093 4099 4111 4127 4129 4133 4139 4153 4157 4159 4177 4201 4211 4217 4219 4229 4231 4241 4243 4253 4259 4261 4271 4273 4283 4289 4297 4327 4337 4339 4349 4357 4363 4373 4391 4397 4409 4421 4423 4441 4447 4451 4457 4463 4481 4483 4493 4507 4513 4517 4519 4523 4547 4549 4561 4567 4583 4591 4597 4603 4621 4637 4639 4643 4649 4651 4657 4663 4673 4679 4691 4703 4721 4723 4729 4733 4751 4759 4783 4787 4789 4793 4799 4801 4813 4817 4831 4861 4871 4877 4889 4903 4909 4919 4931 4933 4937 4943 4951 4957 4967 4969 4973 4987 4993 4999 5003 5009 5011 5021 5023 5039 5051 5059 5077 5081 5087 5099 5101 5107 5113 5119 5147 5153 5167 5171 5179 5189 5197 5209 5227 5231 5233 5237 5261 5273 5279 5281 5297 5303 5309 5323 5333 5347 5351 5381 5387 5393 5399 5407 5413 5417 5419 5431 5437 5441 5443 5449 5471 5477 5479 5483 5501 5503 5507 5519 5521 5527 5531 5557 5563 5569 5573 5581 5591 5623 5639 5641 5647 5651 5653 5657 5659 5669 5683 5689 5693 5701 5711 5717 5737 5741 5743 5749 5779 5783 5791 5801 5807 5813 5821 5827 5839 5843 5849 5851 5857 5861 5867 5869 5879 5881 5897 5903 5923 5927 5939 5953 5981 5987 6007 6011 6029 6037 6043 6047 6053 6067 6073 6079 6089 6091 6101 6113 6121 6131 6133 6143 6151 6163 6173 6197 6199 6203 6211 6217 6221 6229 6247 6257 6263 6269 6271 6277 6287 6299 6301 6311 6317 6323 6329 6337 6343 6353 6359 6361 6367 6373 6379 6389 6397 6421 6427 6449 6451 6469 6473 6481 6491 6521 6529 6547 6551 6553 6563 6569 6571 6577 6581 6599 6607 6619 6637 6653 6659 6661 6673 6679 6689 6691 6701 6703 6709 6719 6733 6737 6761 6763 6779 6781 6791 6793 6803 6823 6827 6829 6833 6841 6857 6863 6869 6871 6883 6899 6907 6911 6917 6947 6949 6959 6961 6967 6971 6977 6983 6991 6997 7001 7013 7019 7027 7039 7043 7057 7069 7079 7103 7109 7121 7127 7129 7151 7159 7177 7187 7193 7207 7211 7213 7219 7229 7237 7243 7247 7253 7283 7297 7307 7309 7321 7331 7333 7349 7351 7369 7393 7411 7417 7433 7451 7457 7459 7477 7481 7487 7489 7499 7507 7517 7523 7529 7537 7541 7547 7549 7559 7561 7573 7577 7583 7589 7591 7603 7607 7621 7639 7643 7649 7669 7673 7681 7687 7691 7699 7703 7717 7723 7727 7741 7753 7757 7759 7789 7793 7817 7823 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9631 9643 9649 9661 9677 9679 9689 9697 9719 9721 9733 9739 9743 9749 9767 9769 9781 9787 9791 9803 9811 9817 9829 9833 9839 9851 9857 9859 9871 9883 9887 9901 9907 9923 9929 9931 9941 9949 9967 9973 10007 10009 10037 10039 10061 10067 10069 10079 10091 10093 10099 10103 10111 10133 10139 10141 10151 10159 10163 10169 10177 10181 10193 10211 10223 10243 10247 10253 10259 10267 10271 10273 10289 10301 10303 10313 10321 10331 10333 10337 10343 10357 10369 10391 10399 10427 10429 10433 10453 10457 10459 10463 10477 10487 10499 10501 10513 10529 10531 10559 10567 10589 10597 10601 10607 10613 10627 10631 10639 10651 10657 10663 10667 10687 10691 10709 10711 10723 10729 10733 10739 10753 10771 10781 10789 10799 10831 10837 10847 10853 10859 10861 10867 10883 10889 10891 10903 10909 10937 10939 10949 10957 10973 10979 10987 10993 11003 11027 11047 11057 11059 11069 11071 11083 11087 11093 11113 11117 11119 11131 11149 11159 11161 11171 11173 11177 11197 11213 11239 11243 11251 11257 11261 11273 11279 11287 11299 11311 11317 11321 11329 11351 11353 11369 11383 11393 11399 11411 11423 11437 11443 11447 11467 11471 11483 11489 11491 11497 11503 11519 11527 11549 11551 11579 11587 11593 11597 11617 11621 11633 11657 11677 11681 11689 11699 11701 11717 11719 11731 11743 11777 11779 11783 11789 11801 11807 11813 11821 11827 11831 11833 11839 11863 11867 11887 11897 11903 11909 11923 11927 11933 11939 11941 11953 11959 11969 11971 11981 11987 12007 12011 12037 12041 12043 12049 12071 12073 12097 12101 12107 12109 12113 12119 12143 12149 12157 12161 12163 12197 12203 12211 12227 12239 12241 12251 12253 12263 12269 12277 12281 12289 12301 12323 12329 12343 12347 12373 12377 12379 12391 12401 12409 12413 12421 12433 12437 12451 12457 12473 12479 12487 12491 12497 12503 12511 12517 12527 12539 12541 12547 12553 12569 12577 12583 12589 12601 12611 12613 12619 12637 12641 12647 12653 12659 12671 12689 12697 12703 12713 12721 12739 12743 12757 12763 12781 12791 12799 12809 12821 12823 12829 12841 12853 12889 12893 12899 12907 12911 12917 12919 12923 12941 12953 12959 12967 12973 12979 12983 13001 13003 13007 13009 13033 13037 13043 13049 13063 13093 13099 13103 13109 13121 13127 13147 13151 13159 13163 13171 13177 13183 13187 13217 13219 13229 13241 13249 13259 13267 13291 13297 13309 13313 13327 13331 13337 13339 13367 13381 13397 13399 13411 13417 13421 13441 13451 13457 13463 13469 13477 13487 13499 13513 13523 13537 13553 13567 13577 13591 13597 13613 13619 13627 13633 13649 13669 13679 13681 13687 13691 13693 13697 13709 13711 13721 13723 13729 13751 13757 13759 13763 13781 13789 13799 13807 13829 13831 13841 13859 13873 13877 13879 13883 13901 13903 13907 13913 13921 13931 13933 13963 13967 13997 13999 14009 14011 14029 14033 14051 14057 14071 14081 14083 14087 14107 14143 14149 14153 14159 14173 14177 14197 14207 14221 14243 14249 14251 14281 14293 14303 14321 14323 14327 14341 14347 14369 14387 14389 14401 14407 14411 14419 14423 14431 14437 14447 14449 14461 14479 14489 14503 14519 14533 14537 14543 14549 14551 14557 14561 14563 14591 14593 14621 14627 14629 14633 14639 14653 14657 14669 14683 14699 14713 14717 14723 14731 14737 14741 14747 14753 14759 14767 14771 14779 14783 14797 14813 14821 14827 14831 14843 14851 14867 14869 14879 14887 14891 14897 14923 14929 14939 14947 14951 14957 14969 14983 15013 15017 15031 15053 15061 15073 15077 15083 15091 15101 15107 15121 15131 15137 15139 15149 15161 15173 15187 15193 15199 15217 15227 15233 15241 15259 15263 15269 15271 15277 15287 15289 15299 15307 15313 15319 15329 15331 15349 15359 15361 15373 15377 15383 15391 15401 15413 15427 15439 15443 15451 15461 15467 15473 15493 15497 15511 15527 15541 15551 15559 15569 15581 15583 15601 15607 15619 15629 15641 15643 15647 15649 15661 15667 15671 15679 15683 15727 15731 15733 15737 15739 15749 15761 15767 15773 15787 15791 15797 15803 15809 15817 15823 15859 15877 15881 15887 15889 15901 15907 15913 15919 15923 15937 15959 15971 15973 15991 16001 16007 16033 16057 16061 16063 16067 16069 16073 16087 16091 16097 16103 16111 16127 16139 16141 16183 16187 16189 16193 16217 16223 16229 16231 16249 16253 16267 16273 16301 16319 16333 16339 16349 16361 16363 16369 16381 16411 16417 16421 16427 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.061s user 0m0.027s sys 0m0.019s '82.51.8' ************** PARI ***************** Host 82.51.81.232 (82.51.81.232) Time: Sat Jan 29 16:50:22 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 20:01:17 2005 Input: 2^57*5^7 Output: ? 11258999068426240000000 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 20:02:02 2005 Input: 3*786 Output: ? 2358 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 20:05:03 2005 Input: { t1 = 1/2 + 14*I; t2 = 1/2 + 15*I; eps = 10^(-50); z1 = zeta(t1); until (norm(z2) < eps, z2 = zeta(t2); if (norm(z2) < norm(z1), t3 = t1; t1 = t2; t2 = t3; z1 = z2 ); t2 = (t1+t2) / 2.; print(t1 ": " z1) ) } Output: ? 1/2 + 14*I: 0.022241142609993589246213199203968626386 - 0.10325812326645005790236309555257383450*I 1/2 + 14*I: 0.022241142609993589246213199203968626386 - 0.10325812326645005790236309555257383450*I 0.50000000000000000000000000000000000000 + 14.250000000000000000000000000000000000*I: -0.010213208887230807522525955767002816511 + 0.091698089621017640081465962929933653198*I 0.50000000000000000000000000000000000000 + 14.125000000000000000000000000000000000*I: 0.0012417291852137510346673085802853350647 - 0.0076067313356130555106430474935370339114*I 0.50000000000000000000000000000000000000 + 14.125000000000000000000000000000000000*I: 0.0012417291852137510346673085802853350647 - 0.0076067313356130555106430474935370339114*I 0.50000000000000000000000000000000000000 + 14.125000000000000000000000000000000000*I: 0.0012417291852137510346673085802853350647 - 0.0076067313356130555106430474935370339114*I 0.50000000000000000000000000000000000000 + 14.140625000000000000000000000000000000*I: -0.00072500707529812503468942479076164825284 + 0.0046253214673438971249880769138653783886*I 0.50000000000000000000000000000000000000 + 14.132812500000000000000000000000000000*I: 0.00023962954107211412834588625490278397267 - 0.0014977447536980232040348813712444919242*I 0.50000000000000000000000000000000000000 + 14.132812500000000000000000000000000000*I: 0.00023962954107211412834588625490278397267 - 0.0014977447536980232040348813712444919242*I 0.50000000000000000000000000000000000000 + 14.134765625000000000000000000000000000*I: -0.0000050477528112895105346089337394953122802 + 0.000031710588793744007891097264313007623870*I 0.50000000000000000000000000000000000000 + 14.134765625000000000000000000000000000*I: -0.0000050477528112895105346089337394953122802 + 0.000031710588793744007891097264313007623870*I 0.50000000000000000000000000000000000000 + 14.134765625000000000000000000000000000*I: -0.0000050477528112895105346089337394953122802 + 0.000031710588793744007891097264313007623870*I 0.50000000000000000000000000000000000000 + 14.134765625000000000000000000000000000*I: -0.0000050477528112895105346089337394953122802 + 0.000031710588793744007891097264313007623870*I 0.50000000000000000000000000000000000000 + 14.134765625000000000000000000000000000*I: -0.0000050477528112895105346089337394953122802 + 0.000031710588793744007891097264313007623870*I 0.50000000000000000000000000000000000000 + 14.134704589843750000000000000000000000*I: 0.0000025629470585022928664553282786112377754 - 0.000016098175959828936822394045075238461739*I 0.50000000000000000000000000000000000000 + 14.134735107421875000000000000000000000*I: -0.0000012426889847373687918207327003320961140 + 0.0000078060994177939847324764298429698262538*I 0.50000000000000000000000000000000000000 + 14.134719848632812500000000000000000000*I: 0.00000066005751036606240409998196372114534632 - 0.0000041460650216441673191517954226161104709*I 0.50000000000000000000000000000000000000 + 14.134727478027343750000000000000000000*I: -0.00000029133361888594635474828658803415387787 + 0.0000018300105105227104907165816658767034581*I 0.50000000000000000000000000000000000000 + 14.134723663330078125000000000000000000*I: 0.00000018435747532388384677381445113139406869 - 0.0000011580289274618373462866323141851235516*I 0.50000000000000000000000000000000000000 + 14.134725570678710937500000000000000000*I: -0.000000053489189386187190268566160316319835330 + 0.00000033599037355679175816071910681797482240*I 0.50000000000000000000000000000000000000 + 14.134725570678710937500000000000000000*I: -0.000000053489189386187190268566160316319835330 + 0.00000033599037355679175816071910681797482240*I 0.50000000000000000000000000000000000000 + 14.134725093841552734375000000000000000*I: 0.0000000059722672404507364302655529844075510389 - 0.000000037514530068051453459458095959312990640*I 0.50000000000000000000000000000000000000 + 14.134725093841552734375000000000000000*I: 0.0000000059722672404507364302655529844075510389 - 0.000000037514530068051453459458095959312990640*I 0.50000000000000000000000000000000000000 + 14.134725093841552734375000000000000000*I: 0.0000000059722672404507364302655529844075510389 - 0.000000037514530068051453459458095959312990640*I 0.50000000000000000000000000000000000000 + 14.134725153446197509765625000000000000*I: -0.0000000014604224777568119054521443839306049290 + 0.0000000091735800278104917820589383501792529841*I 0.50000000000000000000000000000000000000 + 14.134725153446197509765625000000000000*I: -0.0000000014604224777568119054521443839306049290 + 0.0000000091735800278104917820589383501792529841*I 0.50000000000000000000000000000000000000 + 14.134725138545036315917968750000000000*I: 0.00000000039774974715550643150187096082597754920 - 0.0000000024984475726883239646786773010674587327*I 0.50000000000000000000000000000000000000 + 14.134725138545036315917968750000000000*I: 0.00000000039774974715550643150187096082597754920 - 0.0000000024984475726883239646786773010674587327*I 0.50000000000000000000000000000000000000 + 14.134725142270326614379882812500000000*I: -6.6793321862546307166026951304723319480 E-11 + 0.00000000041955932265304704034555983115678186579*I 0.50000000000000000000000000000000000000 + 14.134725142270326614379882812500000000*I: -6.6793321862546307166026951304723319480 E-11 + 0.00000000041955932265304704034555983115678186579*I 0.50000000000000000000000000000000000000 + 14.134725141339004039764404296875000000*I: 4.9342444592593557032601485722012306636 E-11 - 0.00000000030994240148125402160976350267265024432*I 0.50000000000000000000000000000000000000 + 14.134725141804665327072143554687500000*I: -8.7254387015908184768455363910496821172 E-12 + 5.4808460560983316865054125864368132180 E-11*I 0.50000000000000000000000000000000000000 + 14.134725141804665327072143554687500000*I: -8.7254387015908184768455363910496821172 E-12 + 5.4808460560983316865054125864368132180 E-11*I 0.50000000000000000000000000000000000000 + 14.134725141688250005245208740234375000*I: 5.7915321094650672623809602084198113218 E-12 - 3.6379254954247241349789385537925217794 E-11*I 0.50000000000000000000000000000000000000 + 14.134725141746457666158676147460937500*I: -1.4669532971037262854839971039165662123 E-12 + 9.2146028029787691247290358867524080481 E-12*I 0.50000000000000000000000000000000000000 + 14.134725141746457666158676147460937500*I: -1.4669532971037262854839971039165662123 E-12 + 9.2146028029787691247290358867524080481 E-12*I 0.50000000000000000000000000000000000000 + 14.134725141731905750930309295654296875*I: 3.4766805434331259931251678771524941625 E-13 - 2.1838616364007213625735693475677751302 E-12*I 0.50000000000000000000000000000000000000 + 14.134725141731905750930309295654296875*I: 3.4766805434331259931251678771524941625 E-13 - 2.1838616364007213625735693475677751302 E-12*I 0.50000000000000000000000000000000000000 + 14.134725141735543729737401008605957031*I: -1.0598728353064459077231986885952638167 E-13 + 6.6575447343958951746016672211867868257 E-13*I 0.50000000000000000000000000000000000000 + 14.134725141735543729737401008605957031*I: -1.0598728353064459077231986885952638167 E-13 + 6.6575447343958951746016672211867868257 E-13*I 0.50000000000000000000000000000000000000 + 14.134725141734634235035628080368041992*I: 7.4265509370823649435341016782498442409 E-15 - 4.6649554020773311410264298569578535273 E-14*I 0.50000000000000000000000000000000000000 + 14.134725141734634235035628080368041992*I: 7.4265509370823649435341016782498442409 E-15 - 4.6649554020773311410264298569578535273 E-14*I 0.50000000000000000000000000000000000000 + 14.134725141734634235035628080368041992*I: 7.4265509370823649435341016782498442409 E-15 - 4.6649554020773311410264298569578535273 E-14*I 0.50000000000000000000000000000000000000 + 14.134725141734747921873349696397781372*I: -6.7501783714112982326012331467310164508 E-15 + 4.2400949411761647604612625103600418582 E-14*I 0.50000000000000000000000000000000000000 + 14.134725141734691078454488888382911682*I: 3.3818628283454072290737768056313147286 E-16 - 2.1243023045062031383232281602114210256 E-15*I 0.50000000000000000000000000000000000000 + 14.134725141734691078454488888382911682*I: 3.3818628283454072290737768056313147286 E-16 - 2.1243023045062031383232281602114210256 E-15*I 0.50000000000000000000000000000000000000 + 14.134725141734691078454488888382911682*I: 3.3818628283454072290737768056313147286 E-16 - 2.1243023045062031383232281602114210256 E-15*I 0.50000000000000000000000000000000000000 + 14.134725141734691078454488888382911682*I: 3.3818628283454072290737768056313147286 E-16 - 2.1243023045062031383232281602114210256 E-15*I 0.50000000000000000000000000000000000000 + 14.134725141734694631168167688883841037*I: -1.0483650805588237387591771854263320968 E-16 + 6.5852592776051578103033739073469652253 E-16*I 0.50000000000000000000000000000000000000 + 14.134725141734694631168167688883841037*I: -1.0483650805588237387591771854263320968 E-16 + 6.5852592776051578103033739073469652253 E-16*I 0.50000000000000000000000000000000000000 + 14.134725141734693742989747988758608698*I: 5.9191896667226732941060409606611432805 E-18 - 3.7181130306164220709053062987414167102 E-17*I 0.50000000000000000000000000000000000000 + 14.134725141734693742989747988758608698*I: 5.9191896667226732941060409606611432805 E-18 - 3.7181130306164220709053062987414167102 E-17*I 0.50000000000000000000000000000000000000 + 14.134725141734693742989747988758608698*I: 5.9191896667226732941060409606611432805 E-18 - 3.7181130306164220709053062987414167102 E-17*I 0.50000000000000000000000000000000000000 + 14.134725141734693742989747988758608698*I: 5.9191896667226732941060409606611432805 E-18 - 3.7181130306164220709053062987414167102 E-17*I 0.50000000000000000000000000000000000000 + 14.134725141734693798500899220016435720*I: -1.0030414409401563537431020214488710865 E-18 + 6.3005608230032740890924523626967255390 E-18*I 0.50000000000000000000000000000000000000 + 14.134725141734693798500899220016435720*I: -1.0030414409401563537431020214488710865 E-18 + 6.30056082300327408909245236269 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.161s user 0m0.143s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 20:06:10 2005 Input: Pi/2 / intnum(t=0,Pi/2, 1 / sqrt(1 + sin(t)^2)) Output: ? 1.1981402347355922074399224922803238782 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.017s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 20:06:59 2005 Input: solve(t=14,15, imag(zeta(1/2 + I*t))) Output: ? 14.134725141734693790457251983562470270 ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.022s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:06:15 2005 Input: 2^67*7^78 Output: ? 122083460381589536457650361902716139626214171646982979634125726867530305852842203676672 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:07:07 2005 Input: isprime(1169) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:07:34 2005 Input: ifactor(1169) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: ifactor(1169) ^------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:08:19 2005 Input: factor(1169) Output: ? [7 1] [167 1] ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:08:54 2005 Input: gcd(70,245) Output: ? 35 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:09:07 2005 Input: lcm(70,245) Output: ? 490 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:09:25 2005 Input: bin(16,5) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: bin(16,5) ^--------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: bin(x,y) ===> binomial(x,y) binomial(x,y): binomial coefficient x*(x-1)...*(x-y+1)/y! defined for y in Z and any x. Timing: real 0m0.029s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:09:45 2005 Input: binomial(16,5) Output: ? 4368 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:10:23 2005 Input: mod(16,5) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(16,5) ^--------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.013s user 0m0.003s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:10:39 2005 Input: fibo(10) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: fibo(10) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: fibo(x) ===> fibonacci(x) fibonacci(x): fibonacci number of index x (x C-integer). Timing: real 0m0.017s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:11:15 2005 Input: fibonacci(10) Output: ? 55 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:12:10 2005 Input: for (n=1,8,print(isprime(2*(2*n+i)-1))) Output: ? ? Errors (if any) and Timing Info: *** not an integer argument in an arithmetic function Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:12:50 2005 Input: for (n=1,8,print(isprime(2^(2*n+i)-1))) Output: ? ? Errors (if any) and Timing Info: *** not an integer argument in an arithmetic function Timing: real 0m0.020s user 0m0.006s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:14:20 2005 Input: for (n=1,8,print(isprime(2^i))) Output: ? ? Errors (if any) and Timing Info: *** not an integer argument in an arithmetic function Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:14:44 2005 Input: for (n=1,8,print(isprime(2^n))) Output: ? 1 0 0 0 0 0 0 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:14:58 2005 Input: for (n=1,8,print(isprime(2^n-1))) Output: ? 0 1 1 0 1 0 1 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:15:15 2005 Input: for (n=1,8,print(isprime(2^(2*n+1)-1))) Output: ? 1 1 1 0 0 1 0 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:49:55 2005 Input: 2^70 Output: ? 1180591620717411303424 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Jan 30 23:50:07 2005 Input: 2^170 Output: ? 1496577676626844588240573268701473812127674924007424 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '210.15.' ************** PARI ***************** Host 210.15.195.232 (210.15.195.232) Time: Mon Jan 31 05:47:37 2005 Input: factor(136559246467612200625135091586609781477) Output: ? [10264863799845992369 1] [13303561462711375733 1] ? Errors (if any) and Timing Info: Timing: real 0m0.352s user 0m0.317s sys 0m0.019s '195.5.1' ************** PARI ***************** Host 195.5.13.242 (195.5.13.242) Time: Mon Jan 31 05:58:49 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.006s '195.29.' ************** PARI ***************** Host 195.29.134.214 (195.29.134.214) Time: Mon Jan 31 10:55:39 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.223s user 0m0.007s sys 0m0.006s '24.17.1' ************** PARI ***************** Host 24.17.184.11 (24.17.184.11) Time: Mon Jan 31 22:17:41 2005 Input: FindGroupOrder2 := function (p, s) K := GF(p); v := K ! (4*s); u := K ! (s^2-5); x := u^3; b := 4*x*v; a := (v-u)^3*(3*u+v); A := a/b-2; x := x/v^3; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); return FactoredOrder(E); end function; p:=23917104973173909566916321016011885041962486321502513; s:=7917157863480469; FindGroupOrder2(p,s); Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: FindGroupOrder2:=function(p,s) ^-------------- *** unexpected character: K:=GF(p); ^------- *** unexpected character: v:=K!(4*s); ^--------- *** unexpected character: u:=K!(s^2-5); ^----------- *** unexpected character: x:=u^3; ^----- *** unexpected character: b:=4*x*v; ^------- *** unexpected character: a:=(v-u)^3*(3*u+v); ^----------------- *** unexpected character: A:=a/b-2; ^------- *** unexpected character: x:=x/v^3; ^------- *** unexpected character: b:=x^3+A*x^2+x; ^------------- *** unexpected character: E:=EllipticCurve([0,b* ^-------------------- *** expected character: '=' instead of: returnFactoredOrder(E); ^- *** unexpected character: p:=2391710497317390956 ^-------------------- *** unexpected character: s:=7917157863480469; ^------------------ *** expected character: '=' instead of: FindGroupOrder2(p,s); ^- Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '24.17.1' ************** PARI ***************** Host 24.17.184.11 (24.17.184.11) Time: Mon Jan 31 22:18:09 2005 Input: FindGroupOrder2 := function (p, s) K := GF(p); v := K ! (4*s); u := K ! (s^2-5); x := u^3; b := 4*x*v; a := (v-u)^3*(3*u+v); A := a/b-2; x := x/v^3; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); return FactoredOrder(E); end function; p:=23917104973173909566916321016011885041962486321502513; s:=7917157863480469; FindGroupOrder2(p,s); Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: FindGroupOrder2:=function(p,s) ^-------------- *** unexpected character: K:=GF(p); ^------- *** unexpected character: v:=K!(4*s); ^--------- *** unexpected character: u:=K!(s^2-5); ^----------- *** unexpected character: x:=u^3; ^----- *** unexpected character: b:=4*x*v; ^------- *** unexpected character: a:=(v-u)^3*(3*u+v); ^----------------- *** unexpected character: A:=a/b-2; ^------- *** unexpected character: x:=x/v^3; ^------- *** unexpected character: b:=x^3+A*x^2+x; ^------------- *** unexpected character: E:=EllipticCurve([0,b* ^-------------------- *** expected character: '=' instead of: returnFactoredOrder(E); ^- *** unexpected character: p:=2391710497317390956 ^-------------------- *** unexpected character: s:=7917157863480469; ^------------------ *** expected character: '=' instead of: FindGroupOrder2(p,s); ^- Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Feb 1 00:01:03 2005 Input: phi(24) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: phi(24) ^------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: phi(x) ===> eulerphi(x) eulerphi(x): Euler's totient function of x. Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Feb 1 00:01:18 2005 Input: eulerphi(24) Output: ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Feb 1 00:53:58 2005 Input: legendre(15,71) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: legendre(15,71) ^--------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: legendre(n) ===> pollegendre(n) pollegendre(n,{v=x}): legendre polynomial of degree n (n C-integer), in variable v. Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Feb 1 00:56:13 2005 Input: kronecker(15,71) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '129.242' ************** PARI ***************** Host 129.242.21.77 (129.242.21.77) Time: Tue Feb 1 07:32:33 2005 Input: poldisc(x^5+a*x+b) Output: ? 256*a^5 + 3125*b^4 ? Errors (if any) and Timing Info: Timing: real 0m0.302s user 0m0.009s sys 0m0.008s '81.215.' ************** PARI ***************** Host 81.215.60.142 (81.215.60.142) Time: Tue Feb 1 13:43:24 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.229s user 0m0.008s sys 0m0.009s '158.132' ************** PARI ***************** Host 158.132.12.81 (158.132.12.81) Time: Wed Feb 2 01:08:11 2005 Input: bezout(3,8) Output: ? [3, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.006s sys 0m0.007s '128.119' ************** PARI ***************** Host 128.119.47.37 (128.119.47.37) Time: Wed Feb 2 09:32:34 2005 Input: charactertable(Sym(6)); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: charactertable(Sym(6)); ^-------- Timing: real 0m0.356s user 0m0.004s sys 0m0.009s '137.138' ************** PARI ***************** Host 137.138.48.176 (137.138.48.176) Time: Wed Feb 2 12:37:59 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.005s sys 0m0.010s '129.13.' ************** PARI ***************** Host 129.13.186.4 (129.13.186.4) Time: Wed Feb 2 19:36:05 2005 Input: # Output: ? timer = 1 (on) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '129.13.' ************** PARI ***************** Host 129.13.186.3 (129.13.186.3) Time: Wed Feb 2 19:36:27 2005 Input: factor(11111) Output: ? [41 1] [271 1] ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.006s sys 0m0.005s '129.13.' ************** PARI ***************** Host 129.13.186.4 (129.13.186.4) Time: Wed Feb 2 19:36:45 2005 Input: # factor(11111) Output: ? timer = 1 (on) ? time = 1 ms. [41 1] [271 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '129.27.' ************** PARI ***************** Host 129.27.152.89 (129.27.152.89) Time: Thu Feb 3 11:47:12 2005 Input: SetVerbose("Code", true); SetSeed(1); Output: ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: SetVerbose("Code",tr ^-------------------- *** unknown function or error in formal parameters: SetSeed(1); ^----------- Timing: real 0m0.358s user 0m0.004s sys 0m0.004s '82.227.' ************** PARI ***************** Host 82.227.205.96 (82.227.205.96) Time: Thu Feb 3 17:17:10 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.122s user 0m0.005s sys 0m0.007s '193.198' ************** PARI ***************** Host 193.198.139.111 (193.198.139.111) Time: Thu Feb 3 17:39:38 2005 Input: 54545454454*85 Output: ? 4636363628590 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.007s sys 0m0.006s '66.215.' ************** PARI ***************** Host 66.215.153.89 (66.215.153.89) Time: Thu Feb 3 19:18:19 2005 Input: 4a+3b=4x Output: ? 4 ? Errors (if any) and Timing Info: *** Warning: unused characters: a+3b=4x. Timing: real 0m0.377s user 0m0.008s sys 0m0.008s '131.179' ************** PARI ***************** Host 131.179.33.176 (131.179.33.176) Time: Thu Feb 3 22:06:57 2005 Input: A := Graph< 4 | {1,2}, {2,3}, {3,4}>; B := Graph< 4 | {3,1}, {1,4}, {3,2}>; isIsomorphic(A,B); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: A:=Graph<4|{1,2},{2,3} ^-------------------- *** unexpected character: B:=Graph<4|{3,1},{1,4} ^-------------------- *** expected character: '=' instead of: isIsomorphic(A,B); ^- Timing: real 0m0.319s user 0m0.010s sys 0m0.004s '131.179' ************** PARI ***************** Host 131.179.33.176 (131.179.33.176) Time: Thu Feb 3 22:07:48 2005 Input: A := Graph< 4 | { 1, 2 }, { 2, 3 }, { 3, 1 }, { 2, 4 }>; B := Graph< 4 | { 3, 1 }, {1, 4}, {4, 2}, {2, 3}>; IsIsomorphic(A,B); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: A:=Graph<4|{1,2},{2,3} ^-------------------- *** unexpected character: B:=Graph<4|{3,1},{1,4} ^-------------------- *** expected character: '=' instead of: IsIsomorphic(A,B); ^- Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '128.227' ************** PARI ***************** Host 128.227.43.251 (128.227.43.251) Time: Fri Feb 4 16:59:29 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.294s user 0m0.006s sys 0m0.007s '128.227' ************** PARI ***************** Host 128.227.43.251 (128.227.43.251) Time: Fri Feb 4 16:59:40 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.227' ************** PARI ***************** Host 128.227.43.251 (128.227.43.251) Time: Fri Feb 4 16:59:53 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '216.119' ************** PARI ***************** Host 216.119.143.85 (216.119.143.85) Time: Sat Feb 5 10:20:13 2005 Input: forprime(p=2,1000,if(p%10==7,print(p))) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '216.119' ************** PARI ***************** Host 216.119.143.85 (216.119.143.85) Time: Sat Feb 5 10:21:01 2005 Input: forprime(p=2,1000,if((p mod 10)==7,print(p))) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.338s user 0m0.005s sys 0m0.006s '216.119' ************** PARI ***************** Host 216.119.143.85 (216.119.143.85) Time: Sat Feb 5 10:21:16 2005 Input: forprime(p=2,1000,print(p))) Output: ? 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.014s user 0m0.008s sys 0m0.004s '24.34.5' ************** PARI ***************** Host 24.34.51.110 (24.34.51.110) Time: Sat Feb 5 22:55:49 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '24.34.5' ************** PARI ***************** Host 24.34.51.110 (24.34.51.110) Time: Sat Feb 5 22:55:58 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '24.34.5' ************** PARI ***************** Host 24.34.51.110 (24.34.51.110) Time: Sat Feb 5 22:56:09 2005 Input: 6 Output: ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '24.34.5' ************** PARI ***************** Host 24.34.51.110 (24.34.51.110) Time: Sat Feb 5 22:56:17 2005 Input: 6 Output: ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.007s '24.34.5' ************** PARI ***************** Host 24.34.51.110 (24.34.51.110) Time: Sat Feb 5 22:56:21 2005 Input: 6 Output: ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '195.138' ************** PARI ***************** Host 195.138.130.140 (195.138.130.140) Time: Sun Feb 6 09:58:49 2005 Input: 2x + 5 = 10 Output: ? 2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+5=10. Timing: real 0m0.338s user 0m0.006s sys 0m0.008s '67.67.1' ************** PARI ***************** Host 67.67.10.212 (67.67.10.212) Time: Sun Feb 6 12:31:23 2005 Input: for(a=1,100, for(b=a,100, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.047s user 0m0.026s sys 0m0.005s '67.67.1' ************** PARI ***************** Host 67.67.10.212 (67.67.10.212) Time: Sun Feb 6 12:31:47 2005 Input: for(a=1,200, for(b=a,200, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.092s user 0m0.084s sys 0m0.009s '67.67.1' ************** PARI ***************** Host 67.67.10.212 (67.67.10.212) Time: Sun Feb 6 12:32:00 2005 Input: for(a=1,200, for(b=a,200, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.090s user 0m0.085s sys 0m0.005s '67.67.1' ************** PARI ***************** Host 67.67.10.212 (67.67.10.212) Time: Sun Feb 6 12:32:18 2005 Input: for(a=1,200, for(b=a,200, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.090s user 0m0.085s sys 0m0.005s '67.67.1' ************** PARI ***************** Host 67.67.10.212 (67.67.10.212) Time: Sun Feb 6 12:33:14 2005 Input: for(a=1,200, for(b=a,200, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.090s user 0m0.082s sys 0m0.008s '67.67.1' ************** PARI ***************** Host 67.67.10.212 (67.67.10.212) Time: Sun Feb 6 12:33:34 2005 Input: for(a=1,300, for(b=a,300, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 89,233 ? Errors (if any) and Timing Info: Timing: real 0m0.188s user 0m0.181s sys 0m0.007s '195.5.1' ************** PARI ***************** Host 195.5.13.242 (195.5.13.242) Time: Mon Feb 7 05:13:51 2005 Input: K := FunctionField(IntegerRing(),9); F := FreeAlgebra(K,7); B := [x1^3, x2^2, x3^2, x4^2, r1^2, r2^2, r3^2, -r1+x1+s11*x2+s12*x3+s13*x4, -r2+x1+s21*x2+s22*x3+s23*x4, -r3+x1+s31*x2+s32*x3+s33*x4]; I := ideal; GroebnerBasis(I); Output: ? ? ? ? x2*s11 + (-r1 + (x1 + (x3*s12 + x4*s13))) ? x1 + (s21*x2 + (s22*x3 + (s23*x4 - r2))) ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,s12,s13,s21,s22,s23,s31,s32,s33>:=FunctionField(IntegerRing(),9);. *** incorrect type in comparison. *** Warning: unused characters: ,r2,r3,x1,x2,x3,x4>:=FreeAlgebra(K,7);. *** incorrect type in comparison. *** unexpected character: B:=[x1^3,x2^2,x3^2,x4^ ^-------------------- *** Warning: unused characters: ,. *** Warning: unused characters: ,. *** Warning: unused characters: ];. *** unexpected character: I:=ideal; ^------------ *** unknown function or error in formal parameters: GroebnerBasis(I); ^--- Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '194.69.' ************** PARI ***************** Host 194.69.1.21 (194.69.1.21) Time: Mon Feb 7 07:43:44 2005 Input: 2*(7+9) Output: ? 32 ? Errors (if any) and Timing Info: Timing: real 0m0.232s user 0m0.005s sys 0m0.008s '213.103' ************** PARI ***************** Host 213.103.81.183 (213.103.81.183) Time: Mon Feb 7 12:45:09 2005 Input: func(t) = if(t==0,return(0), z = t+I*t*(1-t); real(z^(I/z-1)*(1+I*(1-2*t)))) intnum(t=0,1,func(t)) Output: ? ? 0.32336743167777876139937008795217044452 ? Errors (if any) and Timing Info: Timing: real 0m3.261s user 0m2.983s sys 0m0.018s '213.103' ************** PARI ***************** Host 213.103.81.183 (213.103.81.183) Time: Mon Feb 7 12:46:18 2005 Input: dec=28; default(realprecision,dec); tol=10^(2.0-dec); L=16; vals=vector(L); res=[1.0,1.0]; vals[1]=res[1]; for(nu=2,L, x0=concat(res[2],0*res[2]); res=OperatorNorm(x0,tol); vals[nu]=res[1]); L2=2*L-1; vv=vector(L2,j, if(j%2==1, vals[(j+1)/2], 0)); for(j=2,L, forstep(k=j, L2+1-j, 2, vv[k]=vv[k]+1/(vv[k+1]-vv[k-1]))); result=vector(L,j, vv[2*j-1]) Output: WARNING: PARI command contains unsafe command 'default', so it will not be executed. '213.103' ************** PARI ***************** Host 213.103.81.183 (213.103.81.183) Time: Mon Feb 7 12:46:42 2005 Input: dec=28;tol=10^(2.0-dec); L=16; vals=vector(L); res=[1.0,1.0]; vals[1]=res[1]; for(nu=2,L, x0=concat(res[2],0*res[2]); res=OperatorNorm(x0,tol); vals[nu]=res[1]); L2=2*L-1; vv=vector(L2,j, if(j%2==1, vals[(j+1)/2], 0)); for(j=2,L, forstep(k=j, L2+1-j, 2, vv[k]=vv[k]+1/(vv[k+1]-vv[k-1]))); result=vector(L,j, vv[2*j-1]) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '213.103' ************** PARI ***************** Host 213.103.81.183 (213.103.81.183) Time: Mon Feb 7 12:47:10 2005 Input: dec=28; tol=10^(2.0-dec); L=16; vals=vector(L); res=[1.0,1.0]; vals[1]=res[1]; for(nu=2,L, x0=concat(res[2],0*res[2]); res=OperatorNorm(x0,tol); vals[nu]=res[1]); L2=2*L-1; vv=vector(L2,j, if(j%2==1, vals[(j+1)/2], 0)); for(j=2,L, forstep(k=j, L2+1-j, 2, vv[k]=vv[k]+1/(vv[k+1]-vv[k-1]))); result=vector(L,j, vv[2*j-1]) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '213.103' ************** PARI ***************** Host 213.103.81.183 (213.103.81.183) Time: Mon Feb 7 12:47:49 2005 Input: Meijer's G function as needed for Problem 9 { prob9G(alfa) = local(s,t,sterm,tprod,tsum,z,n); s=0; t=0; n=0; z=alfa^2/16; sterm=1; tprod=1; tsum=1-log(alfa/2)-psi(alfa+1)+2*psi(1); while (1, s=s+sterm; t=t+tsum*tprod; if (1.0+sterm==1, break); n=n+1; sterm=-sterm*z*(alfa-2*n)*(alfa-2*n+1)/(n*(n+1)*(2*n+1)^2); tprod=-tprod*z*(alfa-2*n+1)*(alfa-2*n+2)/(n^2*(2*n-1)*(2*n+1)); tsum=tsum+1/(alfa-2*n+1)+1/(alfa-2*n+2)+1/n+1/(2*n-1)+1/(2*n+1); ); 2^(alfa)*alfa*(2*Pi*z*s+t) } Numerical derivative of prob9G { dprob9G(alfa) = local(h,dh,d2h); h=10^(-precision(0.0)/5.0); dh=(prob9G(alfa+h)-prob9G(alfa-h))/(2*h); d2h=(prob9G(alfa+2*h)-prob9G(alfa-2*h))/(4*h); (4*dh-d2h)/3 } { timings() = default(realprecision,315); gettime; s=psi(Pi/4); print(gettime); s=psi(Pi/4+0.1); print(gettime); s=prob9G(Pi/4); print(gettime); s=dprob9G(Pi/4); print(gettime); default(realprecision,630); gettime; s=psi(Pi/4); print(gettime); s=psi(Pi/4+0.1); print(gettime); s=prob9G(Pi/4); print(gettime); s=dprob9G(Pi/4); print(gettime); default(realprecision,1260); gettime; s=psi(Pi/4); print(gettime); s=psi(Pi/4+0.1); print(gettime); s=prob9G(Pi/4); print(gettime); s=dprob9G(Pi/4); print(gettime); default(realprecision,2520); gettime; s=psi(Pi/4); print(gettime); s=psi(Pi/4+0.1); print(gettime); s=prob9G(Pi/4); print(gettime); s=dprob9G(Pi/4); print(gettime); default(realprecision,5040); gettime; s=psi(Pi/4); print(gettime); } { p9I(alfa) = (2+sin(10*alfa))*prob9G(alfa); } { dp9I(alfa) = (2+sin(10*alfa))*dprob9G(alfa)+10*cos(10*alfa)*prob9G(alfa); } { secant(x1, fx1, x2, fx2) = x2 - fx2*(x1-x2)/(fx1-fx2) } global digits; digits=28; { Digits(n) = n=ceil(n); if (n>28, digits=n; default(realprecision,n));} { main(final) = default(realprecision,28); x1=Pi/4; fx1=dp9I(x1); print(fx1); x2=x1+fx1/100; fx2=dp9I(x2); print(fx2); while (1, x3=secant(x1,fx1,x2,fx2); acc3=floor(1.62*log(abs(x3-x2))/log(0.1)); write(concat("prob9g.",acc3),x3); print("Error estimate = ",acc3); if (acc3>=final, break); if (2*acc3>4/5*digits, Digits(min(2.5*acc3,1.25*final)); x3=precision(x3,digits)); fx3=dp9I(x3); err=floor(2+log(abs(fx3))/log(0.1)); print("Error bound = ",err," Heap state = ",getheap); Digits(1.62*err); x1=precision(x2,digits); fx1=precision(fx2,digits); x2=precision(x3,digits); fx2=precision(fx3,digits); ); x3 } Output: WARNING: PARI command contains unsafe command 'write', so it will not be executed. '213.103' ************** PARI ***************** Host 213.103.81.183 (213.103.81.183) Time: Mon Feb 7 12:48:24 2005 Input: PARI/GP code for computing 275 digits of the result of Problem 3 Working precision dec=279, 15 days computation time (1.6 GHz processor) Transformation (3.30), truncation point T: (3.31), step size 1/r: (3.32) Power iteration enhanced by Wynn's epsilon algorithm, maxiter = 27 Save as PROBLEM3, run (in the background) with "nice +19 gpout&" View the current state of the output file with "more out" {inprod(x,y) = sum(j=1,N1,real(x[j])*real(y[j])-imag(x[j])*imag(y[j]))} {dig(eps) = if(eps==0,dec,-log(abs(eps))/log(10))} {Wynn(vals,L) = L2=2*L-1; vv=vector(L2,j, if(j%2==1, vals[(j+1)/2], 0)); for(j=2,L, forstep(k=j, L2+1-j, 2, vv[k]=vv[k]+1/(vv[k+1]-vv[k-1]))); vector(L,j, vv[2*j-1])} {problem3(T,r,tol,maxiter) = T=truncation limit, r=1/step, tol=error tolerance h=1/r; N=floor(T*r); N1=N+1; s=vector(N1,k,h*(k-N1)); y=vector(N1); t=vector(N1,k,s[k]+s[k]^3/3); dt=vector(N1,k,h*(1+s[k]^2)); t=Phi1(s) z=vector(N1,k,sqrt(1/2)*(cosh(t[k])-I*sinh(t[k]))); zbar=conj(z); contour z1=vector(N1,k, z[k]-1/2); z2=vector(N1,k, -2*z[k]+7/4); auxiliary vectors ct=vector(N1,k,if(abs(imag(z[k]))<925412,cotan(Pi*z[k]),sign(imag(z[k]))/I)); w=vector(N1,k, -ct[k]*zbar[k]*dt[k]); w[N1]=w[N1]/2; x0=vector(N1,j, 2/(z[j]^2+z[j]))~; x=x0/x0[N1]; wbest=0; wbest0=1; iter=0; while ( abs(wbest-wbest0)>tol & iter log(x) log(x,{flag=0}): natural logarithm of x. flag is optional, and can be 0: default, or 1: calls logagm, computed using the agm. Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '194.8.1' ************** PARI ***************** Host 194.8.16.3 (194.8.16.3) Time: Thu Feb 10 08:50:35 2005 Input: x=log(10) Output: ? 2.3025850929940456840179914546843642075 ? Errors (if any) and Timing Info: Timing: real 0m0.052s user 0m0.008s sys 0m0.003s '194.8.1' ************** PARI ***************** Host 194.8.16.3 (194.8.16.3) Time: Thu Feb 10 08:53:23 2005 Input: sqrt(244140625) Output: ? 15625.000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '194.8.1' ************** PARI ***************** Host 194.8.16.3 (194.8.16.3) Time: Thu Feb 10 10:27:27 2005 Input: @preamble("usepackage{url}") @manual{PARI2, organization = "{The PARI~Group}", title = "{PARI/GP, version {tt 2.1.5}}", year = 2004, address = "Bordeaux", note = "available from url{http://pari.math.u-bordeaux.fr/}" } Output: ? ? ? "{The PARI~Group}" ? "{PARI/GP, version {tt 2.1.5}}" ? 2004 ? "Bordeaux" ? "available from url{http://pari.math.u-bordeaux.fr/}" ? ? ? Errors (if any) and Timing Info: *** unexpected character: @preamble("usepackag ^-------------------- *** unexpected character: @manual{PARI2, ^-------------- *** Warning: unused characters: ,. *** Warning: unused characters: ,. *** Warning: unused characters: ,. *** Warning: unused characters: ,. *** unexpected character: } ^- Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '219.164' ************** PARI ***************** Host 219.164.16.253 (219.164.16.253) Time: Thu Feb 10 18:28:43 2005 Input: factor(205475076796438054403559439583) Output: ? [205475076796438054403559439583 1] ? Errors (if any) and Timing Info: Timing: real 0m0.097s user 0m0.008s sys 0m0.007s '219.164' ************** PARI ***************** Host 219.164.16.253 (219.164.16.253) Time: Thu Feb 10 18:28:53 2005 Input: factor(26728282989179919138288092974997722466051480745835285993159902544918880427506555075521675042606752148965728979736958528648574392124680327324609) Output: ? [26728282989179919138288092974997722466051480745835285993159902544918880427506555075521675042606752148965728979736958528648574392124680327324609 1] ? Errors (if any) and Timing Info: Timing: real 0m0.070s user 0m0.062s sys 0m0.007s '24.70.9' ************** PARI ***************** Host 24.70.95.204 (24.70.95.204) Time: Fri Feb 11 17:17:19 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.358s user 0m0.005s sys 0m0.007s '24.70.9' ************** PARI ***************** Host 24.70.95.204 (24.70.95.204) Time: Fri Feb 11 17:17:33 2005 Input: 8x Output: ? 8 ? Errors (if any) and Timing Info: *** Warning: unused characters: x. Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.194' ************** PARI ***************** Host 128.194.144.133 (128.194.144.133) Time: Fri Feb 11 19:13:39 2005 Input: C := BCHCode(GF(3), 13, 3); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: C:=BCHCode(GF(3),13,3) ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '169.229' ************** PARI ***************** Host 169.229.58.122 (169.229.58.122) Time: Fri Feb 11 19:39:38 2005 Input: contfrac((1+sqrt(5))/2) Output: ? [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2] ? Errors (if any) and Timing Info: Timing: real 0m0.046s user 0m0.006s sys 0m0.006s '169.229' ************** PARI ***************** Host 169.229.58.122 (169.229.58.122) Time: Fri Feb 11 19:39:47 2005 Input: contfrac((1+sqrt(5))/2) Output: ? [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.194' ************** PARI ***************** Host 128.194.144.133 (128.194.144.133) Time: Sat Feb 12 03:07:13 2005 Input: q:=2; m:=10; n:=q^m-1; for d:= 4 to n-1 do; C := BCHCode(GF(q),n,d); C; end for; Output: ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: q:=2; ^--- *** unexpected character: m:=10; ^---- *** unexpected character: n:=q^m-1; ^------- *** unexpected character: ford:=4ton-1do; ^---------- *** unexpected character: C:=BCHCode(GF(q),n,d); ^-------------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '68.67.2' ************** PARI ***************** Host 68.67.22.124 (68.67.22.124) Time: Sun Feb 13 03:53:26 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.336s user 0m0.006s sys 0m0.007s '68.67.2' ************** PARI ***************** Host 68.67.22.124 (68.67.22.124) Time: Sun Feb 13 03:53:41 2005 Input: 1234 Output: ? 1234 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '80.58.3' ************** PARI ***************** Host 80.58.33.107 (80.58.33.107) Time: Sun Feb 13 13:53:02 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.100s user 0m0.009s sys 0m0.005s '68.92.2' ************** PARI ***************** Host 68.92.234.162 (68.92.234.162) Time: Sun Feb 13 14:17:11 2005 Input: factor(2^257-1) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 28233 Killed /usr/bin/gp -q -emacs Timing: real 0m21.235s user 0m20.988s sys 0m0.013s '68.92.2' ************** PARI ***************** Host 68.92.234.162 (68.92.234.162) Time: Sun Feb 13 14:18:46 2005 Input: factor(2^211-1) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 28245 Killed /usr/bin/gp -q -emacs Timing: real 0m21.028s user 0m20.962s sys 0m0.038s '66.63.1' ************** PARI ***************** Host 66.63.133.92 (66.63.133.92) Time: Sun Feb 13 21:23:59 2005 Input: m=[0,1,1,1,1;1,0,c,b,d;1,c,0,a,e;1,b,a,0,f;1,d,e,f,0]; matdet(m) Output: ? ? -2*f*c^2 + ((-2*a + (2*e + 2*f))*b + ((2*a + (-2*e + 2*f))*d + (2*f*a + (2*f*e - 2*f^2))))*c + (-2*e*b^2 + ((2*a + (2*e - 2*f))*d + (2*e*a + (-2*e^2 + 2*f*e)))*b + (-2*a*d^2 + (-2*a^2 + (2*e + 2*f)*a)*d - 2*f*e*a)) ? Errors (if any) and Timing Info: Timing: real 0m0.195s user 0m0.005s sys 0m0.008s '66.63.1' ************** PARI ***************** Host 66.63.133.92 (66.63.133.92) Time: Sun Feb 13 21:45:10 2005 Input: m=[0,1,1,1,1;1,0,c,b,d;1,c,0,a,e;1,b,a,0,f;1,d,e,f,0]; n=matdet(m) n-(-2*a*d^2-2*b*e^2-2*c*f^2-2*d*a^2-2*e*b^2-2*f*c^2-2*a*b*c-2*a*e*f-2*b*d*f-2*c*d*e+2*a*(b*(d+e)+c*(d+f)*d*(e+f))+2*b*(c*(e+f)+e*(d+f))+2*c*(f*(d+e))) Output: ? ? -2*f*c^2 + ((-2*a + (2*e + 2*f))*b + ((2*a + (-2*e + 2*f))*d + (2*f*a + (2*f*e - 2*f^2))))*c + (-2*e*b^2 + ((2*a + (2*e - 2*f))*d + (2*e*a + (-2*e^2 + 2*f*e)))*b + (-2*a*d^2 + (-2*a^2 + (2*e + 2*f)*a)*d - 2*f*e*a)) ? ((-2*e - 2*f)*a*d^2 + (-2*f*e + (-2*f^2 + 2))*a*d + 2*f*a)*c + (2*e + 2*f)*a*d ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.006s sys 0m0.006s '66.63.1' ************** PARI ***************** Host 66.63.133.92 (66.63.133.92) Time: Sun Feb 13 21:45:42 2005 Input: m=[0,1,1,1,1;1,0,c,b,d;1,c,0,a,e;1,b,a,0,f;1,d,e,f,0]; n=matdet(m); n-(-2*a*d^2-2*b*e^2-2*c*f^2-2*d*a^2-2*e*b^2-2*f*c^2-2*a*b*c-2*a*e*f-2*b*d*f-2*c*d*e+2*a*(b*(d+e)+c*(d+f)*d*(e+f))+2*b*(c*(e+f)+e*(d+f))+2*c*(f*(d+e))) Output: ? ? ? ((-2*e - 2*f)*a*d^2 + (-2*f*e + (-2*f^2 + 2))*a*d + 2*f*a)*c + (2*e + 2*f)*a*d ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '66.63.1' ************** PARI ***************** Host 66.63.133.92 (66.63.133.92) Time: Sun Feb 13 21:46:37 2005 Input: m=[0,1,1,1,1;1,0,c,b,d;1,c,0,a,e;1,b,a,0,f;1,d,e,f,0]; n=matdet(m); p=(-2*a*d^2-2*b*e^2-2*c*f^2-2*d*a^2-2*e*b^2-2*f*c^2-2*a*b*c-2*a*e*f-2*b*d*f-2*c*d*e+2*a*(b*(d+e)+c*(d+f)*d*(e+f))+2*b*(c*(e+f)+e*(d+f))+2*c*(f*(d+e))); n-p Output: ? ? ? ? ((-2*e - 2*f)*a*d^2 + (-2*f*e + (-2*f^2 + 2))*a*d + 2*f*a)*c + (2*e + 2*f)*a*d ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '66.63.1' ************** PARI ***************** Host 66.63.133.92 (66.63.133.92) Time: Sun Feb 13 21:48:48 2005 Input: m=[0,1,1,1,1;1,0,c,b,d;1,c,0,a,e;1,b,a,0,f;1,d,e,f,0]; n=matdet(m) Output: ? ? -2*f*c^2 + ((-2*a + (2*e + 2*f))*b + ((2*a + (-2*e + 2*f))*d + (2*f*a + (2*f*e - 2*f^2))))*c + (-2*e*b^2 + ((2*a + (2*e - 2*f))*d + (2*e*a + (-2*e^2 + 2*f*e)))*b + (-2*a*d^2 + (-2*a^2 + (2*e + 2*f)*a)*d - 2*f*e*a)) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '66.63.1' ************** PARI ***************** Host 66.63.133.92 (66.63.133.92) Time: Sun Feb 13 22:01:19 2005 Input: m=[0,1,1,1,1;1,0,c,b,d;1,c,0,a,e;1,b,a,0,f;1,d,e,f,0]; n=matdet(m) p=-2*a*d^2-2*b*e^2-2*c*f^2-2*d*a^2-2*e*b^2-2*f*c^2-2*a*b*c-2*a*e*f-2*b*d*f-2*c*d*e+2*a*(b*(d+e)+c*(d+f)+d*(e+f))+2*b*(c*(e+f)+e*(d+f))+2*c*(f*(d+e)); n-p Output: ? ? -2*f*c^2 + ((-2*a + (2*e + 2*f))*b + ((2*a + (-2*e + 2*f))*d + (2*f*a + (2*f*e - 2*f^2))))*c + (-2*e*b^2 + ((2*a + (2*e - 2*f))*d + (2*e*a + (-2*e^2 + 2*f*e)))*b + (-2*a*d^2 + (-2*a^2 + (2*e + 2*f)*a)*d - 2*f*e*a)) ? ? 0 ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '83.112.' ************** PARI ***************** Host 83.112.239.128 (83.112.239.128) Time: Mon Feb 14 14:34:48 2005 Input: .5^(2^24) Output: ? 5.4987797426189993226257377747879918011 E-5050446 ? Errors (if any) and Timing Info: Timing: real 0m0.331s user 0m0.005s sys 0m0.008s '83.112.' ************** PARI ***************** Host 83.112.239.128 (83.112.239.128) Time: Mon Feb 14 14:35:27 2005 Input: .5^(2^52 ) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: .5^(2^52 ^ *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '83.112.' ************** PARI ***************** Host 83.112.239.128 (83.112.239.128) Time: Mon Feb 14 14:35:38 2005 Input: .5^(2^52) Output: ? ? Errors (if any) and Timing Info: *** exponent overflow Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '83.112.' ************** PARI ***************** Host 83.112.239.128 (83.112.239.128) Time: Mon Feb 14 14:36:18 2005 Input: .5^(2^31) Output: ? 5.6766155260037313438164181629489689531 E-646456994 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '83.112.' ************** PARI ***************** Host 83.112.239.128 (83.112.239.128) Time: Mon Feb 14 14:37:16 2005 Input: 1/(2^(2^31)) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '83.112.' ************** PARI ***************** Host 83.112.239.128 (83.112.239.128) Time: Mon Feb 14 14:38:01 2005 Input: (1/2)^(2^31)) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ). *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '83.112.' ************** PARI ***************** Host 83.112.239.128 (83.112.239.128) Time: Mon Feb 14 14:38:21 2005 Input: (1/2)^(2^8)) Output: ? 1/115792089237316195423570985008687907853269984665640564039457584007913129639936 ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '83.112.' ************** PARI ***************** Host 83.112.239.128 (83.112.239.128) Time: Mon Feb 14 14:38:48 2005 Input: (1/2)^(2^8) Output: ? 1/115792089237316195423570985008687907853269984665640564039457584007913129639936 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '83.112.' ************** PARI ***************** Host 83.112.239.128 (83.112.239.128) Time: Mon Feb 14 14:38:59 2005 Input: (1/2)^(2^30) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.011s user 0m0.009s sys 0m0.004s '80.58.4' ************** PARI ***************** Host 80.58.41.235 (80.58.41.235) Time: Mon Feb 14 14:44:16 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s 'form' ************** PARI ***************** Host form (140.247.29.178) Time: Mon Feb 14 16:08:30 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.179s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Feb 14 19:21:51 2005 Input: Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Feb 14 19:22:02 2005 Input: 3+2 Output: ? ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '158.109' ************** PARI ***************** Host 158.109.66.41 (158.109.66.41) Time: Tue Feb 15 03:39:34 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.010s sys 0m0.002s '158.109' ************** PARI ***************** Host 158.109.66.41 (158.109.66.41) Time: Tue Feb 15 03:39:38 2005 Input: "Replace this by some code, then RHAREHREHWE[PARI] or [MAGMA]!" Output: ? "Replace this by some code, then RHAREHREHWE[PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.006s 'form' ************** PARI ***************** Host form (140.247.29.178) Time: Tue Feb 15 14:23:15 2005 Input: e=ellinit([1,2,0,3,5]) Output: ? [1, 2, 0, 3, 5, 9, 6, 20, 36, -63, -3105, -5724, 9261/212, [-2.0000000000000000000000000000000000000, -0.12500000000000000000000000000000000000 - 1.5761900266148114414035782293166390374*I, -0.12500000000000000000000000000000000000 + 1.5761900266148114414035782293166390374*I]~, 3.1990540814167761218801980573647038988, -1.5995270407083880609400990286823519494 + 1.0351878986599847645175181735856514838*I, -1.5828061291933348105050569410853063538 + 5.264988316753567356 E-39*I, 0.79140306459666740525252847054265317690 - 1.4942211925153228296312781359243169145*I, 3.3116220722414802901484104346835229995] ? Errors (if any) and Timing Info: Timing: real 0m0.245s user 0m0.007s sys 0m0.010s 'form' ************** PARI ***************** Host form (140.247.29.178) Time: Tue Feb 15 14:23:27 2005 Input: e=ellinit([1,2,0,3,5]); e.disc Output: ? ? -5724 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.006s 'form' ************** PARI ***************** Host form (140.247.29.178) Time: Tue Feb 15 14:23:35 2005 Input: e=ellinit([1,2,0,3,5]); e.disc; elltors(e) Output: ? ? ? [2, [2], [[-2, 1]]] ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.008s sys 0m0.008s 'form' ************** PARI ***************** Host form (140.247.29.178) Time: Tue Feb 15 14:23:54 2005 Input: e=ellinit([1,2,0,3,5]); print(e.disc); print(elltors(e)); print(ellglobalred(e)[1]); Output: ? ? -5724 ? [2, [2], [[-2, 1]]] ? 954 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.011s sys 0m0.005s '62.254.' ************** PARI ***************** Host 62.254.0.36 (62.254.0.36) Time: Tue Feb 15 17:51:16 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Feb 15 20:03:03 2005 Input: 27*27 Output: ? 729 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Feb 15 20:04:15 2005 Input: 27*27 1./7 Output: ? 729 ? 0.14285714285714285714285714285714285714 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Feb 15 20:15:28 2005 Input: 27*27 1./7 nextprime(46) Output: ? 729 ? 0.14285714285714285714285714285714285714 ? 47 ? Errors (if any) and Timing Info: Timing: real 0m0.050s user 0m0.003s sys 0m0.010s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Feb 15 20:15:36 2005 Input: 27*27 1./7 nextprime(48) Output: ? 729 ? 0.14285714285714285714285714285714285714 ? 53 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Feb 15 22:55:07 2005 Input: Q:=Integers(); P:=PolynomialRing(Q); f:=x^4+1; Kf := NumberField(f); p:=35277617; r:=3464837; q:=143529258889630077742095907121980388447593; a1:=298986817339011281033; b1:=-147338350680808558475; a2:=93203925976548341036; b2:=434121970040227662621; n:=Integers()!Norm((-1951601+35277617)*(a1+b1*a)+1*(a2+b2*a)); XGCD(a1-b1*r,p); (b2*r-a2)*-9353410 mod p; Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: Q:=Integers(); ^------------ *** unexpected character: P:=PolynomialRing(Q); ^-------------------- *** unexpected character: f:=x^4+1; ^------- *** unexpected character: Kf:=NumberField(f); ^----------------- *** unexpected character: p:=35277617; ^---------- *** unexpected character: r:=3464837; ^--------- *** unexpected character: q:=1435292588896300777 ^-------------------- *** unexpected character: a1:=2989868173390112810 ^-------------------- *** unexpected character: b1:=-147338350680808558 ^-------------------- *** unexpected character: a2:=9320392597654834103 ^-------------------- *** unexpected character: b2:=4341219700402276626 ^-------------------- *** unexpected character: n:=Integers()!Norm((-1 ^-------------------- *** expected character: ',' instead of: XGCD(a1-b1*r,p); ^--------- *** Warning: unused characters: modp;. Timing: real 0m0.020s user 0m0.006s sys 0m0.007s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Feb 15 23:10:06 2005 Input: Q:=Integers(); P:=PolynomialRing(Q); f:=x^4+1; Kf := NumberField(f); p:=35277617; r:=3464837; q:=143529258889630077742095907121980388447593; a1:=298986817339011281033; b1:=-147338350680808558475; a2:=93203925976548341036; b2:=434121970040227662621; n:=Integers()!Norm((31826864-2*p)*(a1+b1*a)+3*(a2+b2*a)); Log(2,(n div q) div p); 31826864-0*p; Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: Q:=Integers(); ^------------ *** unexpected character: P:=PolynomialRing(Q); ^-------------------- *** unexpected character: f:=x^4+1; ^------- *** unexpected character: Kf:=NumberField(f); ^----------------- *** unexpected character: p:=35277617; ^---------- *** unexpected character: r:=3464837; ^--------- *** unexpected character: q:=1435292588896300777 ^-------------------- *** unexpected character: a1:=2989868173390112810 ^-------------------- *** unexpected character: b1:=-147338350680808558 ^-------------------- *** unexpected character: a2:=9320392597654834103 ^-------------------- *** unexpected character: b2:=4341219700402276626 ^-------------------- *** unexpected character: n:=Integers()!Norm((31 ^-------------------- *** expected character: ',' instead of: Log(2,(ndivq)divp); ^------ Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '128.243' ************** PARI ***************** Host 128.243.220.41 (128.243.220.41) Time: Wed Feb 16 08:22:12 2005 Input: C := ComplexField(); R := PowerSeriesRing(C); Derivative(Eisenstein(4, z)); z^(1/6); Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: C:=ComplexField(); ^----------------- *** unexpected character: R:=PowerSeriesRing(C) ^-------------------- *** unknown function or error in formal parameters: Derivative( *** Eisenstein(4,z)); ^----------------- *** negative exponent in glog. Timing: real 0m0.456s user 0m0.010s sys 0m0.012s '163.1.1' ************** PARI ***************** Host 163.1.168.218 (163.1.168.218) Time: Wed Feb 16 17:01:59 2005 Input: 2^10 Output: ? 1024 ? Errors (if any) and Timing Info: Timing: real 0m0.203s user 0m0.006s sys 0m0.006s '160.39.' ************** PARI ***************** Host 160.39.38.146 (160.39.38.146) Time: Wed Feb 16 20:06:12 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '160.39.' ************** PARI ***************** Host 160.39.38.146 (160.39.38.146) Time: Wed Feb 16 20:06:25 2005 Input: d Output: ? d ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '160.39.' ************** PARI ***************** Host 160.39.38.146 (160.39.38.146) Time: Wed Feb 16 20:06:37 2005 Input: default() Output: WARNING: PARI command contains unsafe command 'default', so it will not be executed. '160.39.' ************** PARI ***************** Host 160.39.38.146 (160.39.38.146) Time: Wed Feb 16 20:06:54 2005 Input: default(colors) Output: WARNING: PARI command contains unsafe command 'default', so it will not be executed. '160.39.' ************** PARI ***************** Host 160.39.38.146 (160.39.38.146) Time: Wed Feb 16 20:07:18 2005 Input: d Output: ? d ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '158.109' ************** PARI ***************** Host 158.109.66.129 (158.109.66.129) Time: Thu Feb 17 04:50:35 2005 Input: hola Output: ? hola ? Errors (if any) and Timing Info: Timing: real 0m0.253s user 0m0.005s sys 0m0.008s '158.109' ************** PARI ***************** Host 158.109.66.129 (158.109.66.129) Time: Thu Feb 17 04:50:38 2005 Input: hola Output: ? hola ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '137.43.' ************** PARI ***************** Host 137.43.122.54 (137.43.122.54) Time: Thu Feb 17 06:08:55 2005 Input: GolayCode(GF(2),true); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: GolayCode(GF(2),true); ^------------ Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '212.106' ************** PARI ***************** Host 212.106.243.10 (212.106.243.10) Time: Thu Feb 17 10:45:52 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.632s user 0m0.010s sys 0m0.010s '140.247' ************** PARI ***************** Host 140.247.243.16 (140.247.243.16) Time: Thu Feb 17 11:04:49 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.008s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.243.16 (140.247.243.16) Time: Thu Feb 17 11:04:54 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.243.16 (140.247.243.16) Time: Thu Feb 17 11:05:12 2005 Input: factor(9809843835843509838509345) Output: ? [5 1] [83 1] [199 1] [563 1] [7121 1] [29628627921059 1] ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.007s sys 0m0.008s '80.58.3' ************** PARI ***************** Host 80.58.33.107 (80.58.33.107) Time: Thu Feb 17 16:17:06 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '80.58.3' ************** PARI ***************** Host 80.58.33.107 (80.58.33.107) Time: Thu Feb 17 16:17:22 2005 Input: x=3+3 Output: ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '129.105' ************** PARI ***************** Host 129.105.81.140 (129.105.81.140) Time: Thu Feb 17 17:27:12 2005 Input: K := NumberField(2*x^2-3); // doesn't have to be monic > 2*a^2 - 3; 0 > K; Number Field with defining polynomial x^2 - 3/2 over the Rational Field > O := RingOfIntegers(K); > O; Output: ? ? ? 0 ? ? NumberFieldwithdefiningpolynomialx^2 - 3/2 ? Field ? ? ? Errors (if any) and Timing Info: *** unexpected character: K:=NumberField(2*x^2- ^-------------------- *** unexpected character: >2*a^2-3; ^--------- *** unexpected character: >K; ^--- *** Warning: unused characters: overtheRational. *** unexpected character: >O:=RingOfIntegers(K ^-------------------- *** unexpected character: >O; ^--- Timing: real 0m0.035s user 0m0.006s sys 0m0.006s '129.105' ************** PARI ***************** Host 129.105.81.140 (129.105.81.140) Time: Thu Feb 17 17:27:25 2005 Input: > K := NumberField(2*x^2-3); // doesn't have to be monic > 2*a^2 - 3; 0 > K; Number Field with defining polynomial x^2 - 3/2 over the Rational Field > O := RingOfIntegers(K); > O; Output: ? ? ? 0 ? ? NumberFieldwithdefiningpolynomialx^2 - 3/2 ? Field ? ? ? Errors (if any) and Timing Info: *** unexpected character: >K:=NumberField(2 ^-------------------- *** unexpected character: >2*a^2-3; ^--------- *** unexpected character: >K; ^--- *** Warning: unused characters: overtheRational. *** unexpected character: >O:=RingOfIntegers(K ^-------------------- *** unexpected character: >O; ^--- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '129.105' ************** PARI ***************** Host 129.105.81.140 (129.105.81.140) Time: Thu Feb 17 17:27:39 2005 Input: > K := NumberField(2*x^2-3); // doesn't have to be monic > 2*a^2 - 3; 0 > K; Number Field with defining polynomial x^2 - 3/2 over the Rational Field > O := RingOfIntegers(K); > O; Output: ? ? ? 0 ? ? NumberFieldwithdefiningpolynomialx^2 - 3/2 ? Field ? ? ? Errors (if any) and Timing Info: *** unexpected character: >K:=NumberField(2 ^-------------------- *** unexpected character: >2*a^2-3; ^--------- *** unexpected character: >K; ^--- *** Warning: unused characters: overtheRational. *** unexpected character: >O:=RingOfIntegers(K ^-------------------- *** unexpected character: >O; ^--- Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '129.105' ************** PARI ***************** Host 129.105.81.140 (129.105.81.140) Time: Thu Feb 17 17:32:23 2005 Input: > RingOfIntegers(K); Maximal Equation Order with defining polynomial x^3 - 2 over ZZ > RingOfIntegers(L); Maximal Equation Order with defining polynomial x^2 + [0, -1, 0] over its ground order Output: ? ? MaximalEquationOrderwithdefiningpolynomialx^3 - 2 ? ? MaximalEquationOrderwithdefiningpolynomialx^2 + [0, -1, 0] ? overitsgroundorder ? Errors (if any) and Timing Info: *** unexpected character: >RingOfIntegers(K); ^------------------- *** Warning: unused characters: overZZ. *** unexpected character: >RingOfIntegers(L); ^------------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '129.105' ************** PARI ***************** Host 129.105.81.140 (129.105.81.140) Time: Thu Feb 17 17:35:30 2005 Input: K:=NumberField(x^3-2); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: K:=NumberField(x^3-2); ^-------------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '129.105' ************** PARI ***************** Host 129.105.81.140 (129.105.81.140) Time: Thu Feb 17 17:35:52 2005 Input: K:=NumberField(x^3-2); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: K:=NumberField(x^3-2) ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '129.105' ************** PARI ***************** Host 129.105.81.140 (129.105.81.140) Time: Thu Feb 17 17:36:20 2005 Input: K:=NumberField(x^3-2); RingofIntegers(K); Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: K:=NumberField(x^3-2) ^-------------------- *** expected character: '=' instead of: RingofIntegers(K); ^- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '129.105' ************** PARI ***************** Host 129.105.81.140 (129.105.81.140) Time: Thu Feb 17 17:36:44 2005 Input: K:=NumberField(x^3-2); O:=RingofIntegers(K); O; Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: K:=NumberField(x^3-2) ^-------------------- *** expected character: '(' instead of: O:=RingofIntegers(K); ^-------------------- *** expected character: '(' instead of: O; ^- Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '164.223' ************** PARI ***************** Host 164.223.72.7 (164.223.72.7) Time: Fri Feb 18 19:36:55 2005 Input: 231! Output: ? 1792233667382633521618843263044232513197622942259968207385215805123682159320161029848328112148883186161436034535802659466205111867109614573242316954383604389464524535467759401326264883566523043560811873179996072188155290081861628010250468430411854935707396605833540921031884571521279145124581094374547412403086564118143957940727734634769439112260383017302489106932716079961487372942529947238400000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.211s user 0m0.011s sys 0m0.011s '69.140.' ************** PARI ***************** Host 69.140.164.71 (69.140.164.71) Time: Fri Feb 18 20:06:15 2005 Input: 1/999999999999999999991 Output: ? 1/999999999999999999991 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.006s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Sat Feb 19 10:24:37 2005 Input: G:=CyclicGroup(4); G; Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: G:=CyclicGroup(4); ^---------------- Timing: real 0m0.246s user 0m0.006s sys 0m0.008s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Sat Feb 19 11:29:11 2005 Input: G:=CyclicGroup(2); W:=WreathProduct(G, Sym(3)); S:=Subgroups(W); K:=sub; Q:=quo; IsIsomorphic(Q, DirectProduct(CyclicGroup(2),CyclicGroup(2))); Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: G:=CyclicGroup(2); ^---------------- *** unexpected character: W:=WreathProduct(G,Sym ^-------------------- *** unexpected character: S:=Subgroups(W); ^-------------- *** unexpected character: K:=sub; Q:=quo; IsIsomorphic(Q, DirectProduct(CyclicGroup(2),CyclicGroup(2))); Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: G:=CyclicGroup(2); ^---------------- *** unexpected character: W:=WreathProduct(G,Sym ^-------------------- *** unexpected character: S:=Subgroups(W); ^-------------- *** unexpected character: K:=sub0, even and odd distinguished by j%2: p=a*b;z=if(j%2,c+s*floor((n+v*(p-c))/w),c%s); m=if(j%2,2*p-1,-s);g=a*r+b*o+s*z;y=4*p*n;x=g*g-y; while(z>m&&j%2*x>=0, x decreases for odd j if(issquare(x,&h),S=concat(S,[(g+h),(g-h)]/2/a)); k=k+1;z=z-s;g=g-v;x=g*g-y); end test loop j=j+1;q=floor((d-j%2)/a);t=d-q*a;d=a;a=t; Euclid t=e-q*b;e=b;b=t;t=f-q*c;f=c;c=t); now do last j: z=c%s;while(z>-s,if(o>z*d,S=concat(S,n/(o-z*d)));z=z-s); m=1;S=vecsort(S);for(i=1,length(S),t=S[i];if(n>t&&t>m &&t==floor(t)&&n%t==0&&t%s==r,m=t;T=concat(T,t))); [j,k,T])} j=links,k=tests,T={t;t|n,n>t>1,t%s=r} tests: m=121; increase for a bigger workout {ChLenstra(n,r,s)=local(S,T,t); S=divisors(n);T=[];for(i=2,length(S)-1,t=S[i]; if(t%s==r,T=concat(T,t)));S=Lenstra(n,r,s)[3]; if(S!=T,print([n,r,s,S,T]));T} check m>n>s>r>0,gcd(r,s)=1,n%s!=0: {for(n=3,m-1,for(s=2,n-1,for(r=1,s-1, if(gcd(r,s)==1&&n%s!=0,ChLenstra(n,r,s)))))} a couple of 100-digits supercritical factorizations: r=137; s=10^35; n=((2^61-1)*s+r)*((2^31-1)*s+r)*53123477777; print(Lenstra(n,r,s)); check that both factors appear r=1; n=(3*s+r)*(5*s+r)*(11*s+r)*137; print(Lenstra(n,r,s)); check that 7 factors appear Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '219.65.' ************** PARI ***************** Host 219.65.108.176 (219.65.108.176) Time: Sun Feb 20 22:53:45 2005 Input: CP 4.2.11, corrected by DB, 10 Jan 2002 {Lenstra(n,r,s)= usage: 00, even and odd distinguished by j%2: p=a*b;z=if(j%2,c+s*floor((n+v*(p-c))/w),c%s); m=if(j%2,2*p-1,-s);g=a*r+b*o+s*z;y=4*p*n;x=g*g-y; while(z>m&&j%2*x>=0, x decreases for odd j if(issquare(x,&h),S=concat(S,[(g+h),(g-h)]/2/a)); k=k+1;z=z-s;g=g-v;x=g*g-y); end test loop j=j+1;q=floor((d-j%2)/a);t=d-q*a;d=a;a=t; Euclid t=e-q*b;e=b;b=t;t=f-q*c;f=c;c=t); now do last j: z=c%s;while(z>-s,if(o>z*d,S=concat(S,n/(o-z*d)));z=z-s); m=1;S=vecsort(S);for(i=1,length(S),t=S[i];if(n>t&&t>m &&t==floor(t)&&n%t==0&&t%s==r,m=t;T=concat(T,t))); [j,k,T])} j=links,k=tests,T={t;t|n,n>t>1,t%s=r} tests: m=121; increase for a bigger workout {ChLenstra(n,r,s)=local(S,T,t); S=divisors(n);T=[];for(i=2,length(S)-1,t=S[i]; if(t%s==r,T=concat(T,t)));S=Lenstra(n,r,s)[3]; if(S!=T,print([n,r,s,S,T]));T} check m>n>s>r>0,gcd(r,s)=1,n%s!=0: {for(n=3,m-1,for(s=2,n-1,for(r=1,s-1, if(gcd(r,s)==1&&n%s!=0,ChLenstra(n,r,s)))))} a couple of 100-digits supercritical factorizations: r=137; s=10^35; n=((2^61-1)*s+r)*((2^31-1)*s+r)*53123477777; print(Lenstra(n,r,s)); check that both factors appear Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '158.109' ************** PARI ***************** Host 158.109.66.115 (158.109.66.115) Time: Mon Feb 21 05:25:49 2005 Input: l:=[3,2,5]; Sort(l); Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: l:=[3,2,5]; ^--------- *** expected character: '=' instead of: Sort(l); ^- Timing: real 0m0.352s user 0m0.007s sys 0m0.012s '62.173.' ************** PARI ***************** Host 62.173.69.212 (62.173.69.212) Time: Mon Feb 21 08:34:07 2005 Input: ((2x-4)/x)-(5/(x+1)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ((2x-4)/x)-(5/(x+1)) ^----------------- Timing: real 0m0.393s user 0m0.009s sys 0m0.012s '62.173.' ************** PARI ***************** Host 62.173.69.212 (62.173.69.212) Time: Mon Feb 21 08:34:30 2005 Input: ((2x-4)/x)-(5/(x+1))=0 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ((2x-4)/x)-(5/(x+1))=0 ^------------------- Timing: real 0m0.095s user 0m0.005s sys 0m0.010s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Mon Feb 21 10:02:57 2005 Input: W:=WreathProduct(CyclicGroup(2),Sym(3)); K:=sub; IsIsomorphic(K, DihedralGroup(4)); IsIsomorphic(K, DirectProduct(CyclicGroup(4), CyclicGroup(2))); IsIsomorphic(K, DirectProduct(DirectProduct(CyclicGroup(2),CyclicGroup(2)),CyclicGroup(2))); Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: W:=WreathProduct(Cycli ^-------------------- *** unexpected character: K:=subLat Output: ? ? Errors (if any) and Timing Info: *** unexpected character: Lattice(n,Q)->Lat ^---- Timing: real 0m0.759s user 0m0.008s sys 0m0.009s '80.230.' ************** PARI ***************** Host 80.230.114.38 (80.230.114.38) Time: Mon Feb 21 13:30:08 2005 Input: Lattice(3,Q)->Lat Output: ? ? Errors (if any) and Timing Info: *** unexpected character: Lattice(3,Q)->Lat ^---- Timing: real 0m0.019s user 0m0.004s sys 0m0.007s '80.58.5' ************** PARI ***************** Host 80.58.50.107 (80.58.50.107) Time: Mon Feb 21 16:21:29 2005 Input: K:=GF(4); K; m := MatrixRing(K,2); m; Mt := sub < m | Trace(0) >; K![2,2]; Mt; Mf := sub < m | m[1] eq m[2] >; Output: ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: K:=GF(4); ^-------- *** unexpected character: m:=MatrixRing(K,2); ^----------------- *** unexpected character: Mt:=sub; ^----------------- *** this should be an integer: K![2,2]; ^-------- *** unexpected character: Mf:=sub; ^------------------- Timing: real 0m0.683s user 0m0.008s sys 0m0.008s '80.58.5' ************** PARI ***************** Host 80.58.50.107 (80.58.50.107) Time: Mon Feb 21 16:21:51 2005 Input: K:=GF(4); K; m := MatrixRing(K,2); m; Mt := sub < m | Trace(0) >; K![0,2]; Mt; Mf := sub < m | m[1] eq m[2] >; Output: ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: K:=GF(4); ^-------- *** unexpected character: m:=MatrixRing(K,2); ^----------------- *** unexpected character: Mt:=sub; ^----------------- *** this should be an integer: K![0,2]; ^-------- *** unexpected character: Mf:=sub; ^------------------- Timing: real 0m0.117s user 0m0.008s sys 0m0.005s '80.58.5' ************** PARI ***************** Host 80.58.50.107 (80.58.50.107) Time: Mon Feb 21 16:22:11 2005 Input: K:=GF(4); K; m := MatrixRing(K,2); m; Mt := sub < m | Trace(0) >; Mt; Mf := sub < m | m[1] eq m[2] >; Output: ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: K:=GF(4); ^-------- *** unexpected character: m:=MatrixRing(K,2); ^----------------- *** unexpected character: Mt:=sub; ^----------------- *** unexpected character: Mf:=sub; ^------------------- Timing: real 0m0.180s user 0m0.006s sys 0m0.013s '80.58.5' ************** PARI ***************** Host 80.58.50.107 (80.58.50.107) Time: Mon Feb 21 16:23:17 2005 Input: K:=GF(4); K; m := MatrixRing(K,2); m; Mt := sub < m | Trace(0) >; Mt; Output: ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: K:=GF(4); ^-------- *** unexpected character: m:=MatrixRing(K,2); ^----------------- *** unexpected character: Mt:=sub; ^----------------- Timing: real 0m0.017s user 0m0.007s sys 0m0.008s '80.58.5' ************** PARI ***************** Host 80.58.50.107 (80.58.50.107) Time: Mon Feb 21 16:24:06 2005 Input: K:=GF(4); K; m := MatrixRing(K,2); m; Mt := sub < m | Trace(0) >; Mt; K![0,0]; Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: K:=GF(4); ^-------- *** unexpected character: m:=MatrixRing(K,2); ^----------------- *** unexpected character: Mt:=sub; ^----------------- *** this should be an integer: K![0,0]; ^-------- Timing: real 0m0.184s user 0m0.006s sys 0m0.007s '155.207' ************** PARI ***************** Host 155.207.209.187 (155.207.209.187) Time: Mon Feb 21 19:17:08 2005 Input: > R := PolynomialRing(Integers()); > K := NumberField(x^4 - 4*x^2 + 1); > UnitEquation(a,-a,a^2*(a^2-3)); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: >R:=PolynomialRin ^-------------------- *** unexpected character: >K:=NumberField(x ^-------------------- *** unexpected character: >UnitEquation(a,-a,a ^-------------------- Timing: real 0m0.230s user 0m0.008s sys 0m0.003s '18.241.' ************** PARI ***************** Host 18.241.6.162 (18.241.6.162) Time: Mon Feb 21 22:38:26 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.006s sys 0m0.005s '18.241.' ************** PARI ***************** Host 18.241.6.162 (18.241.6.162) Time: Mon Feb 21 22:38:27 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '203.134' ************** PARI ***************** Host 203.134.57.63 (203.134.57.63) Time: Tue Feb 22 02:45:49 2005 Input: GP-PARI Output: ? GP - PARI ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.006s sys 0m0.007s '203.134' ************** PARI ***************** Host 203.134.57.63 (203.134.57.63) Time: Tue Feb 22 02:46:56 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '203.134' ************** PARI ***************** Host 203.134.57.63 (203.134.57.63) Time: Tue Feb 22 02:47:17 2005 Input: isprime(1169) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.073s user 0m0.006s sys 0m0.004s '203.134' ************** PARI ***************** Host 203.134.57.63 (203.134.57.63) Time: Tue Feb 22 02:47:49 2005 Input: fibonacci(10) Output: ? 55 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '18.98.3' ************** PARI ***************** Host 18.98.3.54 (18.98.3.54) Time: Tue Feb 22 03:03:59 2005 Input: 2 + 2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '18.98.3' ************** PARI ***************** Host 18.98.3.54 (18.98.3.54) Time: Tue Feb 22 03:09:15 2005 Input: max(2,3) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '18.98.3' ************** PARI ***************** Host 18.98.3.54 (18.98.3.54) Time: Tue Feb 22 03:09:25 2005 Input: max(2,3) min(5,7) Output: ? 3 ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '158.109' ************** PARI ***************** Host 158.109.66.41 (158.109.66.41) Time: Tue Feb 22 07:18:49 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.392s user 0m0.006s sys 0m0.008s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:18:58 2005 Input: isprime(154875132165) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.287s user 0m0.005s sys 0m0.009s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:19:08 2005 Input: 23! Output: ? 25852016738884976640000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:19:15 2005 Input: 232! Output: ? 415798210832770977015571637026261943061848522604312624113370066788694260962277358924812122018540899189453160012306216996159585953169430580992217533416996218355769692228520181107693452987433346106108354577759088747652027298991897698378108675855550345084116012553381493679397220592936761668902813894894999677516082875409398242248834435266509874044408860014177472808390130551065070522666947759308800000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:19:22 2005 Input: 23122! Output: ? 6596591744323184165203562488290333385434479811656800770306432224649803510329903956077625036361670822518763687766585447368439139050905989722207505479449041613226964622677410200101183245655088032174944567207114713889935798274162183259049559437945328460868769615325326814591728628355013168858118111946720322491528662241462908894711796744397756748809732032612206014427203774311247451355590140803770863804189628767254370731892498482868710016970349208508358502830771973075903758470843398901243319002065221953671560351399316676163150372148493254241098651330255942311883265558951057007043689366871825935169981298578511394901396355872853724660549464062874169197376559741281350762323195309379391480615242268443918574831142805489660922870490097584069724247661748780698806442486833902238558260184321385393285411127921517047739677189239187419352043781221361780313518950793729074195630118810723322485246665505939402326028942594464161293408061884020102636145413086480178598728435409232072249783244745519037803478841979923561539742410993474941545581929370104438329156913210538373792262748436040372704958937209742162229309739051484579883619424576009573851750499372987283103188031606509083404682534024676825762061372186043146132769660683284534842515045743889409855771448556333738443823876943327188376198622434893758312341801377001799245291835065026091889009768982007990155814112740973947874486429285191132809572916824154071503825986420056856819172068445349184516276058619480846510579511470636433863625978545851117518437369124593051537281268968080240837384665809125600571744114689395160025153543370009586428908694246657082215094654584658460311026964708858200231284846523971920691585218040064178976596585650166005196018604036778678302494295585643206414687680107757212518999133818358519309907284615388061652638052457515660456813304348205506772548387184847658684042735889265845228086165039667788988820113630884513393143254749900311877255318502770542750690109536969917070053658334685554923001595400147117244962753571897783957398999803635997291978379339501428319857753480399537143539857841771295986964728369508387197957062313869209042205698086386697532982768565469490231230394831036056580048790264777331756480659295564281900837181101960548942212840556555218102097228082755329898468593322299289842987614282067463367696145524988075720629719811952115979228491785450097222305943952646001339315644618999221656900695168936066679542868430565192030441525763677391205869856326321975020483321641029516348452030694677679570557215980021353717962032190084941679224382476866065278446688552477782784324984836721106303191810642270794284722409771615702317487906709587914725584448821526404290939671024224292950685408902250854665747065535296891656451860510540949594889395675077791266868111712686188194036698180629100182357634184267153071173830544529389199908531372153112103595199714865188904974447246199703971202877734774302126607736205811143000615345568781020810530807460914902867345307821761855279481253932385237223756476137482952262287899740282128419131530128315084107465236091326442915857835838952814645755189374449047330510099025888605349778844286079777734951421095582508365724950589298131855546346105733032366068440814616495560[+++] ? Errors (if any) and Timing Info: Timing: real 0m1.843s user 0m1.828s sys 0m0.011s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:19:41 2005 Input: 231*22 Output: ? 5082 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.005s sys 0m0.008s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:19:48 2005 Input: 231*2252423142210 Output: ? 520309745850510 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:20:30 2005 Input: factor(2^2^7 +1) Output: ? [59649589127497217 1] [5704689200685129054721 1] ? Errors (if any) and Timing Info: Timing: real 0m0.325s user 0m0.267s sys 0m0.017s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:20:42 2005 Input: factor(2^2^7 +1) Output: ? [59649589127497217 1] [5704689200685129054721 1] ? Errors (if any) and Timing Info: Timing: real 0m0.286s user 0m0.263s sys 0m0.023s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:20:56 2005 Input: factor(2^2^7^10 +1) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:22:16 2005 Input: prime(41561) Output: ? 500257 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:22:23 2005 Input: prime(4156234345465461) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:22:57 2005 Input: fibo(22) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: fibo(22) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: fibo(x) ===> fibonacci(x) fibonacci(x): fibonacci number of index x (x C-integer). Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:23:08 2005 Input: fibonacci(22) Output: ? 17711 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:23:15 2005 Input: fibonacci(40) Output: ? 102334155 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:23:21 2005 Input: fibonacci(400) Output: ? 176023680645013966468226945392411250770384383304492191886725992896575345044216019675 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:27:14 2005 Input: fibonacci(4020) Output: ? 603710602013017885633456758374006890118373777109795331504218594372861707732605193831919658199260488137772502079030906456085361445680247193624343530840097623592589327497036626802570701816326806950887145804187450424894884710705483903484007532240172152101230825251787615928848424631597473944726065990142088971471335630021270222844176373647999137896155480529565594097687196746301936040854121882709325108183064306666802164042403372772184970957846159857421524120138943889510482359182184961411965903835740580537370937308538759586359595126398938083409291124465386430599247965345678990005914857713006866269457183407530378187264815884353460494842051001487858918009715037028523984682667893360865030869234615383077218761051710716870925358058012476704008183339514154420470618565609374727746942482753867626462035781624331285922338689124008606690336406640 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:28:15 2005 Input: nextprime(213456489754) Output: ? 213456489769 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:28:25 2005 Input: nextprime(213456531321654987646513216548974351321654489754) Output: ? 213456531321654987646513216548974351321654489897 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.014s sys 0m0.003s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:28:32 2005 Input: nextprime(21345653132165498764651321654897432314354567578687021432451321654489754) Output: ? 21345653132165498764651321654897432314354567578687021432451321654489869 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.017s sys 0m0.004s '129.72.' ************** PARI ***************** Host 129.72.75.151 (129.72.75.151) Time: Tue Feb 22 15:28:38 2005 Input: nextprime(213456531321654987646513216548974323542354353420114354567578687021432451321654489754) Output: ? 213456531321654987646513216548974323542354353420114354567578687021432451321654489867 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.017s sys 0m0.006s '68.66.2' ************** PARI ***************** Host 68.66.22.184 (68.66.22.184) Time: Tue Feb 22 18:36:34 2005 Input: 23 Output: ? 23 ? Errors (if any) and Timing Info: Timing: real 0m0.140s user 0m0.008s sys 0m0.008s '220.41.' ************** PARI ***************** Host 220.41.28.179 (220.41.28.179) Time: Wed Feb 23 04:12:23 2005 Input: F := FreeGroup(7); F7 := quo< F | x1*x2=x3, x2*x3=x4, x3*x4=x5, x4*x5=x6, x5*x6=x7, x6*x7=x1, x7*x1=x2 >; P := TietzeProcess(F7); for i := 7 to 3 by -1 do EliminateGenerators(~P: Generator := i); end for; H := ExtractGroup(P); print H; Output: ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,x2,x3,x4,x5,x6,x7>:=FreeGroup(7);. *** incorrect type in comparison. *** Warning: unused characters: ,x2,x3,x4,x5,x6,x7>:=quo;. *** unexpected character: P:=TietzeProcess(F7); ^------------------- *** unexpected character: fori:=7to3by-1do ^----------- *** unexpected character: EliminateGenerators(~P:Generator:=i); ^----------------- *** Warning: unused characters: ,y>:=ExtractGroup(P);. *** incorrect type in comparison. Timing: real 0m0.151s user 0m0.009s sys 0m0.006s '220.41.' ************** PARI ***************** Host 220.41.28.179 (220.41.28.179) Time: Wed Feb 23 04:18:17 2005 Input: F := FreeGroup(6); F6 := quo< F | x6=x5*x4*x5^-1, x5=x2^-1*x6*x2, x4=x3*x1*x3^-1, x3=x4*x5*x4^-1, x2=x1*x3*x1^-1, x1=x6^-1*x2*x6 >; print F6; Output: ? ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,x2,x3,x4,x5,x6>:=FreeGroup(6);. *** incorrect type in comparison. *** Warning: unused characters: ,x2,x3,x4,x5,x6>:=quo;. Timing: real 0m0.048s user 0m0.004s sys 0m0.007s '220.41.' ************** PARI ***************** Host 220.41.28.179 (220.41.28.179) Time: Wed Feb 23 04:25:49 2005 Input: F := FreeGroup(6); F6 := quo< F | x6=x5*x4*x5^-1, x5=x2^-1*x6*x2, x4=x3*x1*x3^-1, x3=x4*x5*x4^-1, x2=x1*x3*x1^-1, x1=x6^-1*x2*x6>; P := TietzeProcess(F6); for i := 6 to 3 by -1 do EliminateGenerators(~P: Generator := i); end for; H := ExtractGroup(P); print F6; Output: ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,x2,x3,x4,x5,x6>:=FreeGroup(6);. *** incorrect type in comparison. *** Warning: unused characters: ,x2,x3,x4,x5,x6>:=quo;. *** unexpected character: P:=TietzeProcess(F6); ^------------------- *** unexpected character: fori:=6to3by-1do ^----------- *** unexpected character: EliminateGenerators(~P:Generator:=i); ^----------------- *** Warning: unused characters: ,y>:=ExtractGroup(P);. *** incorrect type in comparison. Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '134.157' ************** PARI ***************** Host 134.157.51.2 (134.157.51.2) Time: Wed Feb 23 07:39:54 2005 Input: factor(123456789123456789)) Output: ? [3 2] [7 1] [11 1] [13 1] [19 1] [3607 1] [3803 1] [52579 1] ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.477s user 0m0.009s sys 0m0.009s '134.157' ************** PARI ***************** Host 134.157.51.2 (134.157.51.2) Time: Wed Feb 23 07:42:06 2005 Input: factor(123456789123456789) Output: ? [3 2] [7 1] [11 1] [13 1] [19 1] [3607 1] [3803 1] [52579 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '134.157' ************** PARI ***************** Host 134.157.51.2 (134.157.51.2) Time: Wed Feb 23 07:42:49 2005 Input: factor(123456789123456789123456789) Output: ? [3 3] [757 1] [3607 1] [3803 1] [440334654777631 1] ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.004s sys 0m0.010s '134.157' ************** PARI ***************** Host 134.157.51.2 (134.157.51.2) Time: Wed Feb 23 07:43:10 2005 Input: factor(1234567891234567891234567891) Output: ? [1234567891234567891234567891 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '134.157' ************** PARI ***************** Host 134.157.51.2 (134.157.51.2) Time: Wed Feb 23 07:43:21 2005 Input: factor(12345678912345678912345678912) Output: ? [2 6] [3 1] [7 1] [17 1] [4111 1] [131437506263785848179 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '134.157' ************** PARI ***************** Host 134.157.51.2 (134.157.51.2) Time: Wed Feb 23 07:43:34 2005 Input: factor(12345678912345678912345678912345) Output: ? [3 1] [5 1] [823045260823045260823045260823 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '134.157' ************** PARI ***************** Host 134.157.51.2 (134.157.51.2) Time: Wed Feb 23 07:43:44 2005 Input: factor(123456789123456789123456789123456789) Output: ? [3 2] [7 1] [11 1] [13 1] [19 1] [101 1] [3607 1] [3803 1] [9901 1] [52579 1] [999999000001 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '134.157' ************** PARI ***************** Host 134.157.51.2 (134.157.51.2) Time: Wed Feb 23 07:44:04 2005 Input: factor(123456789123456789123456789123456789123456) Output: ? [2 7] [3 1] [271849 1] [5316163 1] [46584698449 1] [4775451475065443 1] ? Errors (if any) and Timing Info: Timing: real 0m0.094s user 0m0.049s sys 0m0.012s '134.157' ************** PARI ***************** Host 134.157.51.2 (134.157.51.2) Time: Wed Feb 23 09:50:43 2005 Input: 1+1 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.352s user 0m0.005s sys 0m0.010s '158.109' ************** PARI ***************** Host 158.109.66.29 (158.109.66.29) Time: Wed Feb 23 12:56:33 2005 Input: magma Output: ? magma ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '158.109' ************** PARI ***************** Host 158.109.66.29 (158.109.66.29) Time: Wed Feb 23 12:56:48 2005 Input: magma; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.080s user 0m0.005s sys 0m0.007s '158.109' ************** PARI ***************** Host 158.109.66.29 (158.109.66.29) Time: Wed Feb 23 13:07:05 2005 Input: t:= {1..366 by 1}; Output: ? ? Errors (if any) and Timing Info: *** unexpected character: t:={1..366by1}; ^------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '158.109' ************** PARI ***************** Host 158.109.66.29 (158.109.66.29) Time: Wed Feb 23 13:08:17 2005 Input: t:= {1,2,3,4}; Output: ? ? Errors (if any) and Timing Info: *** unexpected character: t:={1,2,3,4}; ^----------- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '158.109' ************** PARI ***************** Host 158.109.66.29 (158.109.66.29) Time: Wed Feb 23 13:09:00 2005 Input: t := {1,2,3,4}; Output: ? ? Errors (if any) and Timing Info: *** unexpected character: t:={1,2,3,4}; ^----------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '81.134.' ************** PARI ***************** Host 81.134.140.150 (81.134.140.150) Time: Wed Feb 23 18:00:07 2005 Input: Pi Output: ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.248s user 0m0.008s sys 0m0.005s '69.157.' ************** PARI ***************** Host 69.157.61.27 (69.157.61.27) Time: Thu Feb 24 12:24:54 2005 Input: ddd Output: ? ddd ? Errors (if any) and Timing Info: Timing: real 0m0.369s user 0m0.004s sys 0m0.010s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Thu Feb 24 13:24:53 2005 Input: ATLASGroupNames(); ATLASGroup(A5); Output: ? ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: ATLASGroupNames(); ^- *** expected character: '=' instead of: ATLASGroup(A5); ^- Timing: real 0m0.396s user 0m0.004s sys 0m0.006s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Thu Feb 24 13:48:06 2005 Input: A:=ATLASGroup("3A6"); B:=ATLASGroup("6A6"); IsNormal(B,A); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: A:=ATLASGroup("3A6"); ^------------------- *** unexpected character: B:=ATLASGroup("6A6"); ^------------------- *** expected character: '=' instead of: IsNormal(B,A); ^- Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '128.101' ************** PARI ***************** Host 128.101.154.160 (128.101.154.160) Time: Thu Feb 24 15:02:25 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.246s user 0m0.006s sys 0m0.008s '81.66.1' ************** PARI ***************** Host 81.66.172.45 (81.66.172.45) Time: Thu Feb 24 16:16:19 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '81.66.1' ************** PARI ***************** Host 81.66.172.45 (81.66.172.45) Time: Thu Feb 24 16:18:00 2005 Input: factor(123456789123456789123456789123456789123456) Output: ? [2 7] [3 1] [271849 1] [5316163 1] [46584698449 1] [4775451475065443 1] ? Errors (if any) and Timing Info: Timing: real 0m0.127s user 0m0.048s sys 0m0.013s '81.66.1' ************** PARI ***************** Host 81.66.172.45 (81.66.172.45) Time: Thu Feb 24 16:18:53 2005 Input: factor(12345678912345678912345678912345678912345612124545787889897878454512122) Output: ? [2 1] [3 1] [43 1] [169219 1] [11742238337442829 1] [24082149946483499472730952614519106699686665659 1] ? Errors (if any) and Timing Info: Timing: real 0m4.804s user 0m4.793s sys 0m0.009s '81.66.1' ************** PARI ***************** Host 81.66.172.45 (81.66.172.45) Time: Thu Feb 24 16:20:24 2005 Input: factor(12345678912345678912345678912345678912345612124545787889897878454512122) Output: ? [2 1] [3 1] [43 1] [169219 1] [11742238337442829 1] [24082149946483499472730952614519106699686665659 1] ? Errors (if any) and Timing Info: Timing: real 0m4.866s user 0m4.857s sys 0m0.004s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Thu Feb 24 18:25:57 2005 Input: G:=GeneralLinearGroup(3,19); x=elt; x; Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: G:=GeneralLinearGroup( ^-------------------- *** Warning: unused characters: ,-1,00,-1,00,0,1>;. *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Thu Feb 24 19:12:45 2005 Input: x=[-1,0,0;0,-1,0;0,0,1] Output: ? [-1 0 0] [0 -1 0] [0 0 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Thu Feb 24 19:13:36 2005 Input: x=[-1,0,0;0,-1,0;0,0,1] y=[0,1,0;0,0,1;1,0,0] a=[a,b,c;d,e,f;g,h,i] a*x-L*x*a Output: ? [-1 0 0] [0 -1 0] [0 0 1] ? [0 1 0] [0 0 1] [1 0 0] ? [a b c] [d e f] [g h i] ? [(L - 1)*a (L - 1)*b (L + 1)*c] [(L - 1)*d (L - 1)*e (L + 1)*f] [(-L - 1)*g (-L - 1)*h (-L + 1)*i] ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.007s sys 0m0.004s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Thu Feb 24 19:16:42 2005 Input: x=[-1,0,0;0,-1,0;0,0,1] y=[0,1,0;0,0,1;1,0,0] a=[a,b,0;d,e,0;0,0,i] a*y-U*y*a Output: ? [-1 0 0] [0 -1 0] [0 0 1] ? [0 1 0] [0 0 1] [1 0 0] ? [a b 0] [d e 0] [0 0 i] ? [-U*d a - U*e b] [0 d e - U*i] [-U*a + i -U*b 0] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Thu Feb 24 19:23:56 2005 Input: x=[-1,0,0;0,-1,0;0,0,1] y=[0,1,0;0,0,1;1,0,0] A=[a,b,0;d,e,0;0,0,i] z=[1,0,0;0,-1,0;0,0,-1] A*y-U*y*A A*z-V*z*A Output: ? [-1 0 0] [0 -1 0] [0 0 1] ? [0 1 0] [0 0 1] [1 0 0] ? [a b 0] [d e 0] [0 0 i] ? [1 0 0] [0 -1 0] [0 0 -1] ? [-U*d a - U*e b] [0 d e - U*i] [-U*a + i -U*b 0] ? [(-V + 1)*a (-V - 1)*b 0] [(V + 1)*d (V - 1)*e 0] [0 0 (V - 1)*i] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Thu Feb 24 19:24:37 2005 Input: x=[-1,0,0;0,-1,0;0,0,1] y=[0,1,0;0,0,1;1,0,0] A=[a,0,0;0,a/U,0;0,0,Ua] z=[1,0,0;0,-1,0;0,0,-1] A*y-U*y*A A*z-V*z*A Output: ? [-1 0 0] [0 -1 0] [0 0 1] ? [0 1 0] [0 0 1] [1 0 0] ? [a 0 0] [0 1/U*a 0] [0 0 Ua] ? [1 0 0] [0 -1 0] [0 0 -1] ? [0 0 0] [0 0 1/U*a - Ua*U] [-U*a + Ua 0 0] ? [(-V + 1)*a 0 0] [0 ((V - 1)/U)*a 0] [0 0 (V - 1)*Ua] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.008s sys 0m0.004s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Thu Feb 24 19:26:29 2005 Input: x=[-1,0,0;0,-1,0;0,0,1] y=[0,1,0;0,0,1;1,0,0] A=[a,0,0;0,a*U^2,0;0,0,Ua] z=[1,0,0;0,-1,0;0,0,-1] A*y-U*y*A A*z-V*z*A Output: ? [-1 0 0] [0 -1 0] [0 0 1] ? [0 1 0] [0 0 1] [1 0 0] ? [a 0 0] [0 U^2*a 0] [0 0 Ua] ? [1 0 0] [0 -1 0] [0 0 -1] ? [0 (-U^3 + 1)*a 0] [0 0 U^2*a - Ua*U] [-U*a + Ua 0 0] ? [(-V + 1)*a 0 0] [0 (V - 1)*U^2*a 0] [0 0 (V - 1)*Ua] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Thu Feb 24 19:26:50 2005 Input: x=[-1,0,0;0,-1,0;0,0,1] y=[0,1,0;0,0,1;1,0,0] A=[a,0,0;0,a*U^2,0;0,0,U*a] z=[1,0,0;0,-1,0;0,0,-1] A*y-U*y*A A*z-V*z*A Output: ? [-1 0 0] [0 -1 0] [0 0 1] ? [0 1 0] [0 0 1] [1 0 0] ? [a 0 0] [0 U^2*a 0] [0 0 U*a] ? [1 0 0] [0 -1 0] [0 0 -1] ? [0 (-U^3 + 1)*a 0] [0 0 0] [0 0 0] ? [(-V + 1)*a 0 0] [0 (V - 1)*U^2*a 0] [0 0 (V - 1)*U*a] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Thu Feb 24 19:29:06 2005 Input: x=[-1,0,0;0,-1,0;0,0,1]; y=[0,1,0;0,0,1;1,0,0]; A=[a,0,0;0,a*U^2,0;0,0,U*a]; z=[1,0,0;0,-1,0;0,0,-1]; B=[-1/2,1/2-t,-t;t-1/2,t,-1/2;t,-1/2,1/2-t] A*B-W*B*A Output: ? ? ? ? ? [-1/2 -t + 1/2 -t] [t - 1/2 t -1/2] [t -1/2 -t + 1/2] ? [(1/2*W - 1/2)*a ((W*t - 1/2*W)*U^2 + (-t + 1/2))*a (W*t*U - t)*a] [((t - 1/2)*U^2 + (-W*t + 1/2*W))*a (-W + 1)*t*U^2*a (-1/2*U^2 + 1/2*W*U)*a] [(t*U - W*t)*a (1/2*W*U^2 - 1/2*U)*a ((W - 1)*t + (-1/2*W + 1/2))*U*a] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '217.82.' ************** PARI ***************** Host 217.82.159.65 (217.82.159.65) Time: Fri Feb 25 09:26:30 2005 Input: forprime(p=2,1000,if(gcd(p+3,10)==10,print(p))) Output: ? 7 17 37 47 67 97 107 127 137 157 167 197 227 257 277 307 317 337 347 367 397 457 467 487 547 557 577 587 607 617 647 677 727 757 787 797 827 857 877 887 907 937 947 967 977 997 ? Errors (if any) and Timing Info: Timing: real 0m0.414s user 0m0.006s sys 0m0.008s '217.82.' ************** PARI ***************** Host 217.82.159.65 (217.82.159.65) Time: Fri Feb 25 09:27:07 2005 Input: forprime(p=2,10000,if(gcd(p+3,10)==10,print(p))) Output: ? 7 17 37 47 67 97 107 127 137 157 167 197 227 257 277 307 317 337 347 367 397 457 467 487 547 557 577 587 607 617 647 677 727 757 787 797 827 857 877 887 907 937 947 967 977 997 1087 1097 1117 1187 1217 1237 1277 1297 1307 1327 1367 1427 1447 1487 1567 1597 1607 1627 1637 1657 1667 1697 1747 1777 1787 1847 1867 1877 1907 1987 1997 2017 2027 2087 2137 2207 2237 2267 2287 2297 2347 2357 2377 2417 2437 2447 2467 2477 2557 2617 2647 2657 2677 2687 2707 2767 2777 2797 2837 2857 2887 2897 2917 2927 2957 3037 3067 3137 3167 3187 3217 3257 3307 3347 3407 3457 3467 3517 3527 3547 3557 3607 3617 3637 3677 3697 3727 3767 3797 3847 3877 3907 3917 3947 3967 4007 4027 4057 4127 4157 4177 4217 4297 4327 4337 4357 4397 4447 4457 4507 4517 4547 4567 4597 4637 4657 4787 4817 4877 4937 4957 4967 4987 5077 5087 5107 5147 5167 5197 5227 5237 5297 5347 5387 5407 5417 5437 5477 5507 5527 5557 5647 5657 5717 5737 5807 5827 5857 5867 5897 5927 5987 6007 6037 6047 6067 6197 6217 6247 6257 6277 6287 6317 6337 6367 6397 6427 6547 6577 6607 6637 6737 6827 6857 6907 6917 6947 6967 6977 6997 7027 7057 7127 7177 7187 7207 7237 7247 7297 7307 7417 7457 7477 7487 7507 7517 7537 7547 7577 7607 7687 7717 7727 7757 7817 7867 7877 7907 7927 7937 8017 8087 8117 8147 8167 8237 8287 8297 8317 8377 8387 8447 8467 8527 8537 8597 8627 8647 8677 8707 8737 8747 8807 8837 8867 8887 9007 9067 9127 9137 9157 9187 9227 9257 9277 9337 9377 9397 9437 9467 9497 9547 9587 9677 9697 9767 9787 9817 9857 9887 9907 9967 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '217.225' ************** PARI ***************** Host 217.225.68.225 (217.225.68.225) Time: Sat Feb 26 05:50:16 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '217.225' ************** PARI ***************** Host 217.225.68.225 (217.225.68.225) Time: Sat Feb 26 05:54:52 2005 Input: mersenne(n)=forprime(p=1,n,if(isprime(2^p-1)==1,print(p,"",2^p-1))) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '217.225' ************** PARI ***************** Host 217.225.68.225 (217.225.68.225) Time: Sat Feb 26 05:55:20 2005 Input: mersenne(20000) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: mersenne(20000) ^--------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '217.225' ************** PARI ***************** Host 217.225.68.225 (217.225.68.225) Time: Sat Feb 26 05:57:38 2005 Input: forprime(p=2,20000,if(isprime(2^p-1)==1,print(p,"",2^p-1))) Output: ? 23 37 531 7127 138191 17131071 19524287 312147483647 612305843009213693951 89618970019642690137449562111 107162259276829213363391578010288127 127170141183460469231731687303715884105727 5216864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151 607531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127 127910407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087 22031475979915214180235084898622737381736312066145333169775147771216478570297878078949377407337049389289382748507531496480477281264838760259191814463365330269540496961201113430156902396093989090226259326935025281409614983499388222831448598601834318536230923772641390209490231836446899608210795482963763094236630945410832793769905399982457186322944729636418890623372171723742105636440368218459649632948538696905872650486914434637457507280441823676813517852099348660847172579408422316678097670224011990280170474894487426924742108823536808485072502240519452587542875349976558572670229633962575212637477897785501552646522609988869914013540483809865681250419497686697771007 2281446087557183758429571151706402101809886208632412859901111991219963404685792820473369112545269003989026153245931124316702395758705693679364790903497461147071065254193353938124978226307947312410798874869040070279328428810311754844108094878252494866760969586998128982645877596028979171536962503068429617331702184750324583009171832104916050157628886606372145501702225925125224076829605427173573964812995250569412480720738476855293681666712844831190877620606786663862190240118570736831901886479225810414714078935386562497968178729127629594924411960961386713946279899275006954917139758796061223803393537381034666494402951052059047968693255388647930440925104186817009640171764133172418132836351 3217259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071 Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 16813 Killed /usr/bin/gp -q -emacs Timing: real 0m21.031s user 0m20.978s sys 0m0.023s '217.225' ************** PARI ***************** Host 217.225.68.225 (217.225.68.225) Time: Sat Feb 26 05:59:37 2005 Input: forprime(p=2,20000,if(isprime(2^p-1)==1,print(p,"t",2^p-1))) Output: ? 2t3 3t7 5t31 7t127 13t8191 17t131071 19t524287 31t2147483647 61t2305843009213693951 89t618970019642690137449562111 107t162259276829213363391578010288127 127t170141183460469231731687303715884105727 521t6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151 607t531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127 1279t10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087 2203t1475979915214180235084898622737381736312066145333169775147771216478570297878078949377407337049389289382748507531496480477281264838760259191814463365330269540496961201113430156902396093989090226259326935025281409614983499388222831448598601834318536230923772641390209490231836446899608210795482963763094236630945410832793769905399982457186322944729636418890623372171723742105636440368218459649632948538696905872650486914434637457507280441823676813517852099348660847172579408422316678097670224011990280170474894487426924742108823536808485072502240519452587542875349976558572670229633962575212637477897785501552646522609988869914013540483809865681250419497686697771007 2281t446087557183758429571151706402101809886208632412859901111991219963404685792820473369112545269003989026153245931124316702395758705693679364790903497461147071065254193353938124978226307947312410798874869040070279328428810311754844108094878252494866760969586998128982645877596028979171536962503068429617331702184750324583009171832104916050157628886606372145501702225925125224076829605427173573964812995250569412480720738476855293681666712844831190877620606786663862190240118570736831901886479225810414714078935386562497968178729127629594924411960961386713946279899275006954917139758796061223803393537381034666494402951052059047968693255388647930440925104186817009640171764133172418132836351 3217t259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071 Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 16819 Killed /usr/bin/gp -q -emacs Timing: real 0m21.003s user 0m20.988s sys 0m0.013s '217.225' ************** PARI ***************** Host 217.225.68.225 (217.225.68.225) Time: Sat Feb 26 06:00:22 2005 Input: forprime(p=2,20000,if(isprime(2^p-1)==1,print(p))) Output: ? 2 3 5 7 13 17 19 31 61 89 107 127 521 607 1279 2203 2281 3217 Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 16825 Killed /usr/bin/gp -q -emacs Timing: real 0m21.161s user 0m20.996s sys 0m0.004s '217.225' ************** PARI ***************** Host 217.225.68.225 (217.225.68.225) Time: Sat Feb 26 06:01:12 2005 Input: forprime(p=3217,2000000,if(isprime(2^p-1)==1,print(p))) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '217.225' ************** PARI ***************** Host 217.225.68.225 (217.225.68.225) Time: Sat Feb 26 06:01:45 2005 Input: forprime(p=3217,200000,if(isprime(2^p-1)==1,print(p))) Output: ? 3217 Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 16888 Killed /usr/bin/gp -q -emacs Timing: real 0m21.008s user 0m20.926s sys 0m0.076s '217.225' ************** PARI ***************** Host 217.225.68.225 (217.225.68.225) Time: Sat Feb 26 06:07:49 2005 Input: nextprime(3217) Output: ? 3217 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '217.225' ************** PARI ***************** Host 217.225.68.225 (217.225.68.225) Time: Sat Feb 26 06:09:05 2005 Input: forprime(p=3221,200000,if(isprime(2^p-1)==1,print(p))) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 16916 Killed /usr/bin/gp -q -emacs Timing: real 0m21.028s user 0m20.988s sys 0m0.012s '217.225' ************** PARI ***************** Host 217.225.68.225 (217.225.68.225) Time: Sat Feb 26 06:28:08 2005 Input: isprime(2^24036583-1) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.032s user 0m0.020s sys 0m0.012s '217.225' ************** PARI ***************** Host 217.225.68.225 (217.225.68.225) Time: Sat Feb 26 06:28:55 2005 Input: allocatemem() Output: WARNING: PARI command contains unsafe command 'allocatemem', so it will not be executed. '217.225' ************** PARI ***************** Host 217.225.68.225 (217.225.68.225) Time: Sat Feb 26 06:29:12 2005 Input: isprime(2^24036583-1) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.031s user 0m0.017s sys 0m0.016s '213.89.' ************** PARI ***************** Host 213.89.33.240 (213.89.33.240) Time: Sat Feb 26 10:06:07 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.192s user 0m0.006s sys 0m0.010s '217.209' ************** PARI ***************** Host 217.209.95.199 (217.209.95.199) Time: Sat Feb 26 10:12:22 2005 Input: prime(123) Output: ? 677 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '129.127' ************** PARI ***************** Host 129.127.41.27 (129.127.41.27) Time: Sat Feb 26 15:26:31 2005 Input: isprime(1169) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.007s sys 0m0.006s '129.127' ************** PARI ***************** Host 129.127.41.27 (129.127.41.27) Time: Sat Feb 26 15:27:00 2005 Input: isprime(5) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '129.127' ************** PARI ***************** Host 129.127.41.27 (129.127.41.27) Time: Sat Feb 26 15:27:06 2005 Input: isprime(6) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '129.127' ************** PARI ***************** Host 129.127.41.27 (129.127.41.27) Time: Sat Feb 26 15:28:01 2005 Input: isprime(6) nextprime(100) gcd(70,245) binomial(16,5) mod(16,5) fibonacci(10) Output: ? 0 ? 101 ? 35 ? 4368 ? ? 55 ? Errors (if any) and Timing Info: *** obsolete function: mod(16,5) ^--------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.039s user 0m0.005s sys 0m0.008s '129.127' ************** PARI ***************** Host 129.127.41.27 (129.127.41.27) Time: Sat Feb 26 15:28:16 2005 Input: isprime(6) nextprime(5) gcd(70,245) binomial(16,5) mod(16,5) fibonacci(10) Output: ? 0 ? 5 ? 35 ? 4368 ? ? 55 ? Errors (if any) and Timing Info: *** obsolete function: mod(16,5) ^--------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '129.127' ************** PARI ***************** Host 129.127.41.27 (129.127.41.27) Time: Sat Feb 26 15:29:29 2005 Input: isprime(6) nextprime(6) gcd(70,245) binomial(16,5) mod(16,5) fibonacci(10) Output: ? 0 ? 7 ? 35 ? 4368 ? ? 55 ? Errors (if any) and Timing Info: *** obsolete function: mod(16,5) ^--------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '129.127' ************** PARI ***************** Host 129.127.41.27 (129.127.41.27) Time: Sat Feb 26 15:29:39 2005 Input: isprime(6) nextprime(14) gcd(70,245) binomial(16,5) mod(16,5) fibonacci(10) Output: ? 0 ? 17 ? 35 ? 4368 ? ? 55 ? Errors (if any) and Timing Info: *** obsolete function: mod(16,5) ^--------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Sat Feb 26 20:20:31 2005 Input: g=[1,1,0,0;-1,1,0,0;0,0,1,1;0,0,-1,1] charpoly(g) Output: ? [1 1 0 0] [-1 1 0 0] [0 0 1 1] [0 0 -1 1] ? x^4 - 4*x^3 + 8*x^2 - 8*x + 4 ? Errors (if any) and Timing Info: Timing: real 0m0.048s user 0m0.007s sys 0m0.004s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Sat Feb 26 20:20:56 2005 Input: g=[1,1,0,0;-1,1,0,0;0,0,1,1;0,0,-1,1] factor(charpoly(g)) Output: ? [1 1 0 0] [-1 1 0 0] [0 0 1 1] [0 0 -1 1] ? [x^2 - 2*x + 2 2] ? Errors (if any) and Timing Info: Timing: real 0m0.046s user 0m0.006s sys 0m0.006s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Sat Feb 26 20:25:46 2005 Input: g=[1,1,0,0;-1,1,0,0;0,0,1,1;0,0,-1,1] g^2 Output: ? [1 1 0 0] [-1 1 0 0] [0 0 1 1] [0 0 -1 1] ? [0 2 0 0] [-2 0 0 0] [0 0 0 2] [0 0 -2 0] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.005s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Sat Feb 26 20:25:56 2005 Input: g=[1,1,0,0;-1,1,0,0;0,0,1,1;0,0,-1,1]; g^2 Output: ? ? [0 2 0 0] [-2 0 0 0] [0 0 0 2] [0 0 -2 0] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Sat Feb 26 20:26:10 2005 Input: g=[1,1,0,0;-1,1,0,0;0,0,1,1;0,0,-1,1]; g^3 Output: ? ? [-2 2 0 0] [-2 -2 0 0] [0 0 -2 2] [0 0 -2 -2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Sat Feb 26 20:26:19 2005 Input: g=[1,1,0,0;-1,1,0,0;0,0,1,1;0,0,-1,1]; g^4 Output: ? ? [-4 0 0 0] [0 -4 0 0] [0 0 -4 0] [0 0 0 -4] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.006s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Sat Feb 26 20:26:47 2005 Input: g=[1,1,0,0;-1,1,0,0;0,0,1,1;0,0,-1,1]; g^5 Output: ? ? [-4 -4 0 0] [4 -4 0 0] [0 0 -4 -4] [0 0 4 -4] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.006s sys 0m0.005s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Sat Feb 26 20:27:00 2005 Input: g=[1,1,0,0;-1,1,0,0;0,0,1,1;0,0,-1,1]; g^6 Output: ? ? [0 -8 0 0] [8 0 0 0] [0 0 0 -8] [0 0 8 0] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Sat Feb 26 20:27:06 2005 Input: g=[1,1,0,0;-1,1,0,0;0,0,1,1;0,0,-1,1]; g^7 Output: ? ? [8 -8 0 0] [8 8 0 0] [0 0 8 -8] [0 0 8 8] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Sat Feb 26 20:27:11 2005 Input: g=[1,1,0,0;-1,1,0,0;0,0,1,1;0,0,-1,1]; g^8 Output: ? ? [16 0 0 0] [0 16 0 0] [0 0 16 0] [0 0 0 16] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '65.96.1' ************** PARI ***************** Host 65.96.160.100 (65.96.160.100) Time: Sat Feb 26 22:39:00 2005 Input: f = x^3 - 2; k = nfinit(f); i = idealfactor(k,3); j = idealfactor(k,5); m = matrix(2,2); m[1,] = i[1,]; m[1,2] = 1; m[2,] = j[1,]; idealchinese(k, m, [x,1]); Output: ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.124s user 0m0.011s sys 0m0.004s '65.96.1' ************** PARI ***************** Host 65.96.160.100 (65.96.160.100) Time: Sat Feb 26 22:39:05 2005 Input: f = x^3 - 2; k = nfinit(f); i = idealfactor(k,3); j = idealfactor(k,5); m = matrix(2,2); m[1,] = i[1,]; m[1,2] = 1; m[2,] = j[1,]; idealchinese(k, m, [x,1]) Output: ? ? ? ? ? ? ? ? ? [0, 0, -1]~ ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.007s '210.136' ************** PARI ***************** Host 210.136.161.200 (210.136.161.200) Time: Sun Feb 27 02:26:16 2005 Input: prime(200) Output: ? 1223 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '210.136' ************** PARI ***************** Host 210.136.161.203 (210.136.161.203) Time: Sun Feb 27 02:26:57 2005 Input: prime(20000) Output: ? 224737 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '210.136' ************** PARI ***************** Host 210.136.161.194 (210.136.161.194) Time: Sun Feb 27 02:27:32 2005 Input: prime(2) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '217.209' ************** PARI ***************** Host 217.209.95.199 (217.209.95.199) Time: Sun Feb 27 07:08:17 2005 Input: isprime(1234567) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '217.209' ************** PARI ***************** Host 217.209.95.199 (217.209.95.199) Time: Sun Feb 27 07:08:32 2005 Input: isprime(11) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '62.175.' ************** PARI ***************** Host 62.175.76.46 (62.175.76.46) Time: Mon Feb 28 09:31:06 2005 Input: t:={n: n in [4..366 by 7]}; Output: ? ? Errors (if any) and Timing Info: *** unexpected character: t:={n:nin[4..366by7]}; ^-------------------- Timing: real 0m0.270s user 0m0.006s sys 0m0.011s '216.23.' ************** PARI ***************** Host 216.23.123.22 (216.23.123.22) Time: Mon Feb 28 11:29:25 2005 Input: Pi Output: ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.043s user 0m0.006s sys 0m0.009s '216.23.' ************** PARI ***************** Host 216.23.123.22 (216.23.123.22) Time: Mon Feb 28 11:29:40 2005 Input: realprecision = 500 Pi Output: ? 500 ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '216.23.' ************** PARI ***************** Host 216.23.123.22 (216.23.123.22) Time: Mon Feb 28 11:30:50 2005 Input: prime(42) Output: ? 181 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '143.106' ************** PARI ***************** Host 143.106.22.196 (143.106.22.196) Time: Tue Mar 1 08:45:50 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.220s user 0m0.010s sys 0m0.004s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Tue Mar 1 10:25:03 2005 Input: 3*5 Output: ? 15 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.008s sys 0m0.006s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Tue Mar 1 10:39:04 2005 Input: bezout(2,7) Output: ? [-3, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.009s sys 0m0.003s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Tue Mar 1 10:39:44 2005 Input: bezout(3,5) Output: ? [2, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.009s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Tue Mar 1 10:39:51 2005 Input: bezout(3,5) Output: ? [2, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Tue Mar 1 10:40:10 2005 Input: bezout(12,33) Output: ? [3, -1, 3] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Tue Mar 1 10:40:20 2005 Input: bezout(12,39) Output: ? [-3, 1, 3] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Tue Mar 1 10:40:28 2005 Input: bezout(12,41) Output: ? [-17, 5, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Tue Mar 1 10:52:23 2005 Input: bezout(374,553) Output: ? [173, -117, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.144' ************** PARI ***************** Host 128.144.90.25 (128.144.90.25) Time: Tue Mar 1 13:38:39 2005 Input: Pi/exp(1) Output: ? 1.1557273497909217179100931833126962991 ? Errors (if any) and Timing Info: Timing: real 0m0.080s user 0m0.009s sys 0m0.005s '128.144' ************** PARI ***************** Host 128.144.90.25 (128.144.90.25) Time: Tue Mar 1 13:39:28 2005 Input: Pi/exp(1) Output: ? 1.1557273497909217179100931833126962991 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '128.144' ************** PARI ***************** Host 128.144.90.25 (128.144.90.25) Time: Tue Mar 1 13:39:47 2005 Input: Pi/(Pi+exp(1)) Output: ? 0.53611944474472277322654673465377758603 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.189.108 (140.247.189.108) Time: Tue Mar 1 17:43:44 2005 Input: R := PolynomialRing(RationalField()); K := NumberField(x^3-2); OK := RingOfIntegers(K); [K!OK.i : i in [1..5]]; Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: R:=PolynomialRing(Rat ^-------------------- *** unexpected character: K:=NumberField(x^3-2) ^-------------------- *** unexpected character: OK:=RingOfIntegers(K); ^------------------- *** ; or ] expected: [K!OK.i:iin[1..5]]; ^---------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '218.102' ************** PARI ***************** Host 218.102.189.231 (218.102.189.231) Time: Wed Mar 2 04:00:47 2005 Input: 111 Output: ? 111 ? Errors (if any) and Timing Info: Timing: real 0m0.148s user 0m0.008s sys 0m0.007s '128.119' ************** PARI ***************** Host 128.119.47.39 (128.119.47.39) Time: Wed Mar 2 09:40:05 2005 Input: 2^18 Output: ? 262144 ? Errors (if any) and Timing Info: Timing: real 0m0.287s user 0m0.007s sys 0m0.008s '128.119' ************** PARI ***************** Host 128.119.47.39 (128.119.47.39) Time: Wed Mar 2 09:40:20 2005 Input: (2^18)/18 Output: ? 131072/9 ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.007s sys 0m0.007s '128.119' ************** PARI ***************** Host 128.119.47.39 (128.119.47.39) Time: Wed Mar 2 09:41:13 2005 Input: factor(2^18) Output: ? [2 18] ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.008s sys 0m0.005s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Wed Mar 2 10:49:13 2005 Input: bezout(10,133) Output: ? [40, -3, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.007s sys 0m0.005s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Wed Mar 2 10:54:09 2005 Input: bezout(22,553) Output: ? [176, -7, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '201.128' ************** PARI ***************** Host 201.128.34.250 (201.128.34.250) Time: Wed Mar 2 15:39:36 2005 Input: g=z*x^3 + ((3*y + 12)*z + y^2)*x^2 + (13*z^3 + 13*y*z^2 + 5*y^2*z + y^3)*x + (10*z^4 + 17*y*z^3 + 11*y^2*z^2 + 4*y^3*z); {for(i=-1000,1000, for(j=-1000,1000, for(k=1000,1000, if(subst(subst(subst(g,x,i),y,j),z,k)==0, print([i,j,k]) ) ) ) ); } Output: ? ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 9264 Killed /usr/bin/gp -q -emacs Timing: real 0m21.233s user 0m20.989s sys 0m0.011s '201.128' ************** PARI ***************** Host 201.128.34.250 (201.128.34.250) Time: Wed Mar 2 15:41:48 2005 Input: g=z*x^3 + ((3*y + 12)*z + y^2)*x^2 + (13*z^3 + 13*y*z^2 + 5*y^2*z + y^3)*x + (10*z^4 + 17*y*z^3 + 11*y^2*z^2 + 4*y^3*z); {for(i=-200,200, for(j=-200,200, for(k=-200,200, if(subst(subst(subst(g,x,i),y,j),z,k)==0, print([i,j,k]) ) ) ) ); } Output: ? ? [-200, 0, 0] [-200, 200, 0] [-199, 0, 0] [-199, 199, 0] [-198, 0, 0] [-198, 198, 0] [-197, 0, 0] [-197, 197, 0] [-196, 0, 0] [-196, 196, 0] [-195, 0, 0] [-195, 195, 0] [-194, 0, 0] [-194, 194, 0] [-193, 0, 0] [-193, 193, 0] [-192, 0, 0] [-192, 144, 48] [-192, 192, 0] [-191, 0, 0] [-191, 191, 0] [-190, 0, 0] [-190, 190, 0] [-189, 0, 0] Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 9290 Killed /usr/bin/gp -q -emacs Timing: real 0m21.010s user 0m20.998s sys 0m0.002s '201.128' ************** PARI ***************** Host 201.128.34.250 (201.128.34.250) Time: Wed Mar 2 15:52:11 2005 Input: g=z*x^3 + ((3*y + 12)*z + y^2)*x^2 + (13*z^3 + 13*y*z^2 + 5*y^2*z + y^3)*x + (10*z^4 + 17*y*z^3 + 11*y^2*z^2 + 4*y^3*z); {for(i=-200,200, for(j=-200,200, for(k=-200,200, if(subst(subst(subst(g,x,i),y,j),z,k)==0, print([i,j,k]) ) ) ) ); } Output: ? ? [-200, 0, 0] [-200, 200, 0] [-199, 0, 0] [-199, 199, 0] [-198, 0, 0] [-198, 198, 0] [-197, 0, 0] [-197, 197, 0] [-196, 0, 0] [-196, 196, 0] [-195, 0, 0] [-195, 195, 0] [-194, 0, 0] [-194, 194, 0] [-193, 0, 0] [-193, 193, 0] [-192, 0, 0] [-192, 144, 48] [-192, 192, 0] [-191, 0, 0] [-191, 191, 0] [-190, 0, 0] [-190, 190, 0] [-189, 0, 0] Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 9422 Killed /usr/bin/gp -q -emacs Timing: real 0m21.028s user 0m20.991s sys 0m0.008s '201.128' ************** PARI ***************** Host 201.128.34.250 (201.128.34.250) Time: Wed Mar 2 15:54:17 2005 Input: g=z*x^3 + (y^2 + 3*z*y + 12*z)*x^2 + (y^3 + 5*z*y^2 + 13*z^2*y + 13*z^3)*x + (4*z*y^3 + 11*z^2*y^2 + 17*z^3*y + 10*z^4); {for(i=-500,500, for(j=-500,500, for(k=1,500, if(subst(subst(subst(g,x,i),y,j),z,k)==0, print([i,j,k]/gcd(gcd(i,j),k)) ) ) ) ); } Output: ? ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 9465 Killed /usr/bin/gp -q -emacs Timing: real 0m21.016s user 0m20.992s sys 0m0.008s '201.128' ************** PARI ***************** Host 201.128.34.250 (201.128.34.250) Time: Wed Mar 2 15:57:53 2005 Input: g=z*x^3 + (y^2 + 3*z*y + 12*z)*x^2 + (y^3 + 5*z*y^2 + 13*z^2*y + 13*z^3)*x + (4*z*y^3 + 11*z^2*y^2 + 17*z^3*y + 10*z^4); {for(i=-300,300, for(j=-300,300, for(k=1,300, if(subst(subst(subst(g,x,i),y,j),z,k)==0, print([i,j,k]/gcd(gcd(i,j),k)) ) ) ) ); } Output: ? ? [-20, 13, 14] [-5, 4, 2] [-21, 10, 3] Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 9499 Killed /usr/bin/gp -q -emacs Timing: real 0m21.049s user 0m20.994s sys 0m0.006s '213.6.5' ************** PARI ***************** Host 213.6.51.99 (213.6.51.99) Time: Wed Mar 2 16:38:44 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.167.29 (140.247.167.29) Time: Wed Mar 2 20:37:56 2005 Input: ? Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.009s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.167.29 (140.247.167.29) Time: Wed Mar 2 20:38:51 2005 Input: ?7 Output: ? O deriv eval factorpadic intformal padicappr polcoeff polcyclo poldegree poldisc poldiscreduced polhensellift polinterpolate polisirreducible pollead pollegendre polrecip polresultant polroots polrootsmod polrootspadic polsturm polsubcyclo polsylvestermatrix polsym poltchebi polzagier serconvol serlaplace serreverse subst taylor thue thueinit ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.167.29 (140.247.167.29) Time: Wed Mar 2 20:39:22 2005 Input: ?polcoeff Output: ? polcoeff(x,s,{v}): coefficient of degree s of x, or the s-th component for vectors or matrices (for which it is simpler to use x[]). With respect to the main variable if v is omitted, with respect to the variable v otherwise. ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.167.29 (140.247.167.29) Time: Wed Mar 2 20:39:42 2005 Input: ?infinit Output: ? ? Errors (if any) and Timing Info: *** infinit: unknown identifier. Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.167.29 (140.247.167.29) Time: Wed Mar 2 20:40:32 2005 Input: ?nfinit Output: ? nfinit(pol,{flag=0}): pol being a nonconstant irreducible polynomial, gives the vector: [pol,[r1,r2],discf,index,[M,MC,T2,T,different] (see manual),r1+r2 first roots, integral basis, matrix of power basis in terms of integral basis, multiplication table of basis]. flag is optional and can be set to 0: default; 1: do not compute different; 2: first use polred to find a simpler polynomial; 3: outputs a two-element vector [nf,Mod(a,P)], where nf is as in 2 and Mod(a,P) is a polymod equal to Mod(x,pol) and P=nf.pol; 4: as 2 but use a partial polred; 5: is to 3 what 4 is to 2. ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.167.29 (140.247.167.29) Time: Wed Mar 2 20:41:15 2005 Input: ?nfbasis Output: ? nfbasis(x,{flag=0},{p}): integral basis of the field Q[a], where a is a root of the polynomial x, using the round 4 algorithm. Second and third args are optional. Binary digits of flag mean 1: assume that no square of a prime>primelimit divides the discriminant of x, 2: use round 2 algorithm instead. If present, p provides the matrix of a partial factorization of the discriminant of x, useful if one wants only an order maximal at certain primes only. ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s 'form' ************** PARI ***************** Host form (140.247.29.178) Time: Thu Mar 3 09:51:27 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.274s user 0m0.004s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.73.183 (140.247.73.183) Time: Thu Mar 3 10:00:36 2005 Input: R := PolynomialRing(RationalField()); K := NumberField(x^5+7*x+1); OK := RingOfIntegers(K); [K!x : x in Basis(OK)]; Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: R:=PolynomialRing(Rat ^-------------------- *** unexpected character: K:=NumberField(x^5+7* ^-------------------- *** unexpected character: OK:=RingOfIntegers(K); ^------------------- *** ; or ] expected: [K!x:xinBasis(OK)]; ^---------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.23.113 (140.247.23.113) Time: Thu Mar 3 12:25:30 2005 Input: K = nfinit(x^5+7*x+1); ? nfbasis(K); Output: ? ? nfbasis(x,{flag=0},{p}): integral basis of the field Q[a], where a is a root of the polynomial x, using the round 4 algorithm. Second and third args are optional. Binary digits of flag mean 1: assume that no square of a prime>primelimit divides the discriminant of x, 2: use round 2 algorithm instead. If present, p provides the matrix of a partial factorization of the discriminant of x, useful if one wants only an order maximal at certain primes only. ? Errors (if any) and Timing Info: Timing: real 0m0.193s user 0m0.009s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.23.113 (140.247.23.113) Time: Thu Mar 3 12:25:40 2005 Input: K = nfinit(x^5+7*x+1); nfbasis(K); Output: ? ? ? Errors (if any) and Timing Info: *** incorrect type in nfbasis00. Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.23.113 (140.247.23.113) Time: Thu Mar 3 12:26:24 2005 Input: K = nfinit(x^5+7*x+1); ?nfbasis(x^5+7x+1); Output: ? ? nfbasis(x,{flag=0},{p}): integral basis of the field Q[a], where a is a root of the polynomial x, using the round 4 algorithm. Second and third args are optional. Binary digits of flag mean 1: assume that no square of a prime>primelimit divides the discriminant of x, 2: use round 2 algorithm instead. If present, p provides the matrix of a partial factorization of the discriminant of x, useful if one wants only an order maximal at certain primes only. ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.015s sys 0m0.002s '140.247' ************** PARI ***************** Host 140.247.23.113 (140.247.23.113) Time: Thu Mar 3 12:26:31 2005 Input: K = nfinit(x^5+7*x+1); nfbasis(x^5+7x+1); Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: nfbasis(x^5+7x+1); ^----- Timing: real 0m0.017s user 0m0.011s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.23.113 (140.247.23.113) Time: Thu Mar 3 12:26:45 2005 Input: K = nfinit(x^5+7*x+1); nfbasis(x^5+7x+1) Output: ? ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: nfbasis(x^5+7x+1) ^---- Timing: real 0m0.017s user 0m0.015s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.23.113 (140.247.23.113) Time: Thu Mar 3 12:26:50 2005 Input: nfbasis(x^5+7x+1) Output: ? ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: nfbasis(x^5+7x+1) ^---- Timing: real 0m0.011s user 0m0.006s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.23.113 (140.247.23.113) Time: Thu Mar 3 12:30:17 2005 Input: nfbasis(x^2-5) Output: ? [1, 1/2*x + 1/2] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.23.113 (140.247.23.113) Time: Thu Mar 3 12:30:37 2005 Input: nfbasis(x^2+7*x+1) Output: ? [1, 1/3*x - 1/3] ? ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.23.113 (140.247.23.113) Time: Thu Mar 3 12:30:49 2005 Input: nfbasis(x^5+7*x+1) Output: ? [1, x, x^2, x^3, 1/9*x^4 + 4/9*x^3 - 2/9*x^2 + 1/9*x + 2/9] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '80.182.' ************** PARI ***************** Host 80.182.117.40 (80.182.117.40) Time: Thu Mar 3 17:04:31 2005 Input: for(d=10^8,10^8+10^5,if(isfundamental(d),h1=quadclassunit(d)[1];h2=quadclassunit(d)[1];if(h1==h2,,print(d," ",h1," ",h2)),)) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 7271 Killed /usr/bin/gp -q -emacs Timing: real 0m21.039s user 0m20.992s sys 0m0.007s '80.182.' ************** PARI ***************** Host 80.182.117.40 (80.182.117.40) Time: Thu Mar 3 17:05:03 2005 Input: for(d=10^8,10^8+10^5,if(isfundamental(d),h1=quadclassunit(d)[1];h2=quadclassunit(d)[1];if(h1==h2,,print(d," ",h1," ",h2)),)) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 7290 Killed /usr/bin/gp -q -emacs Timing: real 0m21.031s user 0m20.986s sys 0m0.013s '80.182.' ************** PARI ***************** Host 80.182.117.40 (80.182.117.40) Time: Thu Mar 3 17:06:30 2005 Input: for(d=10^8,10^8+10^5,if(isfundamental(d),h1=quadclassunit(d)[1];h2=quadclassunit(d)[1];if(h1==h2,,print(d," ",h1," ",h2)),)) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 7311 Killed /usr/bin/gp -q -emacs Timing: real 0m21.014s user 0m20.996s sys 0m0.005s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Thu Mar 3 17:20:21 2005 Input: z=polroots(x^2+x+1)[1] x=[-1,0,0;0,0,-z;0,-z^2,0] charpoly(x) Output: ? -0.50000000000000000000000000000000000000 - 0.86602540378443864676372317075293618346*I ? [-1 0 0] [0 0 0.50000000000000000000000000000000000000 + 0.86602540378443864676372317075293618346*I] [0 0.49999999999999999999999999999999999999 - 0.86602540378443864676372317075293618346*I 0] ? x^3 + x^2 + (-0.99999999999999999999999999999999999999 + 0.E-57*I)*x + (-0.99999999999999999999999999999999999999 + 0.E-57*I) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Thu Mar 3 17:20:46 2005 Input: z=polroots(x^2+x+1)[1] x=[-1,0,0;0,0,-z;0,-z^2,0] charpoly(x) factor(%) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Thu Mar 3 17:20:58 2005 Input: z=polroots(x^2+x+1)[1] x=[-1,0,0;0,0,-z;0,-z^2,0] charpoly(x) factor(charpoly(x)) Output: ? -0.50000000000000000000000000000000000000 - 0.86602540378443864676372317075293618346*I ? [-1 0 0] [0 0 0.50000000000000000000000000000000000000 + 0.86602540378443864676372317075293618346*I] [0 0.49999999999999999999999999999999999999 - 0.86602540378443864676372317075293618346*I 0] ? x^3 + x^2 + (-0.99999999999999999999999999999999999999 + 0.E-57*I)*x + (-0.99999999999999999999999999999999999999 + 0.E-57*I) ? [x + (-0.99999999999999999999999999999999999999 + 0.E-38*I) 1] [x + (1.0000000000000000000000000000000000000 + 0.E-38*I) 1] [x + (0.99999999999999999999999999999999999999 + 0.E-38*I) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.017s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:11:06 2005 Input: (6s^2 -2st+12s+6t^2 +10t+14)^2 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (6s^2-2st+12s+6t^2+10t ^-------------------- Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:11:28 2005 Input: (6(s^2)-2st+12s+6(t^2)+10t+14)^2 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (6(s^2)-2st+12s+6(t^2) ^-------------------- Timing: real 0m0.011s user 0m0.006s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:11:42 2005 Input: (6(s^2)-2st+12s+6(t^2)+10t+14)^2 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (6(s^2)-2st+12s+6(t^2) ^-------------------- Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:11:55 2005 Input: s*s Output: ? s^2 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:12:07 2005 Input: 6s^2 Output: ? 6 ? Errors (if any) and Timing Info: *** Warning: unused characters: s^2. Timing: real 0m0.011s user 0m0.004s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:12:16 2005 Input: 6*s^2 Output: ? 6*s^2 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.009s sys 0m0.002s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:12:24 2005 Input: (6*s^2)^2 Output: ? 36*s^4 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:12:30 2005 Input: (6*s^2-2)^2 Output: ? 36*s^4 - 24*s^2 + 4 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.004s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:13:00 2005 Input: (6*s^2-2st+12s+6t^2+10t+14)^2 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (6*s^2-2st+12s+6t^2+10t+14)^ ^-------------------- Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:13:12 2005 Input: (6*s^2-2st+12s+6t^2+10t+14)^(2) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (6*s^2-2st+12s+6t^2+10t+14)^ ^-------------------- Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:13:21 2005 Input: (6*s^2-2st)^(2) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (6*s^2-2st)^(2) ^------- Timing: real 0m0.011s user 0m0.004s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:13:40 2005 Input: (6*s^2-2st+12s+6t^2+10t+14)*(2) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (6*s^2-2st+12s+6t^2+10t+14)* ^-------------------- Timing: real 0m0.011s user 0m0.003s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:13:58 2005 Input: (6*s^2-2st)^2 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (6*s^2-2st)^2 ^----- Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:14:07 2005 Input: (6*s^2-2st )^2 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (6*s^2-2st)^2 ^----- Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:14:59 2005 Input: (6st)^2 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (6st)^2 ^----- Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:15:04 2005 Input: (6s)^2 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (6s)^2 ^---- Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 22:15:24 2005 Input: (6*s^2-2*s*t+12*s+6*t^2+10*t+14)^2 Output: ? 36*s^4 + (-24*t + 144)*s^3 + (76*t^2 + 72*t + 312)*s^2 + (-24*t^3 + 104*t^2 + 184*t + 336)*s + (36*t^4 + 120*t^3 + 268*t^2 + 280*t + 196) ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.008s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.239.222 (140.247.239.222) Time: Thu Mar 3 22:24:09 2005 Input: (s-(t+1))^2+(2*s-t+2)^2+(-s-2t-3)^2 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...t+1))^2+(2*s-t+2)^2+(-s-2t-3)^2 ^------ Timing: real 0m0.011s user 0m0.008s sys 0m0.002s '140.247' ************** PARI ***************** Host 140.247.239.222 (140.247.239.222) Time: Thu Mar 3 22:24:20 2005 Input: (s-(t+1))^2+(2*s-t+2)^2+(-s-2*t-3)^2 Output: ? 6*s^2 + (-2*t + 12)*s + (6*t^2 + 10*t + 14) ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.239.222 (140.247.239.222) Time: Thu Mar 3 22:24:41 2005 Input: ((s-(t+1))^2+(2*s-t+2)^2+(-s-2*t-3)^2)^2 Output: ? 36*s^4 + (-24*t + 144)*s^3 + (76*t^2 + 72*t + 312)*s^2 + (-24*t^3 + 104*t^2 + 184*t + 336)*s + (36*t^4 + 120*t^3 + 268*t^2 + 280*t + 196) ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.239.222 (140.247.239.222) Time: Thu Mar 3 22:33:05 2005 Input: 3*t-6=0 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 3*t-6=0 ^-- Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.239.222 (140.247.239.222) Time: Thu Mar 3 22:33:12 2005 Input: 3*t-6 Output: ? 3*t - 6 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 23:14:03 2005 Input: (6*t^2+10*t+14+6*s^2-2*s*t+12*s)^2 Output: ? 36*t^4 + (-24*s + 120)*t^3 + (76*s^2 + 104*s + 268)*t^2 + (-24*s^3 + 72*s^2 + 184*s + 280)*t + (36*s^4 + 144*s^3 + 312*s^2 + 336*s + 196) ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 23:14:36 2005 Input: (6*s^2-2*s*t+12*s+6*t^2+10*t+14)^2 Output: ? 36*s^4 + (-24*t + 144)*s^3 + (76*t^2 + 72*t + 312)*s^2 + (-24*t^3 + 104*t^2 + 184*t + 336)*s + (36*t^4 + 120*t^3 + 268*t^2 + 280*t + 196) ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 23:18:04 2005 Input: s*(t^2+(5/3)*t+(7/3))*(-24*t+144) Output: ? (-24*t^3 + 104*t^2 + 184*t + 336)*s ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.239.222 (140.247.239.222) Time: Thu Mar 3 23:23:18 2005 Input: (12*t^2+20*t+28-2*s*t+12*s)^2 Output: ? 144*t^4 + (-48*s + 480)*t^3 + (4*s^2 + 208*s + 1072)*t^2 + (-48*s^2 + 368*s + 1120)*t + (144*s^2 + 672*s + 784) ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 23:36:35 2005 Input: (12*t^2+20*t+28-2*s*t+12*s)^2 Output: ? 144*t^4 + (-48*s + 480)*t^3 + (4*s^2 + 208*s + 1072)*t^2 + (-48*s^2 + 368*s + 1120)*t + (144*s^2 + 672*s + 784) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 23:36:49 2005 Input: (-2*s*t+12*s+12*t^2+20*t+28)^2 Output: ? (4*t^2 - 48*t + 144)*s^2 + (-48*t^3 + 208*t^2 + 368*t + 672)*s + (144*t^4 + 480*t^3 + 1072*t^2 + 1120*t + 784) ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 23:41:08 2005 Input: 6*(6*t^2+10*t+14)^2+(6*t^2+10*t+14)*(76*t^2+72*t+312)+(-48*t^3+208*t^2+368*t^2+784)*s+136*t^4+120*t^3+268*t^2+280*t+196 Output: ? 808*t^4 + (-48*s + 2032)*t^3 + (576*s + 5532)*t^2 + 6088*t + (784*s + 5740) ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.008s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.67.51 (140.247.67.51) Time: Thu Mar 3 23:42:50 2005 Input: s*(-48*t^3+208*t^2+368*t^2+784)+6*(6*t^2+10*t+14)^2+(6*t^2+10*t+14)*(76*t^2+72*t+312)+136*t^4+120*t^3+268*t^2+280*t+196 Output: ? (-48*t^3 + 576*t^2 + 784)*s + (808*t^4 + 2032*t^3 + 5532*t^2 + 6088*t + 5740) ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '62.76.2' ************** PARI ***************** Host 62.76.250.93 (62.76.250.93) Time: Fri Mar 4 03:19:49 2005 Input: AKS(109109) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: AKS(109109) ^----------- Timing: real 0m0.011s user 0m0.004s sys 0m0.009s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Fri Mar 4 05:35:36 2005 Input: bezout(44,133) Output: ? [-3, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Fri Mar 4 05:37:42 2005 Input: bezout(4,133) Output: ? [-33, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.009s sys 0m0.002s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Fri Mar 4 05:50:32 2005 Input: bezout(8,553) Output: ? [-69, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Fri Mar 4 08:43:52 2005 Input: bezout(13,553) Output: ? [-85, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.413s user 0m0.011s sys 0m0.005s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Fri Mar 4 10:00:40 2005 Input: bezout(14,703) Output: ? [-251, 5, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.319s user 0m0.009s sys 0m0.005s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Fri Mar 4 10:03:41 2005 Input: bezout(19,703) Output: ? [1, 0, 19] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Fri Mar 4 10:10:39 2005 Input: bezout(150,703) Output: ? [-314, 67, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Fri Mar 4 10:13:23 2005 Input: bezout(235,703) Output: ? [-350, 117, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Fri Mar 4 10:18:54 2005 Input: bezout(650,703) Output: ? [252, -233, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Fri Mar 4 10:57:05 2005 Input: bezout(588,871) Output: ? [-277, 187, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Fri Mar 4 10:59:18 2005 Input: bezout(21,871) Output: ? [83, -2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.002s sys 0m0.010s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Fri Mar 4 11:00:47 2005 Input: bezout(3,871) Output: ? [-290, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Fri Mar 4 11:02:13 2005 Input: bezout(16,871) Output: ? [-381, 7, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Fri Mar 4 11:02:16 2005 Input: bezout(16,871) Output: ? [-381, 7, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Fri Mar 4 11:05:26 2005 Input: bezout(25,871) Output: ? [-209, 6, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Fri Mar 4 11:06:43 2005 Input: bezout(5,871) Output: ? [-174, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Fri Mar 4 11:11:07 2005 Input: bezout(165,871) Output: ? [-322, 61, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Fri Mar 4 11:12:59 2005 Input: bezout(9,871) Output: ? [-387, 4, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '217.204' ************** PARI ***************** Host 217.204.123.75 (217.204.123.75) Time: Fri Mar 4 12:11:25 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.004s '217.204' ************** PARI ***************** Host 217.204.123.75 (217.204.123.75) Time: Fri Mar 4 12:11:34 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Fri Mar 4 13:50:11 2005 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.006s sys 0m0.008s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Fri Mar 4 14:47:25 2005 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '82.67.1' ************** PARI ***************** Host 82.67.154.177 (82.67.154.177) Time: Fri Mar 4 15:47:17 2005 Input: F:=FiniteField(2); F; R:=PolynomeRing(F); R; Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: F:=FiniteField(2); ^---------------- *** unexpected character: R:=PolynomeRing(F); ^----------------- Timing: real 0m0.012s user 0m0.009s sys 0m0.001s '82.67.1' ************** PARI ***************** Host 82.67.154.177 (82.67.154.177) Time: Fri Mar 4 15:47:21 2005 Input: F:=FiniteField(2); F; R:=PolynomRing(F); R; Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: F:=FiniteField(2); ^---------------- *** unexpected character: R:=PolynomRing(F); ^---------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '82.67.1' ************** PARI ***************** Host 82.67.154.177 (82.67.154.177) Time: Fri Mar 4 15:47:28 2005 Input: F:=FiniteField(2); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: F:=FiniteField(2); ^---------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '132.206' ************** PARI ***************** Host 132.206.150.38 (132.206.150.38) Time: Fri Mar 4 16:27:26 2005 Input: polsubcyclo(5,4) Output: ? x^4 + x^3 + x^2 + x + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.045s user 0m0.009s sys 0m0.002s '140.247' ************** PARI ***************** Host 140.247.161.154 (140.247.161.154) Time: Fri Mar 4 18:23:19 2005 Input: nfint(x^4-4*x^2-5); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: nfint(x^4-4*x^2-5); ^------------ Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.161.154 (140.247.161.154) Time: Fri Mar 4 18:23:33 2005 Input: nfint(x^4-4x^2-5); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: nfint(x^4-4x^2-5); ^------- Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.161.154 (140.247.161.154) Time: Fri Mar 4 18:23:38 2005 Input: nfints(x^4-4x^2-5); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: nfints(x^4-4x^2-5); ^------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.161.154 (140.247.161.154) Time: Fri Mar 4 18:25:05 2005 Input: nfints(x^4-4x^2-x+5); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: nfints(x^4-4x^2-x+5); ^--------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '213.184' ************** PARI ***************** Host 213.184.241.103 (213.184.241.103) Time: Sat Mar 5 09:28:55 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.233s user 0m0.009s sys 0m0.006s '200.103' ************** PARI ***************** Host 200.103.114.134 (200.103.114.134) Time: Sat Mar 5 16:10:55 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.42.' ************** PARI ***************** Host 128.42.62.34 (128.42.62.34) Time: Sat Mar 5 22:23:21 2005 Input: T := PolynomialRing(Rationals()); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: T:=PolynomialRing(Rat ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '67.171.' ************** PARI ***************** Host 67.171.129.172 (67.171.129.172) Time: Sun Mar 6 01:58:53 2005 Input: prime(2) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '67.171.' ************** PARI ***************** Host 67.171.129.172 (67.171.129.172) Time: Sun Mar 6 01:59:09 2005 Input: prime(3) Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.008s sys 0m0.004s '67.171.' ************** PARI ***************** Host 67.171.129.172 (67.171.129.172) Time: Sun Mar 6 01:59:19 2005 Input: prime(5) Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '67.171.' ************** PARI ***************** Host 67.171.129.172 (67.171.129.172) Time: Sun Mar 6 01:59:27 2005 Input: prime(11) Output: ? 31 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '67.171.' ************** PARI ***************** Host 67.171.129.172 (67.171.129.172) Time: Sun Mar 6 01:59:37 2005 Input: prime(31) Output: ? 127 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '67.171.' ************** PARI ***************** Host 67.171.129.172 (67.171.129.172) Time: Sun Mar 6 01:59:49 2005 Input: prime(127) Output: ? 709 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '67.171.' ************** PARI ***************** Host 67.171.129.172 (67.171.129.172) Time: Sun Mar 6 01:59:59 2005 Input: prime(709) Output: ? 5381 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '67.171.' ************** PARI ***************** Host 67.171.129.172 (67.171.129.172) Time: Sun Mar 6 02:00:26 2005 Input: prime(5381) Output: ? 52711 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '67.171.' ************** PARI ***************** Host 67.171.129.172 (67.171.129.172) Time: Sun Mar 6 02:00:37 2005 Input: prime(52711) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '67.171.' ************** PARI ***************** Host 67.171.129.172 (67.171.129.172) Time: Sun Mar 6 02:00:47 2005 Input: prime(52711) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '220.236' ************** PARI ***************** Host 220.236.96.62 (220.236.96.62) Time: Sun Mar 6 06:27:24 2005 Input: isPrime(1987) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: isPrime(1987) ^------------- Timing: real 0m0.229s user 0m0.006s sys 0m0.010s '220.236' ************** PARI ***************** Host 220.236.96.62 (220.236.96.62) Time: Sun Mar 6 06:27:56 2005 Input: isprime(1987) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.058s user 0m0.006s sys 0m0.005s '81.66.1' ************** PARI ***************** Host 81.66.172.45 (81.66.172.45) Time: Sun Mar 6 13:45:07 2005 Input: factor(987654321987654321987654321987654321) Output: ? [3 2] [7 1] [11 1] [13 1] [17 2] [19 1] [101 1] [9901 1] [52579 1] [379721 1] [999999000001 1] ? Errors (if any) and Timing Info: Timing: real 0m0.431s user 0m0.007s sys 0m0.008s '81.66.1' ************** PARI ***************** Host 81.66.172.45 (81.66.172.45) Time: Sun Mar 6 13:45:50 2005 Input: factor(987654321987654321987654321987654321) Output: ? [3 2] [7 1] [11 1] [13 1] [17 2] [19 1] [101 1] [9901 1] [52579 1] [379721 1] [999999000001 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '81.66.1' ************** PARI ***************** Host 81.66.172.45 (81.66.172.45) Time: Sun Mar 6 13:46:25 2005 Input: factor(9876543219876543219876543219876543211) Output: ? [29 1] [67 1] [1708031238233 1] [2976023516680397688469 1] ? Errors (if any) and Timing Info: Timing: real 0m0.134s user 0m0.090s sys 0m0.016s '80.58.4' ************** PARI ***************** Host 80.58.42.235 (80.58.42.235) Time: Sun Mar 6 17:06:07 2005 Input: [i : i in [1..366] | i mod 7 eq 4 ]; Output: ? ? Errors (if any) and Timing Info: *** ; or ] expected: [i:iin[1..366]|imod7eq ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Mon Mar 7 05:45:16 2005 Input: bezout(21,931) Output: ? [-44, 1, 7] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Mon Mar 7 05:45:54 2005 Input: bezout(9,931) Output: ? [207, -2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '83.211.' ************** PARI ***************** Host 83.211.136.87 (83.211.136.87) Time: Mon Mar 7 06:35:08 2005 Input: az98op Output: ? az98op ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.007s sys 0m0.005s '83.211.' ************** PARI ***************** Host 83.211.136.87 (83.211.136.87) Time: Mon Mar 7 06:35:13 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '83.211.' ************** PARI ***************** Host 83.211.136.87 (83.211.136.87) Time: Mon Mar 7 06:35:37 2005 Input: czef34mn Output: ? czef34mn ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '158.109' ************** PARI ***************** Host 158.109.66.121 (158.109.66.121) Time: Mon Mar 7 08:46:49 2005 Input: x:=[2,3,4]; x; K:=GF(4); K; K2:=PolynomialRing(K); T:=[x: x in K2 | x^(7^2) + x^(7^1) + x]; Output: ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: x:=[2,3,4]; ^--------- *** unexpected character: K:=GF(4); ^------- *** unexpected character: K2:=PolynomialRing(K); ^-------------------- *** unexpected character: T:=[x:xinK2|x^(7^2)+x^ ^-------------------- Timing: real 0m0.357s user 0m0.007s sys 0m0.010s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Mon Mar 7 08:47:08 2005 Input: bezout(23,1057) Output: ? [46, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.008s sys 0m0.004s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Mon Mar 7 08:48:25 2005 Input: bezout(3,1057) Output: ? [-352, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Mon Mar 7 08:50:18 2005 Input: bezout(437,1057) Output: ? [-387, 160, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Mon Mar 7 08:53:50 2005 Input: bezout(17,1057) Output: ? [-373, 6, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Mon Mar 7 08:56:40 2005 Input: bezout(25,1057) Output: ? [296, -7, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Mon Mar 7 08:57:44 2005 Input: bezout(4,1057) Output: ? [-264, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Mon Mar 7 09:00:53 2005 Input: bezout(29,1057) Output: ? [-328, 9, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Mon Mar 7 09:00:58 2005 Input: bezout(29,1057) Output: ? [-328, 9, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Mon Mar 7 09:02:12 2005 Input: bezout(8,1057) Output: ? [-132, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '161.116' ************** PARI ***************** Host 161.116.52.50 (161.116.52.50) Time: Mon Mar 7 11:41:32 2005 Input: Prime(5); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Prime(5); ^--------- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '219.164' ************** PARI ***************** Host 219.164.16.253 (219.164.16.253) Time: Mon Mar 7 11:42:36 2005 Input: factor(351293725658528142025984363908540515455299471247490008661682391281288234075835346606964794661872221262643846492958379267355968427671) Output: ? [351293725658528142025984363908540515455299471247490008661682391281288234075835346606964794661872221262643846492958379267355968427671 1] ? Errors (if any) and Timing Info: Timing: real 0m0.075s user 0m0.050s sys 0m0.009s '203.252' ************** PARI ***************** Host 203.252.48.205 (203.252.48.205) Time: Mon Mar 7 21:10:25 2005 Input: n:=7; dmax:=7 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: n:=7;dmax:=7 ^---------- Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '203.252' ************** PARI ***************** Host 203.252.48.205 (203.252.48.205) Time: Mon Mar 7 21:10:35 2005 Input: n:=7; dmax:=7; Output: ? ? Errors (if any) and Timing Info: *** unexpected character: n:=7;dmax:=7; ^----------- Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '203.252' ************** PARI ***************** Host 203.252.48.205 (203.252.48.205) Time: Mon Mar 7 21:11:43 2005 Input: Int:=IntegerRing(); Rat:=Rationals(); RowS:=PowerSeriesRing(Rat,100); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: Int:=IntegerRing(); ^--------------- *** unexpected character: Rat:=Rationals(); ^------------- *** unexpected character: RowS:=PowerSeriesRing(Ra ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '210.98.' ************** PARI ***************** Host 210.98.29.3 (210.98.29.3) Time: Tue Mar 8 01:35:07 2005 Input: ClassicalModularPolynomial(13) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: ClassicalModularPoly ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Tue Mar 8 05:38:59 2005 Input: bezout(992,1057) Output: ? [374, -351, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '82.64.7' ************** PARI ***************** Host 82.64.76.87 (82.64.76.87) Time: Tue Mar 8 07:09:24 2005 Input: 450! Output: ? 17333687331126326593447131461045793996778112652090510155692075095553330016834367506046750882904387106145811284518424097858618583806301650208347296181351667570171918700422280962237272230663528084038062312369342674135036610101508838220494970929739011636793766165023730853896403901590836144149594432684204513784716402303182604094683993315061302563918385303341510606761462420205820006936352095967417183191538725617509521380556781309195429800229273803342553558164591996298912368598547771179158461351340068905647127658164836377126303774923360078072307462008554355068361448126606281145760960499187813428397924840592504537849487425060488481036571447957046788635742936714615176219148469743102979949740714485104716169664052397392602848408694007408998901127492905171514473431386633392492040661522692303043813960541966093224243809225137268851717904303214058238447936111678568236973036238404626507890688000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.308s user 0m0.008s sys 0m0.008s '82.64.7' ************** PARI ***************** Host 82.64.76.87 (82.64.76.87) Time: Tue Mar 8 07:09:35 2005 Input: 450! Output: ? 17333687331126326593447131461045793996778112652090510155692075095553330016834367506046750882904387106145811284518424097858618583806301650208347296181351667570171918700422280962237272230663528084038062312369342674135036610101508838220494970929739011636793766165023730853896403901590836144149594432684204513784716402303182604094683993315061302563918385303341510606761462420205820006936352095967417183191538725617509521380556781309195429800229273803342553558164591996298912368598547771179158461351340068905647127658164836377126303774923360078072307462008554355068361448126606281145760960499187813428397924840592504537849487425060488481036571447957046788635742936714615176219148469743102979949740714485104716169664052397392602848408694007408998901127492905171514473431386633392492040661522692303043813960541966093224243809225137268851717904303214058238447936111678568236973036238404626507890688000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '195.131' ************** PARI ***************** Host 195.131.84.202 (195.131.84.202) Time: Tue Mar 8 07:26:16 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Tue Mar 8 09:32:18 2005 Input: bezout(17,553) Output: ? [-65, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.340s user 0m0.005s sys 0m0.012s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Tue Mar 8 09:36:17 2005 Input: bezout(22,553) Output: ? [176, -7, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Tue Mar 8 09:37:06 2005 Input: bezout(8,553) Output: ? [-69, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Tue Mar 8 09:48:02 2005 Input: bezout(25,703) Output: ? [225, -8, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Tue Mar 8 09:51:04 2005 Input: bezout(9,703) Output: ? [-78, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.205' ************** PARI ***************** Host 128.205.113.174 (128.205.113.174) Time: Tue Mar 8 12:33:32 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '128.205' ************** PARI ***************** Host 128.205.113.174 (128.205.113.174) Time: Tue Mar 8 12:33:49 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.194' ************** PARI ***************** Host 128.194.144.133 (128.194.144.133) Time: Tue Mar 8 16:02:24 2005 Input: c:=MinimumWeight(RandomLinearCode(GF(2),7,4)); c; Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: c:=MinimumWeight(Rando ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.194' ************** PARI ***************** Host 128.194.144.133 (128.194.144.133) Time: Tue Mar 8 16:02:32 2005 Input: c:=MinimumWeight(RandomLinearCode(GF(2),7,3)); c; Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: c:=MinimumWeight(Rando ^-------------------- Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '81.174.' ************** PARI ***************** Host 81.174.201.226 (81.174.201.226) Time: Tue Mar 8 17:57:31 2005 Input: gcd(1,2) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '81.174.' ************** PARI ***************** Host 81.174.201.226 (81.174.201.226) Time: Tue Mar 8 17:57:41 2005 Input: gcd(1,2) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.005s '81.174.' ************** PARI ***************** Host 81.174.201.226 (81.174.201.226) Time: Tue Mar 8 17:57:52 2005 Input: gcd(5,8) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '81.174.' ************** PARI ***************** Host 81.174.201.226 (81.174.201.226) Time: Tue Mar 8 17:58:09 2005 Input: gcd(36,9) Output: ? 9 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '81.174.' ************** PARI ***************** Host 81.174.201.226 (81.174.201.226) Time: Tue Mar 8 17:58:22 2005 Input: isprime(434763483624876284682346234) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.005s '81.174.' ************** PARI ***************** Host 81.174.201.226 (81.174.201.226) Time: Tue Mar 8 17:58:31 2005 Input: isprime(4347634836248762846823462398808098405943954375984739574385783453454) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '81.174.' ************** PARI ***************** Host 81.174.201.226 (81.174.201.226) Time: Tue Mar 8 17:58:47 2005 Input: isprime(4347634836248762846823462398808098405943954375984739574385783453454) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '81.174.' ************** PARI ***************** Host 81.174.201.226 (81.174.201.226) Time: Tue Mar 8 17:58:52 2005 Input: istprime(4347634836248762846823462398808098405943954375984739574385783453454) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: istprime(43476348362 ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '81.174.' ************** PARI ***************** Host 81.174.201.226 (81.174.201.226) Time: Tue Mar 8 17:59:29 2005 Input: isprime(434763483624876284682346239880809840594395437598476823462398808098405943954375984768234623988080984059439543759847682346239880809840594395437598476823462398808098405943954375984768234623988080984059439543759847682346239880809840594395437598476823462398808098405943954375984739574385783453454) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '81.174.' ************** PARI ***************** Host 81.174.201.226 (81.174.201.226) Time: Tue Mar 8 17:59:36 2005 Input: isprime(434763483624876284682346239880809840594395437598476823462398808098405943954375984768234623988080984059439543759847682346239880809840594395437598476823462398808098405943954375984768234623988080984059439543759847682346239880809840594395437598476823462398808098405943954375984739574385783453451) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.013s sys 0m0.006s '81.174.' ************** PARI ***************** Host 81.174.201.226 (81.174.201.226) Time: Tue Mar 8 17:59:58 2005 Input: factor(8) Output: ? [2 3] ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.007s sys 0m0.005s '81.174.' ************** PARI ***************** Host 81.174.201.226 (81.174.201.226) Time: Tue Mar 8 18:00:11 2005 Input: factor(81) Output: ? [3 4] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '81.174.' ************** PARI ***************** Host 81.174.201.226 (81.174.201.226) Time: Tue Mar 8 18:00:19 2005 Input: factor(100) Output: ? [2 2] [5 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '81.174.' ************** PARI ***************** Host 81.174.201.226 (81.174.201.226) Time: Tue Mar 8 18:14:00 2005 Input: factor(100) Output: ? [2 2] [5 2] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.005s '128.205' ************** PARI ***************** Host 128.205.113.174 (128.205.113.174) Time: Tue Mar 8 19:25:17 2005 Input: R:=ReedMullerCode(2,8); #R; MinimumWeight(R); WeightDistribution(R); Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: R:=ReedMullerCode(2,8) ^-------------------- *** unexpected character: #R; ^-- *** expected character: '=' instead of: MinimumWeight(R); ^- *** expected character: '=' instead of: WeightDistribution(R); ^- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.205' ************** PARI ***************** Host 128.205.113.174 (128.205.113.174) Time: Tue Mar 8 20:09:58 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Wed Mar 9 10:20:07 2005 Input: bezout(21,871) Output: ? [83, -2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.352s user 0m0.005s sys 0m0.008s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Wed Mar 9 10:25:17 2005 Input: bezout(330,871) Output: ? [-161, 61, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Wed Mar 9 10:26:58 2005 Input: bezout(28,871) Output: ? [280, -9, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Wed Mar 9 10:28:45 2005 Input: bezout(10,871) Output: ? [-87, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '213.67.' ************** PARI ***************** Host 213.67.160.35 (213.67.160.35) Time: Wed Mar 9 14:48:21 2005 Input: 346/8^23 Output: ? 173/295147905179352825856 ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.008s sys 0m0.006s '213.67.' ************** PARI ***************** Host 213.67.160.35 (213.67.160.35) Time: Wed Mar 9 14:48:50 2005 Input: 234 % 6 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '213.67.' ************** PARI ***************** Host 213.67.160.35 (213.67.160.35) Time: Wed Mar 9 14:49:02 2005 Input: 234 % 6 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '213.67.' ************** PARI ***************** Host 213.67.160.35 (213.67.160.35) Time: Wed Mar 9 14:50:03 2005 Input: factor(234234) Output: ? [2 1] [3 2] [7 1] [11 1] [13 2] ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.008s sys 0m0.005s '213.67.' ************** PARI ***************** Host 213.67.160.35 (213.67.160.35) Time: Wed Mar 9 14:50:17 2005 Input: factor(234232341234123412341234123412341234123412344) Output: ? [2 3] [3 2] [3253226961585047393628251714060294918380727 1] ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.012s sys 0m0.005s '213.67.' ************** PARI ***************** Host 213.67.160.35 (213.67.160.35) Time: Wed Mar 9 14:50:35 2005 Input: factor(234232341234123412341123412341234123412341234123412341234123412341234234123412341234123412344) Output: ? [2 3] [3 1] [11 1] [83 1] [179 1] [16823 1] [29399 1] [675391 1] [16718946899 1] [20669966699 1] [5702508060653020435421 1] [90720604137903114854113451549 1] ? Errors (if any) and Timing Info: Timing: real 0m3.983s user 0m3.907s sys 0m0.043s '202.37.' ************** PARI ***************** Host 202.37.96.11 (202.37.96.11) Time: Wed Mar 9 15:08:26 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.003s sys 0m0.010s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 9 15:15:19 2005 Input: [(a1)*d^3+(a2)*d^4+(a3)*d^5+(a4)*d^6]*[(m1)*d^3+(m2)+(m3)*d^5+(m4)*d^6]+[(b1)*d^3+(b2)*d^4+(b3)*d^5+(b4)*d^6]*[(n1)*d^3+(n2)+(n3)*d^5+(n4)*d^6] Output: ? ? Errors (if any) and Timing Info: *** forbidden multiplication t_VEC * t_VEC. Timing: real 0m0.026s user 0m0.006s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 9 15:15:37 2005 Input: =[(a1)*d^3+(a2)*d^4+(a3)*d^5+(a4)*d^6]*[(m1)*d^3+(m2)+(m3)*d^5+(m4)*d^6]+[(b1)*d^3+(b2)*d^4+(b3)*d^5+(b4)*d^6]*[(n1)*d^3+(n2)+(n3)*d^5+(n4)*d^6] Output: ? ? Errors (if any) and Timing Info: *** unexpected character: =[(a1)*d^3+(a2)*d^4+ ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 9 15:17:17 2005 Input: a1*a2 Output: ? a2*a1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 9 15:17:23 2005 Input: =a1*a2 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: =a1*a2 ^------ Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 9 15:17:31 2005 Input: a1*a2; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 9 15:17:34 2005 Input: a1*a2 Output: ? a2*a1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 9 15:17:44 2005 Input: 3*4 Output: ? 12 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '66.156.' ************** PARI ***************** Host 66.156.201.222 (66.156.201.222) Time: Wed Mar 9 19:12:05 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '67.176.' ************** PARI ***************** Host 67.176.255.108 (67.176.255.108) Time: Wed Mar 9 20:38:57 2005 Input: >RingOfIntegers(K); >Maximal Equation Order with defining polynomial x^3-2 over ZZ Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: >RingOfIntegers(K); ^------------------- *** unexpected character: >MaximalEquationOrde ^-------------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '209.208' ************** PARI ***************** Host 209.208.77.64 (209.208.77.64) Time: Thu Mar 10 02:51:49 2005 Input: 77^78 Output: ? 1400478878861077275204355173497883582881170052805402744623832005974580646666038835482520187434192328057795134300138402634891672631795285274886753369 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '213.228' ************** PARI ***************** Host 213.228.0.12 (213.228.0.12) Time: Thu Mar 10 04:47:26 2005 Input: Mod(x^2,x^3+x+1) Output: ? Mod(x^2, x^3 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '213.228' ************** PARI ***************** Host 213.228.0.12 (213.228.0.12) Time: Thu Mar 10 04:47:35 2005 Input: Mod(x^2,x^3+x+1) Output: ? Mod(x^2, x^3 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '213.228' ************** PARI ***************** Host 213.228.0.12 (213.228.0.12) Time: Thu Mar 10 04:47:43 2005 Input: Mod(x^2,x^3+x+1) Output: ? Mod(x^2, x^3 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '158.109' ************** PARI ***************** Host 158.109.66.104 (158.109.66.104) Time: Thu Mar 10 10:05:20 2005 Input: t := { n : n in [0..364 by 1] | (((n+4) mod(7)) eq 0)}; t; Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: t:={n:nin[0..364by1]|( ^-------------------- Timing: real 0m0.212s user 0m0.003s sys 0m0.009s '192.91.' ************** PARI ***************** Host 192.91.247.212 (192.91.247.212) Time: Thu Mar 10 10:27:51 2005 Input: bezout(90,133) Output: ? [34, -23, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.041s user 0m0.006s sys 0m0.006s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Thu Mar 10 10:42:11 2005 Input: bezout(400,931) Output: ? [-398, 171, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.011s sys 0m0.002s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Thu Mar 10 10:46:23 2005 Input: bezout(250,1057) Output: ? [241, -57, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '70.23.5' ************** PARI ***************** Host 70.23.50.195 (70.23.50.195) Time: Thu Mar 10 14:33:07 2005 Input: cc Output: ? cc ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.010s '70.23.5' ************** PARI ***************** Host 70.23.50.195 (70.23.50.195) Time: Thu Mar 10 14:33:13 2005 Input: 1 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 18:09:45 2005 Input: factor(2^(2^5)+1) Output: ? [641 1] [6700417 1] ? Errors (if any) and Timing Info: Timing: real 0m0.045s user 0m0.005s sys 0m0.007s '69.108.' ************** PARI ***************** Host 69.108.4.113 (69.108.4.113) Time: Thu Mar 10 18:22:32 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 20:31:18 2005 Input: factor(2^(2^5)+1) Output: ? [641 1] [6700417 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 20:43:43 2005 Input: factor(2^(2^5)+1) Output: ? [641 1] [6700417 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 20:43:50 2005 Input: factor(x^6-1) Output: ? [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.047s user 0m0.006s sys 0m0.007s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 20:49:10 2005 Input: for( k=1, 12, print(k, Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: for(k=1,12,print(k, ^ Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 20:51:52 2005 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 20:52:13 2005 Input: for( k=1, 16, print(k,": ",Mod(2^k,17)) ) Output: ? 1: Mod(2, 17) 2: Mod(4, 17) 3: Mod(8, 17) 4: Mod(16, 17) 5: Mod(15, 17) 6: Mod(13, 17) 7: Mod(9, 17) 8: Mod(1, 17) 9: Mod(2, 17) 10: Mod(4, 17) 11: Mod(8, 17) 12: Mod(16, 17) 13: Mod(15, 17) 14: Mod(13, 17) 15: Mod(9, 17) 16: Mod(1, 17) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 21:08:09 2005 Input: collatz(x0,n)= { local(x,i,ans) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 21:09:56 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(x%2 == 0, x/2, (3*x 1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 21:14:26 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x 1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? ? Errors (if any) and Timing Info: *** forbidden division t_POL % t_INT. Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 21:16:57 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 21:17:17 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(190,16) Output: ? ? [190, 95, 143, 215, 323, 485, 728, 364, 182, 91, 137, 206, 103, 155, 233, 350, 175] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 21:17:30 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(190,30) Output: ? ? [190, 95, 143, 215, 323, 485, 728, 364, 182, 91, 137, 206, 103, 155, 233, 350, 175, 263, 395, 593, 890, 445, 668, 334, 167, 251, 377, 566, 283, 425, 638] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 21:17:40 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(190,40) Output: ? ? [190, 95, 143, 215, 323, 485, 728, 364, 182, 91, 137, 206, 103, 155, 233, 350, 175, 263, 395, 593, 890, 445, 668, 334, 167, 251, 377, 566, 283, 425, 638, 319, 479, 719, 1079, 1619, 2429, 3644, 1822, 911, 1367] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 21:17:51 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(190,60) Output: ? ? [190, 95, 143, 215, 323, 485, 728, 364, 182, 91, 137, 206, 103, 155, 233, 350, 175, 263, 395, 593, 890, 445, 668, 334, 167, 251, 377, 566, 283, 425, 638, 319, 479, 719, 1079, 1619, 2429, 3644, 1822, 911, 1367, 2051, 3077, 4616, 2308, 1154, 577, 866, 433, 650, 325, 488, 244, 122, 61, 92, 46, 23, 35, 53, 80] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 21:18:03 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(190,70) Output: ? ? [190, 95, 143, 215, 323, 485, 728, 364, 182, 91, 137, 206, 103, 155, 233, 350, 175, 263, 395, 593, 890, 445, 668, 334, 167, 251, 377, 566, 283, 425, 638, 319, 479, 719, 1079, 1619, 2429, 3644, 1822, 911, 1367, 2051, 3077, 4616, 2308, 1154, 577, 866, 433, 650, 325, 488, 244, 122, 61, 92, 46, 23, 35, 53, 80, 40, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 21:18:17 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(190,68) Output: ? ? [190, 95, 143, 215, 323, 485, 728, 364, 182, 91, 137, 206, 103, 155, 233, 350, 175, 263, 395, 593, 890, 445, 668, 334, 167, 251, 377, 566, 283, 425, 638, 319, 479, 719, 1079, 1619, 2429, 3644, 1822, 911, 1367, 2051, 3077, 4616, 2308, 1154, 577, 866, 433, 650, 325, 488, 244, 122, 61, 92, 46, 23, 35, 53, 80, 40, 20, 10, 5, 8, 4, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 21:21:26 2005 Input: factor(2^(2^5)+1) Output: ? [641 1] [6700417 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 21:23:40 2005 Input: factor(2^(2^5)+1) Output: ? [641 1] [6700417 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 21:23:54 2005 Input: factor(x^6-1) Output: ? [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 21:24:02 2005 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Thu Mar 10 21:24:20 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:11:55 2005 Input: factor(x^6-1) Output: ? [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:13:02 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:21:33 2005 Input: for(a=1,100, for(b=a,100, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? ? ? ? a,b ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: for(a=1,100, ^ *** expected character: ')' instead of: for(b=a,100, ^ *** expected character: ',' instead of: ...ac((a^2+b^2+1)/(a*b))==0, ^ *** Warning: unused characters: ,). *** Warning: unused characters: ). *** Warning: unused characters: ). Timing: real 0m0.015s user 0m0.006s sys 0m0.007s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:24:02 2005 Input: for(a=1,100, for(b=a,100, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: for(a=1,100, ^ *** expected character: ')' instead of: for(b=a,100, ^ *** Warning: unused characters: )). Timing: real 0m0.018s user 0m0.006s sys 0m0.006s '68.91.1' ************** PARI input=for(a=1,100,\ for(b=a,100,\ if( frac((a^2+b^2+1)/(a*b))==0 , \ print(a,",",b), ) \ ) \ ) ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:28:39 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Error in script -- calculator type=PARI input=for(a=1,100,\ for(b=a,100,\ if( frac((a^2+b^2+1)/(a*b))==0 , \ print(a,",",b), ) \ ) \ ) invalid. '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:30:05 2005 Input: for(a=1,100, for(b=a,100, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: for(a=1,100, ^ *** expected character: ')' instead of: for(b=a,100, ^ *** Warning: unused characters: )). Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:33:12 2005 Input: for(a=1,100, for(b=a,100, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: for(a=1,100, ^ *** expected character: ')' instead of: for(b=a,100, ^ *** Warning: unused characters: )). Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:33:57 2005 Input: for(a=1,100, for(b=a,100, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: for(a=1,100,for(b=a,100, ^ *** Warning: unused characters: )). Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:34:10 2005 Input: for(a=1,100, for(b=a,100, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.024s sys 0m0.009s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:36:48 2005 Input: for(a=1,100, for(b=a,100, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.030s sys 0m0.002s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:37:35 2005 Input: for(a=1,100, for(b=1,a, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,1 5,2 13,5 34,13 89,34 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.028s sys 0m0.004s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:38:01 2005 Input: for(a=1,100, for(b=1,a, if( frac((a^2+b^2+1)/(a*b))==0 , print(b,",",a), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.026s sys 0m0.006s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:38:11 2005 Input: for(a=1,100, for(b=1,a, if( frac((a^2+b^2+1)/(a*b))==0 , print(b,",",a), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.026s sys 0m0.006s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:38:20 2005 Input: for(a=1,1000, for(b=1,a, if( frac((a^2+b^2+1)/(a*b))==0 , print(b,",",a), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 89,233 233,610 ? Errors (if any) and Timing Info: Timing: real 0m2.039s user 0m2.029s sys 0m0.010s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:39:46 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.024s sys 0m0.008s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:43:20 2005 Input: for(x=0,20,print(x,":",floor((x+1)*sqrt(2))-floor(x*sqrt(2)))) Output: ? 0:1 1:1 2:2 3:1 4:2 5:1 6:1 7:2 8:1 9:2 10:1 11:1 12:2 13:1 14:2 15:1 16:2 17:1 18:1 19:2 20:1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.006s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:49:09 2005 Input: vector(20,x, floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:55:08 2005 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:55:16 2005 Input: vector(50,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:55:31 2005 Input: vector(100,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:56:06 2005 Input: vector(1000,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.015s sys 0m0.005s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 00:59:55 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.028s sys 0m0.004s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Fri Mar 11 01:00:17 2005 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '158.109' ************** PARI ***************** Host 158.109.66.35 (158.109.66.35) Time: Fri Mar 11 06:33:01 2005 Input: {n : n in [1..10]}; Output: ? ? Errors (if any) and Timing Info: *** Warning: unused characters: };. *** unexpected character: n:nin[1..10]}; ^--------- Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '158.109' ************** PARI ***************** Host 158.109.66.123 (158.109.66.123) Time: Fri Mar 11 11:00:40 2005 Input: P := PolynomialRing(Integers());*/ f := x^3+3*x+1; f; Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: P:=PolynomialRing(Int ^-------------------- *** unexpected character: f:=x^3+3*x+1; ^----------- Timing: real 0m0.196s user 0m0.007s sys 0m0.010s '139.78.' ************** PARI ***************** Host 139.78.112.6 (139.78.112.6) Time: Fri Mar 11 13:11:40 2005 Input: factor(2^(2^5)+1) Output: ? [641 1] [6700417 1] ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.007s sys 0m0.005s '139.78.' ************** PARI ***************** Host 139.78.112.6 (139.78.112.6) Time: Fri Mar 11 13:11:46 2005 Input: factor(x^6-1) Output: ? [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.058s user 0m0.006s sys 0m0.006s '139.78.' ************** PARI ***************** Host 139.78.112.6 (139.78.112.6) Time: Fri Mar 11 13:11:56 2005 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '139.78.' ************** PARI ***************** Host 139.78.112.6 (139.78.112.6) Time: Fri Mar 11 13:12:21 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '139.78.' ************** PARI ***************** Host 139.78.112.6 (139.78.112.6) Time: Fri Mar 11 13:13:47 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.028s sys 0m0.004s '139.78.' ************** PARI ***************** Host 139.78.112.6 (139.78.112.6) Time: Fri Mar 11 13:14:35 2005 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.099s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 11 17:25:28 2005 Input: a=2^64-1; b=2^32+1; gcd(a,b); Output: ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.076s user 0m0.009s sys 0m0.001s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 11 17:25:42 2005 Input: a=2^64-1; b=2^32+1; gcd(a,b) Output: ? ? ? 4294967297 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '219.77.' ************** PARI ***************** Host 219.77.70.172 (219.77.70.172) Time: Sat Mar 12 01:39:21 2005 Input: 11 Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.010s '219.77.' ************** PARI ***************** Host 219.77.70.172 (219.77.70.172) Time: Sat Mar 12 01:39:34 2005 Input: factor(10^2-1) Output: ? [3 2] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '219.77.' ************** PARI ***************** Host 219.77.70.172 (219.77.70.172) Time: Sat Mar 12 01:39:41 2005 Input: factor(10^50-1) Output: ? [3 2] [11 1] [41 1] [251 1] [271 1] [5051 1] [9091 1] [21401 1] [25601 1] [182521213001 1] [78875943472201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.061s user 0m0.023s sys 0m0.012s '219.77.' ************** PARI ***************** Host 219.77.70.172 (219.77.70.172) Time: Sat Mar 12 01:40:14 2005 Input: factor(10^50-1)g4 Output: ? [3 2] [11 1] [41 1] [251 1] [271 1] [5051 1] [9091 1] [21401 1] [25601 1] [182521213001 1] [78875943472201 1] ? Errors (if any) and Timing Info: *** Warning: unused characters: g4. Timing: real 0m0.034s user 0m0.026s sys 0m0.007s '219.77.' ************** PARI ***************** Host 219.77.70.172 (219.77.70.172) Time: Sat Mar 12 01:41:07 2005 Input: factor(10^67-1) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13468 Killed /usr/bin/gp -q -emacs Timing: real 0m41.916s user 0m20.987s sys 0m0.013s '219.77.' ************** PARI ***************** Host 219.77.70.172 (219.77.70.172) Time: Sat Mar 12 01:41:43 2005 Input: factor(10^61-1) Output: ? [3 2] [733 1] [4637 1] [329401 1] [974293 1] [1360682471 1] [106007173861643 1] [7061709990156159479 1] ? Errors (if any) and Timing Info: Timing: real 0m0.186s user 0m0.158s sys 0m0.022s '219.77.' ************** PARI ***************** Host 219.77.70.172 (219.77.70.172) Time: Sat Mar 12 01:42:06 2005 Input: factor(10^62-1) Output: ? [3 2] [11 1] [2791 1] [6943319 1] [57336415063790604359 1] [909090909090909090909090909091 1] ? Errors (if any) and Timing Info: Timing: real 0m6.503s user 0m3.373s sys 0m0.050s '219.77.' ************** PARI ***************** Host 219.77.70.172 (219.77.70.172) Time: Sat Mar 12 01:42:28 2005 Input: factor(10^61-1) factor(10^10-1) Output: ? [3 2] [733 1] [4637 1] [329401 1] [974293 1] [1360682471 1] [106007173861643 1] [7061709990156159479 1] ? [3 2] [11 1] [41 1] [271 1] [9091 1] ? Errors (if any) and Timing Info: Timing: real 0m0.352s user 0m0.166s sys 0m0.010s '219.77.' ************** PARI ***************** Host 219.77.70.172 (219.77.70.172) Time: Sat Mar 12 01:45:12 2005 Input: g4 Output: ? g4 ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.008s sys 0m0.002s '219.77.' ************** PARI ***************** Host 219.77.70.172 (219.77.70.172) Time: Sat Mar 12 01:45:29 2005 Input: factor(10^50-1) Output: ? [3 2] [11 1] [41 1] [251 1] [271 1] [5051 1] [9091 1] [21401 1] [25601 1] [182521213001 1] [78875943472201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.021s sys 0m0.015s '219.77.' ************** PARI ***************** Host 219.77.70.172 (219.77.70.172) Time: Sat Mar 12 01:45:40 2005 Input: factor(10^53-1) Output: ? [3 2] [107 1] [1659431 1] [1325815267337711173 1] [47198858799491425660200071 1] ? Errors (if any) and Timing Info: Timing: real 0m2.806s user 0m1.508s sys 0m0.027s '219.77.' ************** PARI ***************** Host 219.77.70.172 (219.77.70.172) Time: Sat Mar 12 01:45:56 2005 Input: factor(10^60-1) Output: ? [3 3] [7 1] [11 1] [13 1] [31 1] [37 1] [41 1] [61 1] [101 1] [211 1] [241 1] [271 1] [2161 1] [3541 1] [9091 1] [9901 1] [27961 1] [2906161 1] [4188901 1] [39526741 1][+++] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.011s sys 0m0.006s '81.179.' ************** PARI ***************** Host 81.179.248.147 (81.179.248.147) Time: Sat Mar 12 03:38:23 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '81.179.' ************** PARI ***************** Host 81.179.248.147 (81.179.248.147) Time: Sat Mar 12 03:39:23 2005 Input: print(lift(sqrt(Mod(-1,872!+1))^2+1)); Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m4.034s user 0m2.108s sys 0m0.011s '81.179.' ************** PARI ***************** Host 81.179.248.147 (81.179.248.147) Time: Sat Mar 12 05:52:43 2005 Input: print(lift(sqrt(Mod(-1,872!+1))^2+1)); Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m4.042s user 0m2.107s sys 0m0.011s '63.252.' ************** PARI ***************** Host 63.252.67.58 (63.252.67.58) Time: Sat Mar 12 11:23:52 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.364s user 0m0.008s sys 0m0.009s '63.252.' ************** PARI ***************** Host 63.252.67.58 (63.252.67.58) Time: Sat Mar 12 11:24:02 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '63.252.' ************** PARI ***************** Host 63.252.67.58 (63.252.67.58) Time: Sat Mar 12 11:24:17 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Sat Mar 12 16:23:58 2005 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.047s user 0m0.007s sys 0m0.005s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Sat Mar 12 16:33:44 2005 Input: for(x=1,50,print1(x,": ",numdiv(x),",")) Output: ? 1: 1,2: 2,3: 2,4: 3,5: 2,6: 4,7: 2,8: 4,9: 3,10: 4,11: 2,12: 6,13: 2,14: 4,15: 4,16: 5,17: 2,18: 6,19: 2,20: 6,21: 4,22: 4,23: 2,24: 8,25: 3,26: 4,27: 4,28: 6,29: 2,30: 8,31: 2,32: 6,33: 4,34: 4,35: 4,36: 9,37: 2,38: 4,39: 4,40: 8,41: 2,42: 8,43: 2,44: 6,45: 6,46: 4,47: 2,48: 10,49: 3,50: 6, ? Errors (if any) and Timing Info: Timing: real 0m0.054s user 0m0.008s sys 0m0.004s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Sat Mar 12 16:37:13 2005 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Sat Mar 12 16:39:06 2005 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.91.1' ************** PARI ***************** Host 68.91.130.17 (68.91.130.17) Time: Sat Mar 12 16:42:24 2005 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '218.226' ************** PARI ***************** Host 218.226.139.230 (218.226.139.230) Time: Sun Mar 13 06:32:12 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.005s sys 0m0.008s '137.222' ************** PARI ***************** Host 137.222.107.209 (137.222.107.209) Time: Sun Mar 13 09:46:57 2005 Input: N = 126262500008088522679168814217389766997656923509934334666051794317660756997593 Output: ? 126262500008088522679168814217389766997656923509934334666051794317660756997593 ? Errors (if any) and Timing Info: Timing: real 0m0.288s user 0m0.005s sys 0m0.012s '137.222' ************** PARI ***************** Host 137.222.107.209 (137.222.107.209) Time: Sun Mar 13 09:47:16 2005 Input: eulerphi(N) Output: ? ? Errors (if any) and Timing Info: *** not an integer argument in an arithmetic function Timing: real 0m0.156s user 0m0.007s sys 0m0.006s '137.222' ************** PARI ***************** Host 137.222.107.209 (137.222.107.209) Time: Sun Mar 13 09:48:21 2005 Input: eulerphi(126262500008088522679168814217389766997656923509934334666051794317660756997593) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 29105 Killed /usr/bin/gp -q -emacs Timing: real 0m42.582s user 0m20.994s sys 0m0.006s '67.67.8' ************** PARI ***************** Host 67.67.8.43 (67.67.8.43) Time: Sun Mar 13 16:24:07 2005 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.008s sys 0m0.005s '67.67.8' ************** PARI ***************** Host 67.67.8.43 (67.67.8.43) Time: Sun Mar 13 16:24:19 2005 Input: vector(50,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.004s '67.67.8' ************** PARI ***************** Host 67.67.8.43 (67.67.8.43) Time: Sun Mar 13 16:24:37 2005 Input: v=vector(50,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '80.58.3' ************** PARI ***************** Host 80.58.34.107 (80.58.34.107) Time: Sun Mar 13 17:12:33 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.073s user 0m0.008s sys 0m0.002s '80.58.3' ************** PARI ***************** Host 80.58.34.107 (80.58.34.107) Time: Sun Mar 13 17:25:18 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" x:= { n : n in { 4..366 by 7}}; Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? Errors (if any) and Timing Info: *** unexpected character: x:={n:nin{4..366by7}}; ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '80.58.3' ************** PARI ***************** Host 80.58.34.107 (80.58.34.107) Time: Sun Mar 13 17:33:59 2005 Input: "x:={n: n in {4..366 by 7}};" Output: ? "x:={n: n in {4..366 by 7}};" ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '80.58.3' ************** PARI ***************** Host 80.58.34.107 (80.58.34.107) Time: Sun Mar 13 17:38:36 2005 Input: "print "x";" Output: ? "print " ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: x";". Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '80.58.3' ************** PARI ***************** Host 80.58.34.107 (80.58.34.107) Time: Sun Mar 13 17:38:43 2005 Input: "x:={n: n in {4..366 by 7}};" Output: ? "x:={n: n in {4..366 by 7}};" ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '80.58.3' ************** PARI ***************** Host 80.58.34.107 (80.58.34.107) Time: Sun Mar 13 17:45:44 2005 Input: "K:=KG(4); M22:=KMatrixRing(k,2); Mt:={n: n in M22 | Trace(n) eq 0}; Mf:={n: n in M22 | n[1] eq n[2]}; Mtf:={n: n in Mt meet Mf}; " K:=KG(4); Output: ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: '"' instead of: "K:=KG(4); ^ *** unexpected character: M22:=KMatrixRing(k,2); ^------------------ *** unexpected character: Mt:={n:ninM22|Trace(n)e ^-------------------- *** unexpected character: Mf:={n:ninM22|n[1]eqn[2 ^-------------------- *** unexpected character: Mtf:={n:ninMtmeetMf}; ^----------------- *** expected character: '"' instead of: " ^ *** unexpected character: K:=KG(4); ^------- Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '128.250' ************** PARI ***************** Host 128.250.37.103 (128.250.37.103) Time: Sun Mar 13 23:19:41 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '128.250' ************** PARI ***************** Host 128.250.37.103 (128.250.37.103) Time: Sun Mar 13 23:26:38 2005 Input: "200+88" Output: ? "200+88" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.250' ************** PARI ***************** Host 128.250.37.103 (128.250.37.103) Time: Sun Mar 13 23:58:18 2005 Input: // Some Magma code to illustrate Substitution cipher // Orginal text Text:="MEETMEAFTERMIDNIGHTINTTEALLEY"; Text1:=Text; Text2:=""; for i:= 1 to #Text1 do a:=Text1[i]; c1:=StringToCode(a); x:=c1-65; y:= (x+5) mod 26; c1:=y+65; Text2:= Text2 cat CodeToString(c1); end for; // Text 2 is encrypted string by shift cipher with the key k =5 // Decryption Brute force // Trying the decryption with all keys for key:=0 to 25 do Text3:=""; for i:= 1 to #Text2 do a:=Text2[i]; c1:=StringToCode(a); x:=c1-65; y:= (x-key) mod 26; c1:=y+65; Text3:= Text3 cat CodeToString(c1); end for; Text3; end for; // Frequency Analysis FreqP:=[];FreqC:=[]; for i:= 1 to 26 do FreqP[i]:=0; FreqC[i]:=0; end for; for i:= 1 to #Text1 do a:=Text1[i]; c1:=StringToCode(a); x:=c1-65; FreqP[x+1]:=FreqP[x+1]+1; end for; for i:= 1 to #Text2 do a:=Text2[i]; c1:=StringToCode(a); x:=c1-65; FreqC[x+1]:=FreqC[x+1]+1; end for; Output: WARNING: PARI command contains unsafe command 'Str', so it will not be executed. '154.5.8' ************** PARI ***************** Host 154.5.80.105 (154.5.80.105) Time: Mon Mar 14 00:08:04 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:40:24 2005 Input: ZETA(2) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: ZETA(2) ^------- Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:40:32 2005 Input: zeta(2) Output: ? 1.6449340668482264364724151666460251892 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.006s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:40:39 2005 Input: zeta(1+i) Output: ? ? Errors (if any) and Timing Info: *** sorry, zeta of power series is not yet implemented. Timing: real 0m0.022s user 0m0.010s sys 0m0.003s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:40:44 2005 Input: zeta(1+I) Output: ? 0.58215805975200364819946316791425920187 - 0.92684856433080707653642431391750077405*I ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.012s sys 0m0.003s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:41:02 2005 Input: gamma(2) Output: ? 1.0000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:41:17 2005 Input: t=10 zeta(t) Output: ? 10 ? 1.0009945751278180853371459589003190169 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:41:42 2005 Input: t=10 gamma(I*t)/gamma(I*t/2)/gamma(-I*t/2) Output: ? 10 ? 0.59587263966472006251756027678049871355 - 0.20693756311679846742344032583780092659*I ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:42:01 2005 Input: t=10 gamma(I*t)/gamma(I*t/2)/gamma(-I*t/2)*2 PI Output: ? 10 ? 1.1917452793294401250351205535609974271 - 0.41387512623359693484688065167560185318*I ? PI ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:42:05 2005 Input: t=10 gamma(I*t)/gamma(I*t/2)/gamma(-I*t/2)*2 pi Output: ? 10 ? 1.1917452793294401250351205535609974271 - 0.41387512623359693484688065167560185318*I ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.006s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:42:20 2005 Input: t=10 gamma(I*t)/gamma(I*t/2)/gamma(-I*t/2)*2 2*PI Output: ? 10 ? 1.1917452793294401250351205535609974271 - 0.41387512623359693484688065167560185318*I ? 2*PI ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.006s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:42:27 2005 Input: t=10 gamma(I*t)/gamma(I*t/2)/gamma(-I*t/2)*2 2*PI() Output: ? 10 ? 1.1917452793294401250351205535609974271 - 0.41387512623359693484688065167560185318*I ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: 2*PI() ^ Timing: real 0m0.015s user 0m0.009s sys 0m0.008s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:42:34 2005 Input: t=10 gamma(I*t)/gamma(I*t/2)/gamma(-I*t/2)*2 2*pi Output: ? 10 ? 1.1917452793294401250351205535609974271 - 0.41387512623359693484688065167560185318*I ? 2*pi ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.011s sys 0m0.004s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:42:51 2005 Input: t=10 t^2 gamma(I*t)/gamma(I*t/2)/gamma(-I*t/2)*2/(2*pi) 2*pi Output: ? 10 ? 100 ? (0.59587263966472006251756027678049871355 - 0.20693756311679846742344032583780092659*I)/pi ? 2*pi ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.010s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:43:05 2005 Input: t=10 t^2 gamma(I*t)/gamma(I*t/2)/gamma(-I*t/2)*2/((2*pi)^(I*t) 2*pi Output: ? 10 ? 100 ? ? 2*pi ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...a(-I*t/2)*2/((2*pi)^(I*t) ^ Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:43:18 2005 Input: t=10 t^2 gamma(I*t)/gamma(I*t/2)/gamma(-I*t/2)*2/((2*pi)^(I*t)) 2*pi Output: ? 10 ? 100 ? ? 2*pi ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m0.015s user 0m0.010s sys 0m0.006s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:45:05 2005 Input: t=10 t^2 gamma(I*t)/gamma(I*t/2)/gamma(-I*t/2)*2/((2*Pi)^(I*t)) 2*pi Output: ? 10 ? 100 ? 1.2498262170505175613315934547992106970 + 0.17170864303253238437947582572231585279*I ? 2*pi ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.008s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:45:24 2005 Input: t=10 t^2 gamma(I*t)/gamma(I*t/2)/gamma(-I*t/2)*2/((2*Pi)^(I*t)) zeta(I*t)/zeta(1+I*t) Output: ? 10 ? 100 ? 1.2498262170505175613315934547992106970 + 0.17170864303253238437947582572231585279*I ? 1.2612861514758651024101268469505500595 + 0.026583359721490025421650847378551510793*I ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.015s sys 0m0.006s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:46:25 2005 Input: t=10 t^2 gamma(I*t)/gamma(I*t/2)/gamma(-I*t/2)*2/((2*Pi)^(I*t)) zeta(I*t)/zeta(1+I*t) conj(1+I*t) Output: ? 10 ? 100 ? 1.2498262170505175613315934547992106970 + 0.17170864303253238437947582572231585279*I ? 1.2612861514758651024101268469505500595 + 0.026583359721490025421650847378551510793*I ? 1 - 10*I ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.018s sys 0m0.001s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:46:38 2005 Input: t=10 t^2 gamma(I*t)/gamma(I*t/2)/gamma(-I*t/2)*2/((2*Pi)^(I*t)) conj(zeta(I*t))/zeta(1+I*t) Output: ? 10 ? 100 ? 1.2498262170505175613315934547992106970 + 0.17170864303253238437947582572231585279*I ? 1.2498262170505175613315934547992200999 + 0.17170864303253238437947582572234688298*I ? ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.016s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:46:53 2005 Input: t=20 t^2 gamma(I*t)/gamma(I*t/2)/gamma(-I*t/2)*2/((2*Pi)^(I*t)) conj(zeta(I*t))/zeta(1+I*t) Output: ? 20 ? 400 ? -1.2757965820490598857675103087623580873 + 1.2471735817719372788046498205246185627*I ? -1.2757965820490598857675103087623307098 + 1.2471735817719372788046498205245917999*I ? ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.015s sys 0m0.006s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:48:02 2005 Input: t=20 norm(1+I*t) t^2 gamma(I*t)/gamma(I*t/2)/gamma(-I*t/2)*2/((2*Pi)^(I*t)) conj(zeta(I*t))/zeta(1+I*t) Output: ? 20 ? 401 ? 400 ? -1.2757965820490598857675103087623580873 + 1.2471735817719372788046498205246185627*I ? -1.2757965820490598857675103087623307098 + 1.2471735817719372788046498205245917999*I ? ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.011s sys 0m0.010s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:49:33 2005 Input: t=30 zeta(1+I*t) Output: ? 30 ? 0.42426477808417825432348840585750580352 - 0.48082945406920911010915188090907751081*I ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.009s sys 0m0.007s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:49:41 2005 Input: t=30 sqrt(norm(zeta(1+I*t))) Output: ? 30 ? 0.64124688367532102497019143300135730069 ? ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.009s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:49:45 2005 Input: t=36 sqrt(norm(zeta(1+I*t))) Output: ? 36 ? 1.8610625811663303075988038249459298255 ? ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.012s sys 0m0.003s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:49:49 2005 Input: t=360 sqrt(norm(zeta(1+I*t))) Output: ? 360 ? 0.97969323920735490569868579754698602463 ? ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.024s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:49:53 2005 Input: t=361 sqrt(norm(zeta(1+I*t))) Output: ? 361 ? 1.1839783293726770170212341776780125087 ? ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.023s sys 0m0.007s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:49:58 2005 Input: t=363 sqrt(norm(zeta(1+I*t))) Output: ? 363 ? 1.3446103863618223117015244650199786132 ? ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.022s sys 0m0.008s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:50:02 2005 Input: t=364 sqrt(norm(zeta(1+I*t))) Output: ? 364 ? 1.1194441844506027528128012728106522473 ? ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.023s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:50:06 2005 Input: t=365 sqrt(norm(zeta(1+I*t))) Output: ? 365 ? 0.88180627864636284689797391586301906298 ? ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.023s sys 0m0.008s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:50:10 2005 Input: t=366 sqrt(norm(zeta(1+I*t))) Output: ? 366 ? 0.83607337663275570269769685046292903245 ? ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.026s sys 0m0.002s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:50:13 2005 Input: t=367 sqrt(norm(zeta(1+I*t))) Output: ? 367 ? 1.0454213698740389176062010636622289337 ? ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.022s sys 0m0.007s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:50:17 2005 Input: t=366 sqrt(norm(zeta(1+I*t))) Output: ? 366 ? 0.83607337663275570269769685046292903245 ? ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.025s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:50:21 2005 Input: t=365.9 sqrt(norm(zeta(1+I*t))) Output: ? 365.89999999999999999999999999999999999 ? 0.87882835797624275389148267393338090016 ? ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.025s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:50:28 2005 Input: t=366.1 sqrt(norm(zeta(1+I*t))) Output: ? 366.09999999999999999999999999999999999 ? 0.80487761776396641095215721562059247946 ? ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.025s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:50:32 2005 Input: t=366.2 sqrt(norm(zeta(1+I*t))) Output: ? 366.19999999999999999999999999999999999 ? 0.79242348258994703599143255879135190925 ? ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.024s sys 0m0.006s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:50:35 2005 Input: t=366.3 sqrt(norm(zeta(1+I*t))) Output: ? 366.29999999999999999999999999999999999 ? 0.80211028768677024679852281109759785561 ? ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.021s sys 0m0.009s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 00:50:39 2005 Input: t=366.2 sqrt(norm(zeta(1+I*t))) Output: ? 366.19999999999999999999999999999999999 ? 0.79242348258994703599143255879135190925 ? ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.021s sys 0m0.010s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 01:32:53 2005 Input: t=400 gamma(I*t) Output: ? 400 ? -1.0527505496248498564719610464116575656 E-274 - 1.2967459797256968353984532866473467495 E-274*I ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 01:33:06 2005 Input: t=100 gamma(I*t) Output: ? 100 ? -2.7908215556174776333119816976983244755 E-71 + 1.5142531804977559697806825347866576827 E-69*I ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 01:33:18 2005 Input: t=100 gamma(I*t)/sqrt(norm(gamma(I*t))) Output: ? 100 ? -0.018427220244457262399699782637659327266 + 0.99983020436175174814967998701980710093*I ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 01:33:25 2005 Input: t=120 gamma(I*t)/sqrt(norm(gamma(I*t))) Output: ? 120 ? 0.24471129114809869696502518711303114017 + 0.96959599008279240733645876695137873946*I ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 01:33:47 2005 Input: t=120 gamma(I*t)/sqrt(norm(gamma(I*t))) exp(I*(t*log(t)-t-Pi/4)) Output: ? 120 ? 0.24471129114809869696502518711303114017 + 0.96959599008279240733645876695137873946*I ? 0.24403790008822476755860339864020196988 + 0.96976569506274536293135220108286456029*I ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '84.175.' ************** PARI ***************** Host 84.175.181.169 (84.175.181.169) Time: Mon Mar 14 10:22:02 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.190s user 0m0.008s sys 0m0.004s '82.127.' ************** PARI ***************** Host 82.127.188.203 (82.127.188.203) Time: Mon Mar 14 10:42:29 2005 Input: 87451-64541 Output: ? 22910 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.008s sys 0m0.005s '82.127.' ************** PARI ***************** Host 82.127.188.203 (82.127.188.203) Time: Mon Mar 14 10:43:09 2005 Input: 985411241*51411123 Output: ? 50661098516633643 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.004s sys 0m0.011s '82.127.' ************** PARI ***************** Host 82.127.188.203 (82.127.188.203) Time: Mon Mar 14 10:44:16 2005 Input: prime(50) Output: ? 229 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:26:12 2005 Input: t=100 zeta(1+I*t) Output: ? 100 ? 1.6328335066867118666107050494664601752 - 0.068131203841812490101205482141125534704*I ? Errors (if any) and Timing Info: Timing: real 0m0.066s user 0m0.012s sys 0m0.008s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:26:14 2005 Input: t=1000 zeta(1+I*t) Output: ? 1000 ? 0.94093686829275331080101380029530083963 + 0.045226652072095099088656444101620262768*I ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.052s sys 0m0.008s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:26:48 2005 Input: t=1000 zeta(1+I*t) int(Pi) m=sqrt(t/2/Pi) Output: ? 1000 ? 0.94093686829275331080101380029530083963 + 0.045226652072095099088656444101620262768*I ? ? 12.615662610100800241235747611828419732 ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: int(Pi) ^--- Timing: real 0m0.060s user 0m0.056s sys 0m0.006s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:26:59 2005 Input: t=1000 zeta(1+I*t) Pi int(Pi) m=sqrt(t/2/Pi) Output: ? 1000 ? 0.94093686829275331080101380029530083963 + 0.045226652072095099088656444101620262768*I ? 3.1415926535897932384626433832795028841 ? ? 12.615662610100800241235747611828419732 ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: int(Pi) ^--- Timing: real 0m0.059s user 0m0.053s sys 0m0.008s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:27:12 2005 Input: t=1000 zeta(1+I*t) Pi floor(Pi) m=sqrt(t/2/Pi) Output: ? 1000 ? 0.94093686829275331080101380029530083963 + 0.045226652072095099088656444101620262768*I ? 3.1415926535897932384626433832795028841 ? 3 ? 12.615662610100800241235747611828419732 ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.056s sys 0m0.004s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:28:07 2005 Input: t=1000 zeta(1+I*t) m=floor(sqrt(t/2/Pi)) sum(n=1,m,n^(-I*t)/n) Output: ? 1000 ? 0.94093686829275331080101380029530083963 + 0.045226652072095099088656444101620262768*I ? 12 ? 0.82566055127504742550321833399950453406 + 0.015340542571715150333389729878880500420*I ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.056s sys 0m0.005s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:28:15 2005 Input: t=5000 zeta(1+I*t) m=floor(sqrt(t/2/Pi)) sum(n=1,m,n^(-I*t)/n) Output: ? 5000 ? 0.62529369633261620142177985069641604591 - 0.072852846940554152624795391266803027935*I ? 28 ? 0.68337183620343274556808111473244078364 - 0.015382358920902926345514511021897448922*I ? Errors (if any) and Timing Info: Timing: real 0m0.320s user 0m0.314s sys 0m0.007s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:28:31 2005 Input: t=50000 zeta(1+I*t) m=floor(sqrt(t/2/Pi)) sum(n=1,m,n^(-I*t)/n) Output: ? 50000 ? 1.1153301899039131537521920273904790635 + 0.46172648910435617013821497880456373173*I ? 89 ? 1.0496173905499787383170306758070626213 + 0.52298371952155504027621120141840627492*I ? Errors (if any) and Timing Info: Timing: real 0m8.296s user 0m5.397s sys 0m0.011s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:28:33 2005 Input: t=50000 zeta(1+I*t) m=floor(sqrt(t/2/Pi)) sum(n=1,m,n^(-I*t)/n) Output: ? 50000 ? 1.1153301899039131537521920273904790635 + 0.46172648910435617013821497880456373173*I ? 89 ? 1.0496173905499787383170306758070626213 + 0.52298371952155504027621120141840627492*I ? Errors (if any) and Timing Info: Timing: real 0m8.162s user 0m5.468s sys 0m0.027s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:30:35 2005 Input: t=50000 zeta(1+I*t) m=floor(sqrt(t/2/Pi)) chi = 2*(2*pi)^(I*t)*gamma(-I*t)*cos(Pi/2*I*t) sum(n=1,m,n^(-I*t)/n) sum(n=1,m,n^(-I*t)/n) + chi*sum(n=1,m,n^(I*t)) Output: ? 50000 ? 1.1153301899039131537521920273904790635 + 0.46172648910435617013821497880456373173*I ? 89 ? ? 1.0496173905499787383170306758070626213 + 0.52298371952155504027621120141840627492*I ? (-2.5946812914211841086652333175233650651 - 7.4433724772618405193956081026493738500*I)*chi + (1.0496173905499787383170306758070626213 + 0.52298371952155504027621120141840627492*I) ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m5.419s user 0m5.389s sys 0m0.017s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:31:05 2005 Input: t=5000 zeta(1+I*t) m=floor(sqrt(t/2/Pi)) chi = 2*(2*pi)^(I*t)*gamma(-I*t)*cos(Pi/2*I*t) sum(n=1,m,n^(-I*t)/n) sum(n=1,m,n^(-I*t)/n) + chi*sum(n=1,m,n^(I*t)) Output: ? 5000 ? 0.62529369633261620142177985069641604591 - 0.072852846940554152624795391266803027935*I ? 28 ? ? 0.68337183620343274556808111473244078364 - 0.015382358920902926345514511021897448922*I ? (1.9404778161744263906428759632440138455 - 1.1094270689900451485035832243658005351*I)*chi + (0.68337183620343274556808111473244078364 - 0.015382358920902926345514511021897448922*I) ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m0.323s user 0m0.314s sys 0m0.008s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:31:39 2005 Input: t=5000 zeta(1+I*t) m=floor(sqrt(t/2/Pi)) chi = 2*(2*pi)^(I*t)*gamma(-I*t)*cos(Pi/2*I*t) sum(n=1,m,n^(-I*t)/n) sum(n=1,m,n^(-I*t)/n) + sum(n=1,m,n^(I*t)) Output: ? 5000 ? 0.62529369633261620142177985069641604591 - 0.072852846940554152624795391266803027935*I ? 28 ? ? 0.68337183620343274556808111473244078364 - 0.015382358920902926345514511021897448922*I ? 2.6238496523778591362109570779764546292 - 1.1248094279109480748490977353876979840*I ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m0.323s user 0m0.315s sys 0m0.008s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:31:48 2005 Input: t=5000 zeta(1+I*t) m=floor(sqrt(t/2/Pi)) chi=2*(2*pi)^(I*t)*gamma(-I*t)*cos(Pi/2*I*t) sum(n=1,m,n^(-I*t)/n) sum(n=1,m,n^(-I*t)/n) + sum(n=1,m,n^(I*t)) Output: ? 5000 ? 0.62529369633261620142177985069641604591 - 0.072852846940554152624795391266803027935*I ? 28 ? ? 0.68337183620343274556808111473244078364 - 0.015382358920902926345514511021897448922*I ? 2.6238496523778591362109570779764546292 - 1.1248094279109480748490977353876979840*I ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m0.323s user 0m0.316s sys 0m0.008s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:32:02 2005 Input: t=5000 gamma(3) zeta(1+I*t) m=floor(sqrt(t/2/Pi)) chi=2*(2*pi)^(I*t)*gamma(-I*t)*cos(Pi/2*I*t) sum(n=1,m,n^(-I*t)/n) sum(n=1,m,n^(-I*t)/n) + sum(n=1,m,n^(I*t)) Output: ? 5000 ? 2.0000000000000000000000000000000000000 ? 0.62529369633261620142177985069641604591 - 0.072852846940554152624795391266803027935*I ? 28 ? ? 0.68337183620343274556808111473244078364 - 0.015382358920902926345514511021897448922*I ? 2.6238496523778591362109570779764546292 - 1.1248094279109480748490977353876979840*I ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m0.324s user 0m0.316s sys 0m0.009s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:32:11 2005 Input: t=5000 gamma(-I*t) zeta(1+I*t) m=floor(sqrt(t/2/Pi)) chi=2*(2*pi)^(I*t)*gamma(-I*t)*cos(Pi/2*I*t) sum(n=1,m,n^(-I*t)/n) sum(n=1,m,n^(-I*t)/n) + sum(n=1,m,n^(I*t)) Output: ? 5000 ? 2.7293148025759377095396117522013212079 E-3413 + 3.0081881775021235640004094670477056680 E-3413*I ? 0.62529369633261620142177985069641604591 - 0.072852846940554152624795391266803027935*I ? 28 ? ? 0.68337183620343274556808111473244078364 - 0.015382358920902926345514511021897448922*I ? 2.6238496523778591362109570779764546292 - 1.1248094279109480748490977353876979840*I ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m0.324s user 0m0.318s sys 0m0.005s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:32:21 2005 Input: t=5000 zeta(1+I*t) m=floor(sqrt(t/2/Pi)) chi=2*(2*pi)^(I*t)*gamma(-I*t)*cos(Pi/2*I*t) sum(n=1,m,n^(-I*t)/n) sum(n=1,m,n^(-I*t)/n) + sum(n=1,m,n^(I*t)) Output: ? 5000 ? 0.62529369633261620142177985069641604591 - 0.072852846940554152624795391266803027935*I ? 28 ? ? 0.68337183620343274556808111473244078364 - 0.015382358920902926345514511021897448922*I ? 2.6238496523778591362109570779764546292 - 1.1248094279109480748490977353876979840*I ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m0.323s user 0m0.316s sys 0m0.007s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:32:31 2005 Input: t=5000 zeta(1+I*t) m=floor(sqrt(t/2/Pi)) chi=2*(2*Pi)^(I*t)*gamma(-I*t)*cos(Pi/2*I*t) sum(n=1,m,n^(-I*t)/n) sum(n=1,m,n^(-I*t)/n) + sum(n=1,m,n^(I*t)) Output: ? 5000 ? 0.62529369633261620142177985069641604591 - 0.072852846940554152624795391266803027935*I ? 28 ? -0.017305764881189916046903163247424766295 - 0.030937801526819759891391305582991428232*I ? 0.68337183620343274556808111473244078364 - 0.015382358920902926345514511021897448922*I ? 2.6238496523778591362109570779764546292 - 1.1248094279109480748490977353876979840*I ? Errors (if any) and Timing Info: Timing: real 0m0.324s user 0m0.316s sys 0m0.008s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:32:40 2005 Input: t=5000 zeta(1+I*t) m=floor(sqrt(t/2/Pi)) chi=2*(2*Pi)^(I*t)*gamma(-I*t)*cos(Pi/2*I*t) sum(n=1,m,n^(-I*t)/n) sum(n=1,m,n^(-I*t)/n) + chi*sum(n=1,m,n^(I*t)) Output: ? 5000 ? 0.62529369633261620142177985069641604591 - 0.072852846940554152624795391266803027935*I ? 28 ? -0.017305764881189916046903163247424766295 - 0.030937801526819759891391305582991428232*I ? 0.68337183620343274556808111473244078364 - 0.015382358920902926345514511021897448922*I ? 0.61546714889065786580285800713016046051 - 0.056216992456134583027107044127432128073*I ? Errors (if any) and Timing Info: Timing: real 0m0.324s user 0m0.320s sys 0m0.003s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:32:57 2005 Input: t=50000 zeta(1+I*t) m=floor(sqrt(t/2/Pi)) chi=2*(2*Pi)^(I*t)*gamma(-I*t)*cos(Pi/2*I*t) sum(n=1,m,n^(-I*t)/n) sum(n=1,m,n^(-I*t)/n) + chi*sum(n=1,m,n^(I*t)) Output: ? 50000 ? 1.1153301899039131537521920273904790635 + 0.46172648910435617013821497880456373173*I ? 89 ? 0.0051959665909392683921021481226770710703 + 0.0099330578035887160072668189151502906349*I ? 1.0496173905499787383170306758070626213 + 0.52298371952155504027621120141840627492*I ? 1.1100709623159023075162939327007537276 + 0.45853508555620881757689607406131115969*I ? Errors (if any) and Timing Info: Timing: real 0m5.339s user 0m5.321s sys 0m0.012s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:33:32 2005 Input: t=5000 zeta(1+I*t) m=floor(sqrt(t/2/Pi)) chi=2*(2*Pi)^(I*t)*gamma(-I*t)*cos(Pi/2*I*t) sum(n=1,m,n^(-I*t)/n) sum(n=1,m,n^(-I*t)/n) + chi*sum(n=1,m,n^(I*t)) Output: ? 5000 ? 0.62529369633261620142177985069641604591 - 0.072852846940554152624795391266803027935*I ? 28 ? -0.017305764881189916046903163247424766295 - 0.030937801526819759891391305582991428232*I ? 0.68337183620343274556808111473244078364 - 0.015382358920902926345514511021897448922*I ? 0.61546714889065786580285800713016046051 - 0.056216992456134583027107044127432128073*I ? Errors (if any) and Timing Info: Timing: real 0m0.324s user 0m0.315s sys 0m0.008s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:37:08 2005 Input: t=5000 zeta(1+I*t) m=floor(sqrt(t/2/Pi)) chi=2*(2*Pi)^(I*t)*gamma(-I*t)*cos(Pi/2*I*t) sum(n=1,m,n^(-I*t)/n) sum(n=1,m,n^(-I*t)/n) + chi*sum(n=1,m,n^(I*t)) Output: ? 5000 ? 0.62529369633261620142177985069641604591 - 0.072852846940554152624795391266803027935*I ? 28 ? -0.017305764881189916046903163247424766295 - 0.030937801526819759891391305582991428232*I ? 0.68337183620343274556808111473244078364 - 0.015382358920902926345514511021897448922*I ? 0.61546714889065786580285800713016046051 - 0.056216992456134583027107044127432128073*I ? Errors (if any) and Timing Info: Timing: real 0m0.332s user 0m0.317s sys 0m0.012s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:37:18 2005 Input: t=500000 zeta(1+I*t) m=floor(sqrt(t/2/Pi)) chi=2*(2*Pi)^(I*t)*gamma(-I*t)*cos(Pi/2*I*t) sum(n=1,m,n^(-I*t)/n) sum(n=1,m,n^(-I*t)/n) + chi*sum(n=1,m,n^(I*t)) Output: ** WARNING: Computation used more memory than allowed. ** ? 500000 ? ? 282 ? -0.00091988176523007068319184648667496737762 - 0.0034234760335595139195218724097566440694*I ? 1.2992683366454613675956277485855863233 + 1.6374612992495244318367191197225858044*I ? 1.1834556634349433606645965344651040247 + 1.6826734499822361507512638397194621497*I ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m1.889s user 0m1.868s sys 0m0.016s '65.248.' ************** PARI ***************** Host 65.248.243.100 (65.248.243.100) Time: Mon Mar 14 13:37:34 2005 Input: t=50000 zeta(1+I*t) m=floor(sqrt(t/2/Pi)) chi=2*(2*Pi)^(I*t)*gamma(-I*t)*cos(Pi/2*I*t) sum(n=1,m,n^(-I*t)/n) sum(n=1,m,n^(-I*t)/n) + chi*sum(n=1,m,n^(I*t)) Output: ? 50000 ? 1.1153301899039131537521920273904790635 + 0.46172648910435617013821497880456373173*I ? 89 ? 0.0051959665909392683921021481226770710703 + 0.0099330578035887160072668189151502906349*I ? 1.0496173905499787383170306758070626213 + 0.52298371952155504027621120141840627492*I ? 1.1100709623159023075162939327007537276 + 0.45853508555620881757689607406131115969*I ? Errors (if any) and Timing Info: Timing: real 0m5.474s user 0m5.381s sys 0m0.063s '80.58.3' ************** PARI ***************** Host 80.58.32.107 (80.58.32.107) Time: Mon Mar 14 15:39:43 2005 Input: Factorial(5); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorial(5); ^------------- Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '80.58.3' ************** PARI ***************** Host 80.58.32.107 (80.58.32.107) Time: Mon Mar 14 15:40:34 2005 Input: Factorial(5) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorial(5) ^------------ Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '80.58.3' ************** PARI ***************** Host 80.58.32.107 (80.58.32.107) Time: Mon Mar 14 15:40:43 2005 Input: Factorial(5); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorial(5); ^------------- Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.167.29 (140.247.167.29) Time: Mon Mar 14 20:21:44 2005 Input: Factorization(2^200+9); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorization(2^200+ ^-------------------- Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Mon Mar 14 21:09:43 2005 Input: isprime(7) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Mon Mar 14 21:10:07 2005 Input: isprime(7) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Mon Mar 14 21:11:29 2005 Input: isprime(4) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Mon Mar 14 21:11:53 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Mon Mar 14 21:13:04 2005 Input: gp> pi Output: ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Mon Mar 14 21:13:18 2005 Input: gp> (pi) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Mon Mar 14 21:13:34 2005 Input: gp>isprime(7) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Mon Mar 14 21:13:54 2005 Input: 2*3 Output: ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Mon Mar 14 21:14:27 2005 Input: ?pi Output: ? ? Errors (if any) and Timing Info: *** obsolete function: pi ^-- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: pi ===> Pi Pi=Pi(): the constant pi, with current precision. Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Mon Mar 14 21:15:46 2005 Input: Pi Output: ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Mon Mar 14 21:17:32 2005 Input: gcd(16,24) Output: ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Mon Mar 14 21:17:51 2005 Input: nextprime(1077953) Output: ? 1077971 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Mon Mar 14 21:18:16 2005 Input: factor(5240) Output: ? [2 3] [5 1] [131 1] ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.007s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:40:16 2005 Input: t=120 zeta(1+I*t) Output: ? 120 ? 1.5516529576358822105144558967789947047 - 0.50392813731944322425963050972764895235*I ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.015s sys 0m0.003s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:40:30 2005 Input: t=120 sqrt(norm(zeta(1+I*120))) Output: ? 120 ? 1.6314320300038320936852444460555870511 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.013s sys 0m0.006s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:40:34 2005 Input: t=120 sqrt(norm(zeta(1+I*121))) Output: ? 120 ? 0.84365690323483344649880401532095281810 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.013s sys 0m0.007s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:40:38 2005 Input: t=120 sqrt(norm(zeta(1+I*122))) Output: ? 120 ? 0.63895827041931496773902568573377785545 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.011s sys 0m0.008s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:40:43 2005 Input: t=120 sqrt(norm(zeta(1+I*122.5))) Output: ? 120 ? 0.54155032170091446636685370662854301186 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.013s sys 0m0.006s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:40:47 2005 Input: t=120 sqrt(norm(zeta(1+I*122.6))) Output: ? 120 ? 0.50697492025054951365039173560910876929 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.014s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:40:51 2005 Input: t=120 sqrt(norm(zeta(1+I*122.7))) Output: ? 120 ? 0.47465834021553825535224584947281276452 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.013s sys 0m0.006s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:40:56 2005 Input: t=120 sqrt(norm(zeta(1+I*122.8))) Output: ? 120 ? 0.44893751295411038773190309672015710581 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.011s sys 0m0.007s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:41:00 2005 Input: t=120 sqrt(norm(zeta(1+I*122.9))) Output: ? 120 ? 0.43371267254552551561942101803912241428 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.015s sys 0m0.004s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:41:04 2005 Input: t=120 sqrt(norm(zeta(1+I*123))) Output: ? 120 ? 0.43122704301421172026351009457415675979 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.010s sys 0m0.011s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:41:09 2005 Input: t=120 sqrt(norm(zeta(1+I*123.1))) Output: ? 120 ? 0.44111398274568426873755111310884033522 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.016s sys 0m0.003s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:41:23 2005 Input: t=120 zet(1+I*123) sqrt(norm(zeta(1+I*123.1))) Output: ? 120 ? ? 0.44111398274568426873755111310884033522 ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: zet(1+I*123) ^------------ Timing: real 0m0.019s user 0m0.013s sys 0m0.007s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:42:09 2005 Input: t=120 zeta(1+I*123) d=zeta(1+I*123)/(zeta(1+I*123.1)-zeta(1+I*122.9)) sqrt(norm(zeta(1+I*123))) Output: ? 120 ? 0.42880690806325920570474562266165890441 + 0.045622343473438235962956764652608612082*I ? 0.38856172076779367885502841438759181336 - 4.6650426190670339774785579295590074157*I ? 0.43122704301421172026351009457415675979 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.028s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:42:30 2005 Input: t=120 zeta(1+I*123) d=5*zeta(1+I*123)/(zeta(1+I*123.1)-zeta(1+I*122.9)) sqrt(norm(zeta(1+I*123))) Output: ? 120 ? 0.42880690806325920570474562266165890441 + 0.045622343473438235962956764652608612082*I ? 1.9428086038389683942751420719379590668 - 23.325213095335169887392789647795037078*I ? 0.43122704301421172026351009457415675979 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.026s sys 0m0.007s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:43:08 2005 Input: t=120 zeta(1+I*123) d=zeta(1+I*123)/((zeta(1+I*123.1)-zeta(1+I*122.9))/.2) sqrt(norm(zeta(1+I*123))) Output: ? 120 ? 0.42880690806325920570474562266165890441 + 0.045622343473438235962956764652608612082*I ? 0.077712344153558735771005682877518362671 - 0.93300852381340679549571158591180148315*I ? 0.43122704301421172026351009457415675979 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.025s sys 0m0.008s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:43:28 2005 Input: t=120 zeta(1+I*123) d=I*(zeta(1+I*123)/((zeta(1+I*123.1)-zeta(1+I*122.9))/.2)) sqrt(norm(zeta(1+I*123))) Output: ? 120 ? 0.42880690806325920570474562266165890441 + 0.045622343473438235962956764652608612082*I ? 0.93300852381340679549571158591180148315 + 0.077712344153558735771005682877518362670*I ? 0.43122704301421172026351009457415675979 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.030s sys 0m0.003s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Mon Mar 14 22:44:28 2005 Input: t=120 zeta(1+I*123) d=I*(zeta(1+I*123)/((zeta(1+I*123.01)-zeta(1+I*122.99))/.02)) sqrt(norm(zeta(1+I*123))) Output: ? 120 ? 0.42880690806325920570474562266165890441 + 0.045622343473438235962956764652608612082*I ? 0.92417316570979513761946890951128960990 + 0.079674143626255244575203363499377605476*I ? 0.43122704301421172026351009457415675979 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.028s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Tue Mar 15 01:05:41 2005 Input: isprime(1087251) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.003s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Tue Mar 15 01:06:59 2005 Input: isprime(230484) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Tue Mar 15 01:07:25 2005 Input: isprime(82896111) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Tue Mar 15 01:07:42 2005 Input: isprime(82896111) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.258s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Tue Mar 15 01:08:00 2005 Input: isprime(5109) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Tue Mar 15 01:09:00 2005 Input: factor(1087251) Output: ? [3 1] [11 1] [47 1] [701 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Tue Mar 15 01:10:03 2005 Input: factor(82896111) Output: ? [3 2] [9210679 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Tue Mar 15 01:11:04 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.228.137 (192.43.228.137) Time: Tue Mar 15 01:14:58 2005 Input: prime(5109) Output: ? 49747 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:42:40 2005 Input: t=20 zeta(1+I*t)/(2*Pi)^(I*t)*t/Pi*sinh(Pi*t/2)*gamma(I*t) zeta(-I*t) Output: ? 20 ? -0.053873381229703653134536555019609611147 + 1.7306610438309434764849072038468199692*I ? -0.053873381229703653134536555019609610804 + 1.7306610438309434764849072038468199694*I ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.011s sys 0m0.008s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:43:09 2005 Input: t=20 zeta(1+I*t)/(2*Pi)^(I*t)*t/Pi*sinh(Pi*t/2)*gamma(I*t)-zeta(-I*t) Output: ? 20 ? -3.425464006693072191 E-37 - 1.293043785904516258 E-37*I ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.015s sys 0m0.003s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:43:16 2005 Input: t=25 zeta(1+I*t)/(2*Pi)^(I*t)*t/Pi*sinh(Pi*t/2)*gamma(I*t)-zeta(-I*t) Output: ? 25 ? 4.408103815583578154 E-38 - 1.146106992051730320 E-37*I ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.014s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:43:21 2005 Input: t=25 zeta(1+I*t)/(2*Pi)^(I*t)*t/Pi*sinh(Pi*t/2)*gamma(I*t)-zeta(-I*t) Output: ? 25 ? 4.408103815583578154 E-38 - 1.146106992051730320 E-37*I ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.016s sys 0m0.004s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:43:58 2005 Input: t=25 zeta(1+I*t)/(2*Pi)^(I*t)*t/Pi*sinh(Pi*t/2)*gamma(I*t)-zeta(-I*t) Output: ? 25 ? 4.408103815583578154 E-38 - 1.146106992051730320 E-37*I ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.015s sys 0m0.004s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:44:32 2005 Input: t=25 zeta(1+I*t)/(2*Pi)^(I*t)*sqrt(t/Pi)*sinh(Pi*t/2)/sqrt(sinh(Pi*t)) Output: ? 25 ? -0.13452252256439591660513394174047228421 - 0.97806649906256984471745324385156460430*I ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.009s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:44:39 2005 Input: t=20 zeta(1+I*t)/(2*Pi)^(I*t)*sqrt(t/Pi)*sinh(Pi*t/2)/sqrt(sinh(Pi*t)) Output: ? 20 ? 1.7047672210270262339013893035137904683 + 0.30308202182069811221871945546178118377*I ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.010s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:44:56 2005 Input: t=20 zeta(1+I*t)/(2*Pi)^(I*t)*sqrt(t/Pi)*sinh(Pi*t/2)/sqrt(sinh(Pi*t))/zeta(-I*t) Output: ? 20 ? 0.14432211018039774070520471923330827523 - 0.98953076178210707246530414642905272343*I ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.015s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:45:04 2005 Input: t=20 norm(zeta(1+I*t)/(2*Pi)^(I*t)*sqrt(t/Pi)*sinh(Pi*t/2)/sqrt(sinh(Pi*t))/zeta(-I*t)) Output: ? 20 ? 0.99999999999999999999999999999999999997 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.012s sys 0m0.006s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:45:09 2005 Input: t=27 norm(zeta(1+I*t)/(2*Pi)^(I*t)*sqrt(t/Pi)*sinh(Pi*t/2)/sqrt(sinh(Pi*t))/zeta(-I*t)) Output: ? 27 ? 0.99999999999999999999999999999999999997 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.013s sys 0m0.008s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:45:14 2005 Input: t=30 norm(zeta(1+I*t)/(2*Pi)^(I*t)*sqrt(t/Pi)*sinh(Pi*t/2)/sqrt(sinh(Pi*t))/zeta(-I*t)) Output: ? 30 ? 0.99999999999999999999999999999999999997 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.013s sys 0m0.006s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:45:17 2005 Input: t=3 norm(zeta(1+I*t)/(2*Pi)^(I*t)*sqrt(t/Pi)*sinh(Pi*t/2)/sqrt(sinh(Pi*t))/zeta(-I*t)) Output: ? 3 ? 0.99999999999999999999999999999999999995 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.014s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:45:36 2005 Input: t=3 zeta(1+I*t)/(2*Pi)^(I*t)*sqrt(t/Pi)*sinh(Pi*t/2)/sqrt(sinh(Pi*t)) Output: ? 3 ? 0.36373298714156893359198802493146258063 + 0.24899354120646507604651877083295329150*I ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.009s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:45:47 2005 Input: t=20 arg(2+I*t) zeta(1+I*t)/(2*Pi)^(I*t)*sqrt(t/Pi)*sinh(Pi*t/2)/sqrt(sinh(Pi*t)) Output: ? 20 ? 1.4711276743037345918528755717617308518 ? 1.7047672210270262339013893035137904683 + 0.30308202182069811221871945546178118377*I ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.010s sys 0m0.004s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:46:11 2005 Input: t=20 arg(2+I*t) exp(I*arg(2+I*t))*sqrt(5) zeta(1+I*t)/(2*Pi)^(I*t)*sqrt(t/Pi)*sinh(Pi*t/2)/sqrt(sinh(Pi*t)) Output: ? 20 ? 1.4711276743037345918528755717617308518 ? 0.22249707974499239469899148955931365771 + 2.2249707974499239469899148955931365772*I ? 1.7047672210270262339013893035137904683 + 0.30308202182069811221871945546178118377*I ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.012s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:46:51 2005 Input: t=20 arg(2+I) exp(I*arg(2+I))*sqrt(5) zeta(1+I*t)/(2*Pi)^(I*t)*sqrt(t/Pi)*sinh(Pi*t/2)/sqrt(sinh(Pi*t)) Output: ? 20 ? 0.46364760900080611621425623146121440202 ? 2.0000000000000000000000000000000000000 + 0.99999999999999999999999999999999999999*I ? 1.7047672210270262339013893035137904683 + 0.30308202182069811221871945546178118377*I ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.013s sys 0m0.004s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:47:16 2005 Input: t=20 zeta(1+I*t)/(2*Pi)^(I*t)*sqrt(t/Pi)*sinh(Pi*t/2)/sqrt(sinh(Pi*t))*exp(I*arg(gamma(I*t))) Output: ? 20 ? -0.053873381229703653134536555019609611154 + 1.7306610438309434764849072038468199693*I ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.011s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:47:27 2005 Input: t=20 zeta(1+I*t)/(2*Pi)^(I*t)*sqrt(t/Pi)*sinh(Pi*t/2)/sqrt(sinh(Pi*t))*exp(I*arg(gamma(I*t))) zeta(-I*t) Output: ? 20 ? -0.053873381229703653134536555019609611154 + 1.7306610438309434764849072038468199693*I ? -0.053873381229703653134536555019609610804 + 1.7306610438309434764849072038468199694*I ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.014s sys 0m0.005s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 01:47:32 2005 Input: t=2 zeta(1+I*t)/(2*Pi)^(I*t)*sqrt(t/Pi)*sinh(Pi*t/2)/sqrt(sinh(Pi*t))*exp(I*arg(gamma(I*t))) zeta(-I*t) Output: ? 2 ? 0.31472576404209958223490432211550805735 + 0.23167964875052068322446450582306984884*I ? 0.31472576404209958223490432211550805735 + 0.23167964875052068322446450582306984884*I ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.012s sys 0m0.009s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:45:00 2005 Input: isprime(13) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.092s user 0m0.007s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:45:35 2005 Input: factor(24) Output: ? [2 3] [3 1] ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.007s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:45:56 2005 Input: isprime(19) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.041s user 0m0.009s sys 0m0.002s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:46:05 2005 Input: isprime(18) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:46:26 2005 Input: isprime(281) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m1.504s user 0m0.005s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:46:36 2005 Input: isprime(5107) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:46:48 2005 Input: isprime(317) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.307s user 0m0.006s sys 0m0.007s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:47:02 2005 Input: isprime(177501) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:47:25 2005 Input: isprime(317) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:47:38 2005 Input: isprime(177501) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:47:46 2005 Input: factor(177501) Output: ? [3 1] [59167 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:52:31 2005 Input: 2^2*3*5*23*59167 Output: ? ? 81650460 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:53:35 2005 Input: prime(1105173) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.066s user 0m0.006s sys 0m0.007s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:54:11 2005 Input: prime(81650460) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:54:33 2005 Input: gcd(1105173,61284) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:55:06 2005 Input: gcd(16,24) Output: ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:55:39 2005 Input: gcd(61284,20) Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:55:52 2005 Input: gcd(61284,20,1105173) Output: ? ? Errors (if any) and Timing Info: *** invalid flag in gcd. Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:56:21 2005 Input: gcd(61284,gcd(20,1105173)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:56:48 2005 Input: gcd(1105173,gcd(61284,20)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:57:14 2005 Input: prime(5072) Output: ? 49367 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.005s sys 0m0.009s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:58:07 2005 Input: fibonnaci(10) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: fibonnaci(10) ^------------- Timing: real 0m0.020s user 0m0.007s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:58:33 2005 Input: fibonnaci(10) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: fibonnaci(10) ^------------- Timing: real 0m0.476s user 0m0.005s sys 0m0.007s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:59:20 2005 Input: Mod(1105173,20) Output: ? Mod(13, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:59:46 2005 Input: Mod(16,5) Output: ? Mod(1, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 06:59:57 2005 Input: Mod(1105173,20) Output: ? Mod(13, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.133s user 0m0.008s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:00:33 2005 Input: Mod(81650460,20) Output: ? Mod(0, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:01:10 2005 Input: Mod(81650460,20) 81650460/20 Output: ? Mod(0, 20) ? ? 4082523 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:02:00 2005 Input: binomial(5072,20) Output: ? 50253981227903680115713195525576903473426247993895571856 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.005s sys 0m0.007s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:02:46 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.007s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:03:13 2005 Input: pi+1^10 Output: ? pi + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:03:31 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.112s user 0m0.007s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:04:35 2005 Input: ?pi Output: ? ? Errors (if any) and Timing Info: *** obsolete function: pi ^-- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: pi ===> Pi Pi=Pi(): the constant pi, with current precision. Timing: real 0m0.025s user 0m0.010s sys 0m0.003s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:04:44 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:05:12 2005 Input: p 32 pi Output: ? p32 ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:05:59 2005 Input: p 32 pi Output: ? p32 ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:07:00 2005 Input: 1/7 Output: ? 1/7 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:07:32 2005 Input: 2/24 Output: ? 1/12 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:07:54 2005 Input: 1./7 Output: ? 0.14285714285714285714285714285714285714 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.004s sys 0m0.010s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:08:00 2005 Input: 1./7 1/7 Output: ? 0.14285714285714285714285714285714285714 ? 1/7 ? Errors (if any) and Timing Info: Timing: real 0m0.348s user 0m0.007s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:08:59 2005 Input: 1./7 1/7 Pi Output: ? 0.14285714285714285714285714285714285714 ? 1/7 ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.008s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:09:35 2005 Input: p 32 Pi Output: ? p32 ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:09:52 2005 Input: Pi Output: ? ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.246s user 0m0.006s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:11:12 2005 Input: prime(1105173) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:15:14 2005 Input: ithprime(1105173) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: ithprime(1105173) ^----------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:15:29 2005 Input: prime(3) Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:15:42 2005 Input: prime(1) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:16:00 2005 Input: prime(1) prime(2) prime(3) Output: ? 2 ? 3 ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:16:15 2005 Input: prime(81650460) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:17:11 2005 Input: fibonacci(1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.008s sys 0m0.002s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:17:17 2005 Input: fibonacci(3) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.005s sys 0m0.011s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:17:23 2005 Input: fibonacci(10) Output: ? 55 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:17:46 2005 Input: fibonacci(50) Output: ? 12586269025 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:18:01 2005 Input: fibonacci(20) Output: ? 6765 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:18:11 2005 Input: fibonacci(19) Output: ? 4181 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:18:21 2005 Input: fibonacci(20) Output: ? 6765 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:18:32 2005 Input: fibonacci(30) Output: ? 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.065s user 0m0.009s sys 0m0.002s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:18:43 2005 Input: fibonacci(40) Output: ? 102334155 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.011s sys 0m0.001s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:18:55 2005 Input: fibonacci(35) Output: ? 9227465 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.003s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:19:14 2005 Input: fibonacci(30) Output: ? 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:19:40 2005 Input: fibonacci(31) fibonacci(32) fibonacci(33) fibonacci(34) fibonacci(35) Output: ? 1346269 ? 2178309 ? 3524578 ? 5702887 ? 9227465 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:20:06 2005 Input: fibonacci(28) fibonacci(29) fibonacci(30) fibonacci(31) fibonacci(32) Output: ? 317811 ? 514229 ? 832040 ? 1346269 ? 2178309 ? Errors (if any) and Timing Info: Timing: real 0m0.418s user 0m0.006s sys 0m0.007s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:21:11 2005 Input: prime(200) Output: ? 1223 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:21:25 2005 Input: prime(61284) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.013s user 0m0.006s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:21:32 2005 Input: prime(10000) Output: ? 104729 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:21:38 2005 Input: prime(10001) Output: ? 104743 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:21:45 2005 Input: prime(15000) Output: ? 163841 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:21:54 2005 Input: prime(35000) Output: ? 414977 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.006s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:22:00 2005 Input: prime(65000) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:22:15 2005 Input: prime(55000) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.018s user 0m0.005s sys 0m0.007s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:22:21 2005 Input: prime(50000) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:22:26 2005 Input: prime(40000) Output: ? 479909 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:22:31 2005 Input: prime(45000) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:22:39 2005 Input: prime(40500) Output: ? 486653 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:22:52 2005 Input: prime(44000) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.235s user 0m0.007s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:22:58 2005 Input: prime(41000) Output: ? 493127 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:23:02 2005 Input: prime(42000) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:23:10 2005 Input: prime(41900) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.377s user 0m0.008s sys 0m0.003s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:23:15 2005 Input: prime(41700) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:23:20 2005 Input: prime(41500) Output: ? 499523 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:23:25 2005 Input: prime(41600) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:23:30 2005 Input: prime(41550) Output: ? 500167 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:23:36 2005 Input: prime(41580) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:23:41 2005 Input: prime(41560) Output: ? 500249 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:23:47 2005 Input: prime(41570) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:23:53 2005 Input: prime(41565) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:23:58 2005 Input: prime(41563) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:24:03 2005 Input: prime(41561) Output: ? 500257 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:24:09 2005 Input: prime(41562) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:24:15 2005 Input: prime(41561) Output: ? 500257 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:24:28 2005 Input: prime(41561) prime(41562) Output: ? 500257 ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:25:53 2005 Input: factor(81650460) Output: ? [2 2] [3 1] [5 1] [23 1] [59167 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:27:15 2005 Input: isprime(81650460) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:27:26 2005 Input: isprime(1105173) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:27:30 2005 Input: isprime(1105171) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.004s sys 0m0.009s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:27:57 2005 Input: isprime(1105177) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:28:31 2005 Input: isprime(1105173) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.004s sys 0m0.010s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:28:50 2005 Input: factor(1105171) factor(1105177) Output: ? [1105171 1] ? [1105177 1] ? Errors (if any) and Timing Info: Timing: real 0m0.041s user 0m0.008s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:30:02 2005 Input: factor(8150459) factor(8150461) Output: ? [8150459 1] ? [11 1] [740951 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.007s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:30:49 2005 Input: factor(81650459) factor(81650461) Output: ? [11 1] [127 1] [211 1] [277 1] ? [81650461 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:31:24 2005 Input: factor(81650457) factor(81650461) Output: ? [3 3] [7 1] [29 1] [14897 1] ? [81650461 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:31:32 2005 Input: factor(81650453) factor(81650461) Output: ? [37 1] [2206769 1] ? [81650461 1] ? Errors (if any) and Timing Info: Timing: real 0m0.182s user 0m0.008s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:31:38 2005 Input: factor(81650451) factor(81650461) Output: ? [3 1] [281 1] [96857 1] ? [81650461 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.003s sys 0m0.011s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:31:48 2005 Input: factor(81650449) factor(81650461) Output: ? [163 1] [500923 1] ? [81650461 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:32:00 2005 Input: factor(81650447) factor(81650461) Output: ? [81650447 1] ? [81650461 1] ? Errors (if any) and Timing Info: Timing: real 0m0.428s user 0m0.008s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:33:39 2005 Input: isprime(81650447) isprime(81650449) isprime(81650451) isprime(81650453) isprime(81650457) isprime(81650459) factor(81650461) Output: ? 1 ? 0 ? 0 ? 0 ? 0 ? 0 ? ? [81650461 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:35:48 2005 Input: fibonnaci(10) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: fibonnaci(10) ^------------- Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:35:57 2005 Input: fibonacci(10) Output: ? 55 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:36:03 2005 Input: fibonacci(15) Output: ? 610 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:36:13 2005 Input: fibonacci(20) Output: ? 6765 ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.009s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:36:36 2005 Input: fibonacci(19) fibonacci(20) fibonacci(29) fibonacci(30) Output: ? 4181 ? 6765 ? ? 514229 ? 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:36:58 2005 Input: fibonacci(19) fibonacci(20) fibonacci(30) fibonacci(31) Output: ? 4181 ? 6765 ? ? 832040 ? 1346269 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:37:38 2005 Input: fibonacci(5) fibonacci(6) fibonacci(19) fibonacci(20) fibonacci(30) fibonacci(31) Output: ? 5 ? 8 ? ? 4181 ? 6765 ? ? 832040 ? 1346269 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:37:44 2005 Input: fibonacci(7) fibonacci(8) fibonacci(19) fibonacci(20) fibonacci(30) fibonacci(31) Output: ? 13 ? 21 ? ? 4181 ? 6765 ? ? 832040 ? 1346269 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:39:14 2005 Input: factor(1105173) factor(61284) factor(20) factor(81650460) factor(18) factor(5072) Output: ? [3 2] [19 1] [23 1] [281 1] ? [2 2] [3 1] [5107 1] ? [2 2] [5 1] ? [2 2] [3 1] [5 1] [23 1] [59167 1] ? [2 1] [3 2] ? [2 4] [317 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:41:03 2005 Input: Mod(1105173,20) Mod(81650460,20) Output: ? Mod(13, 20) ? Mod(0, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:42:08 2005 Input: prime(5072) Output: ? 49367 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:43:16 2005 Input: lcm(20,18) lcm(18,5072) Output: ? 180 ? 45648 ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.009s sys 0m0.003s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:43:34 2005 Input: lcm(20,18,5072) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: lcm(20,18,5072) ^------ Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 15 07:43:45 2005 Input: lcm(20,lcm(18,5072)) Output: ? 228240 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '212.144' ************** PARI ***************** Host 212.144.198.64 (212.144.198.64) Time: Tue Mar 15 07:54:07 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '193.226' ************** PARI ***************** Host 193.226.29.100 (193.226.29.100) Time: Tue Mar 15 09:52:04 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.351s user 0m0.002s sys 0m0.013s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:01:52 2005 Input: factor(203) Output: ? [7 1] [29 1] ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:02:03 2005 Input: factor(20334534) Output: ? [2 1] [3 1] [11 2] [37 1] [757 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:02:10 2005 Input: factor(345345345345345) Output: ? [3 1] [5 1] [23 1] [31 1] [41 1] [271 1] [2906161 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:02:22 2005 Input: prime(349328547293472391) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:02:28 2005 Input: isprime(349328547293472391) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:02:34 2005 Input: isprime(349328547293472393) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:04:15 2005 Input: inversemod(3,7) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: inversemod(3,7) ^--------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:04:27 2005 Input: 3^(-1)%7 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:04:40 2005 Input: modinverse(3,7) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: modinverse(3,7) ^--------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:06:18 2005 Input: bezout(3,7)[1] Output: ? -2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:07:10 2005 Input: phi(7) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: phi(7) ^------ For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: phi(x) ===> eulerphi(x) eulerphi(x): Euler's totient function of x. Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:07:19 2005 Input: eulerphi(7) Output: ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:07:23 2005 Input: eulerphi(1644288286138814381718931386493997) Output: ? 1644288286138814298881724179241756 ? Errors (if any) and Timing Info: Timing: real 0m0.109s user 0m0.068s sys 0m0.016s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:07:56 2005 Input: bezout(7,1644288286138814381718931386493997) Output: ? [469796653182518394776837538998285, -2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:08:00 2005 Input: bezout(7,1644288286138814381718931386493997)[1] Output: ? 469796653182518394776837538998285 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:12:23 2005 Input: Mod(2,7)^100 Output: ? Mod(2, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:12:29 2005 Input: Mod(2,7)^101 Output: ? Mod(4, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:12:42 2005 Input: Mod(3,7)^(-1) Output: ? Mod(5, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:20:11 2005 Input: p=7 Output: ? 7 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 12:20:15 2005 Input: p Output: ? p ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 16:01:17 2005 Input: factor(9672075774620220110296926718055724247) Output: ? [2934729884729384723 1] [3295729472394729389 1] ? Errors (if any) and Timing Info: Timing: real 0m0.221s user 0m0.205s sys 0m0.016s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 16:01:29 2005 Input: eulerphi(9672075774620220110296926718055724247) Output: ? 9672075774620220104066467360931610136 ? Errors (if any) and Timing Info: Timing: real 0m0.221s user 0m0.206s sys 0m0.016s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 16:01:49 2005 Input: Mod(923492472974291,9672075774620220104066467360931610136)^(-1) Output: ? Mod(8415944787552510294425543088234566123, 9672075774620220104066467360931610136) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.72 (128.197.60.72) Time: Tue Mar 15 16:02:34 2005 Input: Mod(8922937353667053919136497562228780869,9672075774620220110296926718055724247)^8415944787552510294425543088234566123 Output: ? Mod(13, 9672075774620220110296926718055724247) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '62.101.' ************** PARI ***************** Host 62.101.126.231 (62.101.126.231) Time: Tue Mar 15 18:55:43 2005 Input: (t^2+2*t+1)*(t^2+2*t+2) Output: ? t^4 + 4*t^3 + 7*t^2 + 6*t + 2 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.008s sys 0m0.003s '24.15.8' ************** PARI ***************** Host 24.15.8.150 (24.15.8.150) Time: Tue Mar 15 22:14:27 2005 Input: t=2 zeta(1+I*t)/(2*Pi)^(I*t)*sqrt(t/Pi)*sinh(Pi*t/2)/sqrt(sinh(Pi*t))*exp(I*arg(gamma(I*t))) zeta(-I*t) Output: ? 2 ? 0.31472576404209958223490432211550805735 + 0.23167964875052068322446450582306984884*I ? 0.31472576404209958223490432211550805735 + 0.23167964875052068322446450582306984884*I ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.014s sys 0m0.004s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Tue Mar 15 22:21:24 2005 Input: 1+1 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '68.3.63' ************** PARI ***************** Host 68.3.63.241 (68.3.63.241) Time: Tue Mar 15 22:26:45 2005 Input: w%solutions modp Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '68.3.63' ************** PARI ***************** Host 68.3.63.241 (68.3.63.241) Time: Tue Mar 15 22:27:07 2005 Input: w %2 solutions modp Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 00:41:57 2005 Input: factor(N) Output: ? [N 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 00:42:05 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.118s user 0m0.101s sys 0m0.017s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 00:42:35 2005 Input: (294729472947294397-1)*(328497239427384289-1) Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 00:43:01 2005 Input: Mod(13, 96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 00:43:51 2005 Input: Mod(41216345596225937530422932747005437,96817818241074148177594033335528733)^ 52132671360578387144659326671226949 Output: ? Mod(605130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.005s sys 0m0.008s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 00:45:16 2005 Input: Mod(17,10600)^(-1) Output: ? Mod(9353, 10600) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 00:45:41 2005 Input: Mod(4441,101*107)^9353 Output: ? Mod(10531, 10807) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 00:46:13 2005 Input: Mod(17,10600)^(-1) Output: ? Mod(9353, 10600) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 00:46:50 2005 Input: Mod(4441,101*107)^9353 Output: ? Mod(10531, 10807) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 00:58:03 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 24499 Killed /usr/bin/gp -q -emacs Timing: real 0m21.028s user 0m20.994s sys 0m0.007s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 01:01:02 2005 Input: eulerphi(1022117) Output: ? 1020096 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 01:01:13 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 01:01:29 2005 Input: 1008*1012 Output: ? 1020096 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 01:01:55 2005 Input: Mod(13, 1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 01:02:30 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 01:03:17 2005 Input: bezout(29,11) Output: ? [-3, 8, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 01:03:40 2005 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 01:04:41 2005 Input: eulerphi(96817818241074148177594033335528733) Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.118s user 0m0.097s sys 0m0.021s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 01:05:05 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 01:05:42 2005 Input: Mod(41216345596225937530422932747005437,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(605130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 01:09:37 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 01:10:44 2005 Input: eulerphi(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 24757 Killed /usr/bin/gp -q -emacs Timing: real 0m21.023s user 0m20.991s sys 0m0.008s '70.19.2' ************** PARI ***************** Host 70.19.203.130 (70.19.203.130) Time: Wed Mar 16 01:14:35 2005 Input: factor(15) Output: ? [3 1] [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '220.233' ************** PARI ***************** Host 220.233.92.248 (220.233.92.248) Time: Wed Mar 16 04:41:10 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 08:32:11 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 28394 Killed /usr/bin/gp -q -emacs Timing: real 0m21.560s user 0m20.973s sys 0m0.028s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 08:33:23 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 28408 Killed /usr/bin/gp -q -emacs Timing: real 0m21.617s user 0m20.721s sys 0m0.280s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 08:39:20 2005 Input: factor (2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 28445 Killed /usr/bin/gp -q -emacs Timing: real 0m21.269s user 0m20.990s sys 0m0.012s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 08:45:17 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.065s user 0m0.005s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 08:45:25 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 08:46:45 2005 Input: factor(5) Output: ? [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 08:46:54 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 28512 Killed /usr/bin/gp -q -emacs Timing: real 0m21.047s user 0m20.963s sys 0m0.037s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 08:46:57 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 28516 Killed /usr/bin/gp -q -emacs Timing: real 0m21.648s user 0m20.992s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 08:46:59 2005 Input: factor(10) Output: ? [2 1] [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 08:47:25 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 09:04:58 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.009s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 09:06:12 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.008s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 09:10:07 2005 Input: Mod(167366,1020096)^78469 Output: ? Mod(845120, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 09:14:54 2005 Input: mod(167366,1022117)^78469 Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(167366,1022117)^ ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.033s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 09:15:13 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 09:16:57 2005 Input: Factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(2179575060383 ^-------------------- Timing: real 0m0.014s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 09:17:26 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 28866 Killed /usr/bin/gp -q -emacs Timing: real 0m21.057s user 0m20.979s sys 0m0.020s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Wed Mar 16 09:18:05 2005 Input: 111^3 -11^2 Output: ? 1367510 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.005s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 09:20:24 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 09:22:08 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 09:23:48 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 09:24:59 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.180s user 0m0.103s sys 0m0.019s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 09:27:18 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.118s user 0m0.100s sys 0m0.018s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 09:29:12 2005 Input: 294729472947294397*328497239427384289 Output: ? 96817818241074148177594033335528733 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 09:35:42 2005 Input: (13,96817818241074148177594033335528733)^(-1) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (13,9681781824107414817 ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 09:37:36 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.118s user 0m0.104s sys 0m0.015s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 09:38:20 2005 Input: 294729472947294396*328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 09:40:01 2005 Input: (13,96817818241074147554367320960850048)^(-1) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (13,9681781824107414755 ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 09:51:12 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.118s user 0m0.096s sys 0m0.022s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 09:52:39 2005 Input: 328497239427384289*294729472947294397 Output: ? 96817818241074148177594033335528733 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.159 (128.197.150.159) Time: Wed Mar 16 09:53:00 2005 Input: 328497239427384288*294729472947294396 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Wed Mar 16 09:59:53 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.119s user 0m0.104s sys 0m0.014s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Wed Mar 16 10:00:41 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 29407 Killed /usr/bin/gp -q -emacs Timing: real 0m21.007s user 0m20.995s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Wed Mar 16 10:04:04 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 29453 Killed /usr/bin/gp -q -emacs Timing: real 0m21.011s user 0m20.981s sys 0m0.020s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Wed Mar 16 10:18:39 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Wed Mar 16 10:21:07 2005 Input: Mod(167366,1022117)^(78469) Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Wed Mar 16 10:25:40 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 29518 Killed /usr/bin/gp -q -emacs Timing: real 0m21.002s user 0m20.994s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Wed Mar 16 10:25:47 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.121s user 0m0.108s sys 0m0.013s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Wed Mar 16 10:27:31 2005 Input: 294729472947294397*328497239427384289 Output: ? 96817818241074148177594033335528733 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.001s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Wed Mar 16 10:29:02 2005 Input: Mod(13,96817818241074148177594033335528733)^(-1) Output: ? Mod(52132671360578387480242941026823164, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Wed Mar 16 10:38:16 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387480242941026823164 Output: ? Mod(83293387193180743506542113087832284, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Wed Mar 16 10:39:19 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.118s user 0m0.107s sys 0m0.012s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Wed Mar 16 10:39:46 2005 Input: (294729472947294397-1)*(328497239427384289-1) Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Wed Mar 16 10:40:24 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Wed Mar 16 10:41:30 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^(52132671360578387144659326671226949) Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Wed Mar 16 10:43:19 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 29601 Killed /usr/bin/gp -q -emacs Timing: real 0m21.002s user 0m20.994s sys 0m0.006s '128.119' ************** PARI ***************** Host 128.119.47.17 (128.119.47.17) Time: Wed Mar 16 10:57:35 2005 Input: G:=GL(2,11); x:=elt; y:=elt; z:=y*y*x*y*y*x*y*y*x*y*x*y*x; Order(z); Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: G:=GL(2,11); ^---------- *** unexpected character: x:=elt; ^---------------- *** unexpected character: y:=elt; ^------------------ *** unexpected character: z:=y*y*x*y*y*x*y*y*x*y ^-------------------- *** expected character: '=' instead of: Order(z); ^- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 13:28:49 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 13:29:15 2005 Input: factor(1022117); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 13:29:19 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 13:41:58 2005 Input: 167366^78469 Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31223 Killed /usr/bin/gp -q -emacs Timing: real 0m21.053s user 0m20.985s sys 0m0.015s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 13:49:23 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 13:52:16 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.119s user 0m0.102s sys 0m0.018s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 13:52:21 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.118s user 0m0.097s sys 0m0.021s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 13:53:46 2005 Input: 96817818241074148177594033335528733 - 294729472947294397 - 328497239427384289 + 1 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 13:56:54 2005 Input: 96817818241074148177594033335528733 - 294729472947294397 - 328497239427384289 + 1 Output: ? 96817818241074147554367320960850048 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 13:56:57 2005 Input: 96817818241074148177594033335528733 - 294729472947294397 - 328497239427384289 + 1 Output: ? 96817818241074147554367320960850048 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 13:56:58 2005 Input: 96817818241074148177594033335528733 - 294729472947294397 - 328497239427384289 + 1 Output: ? 96817818241074147554367320960850048 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 13:57:26 2005 Input: (13,96817818241074147554367320960850048)^(-1) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (13,9681781824107414755 ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 13:58:08 2005 Input: (13,96817818241074147554367320960850048)^(-1) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (13,9681781824107414755 ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 14:00:56 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 14:04:58 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^(52132671360578387144659326671226949) Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Wed Mar 16 14:48:52 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.007s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Wed Mar 16 14:49:59 2005 Input: Mod(13,1022117)^(-1) Output: ? Mod(393122, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Wed Mar 16 14:50:05 2005 Input: Mod(13,1022117)^(-1) Output: ? Mod(393122, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Wed Mar 16 14:51:52 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Wed Mar 16 14:52:56 2005 Input: 1008 * 1012 Output: ? 1020096 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Wed Mar 16 14:55:07 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Wed Mar 16 14:56:51 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 14:56:53 2005 Input: Mod(121512,1022117)^(13) Output: ? Mod(167366, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Wed Mar 16 14:58:54 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.118s user 0m0.106s sys 0m0.012s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Wed Mar 16 14:59:21 2005 Input: 294729472947294396 * 328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Wed Mar 16 15:00:41 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Wed Mar 16 15:02:53 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Wed Mar 16 15:05:06 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31949 Killed /usr/bin/gp -q -emacs Timing: real 0m21.014s user 0m20.972s sys 0m0.029s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Wed Mar 16 15:06:15 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31955 Killed /usr/bin/gp -q -emacs Timing: real 0m21.007s user 0m20.981s sys 0m0.019s '128.197' ************** PARI ***************** Host 128.197.87.60 (128.197.87.60) Time: Wed Mar 16 15:07:45 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31961 Killed /usr/bin/gp -q -emacs Timing: real 0m21.006s user 0m20.986s sys 0m0.014s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Wed Mar 16 15:08:10 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31968 Killed /usr/bin/gp -q -emacs Timing: real 0m21.011s user 0m20.974s sys 0m0.025s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Wed Mar 16 15:12:25 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31988 Killed /usr/bin/gp -q -emacs Timing: real 0m21.037s user 0m20.972s sys 0m0.029s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 16 15:14:08 2005 Input: 167366 Output: ? 167366 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 16 15:14:31 2005 Input: factor(167366) Output: ? [2 1] [67 1] [1249 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '84.72.1' ************** PARI ***************** Host 84.72.117.212 (84.72.117.212) Time: Wed Mar 16 15:28:49 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '84.72.1' ************** PARI ***************** Host 84.72.117.212 (84.72.117.212) Time: Wed Mar 16 15:29:11 2005 Input: 2+4 Output: ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 15:59:18 2005 Input: 294729472947294396x328497239427384288 Output: ? 294729472947294396 ? Errors (if any) and Timing Info: *** Warning: unused characters: x328497239427384288. Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 16:03:07 2005 Input: 294729472947294396 x 328497239427384288 Output: ? 294729472947294396 ? Errors (if any) and Timing Info: *** Warning: unused characters: x328497239427384288. Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 16:09:32 2005 Input: 294729472947294396 * 328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 16:13:51 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 16:15:39 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 16:17:41 2005 Input: 23984723984723947234231323422342323492*90873468536548724562875427633324423460 Output: ? 2179575060383617170819849823956766088050949934328875366459377192327713922320 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.001s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 16:20:47 2005 Input: Mod(17,2179575060383617170819849823956766088050949934328875366459377192327713922320)^(-1) Output: ? Mod(128210297669624539459991166115103887532408819666404433321139834842806701313, 2179575060383617170819849823956766088050949934328875366459377192327713922320) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 16:22:45 2005 Input: Mod(808646506926052224264347178889859829860987198492865627794079793528086106381,2179575060383617170819849823956766088165808126850148038256483943383380669273)^(17) Output: ? Mod(217367901969495696162502455728774489711555540053426585804309460798884742101, 2179575060383617170819849823956766088165808126850148038256483943383380669273) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.159.87 (168.122.159.87) Time: Wed Mar 16 16:23:46 2005 Input: Mod(808646506926052224264347178889859829860987198492865627794079793528086106381,2179575060383617170819849823956766088165808126850148038256483943383380669273)^(128 210297669624539459991166115103887532408819666404433321139834842806701313) Output: ? Mod(701211919, 2179575060383617170819849823956766088165808126850148038256483943383380669273) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 18:05:32 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.893s user 0m0.004s sys 0m0.010s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 18:08:08 2005 Input: factor(1009) Output: ? [1009 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 18:17:28 2005 Input: Mod(167366, 1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.237s user 0m0.009s sys 0m0.011s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 18:33:08 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m4.018s user 0m0.098s sys 0m0.023s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 18:36:39 2005 Input: factor(294729472947294397) Output: ? [294729472947294397 1] ? Errors (if any) and Timing Info: Timing: real 0m0.533s user 0m0.007s sys 0m0.005s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 18:37:14 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m6.276s user 0m0.106s sys 0m0.014s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 18:38:48 2005 Input: 294729472947294397*328497239427384289 Output: ? 96817818241074148177594033335528733 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.007s sys 0m0.005s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 18:41:42 2005 Input: (96817818241074148177594033335528733+1)/13 Output: ? 96817818241074148177594033335528734/13 ? Errors (if any) and Timing Info: Timing: real 0m3.393s user 0m0.007s sys 0m0.006s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 18:43:05 2005 Input: 96817818241074148177594033335528734/13 Output: ? 96817818241074148177594033335528734/13 ? Errors (if any) and Timing Info: Timing: real 0m2.262s user 0m0.005s sys 0m0.006s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 18:51:26 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m2.788s user 0m0.103s sys 0m0.016s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 18:51:51 2005 Input: 294729472947294396*328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.775s user 0m0.005s sys 0m0.009s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 18:59:55 2005 Input: Mod(10424944469828754080284344711353162, 96817818241074148177594033335528733)^7447524480082626734951332381603849 Output: ? Mod(538645420281165792789187802305314, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.650s user 0m0.007s sys 0m0.004s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 19:20:08 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m5.708s user 0m0.102s sys 0m0.021s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 19:22:16 2005 Input: 294729472947294396*328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.005s sys 0m0.007s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 19:22:45 2005 Input: 96817818241074147554367320960850048+1 Output: ? 96817818241074147554367320960850049 ? Errors (if any) and Timing Info: Timing: real 0m0.903s user 0m0.008s sys 0m0.007s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 19:23:09 2005 Input: 96817818241074147554367320960850049/13 Output: ? 96817818241074147554367320960850049/13 ? Errors (if any) and Timing Info: Timing: real 0m4.478s user 0m0.004s sys 0m0.007s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 19:41:16 2005 Input: 96817818241074147554367320960850049/13 Output: ? 96817818241074147554367320960850049/13 ? Errors (if any) and Timing Info: Timing: real 0m0.201s user 0m0.006s sys 0m0.011s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Wed Mar 16 19:42:50 2005 Input: 96817818241074147554367320960850049/13 Output: ? 96817818241074147554367320960850049/13 ? Errors (if any) and Timing Info: Timing: real 0m2.138s user 0m0.005s sys 0m0.007s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Wed Mar 16 22:06:16 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.448s user 0m0.006s sys 0m0.009s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Wed Mar 16 22:07:44 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.006s sys 0m0.007s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Wed Mar 16 22:08:46 2005 Input: 1009*1013 Output: ? 1022117 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.008s sys 0m0.004s '133.30.' ************** PARI ***************** Host 133.30.64.210 (133.30.64.210) Time: Wed Mar 16 23:10:55 2005 Input: > k := Rationals(); > P2 := ProjectiveSpace(k,2); > f := (y^4+8*z*y^3-10*z^2*y^2-8*z^3*y-7*z^4)*x^5 +(-4*z*y^4+34*z^2*y^3-18*z^3*y^2-18*z^4*y-10*z^5)*x^4 +(-17*z^2*y^4+56*z^3*y^3+3*z^4*y^2-26*z^5*y-12*z^6)*x^3 +(-25*z^3*y^4+36*z^4*y^3+29*z^5*y^2-8*z^6*y-8*z^7)*x^2 +(-17*z^4*y^4+3*z^5*y^3+19*z^6*y^2+8*z^7*y)*x -5*z^5*y^4-6*z^6*y^3-2*z^7*y^2; > C := Curve(P2,f); > Genus(C); Output: ? ? ? ? @ Euler I List Mat Mod O Pi Pol Polrev Qfb Ser Set Str Vec abs acos acosh addhelp addprimes agm algdep alias allocatemem arg asin asinh atan atanh bernfrac bernreal bernvec besseljh besselk bestappr bezout bezoutres bigomega binary binomial bitand bitneg bitnegimply bitor bittest bitxor bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark break ceil centerlift changevar charpoly chinese component concat conj conjvec content contfrac contfracpnqn core coredisc cos cosh cotan default denominator deriv dilog dirdiv direuler dirmul dirzetak divisors divrem eint1 elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint erfc error eta eulerphi eval exp extern factor factorback factorcantor factorff factorial factorint factormod factornf factorpadic ffinit fibonacci floor for fordiv forprime forstep forsubgroup forvec frac galoisfixedfield galoisinit galoispermtopol galoissubcyclo gamma gammah gcd getheap getrand getstack gettime global hilbert hyperu idealadd idealaddtoone idealappr idealchinese idealcoprime idealdiv idealfactor idealhnf idealintersect idealinv ideallist ideallistarch ideallog idealmin idealmul idealnorm idealpow idealprimedec idealprincipal idealred idealstar idealtwoelt idealval ideleprincipal if imag incgam incgamc input install intformal intnum isfundamental isprime ispseudoprime issquare issquarefree kill kronecker lcm length lex lift lindep listcreate listinsert listkill listput listsort lngamma log matadjoint matalgtobasis matbasistoalg matcompanion matdet matdetint matdiagonal mateigen mathess mathilbert mathnf mathnfmod mathnfmodid matid matimage matimagecompl matindexrank matintersect matinverseimage matisdiagonal matker matkerint matmuldiagonal matmultodiagonal matpascal matrank matrix matrixqz matsize matsnf matsolve matsolvemod matsupplement mattranspose max min modreverse moebius newtonpoly next nextprime nfalgtobasis nfbasis nfbasistoalg nfdetint nfdisc nfeltdiv nfeltdiveuc nfeltdivmodpr nfeltdivrem nfeltmod nfeltmul nfeltmulmodpr nfeltpow nfeltpowmodpr nfeltreduce nfeltreducemodpr nfeltval nffactor nffactormod nfgaloisapply nfgaloisconj nfhilbert nfhnf nfhnfmod nfinit nfisideal nfisincl nfisisom nfkermodpr nfmodprinit nfnewprec nfroots nfrootsof1 nfsnf nfsolvemodpr nfsubfields norm norml2 numdiv numerator numtoperm omega padicappr padicprec permtonum plot plotbox plotclip plotcolor plotcopy plotcursor plotdraw plotfile ploth plothraw plothsizes plotinit plotkill plotlines plotlinetype plotmove plotpoints plotpointsize plotpointtype plotrbox plotrecth plotrecthraw plotrline plotrmove plotrpoint plotscale plotstring plotterm polcoeff polcompositum polcyclo poldegree poldisc poldiscreduced polgalois polhensellift polinterpolate polisirreducible pollead pollegendre polrecip polred polredabs polredord polresultant polroots polrootsmod polrootspadic polsturm polsubcyclo polsylvestermatrix polsym poltchebi poltschirnhaus polylog polzagier precision precprime prime primes print print1 printp printp1 printtex prod prodeuler prodinf psdraw psi psploth psplothraw qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfgaussred qfjacobi qflll qflllgram qfminim qfperfection qfsign quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit quit random read real removeprimes reorder return rnfalgtobasis rnfbasis rnfbasistoalg rnfcharpoly rnfconductor rnfdedekind rnfdet rnfdisc rnfeltabstorel rnfeltdown rnfeltreltoabs rnfeltup rnfequation rnfhnfbasis rnfidealabstorel rnfidealdown rnfidealhnf rnfidealmul rnfidealnormabs rnfidealnormrel rnfidealreltoabs rnfidealtwoelt rnfidealup rnfinit rnfisfree rnfisnorm rnfkummer rnflllgram rnfnormgroup rnfpolred rnfpolredabs rnfpseudobasis rnfsteinitz round serconvol serlaplace serreverse setintersect setisset setminus setrand setsearch setunion shift shiftmul sigma sign simplify sin sinh sizebyte sizedigit solve sqr sqrt sqrtint sqrtn subgrouplist subst sum sumalt sumdiv suminf sumpos system tan tanh taylor teichmuller theta thetanullk thue thueinit trace trap truncate type until valuation variable vecextract vecmax vecmin vecsort vector vectorv weber whatnow while write write1 writetex x zeta zetak zetakinit znlog znorder znprimroot znstar @E_N_D@ Euler I List Mat Mod O Pi Pol Polrev Qfb Ser Set Str Vec abs acos acosh addhelp addprimes agm algdep alias allocatemem arg asin asinh atan atanh bernfrac bernreal bernvec besseljh besselk bestappr bezout bezoutres bigomega binary binomial bitand bitneg bitnegimply bitor bittest bitxor bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark break ceil centerlift changevar charpoly chinese component concat conj conjvec content contfrac contfracpnqn core coredisc cos cosh cotan default denominator ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** unexpected character: >k:=Rationals(); ^---------------- *** unexpected character: >P2:=Projecti ^-------------------- *** unexpected character: >f:=(y^4+8*z*y^3-10* ^-------------------- *** unexpected character: __+(-4*z*y^4+34*z^2* ^-------------------- *** unexpected character: __+(-17*z^2*y^4+56*z ^-------------------- *** unexpected character: __+(-25*z^3*y^4+36*z ^-------------------- *** unexpected character: __+(-17*z^4*y^4+3*z^ ^-------------------- *** unexpected character: __-5*z^5*y^4-6*z^6*y ^-------------------- *** unexpected character: >C:=Curve(P2,f); ^---------------- *** unexpected character: >Genus(C); ^---------- Timing: real 0m0.355s user 0m0.007s sys 0m0.015s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:31:20 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.354s user 0m0.008s sys 0m0.006s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:33:08 2005 Input: mod(4,5) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(4,5) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.016s user 0m0.008s sys 0m0.005s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:33:20 2005 Input: Mod(4,5) Output: ? Mod(4, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.006s sys 0m0.008s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:33:33 2005 Input: Mod(4,5)^2 Output: ? Mod(1, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.003s sys 0m0.011s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:33:46 2005 Input: Mod(4,5)^3 Output: ? Mod(4, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.005s sys 0m0.007s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:34:29 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.264s user 0m0.097s sys 0m0.024s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:35:08 2005 Input: (294729472947294397-1)(328497239427384289-1) Output: ? 294729472947294396 ? Errors (if any) and Timing Info: *** Warning: unused characters: (328497239427384289-1). Timing: real 0m0.022s user 0m0.005s sys 0m0.008s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:35:19 2005 Input: (294729472947294397-1)*(328497239427384289-1) Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:36:01 2005 Input: ((294729472947294397-1)*(328497239427384289-1)+1)/13 Output: ? 96817818241074147554367320960850049/13 ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.008s sys 0m0.005s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:36:10 2005 Input: ((294729472947294397-1)*(328497239427384289-1)*2+1)/13 Output: ? 193635636482148295108734641921700097/13 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.004s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:36:15 2005 Input: ((294729472947294397-1)*(328497239427384289-1)*3+1)/13 Output: ? 290453454723222442663101962882550145/13 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.003s sys 0m0.009s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:36:18 2005 Input: ((294729472947294397-1)*(328497239427384289-1)*4+1)/13 Output: ? 387271272964296590217469283843400193/13 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.006s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:36:21 2005 Input: ((294729472947294397-1)*(328497239427384289-1)*5+1)/13 Output: ? 484089091205370737771836604804250241/13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:36:25 2005 Input: ((294729472947294397-1)*(328497239427384289-1)*6+1)/13 Output: ? 580906909446444885326203925765100289/13 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.005s sys 0m0.011s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:36:36 2005 Input: ((294729472947294397-1)*(328497239427384289-1)*7+1)/13 Output: ? 52132671360578387144659326671226949 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:37:53 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.003s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:45:30 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 22753 Killed /usr/bin/gp -q -emacs Timing: real 0m21.534s user 0m20.972s sys 0m0.029s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:46:20 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 22769 Killed /usr/bin/gp -q -emacs Timing: real 0m21.653s user 0m20.924s sys 0m0.076s '24.60.9' ************** PARI ***************** Host 24.60.9.255 (24.60.9.255) Time: Thu Mar 17 00:51:43 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 22816 Killed /usr/bin/gp -q -emacs Timing: real 0m21.172s user 0m20.988s sys 0m0.012s '80.94.1' ************** PARI ***************** Host 80.94.101.50 (80.94.101.50) Time: Thu Mar 17 05:54:34 2005 Input: 1.0*17 Output: ? 17.000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.314s user 0m0.008s sys 0m0.006s '80.94.1' ************** PARI ***************** Host 80.94.101.50 (80.94.101.50) Time: Thu Mar 17 05:54:47 2005 Input: 1.0/17 Output: ? 0.058823529411764705882352941176470588235 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '80.94.1' ************** PARI ***************** Host 80.94.101.50 (80.94.101.50) Time: Thu Mar 17 05:55:16 2005 Input: 1.0/17 Output: ? 0.058823529411764705882352941176470588235 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '80.94.1' ************** PARI ***************** Host 80.94.101.50 (80.94.101.50) Time: Thu Mar 17 05:55:21 2005 Input: 1.0/17 Output: ? 0.058823529411764705882352941176470588235 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '80.94.1' ************** PARI ***************** Host 80.94.101.50 (80.94.101.50) Time: Thu Mar 17 05:57:06 2005 Input: exp(log(1)) Output: ? 1.0000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '80.94.1' ************** PARI ***************** Host 80.94.101.50 (80.94.101.50) Time: Thu Mar 17 05:57:19 2005 Input: exp(log(1)) Output: ? 1.0000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '80.94.1' ************** PARI ***************** Host 80.94.101.50 (80.94.101.50) Time: Thu Mar 17 05:57:53 2005 Input: cos(3*Pi)) Output: ? -1.0000000000000000000000000000000000000 ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.020s user 0m0.008s sys 0m0.002s '217.209' ************** PARI ***************** Host 217.209.95.199 (217.209.95.199) Time: Thu Mar 17 09:23:08 2005 Input: 23! Output: ? 25852016738884976640000 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:12:54 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.041s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:22:07 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:24:40 2005 Input: Mod(16,1022117)^78469 Output: ? Mod(703245, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:25:19 2005 Input: Factor(1022117) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(1022117) ^--------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:25:33 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:27:09 2005 Input: Mod(13,1022117)^(-1) Output: ? Mod(393122, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:27:23 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:28:20 2005 Input: Mod(16,1022117)^(78469) Output: ? Mod(703245, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:28:24 2005 Input: Mod(16,1022117)^(78469) Output: ? Mod(703245, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:28:24 2005 Input: Mod(16,1022117)^(78469) Output: ? Mod(703245, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:31:23 2005 Input: Mod(16,1022117)^(78469) Output: ? Mod(703245, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:31:25 2005 Input: Mod(16,1022117)^(78469) Output: ? Mod(703245, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:31:28 2005 Input: Mod(16,1022117)^(78469) Output: ? Mod(703245, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:34:00 2005 Input: Mod(66,1022117)^(78469) Output: ? Mod(1002067, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:35:27 2005 Input: Mod(16,1022117)^(78469) Output: ? Mod(703245, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:35:50 2005 Input: Mod(703245,26)^(1) Output: ? Mod(23, 26) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.001s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Thu Mar 17 11:36:42 2005 Input: Mod(16,1022117)^(78469) Output: ? Mod(703245, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:45:43 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:50:16 2005 Input: mod(13,1020096)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:50:26 2005 Input: mod(13,1020096)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:50:40 2005 Input: mod(13,1020096)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:51:45 2005 Input: mod(13,1020096)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:51:46 2005 Input: mod(13,1020096)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:51:48 2005 Input: mod(13,1020096)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:51:49 2005 Input: mod(13,1020096)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:51:49 2005 Input: mod(13,1020096)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:51:50 2005 Input: mod(13,1020096)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:52:42 2005 Input: mod(13,1020096) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096) ^--------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:52:43 2005 Input: mod(13,1020096) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096) ^--------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:52:57 2005 Input: mod(13,1020096) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096) ^--------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:53:14 2005 Input: mod(13,1020096) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096) ^--------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:55:29 2005 Input: mod(167366,1020096)^78469 Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(167366,1020096)^ ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:55:51 2005 Input: mod(167366,1020096)^78469 Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(167366,1020096)^ ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:55:52 2005 Input: mod(167366,1020096)^78469 Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(167366,1020096)^ ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:56:18 2005 Input: Mod(167366,1020096)^78469 Output: ? Mod(845120, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:57:14 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:58:53 2005 Input: Mod(167366,1020096)^(78469) Output: ? Mod(845120, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:59:41 2005 Input: Factor(1022117) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(1022117) ^--------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 11:59:55 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 12:01:06 2005 Input: Mod(167366,102217)^(78469)) Output: ? Mod(33446, 102217) ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 12:03:20 2005 Input: Mod(13,1020096)^(-1)) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 12:04:34 2005 Input: Mod(167366,1022117)^(78469)) Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 12:05:54 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.164s user 0m0.109s sys 0m0.011s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 12:08:08 2005 Input: Mod (13,(294729472947294396*328497239427384288))^(-1)) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.214 (128.197.150.214) Time: Thu Mar 17 12:10:00 2005 Input: Mod (10424944469828754080284344711353162,96817818241074148177594033335528733)^(52132671360578387144659326671226949)) Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.89.101 (128.197.89.101) Time: Thu Mar 17 12:15:18 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.89.101 (128.197.89.101) Time: Thu Mar 17 12:17:30 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.89.101 (128.197.89.101) Time: Thu Mar 17 12:23:31 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.119s user 0m0.107s sys 0m0.012s '128.197' ************** PARI ***************** Host 128.197.89.101 (128.197.89.101) Time: Thu Mar 17 12:29:49 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.89.101 (128.197.89.101) Time: Thu Mar 17 12:31:54 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.89.101 (128.197.89.101) Time: Thu Mar 17 12:33:33 2005 Input: 2947(2) Output: ? 2947 ? Errors (if any) and Timing Info: *** Warning: unused characters: (2). Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.89.101 (128.197.89.101) Time: Thu Mar 17 12:33:45 2005 Input: 2947*(2) Output: ? 5894 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.89.101 (128.197.89.101) Time: Thu Mar 17 12:34:27 2005 Input: 294729472947294396*328497239427384289 Output: ? 96817818241074147849096793908144444 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.89.101 (128.197.89.101) Time: Thu Mar 17 12:36:42 2005 Input: Mod(13,96817818241074147849096793908144444)^(-1) Output: ? Mod(74475244800826267576228303006264957, 96817818241074147849096793908144444) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.89.101 (128.197.89.101) Time: Thu Mar 17 12:40:24 2005 Input: Mod(10424944469828754080284344711353162,96817818241074147849096793908144444)^74475244800826267576228303006264957 Output: ? Mod(12218668913034385158446554937336324, 96817818241074147849096793908144444) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.89.101 (128.197.89.101) Time: Thu Mar 17 12:47:41 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.120s user 0m0.105s sys 0m0.013s '128.197' ************** PARI ***************** Host 128.197.89.101 (128.197.89.101) Time: Thu Mar 17 12:48:54 2005 Input: 294729472947294396*328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.89.101 (128.197.89.101) Time: Thu Mar 17 12:51:10 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.89.101 (128.197.89.101) Time: Thu Mar 17 12:54:24 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.89.101 (128.197.89.101) Time: Thu Mar 17 12:56:32 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 29819 Killed /usr/bin/gp -q -emacs Timing: real 0m21.013s user 0m20.993s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 13:29:34 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 13:30:06 2005 Input: "factor(1022117)" Output: ? "factor(1022117)" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 13:30:22 2005 Input: "factor(1022117)" Output: ? "factor(1022117)" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 13:42:45 2005 Input: "factor(1022117)" Output: ? "factor(1022117)" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 13:42:48 2005 Input: "factor(1022117)" Output: ? "factor(1022117)" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 13:43:54 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 13:54:35 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 14:05:38 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 14:08:58 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.119s user 0m0.104s sys 0m0.016s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 14:15:37 2005 Input: 294729472947294396*328497239427384289 Output: ? 96817818241074147849096793908144444 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 17 14:18:03 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 14:20:37 2005 Input: Mod(13,96817818241074147849096793908144444)^(-1) Output: ? Mod(74475244800826267576228303006264957, 96817818241074147849096793908144444) ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.007s sys 0m0.004s '67.22.4' ************** PARI ***************** Host 67.22.46.56 (67.22.46.56) Time: Thu Mar 17 14:25:35 2005 Input: 1/2+1/3 Output: ? 5/6 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 17 14:31:49 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.136s user 0m0.107s sys 0m0.012s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 17 14:35:22 2005 Input: Mod(13,(294729472947294396)*(328497239427384288 ) ) Output: ? Mod(13, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 17 14:35:50 2005 Input: Mod(13,(294729472947294396)*(328497239427384288 ) ^(-1)) Output: ? ? Errors (if any) and Timing Info: *** forbidden division t_INT % t_FRAC. Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 17 14:36:22 2005 Input: Mod(13,(294729472947294396*328497239427384288) ^(-1)) Output: ? ? Errors (if any) and Timing Info: *** forbidden division t_INT % t_FRAC. Timing: real 0m0.014s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 17 14:36:24 2005 Input: Mod(13,(294729472947294396*328497239427384288) ^(-1)) Output: ? ? Errors (if any) and Timing Info: *** forbidden division t_INT % t_FRAC. Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 17 14:36:40 2005 Input: Mod(13,294729472947294396*328497239427384288) ^(-1)) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 14:44:56 2005 Input: Mod(10424944469828754080284344711353162 ,96817818241074148177594033335528733)^74475244800826267576228303006264957 Output: ? Mod(36641192803627843555373023787022524, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 17 14:45:52 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733) ^(52132671360578387144659326671226949)) Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 17 14:51:33 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 30792 Killed /usr/bin/gp -q -emacs Timing: real 0m21.305s user 0m20.845s sys 0m0.154s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 15:10:18 2005 Input: Factor(96817818241074148177594033335528733) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(9681781824107 ^-------------------- Timing: real 0m0.021s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 15:10:23 2005 Input: Factor(96817818241074148177594033335528733) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(9681781824107 ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 15:10:28 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.119s user 0m0.100s sys 0m0.018s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 15:18:06 2005 Input: 294729472947294397*328497239427384289 Output: ? 96817818241074148177594033335528733 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 15:25:50 2005 Input: 294729472947294396*328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 15:28:14 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.007s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 15:36:34 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^(52132671360578387144659326671226949) Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.469s user 0m0.008s sys 0m0.012s '168.122' ************** PARI ***************** Host 168.122.193.213 (168.122.193.213) Time: Thu Mar 17 15:43:35 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 30956 Killed /usr/bin/gp -q -emacs Timing: real 0m21.683s user 0m20.726s sys 0m0.275s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 15:54:11 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.321s user 0m0.105s sys 0m0.021s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Thu Mar 17 15:54:30 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Thu Mar 17 16:00:14 2005 Input: Mod(7,33)^r Output: ? ? Errors (if any) and Timing Info: *** incorrect type in glog. Timing: real 0m0.040s user 0m0.008s sys 0m0.005s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Thu Mar 17 16:00:22 2005 Input: Mod(7,33)^20 Output: ? Mod(1, 33) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:00:30 2005 Input: 294729472947294396*328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.004s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Thu Mar 17 16:00:39 2005 Input: Mod(7,33)^3 Output: ? Mod(13, 33) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:01:26 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Thu Mar 17 16:02:30 2005 Input: Mod(7,33)^(-1) Output: ? Mod(19, 33) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:07:54 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Thu Mar 17 16:09:04 2005 Input: Mod(7,33)^r Output: ? ? Errors (if any) and Timing Info: *** incorrect type in glog. Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Thu Mar 17 16:09:19 2005 Input: Mod(1,33)^7 Output: ? Mod(1, 33) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.006s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Thu Mar 17 16:09:36 2005 Input: Mod(7,20)^1 Output: ? Mod(7, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Thu Mar 17 16:09:41 2005 Input: Mod(7,20)^r Output: ? ? Errors (if any) and Timing Info: *** incorrect type in glog. Timing: real 0m0.014s user 0m0.007s sys 0m0.006s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Thu Mar 17 16:10:07 2005 Input: Mod((1/7),20)^1 Output: ? Mod(3, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.006s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:11:12 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31247 Killed /usr/bin/gp -q -emacs Timing: real 0m21.257s user 0m20.990s sys 0m0.011s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Thu Mar 17 16:11:32 2005 Input: Mod(7,20)^(-1) Output: ? Mod(3, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.005s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Thu Mar 17 16:11:36 2005 Input: Mod(7,20)^(-1) Output: ? Mod(3, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.133s user 0m0.005s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:11:47 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31257 Killed /usr/bin/gp -q -emacs Timing: real 0m30.153s user 0m20.983s sys 0m0.017s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:12:08 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31253 Killed /usr/bin/gp -q -emacs Timing: real 0m52.707s user 0m20.715s sys 0m0.287s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:12:19 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31261 Killed /usr/bin/gp -q -emacs Timing: real 1m0.871s user 0m20.493s sys 0m0.508s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Thu Mar 17 16:12:25 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:12:31 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31271 Killed /usr/bin/gp -q -emacs Timing: real 0m57.318s user 0m20.912s sys 0m0.089s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:12:36 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31293 Killed /usr/bin/gp -q -emacs Timing: real 0m53.931s user 0m20.989s sys 0m0.013s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:12:36 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31275 Killed /usr/bin/gp -q -emacs Timing: real 1m1.425s user 0m20.493s sys 0m0.508s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:12:41 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31289 Killed /usr/bin/gp -q -emacs Timing: real 0m59.194s user 0m20.619s sys 0m0.383s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:13:16 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31319 Killed /usr/bin/gp -q -emacs Timing: real 0m43.206s user 0m20.981s sys 0m0.020s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:13:20 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31314 Killed /usr/bin/gp -q -emacs Timing: real 0m49.129s user 0m20.655s sys 0m0.346s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:13:23 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31329 Killed /usr/bin/gp -q -emacs Timing: real 0m43.443s user 0m20.991s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:13:26 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31325 Killed /usr/bin/gp -q -emacs Timing: real 0m48.871s user 0m20.685s sys 0m0.315s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:14:04 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31340 Killed /usr/bin/gp -q -emacs Timing: real 0m57.781s user 0m20.341s sys 0m0.660s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:14:14 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31350 Killed /usr/bin/gp -q -emacs Timing: real 0m51.868s user 0m20.998s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:14:15 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31346 Killed /usr/bin/gp -q -emacs Timing: real 0m53.522s user 0m20.230s sys 0m0.771s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:14:15 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31354 Killed /usr/bin/gp -q -emacs Timing: real 0m52.984s user 0m20.844s sys 0m0.156s '168.122' ************** PARI ***************** Host 168.122.35.39 (168.122.35.39) Time: Thu Mar 17 16:14:20 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31360 Killed /usr/bin/gp -q -emacs Timing: real 0m49.605s user 0m20.889s sys 0m0.113s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Thu Mar 17 16:15:55 2005 Input: Mod(13,1022117)^78469 Output: ? Mod(370260, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.006s sys 0m0.008s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 17 16:18:14 2005 Input: 167366^78469 Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 31417 Killed /usr/bin/gp -q -emacs Timing: real 0m21.731s user 0m20.597s sys 0m0.405s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Thu Mar 17 16:25:32 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.327s user 0m0.007s sys 0m0.008s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Thu Mar 17 16:26:04 2005 Input: Mod(13,1020096)^(1) Output: ? Mod(13, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.004s sys 0m0.009s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Thu Mar 17 16:26:11 2005 Input: Mod(1,1020096)^(13) Output: ? Mod(1, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.008s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 17 16:35:56 2005 Input: Mod(167366,1020096)^(78469) Output: ? Mod(845120, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.041s user 0m0.006s sys 0m0.007s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Thu Mar 17 16:37:20 2005 Input: Mod(16,1020096)^(78469) Output: ? Mod(420352, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '170.224' ************** PARI ***************** Host 170.224.224.154 (170.224.224.154) Time: Thu Mar 17 17:12:43 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.336s user 0m0.008s sys 0m0.008s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 17 17:16:36 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.416s user 0m0.104s sys 0m0.041s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 17:16:43 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.005s sys 0m0.009s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Thu Mar 17 17:19:21 2005 Input: 294729472947294396*328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.004s sys 0m0.008s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Thu Mar 17 17:21:36 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.006s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Thu Mar 17 17:24:23 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 17:27:53 2005 Input: Mod(13,1021104)^(-1) Output: ? Mod(157093, 1021104) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 17:28:28 2005 Input: 107093 * 13 Output: ? 1392209 ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 17:28:50 2005 Input: 157093 * 13 Output: ? 2042209 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 17:29:13 2005 Input: 2042209 - 1 Output: ? 2042208 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 17:29:33 2005 Input: 2042208 / 1021104 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 17:31:48 2005 Input: Mod(167366,1022117)^157093 Output: ? Mod(47855, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 17:31:53 2005 Input: Mod(167366,1022117)^157093 Output: ? Mod(47855, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:40:05 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.314s user 0m0.004s sys 0m0.017s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 17:40:39 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 17:41:08 2005 Input: 1008*1012 Output: ? 1020096 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 17:41:44 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 17:43:57 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.009s sys 0m0.004s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:45:20 2005 Input: factor(1022117) mod(13, 1020096)^(-1) Output: ? [1009 1] [1013 1] ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.073s user 0m0.008s sys 0m0.005s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Thu Mar 17 17:45:35 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Thu Mar 17 17:45:38 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:45:45 2005 Input: factor(1022117) mod(13, 1020096)^(-1) Output: ? [1009 1] [1013 1] ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 17:45:46 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.010s sys 0m0.004s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:45:54 2005 Input: mod(13, 1020096)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:46:07 2005 Input: mod(13,1020096)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:46:09 2005 Input: mod(13,1020096)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Thu Mar 17 17:46:18 2005 Input: 1008 * 1012 Output: ? 1020096 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:46:32 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:47:51 2005 Input: Mod(78469, 1022117)^78469 Output: ? Mod(257142, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Thu Mar 17 17:48:05 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.004s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:48:36 2005 Input: Mod(167366, 1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.005s sys 0m0.009s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Thu Mar 17 17:50:27 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.048s user 0m0.007s sys 0m0.008s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:50:52 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.242s user 0m0.102s sys 0m0.018s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:52:37 2005 Input: 294729472947294397*328497239427384289 Output: ? 96817818241074148177594033335528733 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.008s sys 0m0.005s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:52:56 2005 Input: 5*4 Output: ? 20 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:53:02 2005 Input: 5294729472947294397*328497239427384289 Output: ? 1739304015377995593177594033335528733 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:53:23 2005 Input: 294729472947294396*328497239427384288 Output: ? 96817818241074147554367320960850048 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:54:40 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.006s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:56:37 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.005s sys 0m0.009s '68.163.' ************** PARI ***************** Host 68.163.160.111 (68.163.160.111) Time: Thu Mar 17 17:58:41 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 32209 Killed /usr/bin/gp -q -emacs Timing: real 0m21.889s user 0m20.915s sys 0m0.087s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 18:36:45 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.327s user 0m0.007s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 18:36:55 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 18:42:45 2005 Input: mod(13,1020096) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096) ^--------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 18:42:59 2005 Input: Mod(13,1020096) Output: ? Mod(13, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 18:43:08 2005 Input: Mod(13,1020096) Output: ? Mod(13, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 18:43:32 2005 Input: Mod(13,1020096)^r Output: ? ? Errors (if any) and Timing Info: *** incorrect type in glog. Timing: real 0m0.021s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 18:43:56 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.057s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 18:44:55 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.003s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 18:48:03 2005 Input: Mod(16, 1020096)^(78469) Output: ? Mod(420352, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 18:48:26 2005 Input: Mod(73, 1020096)^(78469) Output: ? Mod(429481, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 18:48:47 2005 Input: Mod(63, 1020096)^(78469) Output: ? Mod(36351, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 18:54:42 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.243s user 0m0.102s sys 0m0.019s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:00:11 2005 Input: 294729472947294397*328497239427384289 Output: ? 96817818241074148177594033335528733 ? Errors (if any) and Timing Info: Timing: real 0m0.279s user 0m0.012s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:00:54 2005 Input: 294729472947294396*328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:02:17 2005 Input: Mod(13, 96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:04:54 2005 Input: Mod(1, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(1, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:05:15 2005 Input: Mod(4, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(16274367132960748053694809699778971, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:08:37 2005 Input: Mod(24, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(34759820670608639654184791399385648, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:09:41 2005 Input: Mod(24, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(34759820670608639654184791399385648, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:10:08 2005 Input: Mod(4, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(16274367132960748053694809699778971, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:10:38 2005 Input: Mod(24, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(34759820670608639654184791399385648, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:11:01 2005 Input: Mod(94, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(69795702155784541708979918970324124, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:11:27 2005 Input: Mod(44, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(51809573351621068819588386777045626, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:12:04 2005 Input: Mod(69, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(13568826152754765968955354852877538, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:12:20 2005 Input: Mod(82, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(8290996635940431853287826191779401, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:12:42 2005 Input: Mod(87, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(59907538109224536249539826643610171, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:13:00 2005 Input: Mod(54, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(39649049161368418136739204355038723, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:13:17 2005 Input: Mod(8, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(78917709523061959739891342678054692, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:13:31 2005 Input: Mod(2, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(92075324895587693122872357831582195, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:13:49 2005 Input: Mod(84, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(77680756510522574499446330676034231, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:14:04 2005 Input: Mod(34, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(16355344418146653481888405861643295, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:14:09 2005 Input: Mod(34, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(16355344418146653481888405861643295, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:14:31 2005 Input: Mod(47, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(37079296383645050767429707937405337, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:14:48 2005 Input: Mod(11, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(28314033499679457071142404765639744, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:15:03 2005 Input: Mod(35, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(24331390246114943732768518700851145, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:15:20 2005 Input: Mod(31, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(10237929247022744218835021313721062, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.237.146 (168.122.237.146) Time: Thu Mar 17 19:15:39 2005 Input: Mod(62, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(76769815458547309936655323583324816, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 17 19:21:55 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.095s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 17 19:30:00 2005 Input: factor (1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.067s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 17 19:30:45 2005 Input: factor (96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.269s user 0m0.107s sys 0m0.018s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 17 19:37:03 2005 Input: mod (13,1020096)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.251s user 0m0.009s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 17 19:37:28 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.062s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 17 19:38:25 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.006s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 17 19:39:17 2005 Input: 167366^78469 Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 740 Killed /usr/bin/gp -q -emacs Timing: real 0m22.351s user 0m20.523s sys 0m0.479s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 17 19:40:51 2005 Input: 167366^78469 Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 749 Killed /usr/bin/gp -q -emacs Timing: real 0m21.788s user 0m20.861s sys 0m0.141s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 17 19:41:18 2005 Input: Mod(7,20)^(-1) Output: ? Mod(3, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 17 19:43:21 2005 Input: 167366^78469 Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 775 Killed /usr/bin/gp -q -emacs Timing: real 0m22.247s user 0m20.224s sys 0m0.777s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 17 19:45:00 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.274s user 0m0.102s sys 0m0.031s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 17 19:49:07 2005 Input: 294729472947294396 * 328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.283s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 17 19:50:23 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 17 19:51:57 2005 Input: (10424944469828754080284344711353162)^(52132671360578387144659326671226949) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m4.493s user 0m4.131s sys 0m0.094s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 17 19:53:32 2005 Input: (167366)^(78469) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 878 Killed /usr/bin/gp -q -emacs Timing: real 0m21.135s user 0m20.983s sys 0m0.019s '151.204' ************** PARI ***************** Host 151.204.250.33 (151.204.250.33) Time: Thu Mar 17 20:02:51 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 1007 Killed /usr/bin/gp -q -emacs Timing: real 0m21.897s user 0m20.713s sys 0m0.288s '151.204' ************** PARI ***************** Host 151.204.250.33 (151.204.250.33) Time: Thu Mar 17 20:03:34 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 1014 Killed /usr/bin/gp -q -emacs Timing: real 0m21.760s user 0m20.471s sys 0m0.529s '151.204' ************** PARI ***************** Host 151.204.250.33 (151.204.250.33) Time: Thu Mar 17 20:04:13 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 1027 Killed /usr/bin/gp -q -emacs Timing: real 0m22.250s user 0m20.226s sys 0m0.775s '4.156.2' ************** PARI ***************** Host 4.156.216.92 (4.156.216.92) Time: Thu Mar 17 20:25:06 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.354s user 0m0.011s sys 0m0.008s '4.156.2' ************** PARI ***************** Host 4.156.216.92 (4.156.216.92) Time: Thu Mar 17 20:27:00 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.325s user 0m0.098s sys 0m0.032s '4.156.2' ************** PARI ***************** Host 4.156.216.92 (4.156.216.92) Time: Thu Mar 17 20:29:54 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 1190 Killed /usr/bin/gp -q -emacs Timing: real 0m21.104s user 0m20.974s sys 0m0.026s '4.156.2' ************** PARI ***************** Host 4.156.216.92 (4.156.216.92) Time: Thu Mar 17 20:51:32 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.324s user 0m0.007s sys 0m0.009s '4.156.2' ************** PARI ***************** Host 4.156.216.92 (4.156.216.92) Time: Thu Mar 17 20:52:46 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.003s sys 0m0.012s '4.156.2' ************** PARI ***************** Host 4.156.216.92 (4.156.216.92) Time: Thu Mar 17 20:56:25 2005 Input: Mod(1,1022117)^78469 Output: ? Mod(1, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.007s '4.156.2' ************** PARI ***************** Host 4.156.216.92 (4.156.216.92) Time: Thu Mar 17 20:56:40 2005 Input: Mod(6,1022117)^78469 Output: ? Mod(702675, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 20:57:07 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.009s sys 0m0.008s '4.156.2' ************** PARI ***************** Host 4.156.216.92 (4.156.216.92) Time: Thu Mar 17 20:57:18 2005 Input: Mod(167366 ,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:00:11 2005 Input: mod(7,20) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(7,20) ^--------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.030s user 0m0.006s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:00:26 2005 Input: mod(7,20)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(7,20)^(-1) ^-------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.022s user 0m0.009s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:00:28 2005 Input: mod(7,20)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(7,20)^(-1) ^-------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.022s user 0m0.004s sys 0m0.009s '4.156.2' ************** PARI ***************** Host 4.156.216.92 (4.156.216.92) Time: Thu Mar 17 21:00:29 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.229s user 0m0.099s sys 0m0.022s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:00:31 2005 Input: mod(7,20)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(7,20)^(-1) ^-------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.013s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:00:38 2005 Input: Mod(7,20)^(-1) Output: ? Mod(3, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:00:57 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '4.156.2' ************** PARI ***************** Host 4.156.216.92 (4.156.216.92) Time: Thu Mar 17 21:02:45 2005 Input: Mod(13,294729472947294396*328497239427384288)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.005s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:03:47 2005 Input: Mod(16,1022117)^78469 Output: ? Mod(703245, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:04:42 2005 Input: Mod(16,1022117)^78469 Output: ? Mod(703245, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:04:42 2005 Input: Mod(16,1022117)^78469 Output: ? Mod(703245, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.006s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:04:43 2005 Input: Mod(16,1022117)^78469 Output: ? Mod(703245, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.007s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:04:51 2005 Input: Mod(1,1022117)^78469 Output: ? Mod(1, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:05:01 2005 Input: Mod(67,1022117)^78469 Output: ? Mod(851309, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.005s sys 0m0.008s '4.156.2' ************** PARI ***************** Host 4.156.216.92 (4.156.216.92) Time: Thu Mar 17 21:05:08 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.004s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:05:47 2005 Input: 16^78469 Output: ? 1232874947851136791856689909456930366777586745424362948844233814487557089184019270182941569084360078762552707845287313130922162483837346566159598031495851965579440132940198475437912900984262743879258714186241925113120851150017850875496100655962147616822699196156548752885281508209110991072876411571048386186729163554189101786985999297677784289759346382971721371091852351200402458679940710745755087084597334037843476605056362663622840575793800018903268691784613920271689856910618363519541636084301733062420270792561171601594421519288332081389211090877409774866822866519302620766732093046513425603420505960690406780638255131427945861357077270076768213608093863541355301638614935196629652702869075151788954029175280102861669218347373114347719224351922874517872634511096699514167193827097883348800305412896753019223536399474756976654515213217201803687233247581365237165933074110927975110780468767455046646343824762127830354569614420420699635486709396670271382501193891021442393806740842939222992971394958272254471583506786198711765523113670015188622314927074322306332160158232617601541080503698118284410295002113212377825211502606978029637394382031598774527822197473272858203212304736088480475139864928282480253231086193825354846048104730524381724066243035728547456118950881043812766717356150447564821252158416651919080749257920510717360382924430973470316423124824756015093108882935730665909301222810484275105191269101893619684101621983153033319884411654298347117312677540724780166394409614007522935898997348078508366169760244552251239182919373359013570737335982896854005223554195516210213615649882811764482014806777801578661719150526637979115478843112794297785960043541852500568635851758175572293635556981160284495520280844977804996410608449051775203073221275338844244575886672905091280095569157498228720584074952090427265562968268952331623887825966384568053099399753393400352820437253415911711740440581780014394982034387341354996290876691922386721128955449718469820126651774603277877651184662471936377804040556607996119121310493196018524729409511479712939741013789514062147766451973855773542401907858783108642984189018735109131477247184636744466832608941527230280769241649154949693716909572355898321971576357825524348000306975009677928994167051041017934882997782996975398553477359705499858786551851827870025401341152922329212862345621361525775665769379495496629502322954603411083034669683073362441380851336113501957466130842457669365412475247758513135328182537975725487592758332855156704943590119301358893552539244723144546128414895170544378416699813590052612997419725773098041856770313916940675305468007966758100736747722627717863856538829784363178852341665887223556930316798666646762833965627175812560659627233068867019958799851245669248804634455952670735978980022464132418052658919463355457936808034186254210937967934127835066457276858034168552700151027971972905831720467749245814276379898622534951044138216683022477881457716774853993084626566045089762227168957284732880160500658654808554116376923750071286771746767779903058148643035405099206533958070062092951495262051133609880624772045451035074575287116499655614356446429915218400701529544210842941958292397392129598327303235750321098686[+++] ? Errors (if any) and Timing Info: Timing: real 0m2.037s user 0m1.930s sys 0m0.022s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:07:07 2005 Input: Mod(167366,1022117)^(78469) Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:12:13 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.226s user 0m0.105s sys 0m0.037s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:14:10 2005 Input: 294729472947294397*328497239427384289 Output: ? 96817818241074148177594033335528733 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 21:14:16 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.124s user 0m0.101s sys 0m0.018s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:14:47 2005 Input: (294729472947294397-1)*(328497239427384289-1) Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.009s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:16:07 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:16:26 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.002s sys 0m0.011s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 21:17:40 2005 Input: 294729472947294397 * 328497239427384289 Output: ? 96817818241074148177594033335528733 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 21:18:09 2005 Input: 294729472947294396 * 328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 21:19:00 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.125s user 0m0.105s sys 0m0.013s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 21:19:22 2005 Input: 294729472947294396 * 328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:20:36 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^(52132671360578387144659326671226949) Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.007s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 21:22:33 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.010s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 17 21:23:02 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 1824 Killed /usr/bin/gp -q -emacs Timing: real 0m22.234s user 0m20.425s sys 0m0.575s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 21:26:36 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 17 21:33:38 2005 Input: Mod(13,1020096)^78469 Output: ? Mod(575581, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.056s user 0m0.004s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 17 21:34:48 2005 Input: Mod(6,1022117)^78469 Output: ? Mod(702675, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 17 21:39:01 2005 Input: Mod(7,1022117)^78469 Output: ? Mod(504080, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.004s '170.224' ************** PARI ***************** Host 170.224.224.154 (170.224.224.154) Time: Thu Mar 17 21:39:14 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 1966 Killed /usr/bin/gp -q -emacs Timing: real 0m21.967s user 0m20.687s sys 0m0.312s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 17 21:39:35 2005 Input: Mod(3,1022117)^78469 Output: ? Mod(242263, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.005s sys 0m0.011s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 17 21:40:13 2005 Input: Mod(3,1022117)^78469 Output: ? Mod(242263, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.007s sys 0m0.010s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Thu Mar 17 21:42:22 2005 Input: Factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(2179575060383 ^-------------------- Timing: real 0m0.023s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 21:42:30 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 2021 Killed /usr/bin/gp -q -emacs Timing: real 0m21.501s user 0m20.676s sys 0m0.325s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Thu Mar 17 21:42:58 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 2035 Killed /usr/bin/gp -q -emacs Timing: real 0m21.044s user 0m20.991s sys 0m0.010s '155.41.' ************** PARI ***************** Host 155.41.162.41 (155.41.162.41) Time: Thu Mar 17 21:56:08 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.465s user 0m0.008s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 17 21:59:19 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.245s user 0m0.110s sys 0m0.016s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:08:42 2005 Input: isprime(1079007); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.038s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:08:57 2005 Input: isprime(1079007) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.005s sys 0m0.011s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:09:26 2005 Input: isprime(1079007) isprime(210283) Output: ? 0 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:09:38 2005 Input: isprime(210283) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:09:56 2005 Input: isprime(22) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:11:16 2005 Input: factor(1079007) Output: ? [3 1] [17 1] [21157 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.007s '155.41.' ************** PARI ***************** Host 155.41.162.41 (155.41.162.41) Time: Thu Mar 17 22:11:29 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:12:04 2005 Input: nextprime(1079007) Output: ? 1079009 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:12:31 2005 Input: nextprime(83393192) Output: ? 83393197 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:13:01 2005 Input: prevprime(83393192) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: prevprime(83393192) ^------------------- Timing: real 0m0.023s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:13:42 2005 Input: nextprime(83393190) Output: ? 83393197 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:13:50 2005 Input: nextprime(83393188) Output: ? 83393197 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:13:56 2005 Input: nextprime(83393186) Output: ? 83393197 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:14:08 2005 Input: nextprime(83393182) Output: ? 83393197 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:14:16 2005 Input: nextprime(83393180) Output: ? 83393197 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:14:22 2005 Input: nextprime(83393178) Output: ? 83393179 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.004s '155.41.' ************** PARI ***************** Host 155.41.162.41 (155.41.162.41) Time: Thu Mar 17 22:14:47 2005 Input: Mod(13, 1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:14:57 2005 Input: gcd(1079007,210283) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:15:19 2005 Input: gcd(210283,22) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:15:42 2005 Input: gcd(1079007,210283,22) Output: ? ? Errors (if any) and Timing Info: *** invalid flag in gcd. Timing: real 0m0.014s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:16:09 2005 Input: gcd(1079007,22) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '155.41.' ************** PARI ***************** Host 155.41.162.41 (155.41.162.41) Time: Thu Mar 17 22:16:38 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:16:40 2005 Input: lcm(22,37) Output: ? 814 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:17:00 2005 Input: lcm(37,5152) Output: ? 190624 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:18:38 2005 Input: Mod(1079007,22) Output: ? Mod(17, 22) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:19:06 2005 Input: Mod(17,22) Output: ? Mod(17, 22) ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.005s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:19:26 2005 Input: Mod(83393192,22) Output: ? Mod(14, 22) ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:20:37 2005 Input: fibonacci(1079007) Output: ? 5987674821202286039628774715227675506638557226213838281299746602618692737949391956377826749703049538941723817499908965359357207822129855323077106690748832727058626006336750786937176391442435830903867434719541225332841272375590043612197638231333026870156718084930329559122781329260955134851266679732900635223387411622364594503346631009875847542160137214293327760295562718217800178779519060682089547871486161746495902860575462109238883185315919903942548841725121537005812902266372218947731170069722077050186587136820720661139806483104156986547762099841615659375066333777116895539828042601613883374700575877459971756359185620199399242607425032307314074498119174259478931368031515181073404981335846382106612280431572744372031637742524988680087510722328897604694445037478692586386199943394244046518934889601505653815149370832881695159124936730675554633279961152252855612161067818707149228304637383557314360409472839700385419579933624631343430546132466308594541769836646241137824080562559645066826157565011482535176694598310394366991386118134764377673173480461343437445404205061909282313357182079427199137793263181028270133757472524327530569149225812699592124245407297505900282946062572287762793551028149477227501890524384683675790202443580997172607651166014796550468561017691798667204821248467313637010549649482253683284273336397246444680586616619085238255561161612041190920743272265104063652277853351472501264852459234377119322344323430264097712496062544582918448980462468148273171568264263887804500281133261647466926076440697477448340472616116886837273031595677296243740780354479520120740930513269444062160996828944201048878567660560887224950694516205749139545764895845191881615739744750230533791420878429228240061592790712775224008567462698115648717469475606847707909446863525184513386725640466259597815792952625991638300862201581851045882716873351004453079924111769456837406349633294806311525366480111413272163531280129240388264437319292781330599354639889670036142396302586000438113221180680624129494784894883261094574349746399490682308065310476830997848200079323224909881191127774718572371016057793481845681751683425223142877767478699794195456689567571860895677137623082177010607792301879843801173808597231696963822157585145602353173921585184159335610667142908078875354198574879496675245827834146219113066044345419282821005695749571664680055388873344993957110413831408942921081866350795439311573542523470335826605187742583357566018307529278665690991064655925015577147356000809958128625000398923835219558851234000302026023284893795860153501033073328605045908525510572897857884580700397762007910745022591829140083147647318988129841403628259450785417272093434540745428360479108180468817464405544359640197511469378228359575906310606333411322517521686140406968622413840400927790032900994242746452526889508906767928298208251311830944467058570980801500949226972134912392501447691479077058220678540543270562070520970638396689832701220030591468155751339221393164899615049727428412673113863856436102139463604969195415973359588332327418469183441660325628540614982748249316921669384656189977522873866302902677752518710464038952054088661085504711139550325351276708301262887875625003177264393421098821891[+++] ? Errors (if any) and Timing Info: Timing: real 0m12.404s user 0m11.194s sys 0m0.485s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:21:15 2005 Input: fibonacci(8) Output: ? 21 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.005s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:22:00 2005 Input: fibonacci(20) Output: ? 6765 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.006s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:22:06 2005 Input: fibonacci(50) Output: ? 12586269025 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:22:13 2005 Input: fibonacci(40) Output: ? 102334155 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:22:23 2005 Input: fibonacci(35) Output: ? 9227465 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:22:34 2005 Input: fibonacci(33) Output: ? 3524578 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:22:41 2005 Input: fibonacci(30) Output: ? 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:22:51 2005 Input: fibonacci(31) Output: ? 1346269 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.003s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:23:11 2005 Input: fibonacci(8) Output: ? 21 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:23:23 2005 Input: fibonacci(18) Output: ? 2584 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:23:29 2005 Input: fibonacci(21) Output: ? 10946 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:23:34 2005 Input: fibonacci(20) Output: ? 6765 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.004s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.162.41 (155.41.162.41) Time: Thu Mar 17 22:23:35 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.156s user 0m0.110s sys 0m0.015s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:23:44 2005 Input: fibonacci(19) Output: ? 4181 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 22:23:51 2005 Input: zp = Mod(x, sum(n=0, 36, x^n)); zp^37; Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.054s user 0m0.007s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 22:24:24 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.003s sys 0m0.012s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 22:24:30 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); zp Output: ? ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.006s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 22:24:39 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) zp Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:24:46 2005 Input: binomial(5152,22) Output: ? 3919246839680430912247695238791336868564501407496391836080880 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.009s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 22:24:56 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) zp^37 Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:25:23 2005 Input: prime(5152) Output: ? 50159 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:25:46 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 22:25:59 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) zp^37 zp^5+1/zp^5 Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(x^32 + x^5, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 17 22:26:01 2005 Input: pi(38) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: pi(38) ^------ For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: pi ===> Pi Pi=Pi(): the constant pi, with current precision. Timing: real 0m0.027s user 0m0.005s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 22:26:50 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) zp^37 b(n)=zp^n+1/zp^n Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.009s sys 0m0.009s '155.41.' ************** PARI ***************** Host 155.41.162.41 (155.41.162.41) Time: Thu Mar 17 22:27:03 2005 Input: factor(3*10) Output: ? [2 1] [3 1] [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 22:27:19 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) zp^37 b(n):=zp^n+1/zp^n Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? Errors (if any) and Timing Info: *** unexpected character: b(n):=zp^n+1/zp^n ^------------ Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 22:27:25 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) zp^37 b(n);=zp^n+1/zp^n Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? Errors (if any) and Timing Info: *** unexpected character: b(n);=zp^n+1/zp^n ^------------ Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 22:27:49 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) zp^37 b(n)=zp^n+1/zp^n Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 22:28:02 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) zp^37 b(n)=zp^n+1/zp^n b(1) Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? Mod(-x^35 - x^34 - x^33 - x^32 - x^31 - x^30 - x^29 - x^28 - x^27 - x^26 - x^25 - x^24 - x^23 - x^22 - x^21 - x^20 - x^19 - x^18 - x^17 - x^16 - x^15 - x^14 - x^13 - x^12 - x^11 - x^10 - x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 22:28:16 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) zp^37 b(n)=zp^n+1/zp^n b(2) Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? Mod(x^35 + x^2, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 22:28:51 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) b(n)=zp^n+1/zp^n lift(b(2)) Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? x^35 + x^2 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.006s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 22:29:51 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) b(n)=zp^n+1/zp^n c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))) Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 22:30:06 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) b(n)=zp^n+1/zp^n c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))) c(1) c(3) c(5) Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? Mod(-1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.130s user 0m0.091s sys 0m0.018s '155.41.' ************** PARI ***************** Host 155.41.162.41 (155.41.162.41) Time: Thu Mar 17 22:33:12 2005 Input: Mod(13,294729472947294396*328497239427384288)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.006s sys 0m0.008s '155.41.' ************** PARI ***************** Host 155.41.162.41 (155.41.162.41) Time: Thu Mar 17 22:37:54 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 22:38:11 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 22:38:45 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.006s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 22:45:39 2005 Input: Mod(13,1020096) Output: ? Mod(13, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.215s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 22:46:07 2005 Input: Mod(13,1020096)^-1 Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.149s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 22:51:00 2005 Input: Mod(16,1022117)^78469 Output: ? Mod(703245, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 22:51:13 2005 Input: Mod(1,1022117)^78469 Output: ? Mod(1, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 22:52:10 2005 Input: Mod(6,1022117)^78469 Output: ? Mod(702675, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 22:53:31 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 22:57:15 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.293s user 0m0.110s sys 0m0.020s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 23:00:54 2005 Input: Mod(13,96817818241074147554367320960850048)^-1 Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:02:00 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) b(n)=zp^n+1/zp^n c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))) c(1) c(3) c(5) c(35) Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? Mod(-1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.177s user 0m0.114s sys 0m0.013s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:02:18 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) b(n)=zp^n+1/zp^n c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))) c(1) c(3) c(5) c(34) Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? Mod(-1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-1791295882829801915623514510354762556780231801984329112*x^35 + 1092574623512842289500172232076095738085757348380787578*x^34 + 2132753460634957186380315057081651551393438801257294602*x^33 - 988823635337416352196145075077287094357155821201264899*x^32 - 1249057741916119710001928965469659482275688329723199228*x^31 + 1927608666199914330352326506047409104939921749638344626*x^30 + 1407008425614303298534108385272758020242889992165274476*x^29 - 1657489396461923908531169723733770719304962970578423821*x^28 - 360666270111803442941312840799291779609163039996099364*x^27 + 2397172870317220180752486900372125762781225718775535208*x^26 + 374936878863789370142111501263344266597024963457135667*x^25 - 1862441182305396234162017237332040666650970707649029163*x^24 + 744975088218649544224638340626753523077071083208703160*x^23 + 2293248003879706335736309627975250966986026719098788444*x^22 - 692503990580283065961362610383691503187079719884172325*x^21 - 1473377136355156370727316929758696245123357310394089972*x^20 + 1685164529676120884981703664581029741918593725505139201*x^19 + 1685164529676120884981703664581029741918593725505139201*x^18 - 1473377136355156370727316929758696245123357310394089972*x^17 - 692503990580283065961362610383691503187079719884172325*x^16 + 2293248003879706335736309627975250966986026719098788444*x^15 + 744975088218649544224638340626753523077071083208703160*x^14 - 1862441182305396234162017237332040666650970707649029163*x^13 + 374936878863789370142111501263344266597024963457135667*x^12 + 2397172870317220180752486900372125762781225718775535208*x^11 - 360666270111803442941312840799291779609163039996099364*x^10 - 1657489396461923908531169723733770719304962970578423821*x^9 + 1407008425614303298534108385272758020242889992165274476*x^8 + 1927608666199914330352326506047409104939921749638344626*x^7 - 1249057741916119710001928965469659482275688329723199228*x^6 - 988823635337416352196145075077287094357155821201264899*x^5 + 2132753460634957186380315057081651551393438801257294602*x^4 + 1092574623512842289500172232076095738085757348380787578*x^3 - 1791295882829801915623514510354762556780231801984329112*x^2 + 2433338721014269014518308029682288911327975112736918407, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.155s user 0m0.119s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:02:59 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) b(n)=zp^n+1/zp^n c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))) c(1) c(3) c(5) c(32) Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? Mod(-1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(12737464052481102881460945669707673*x^35 + 1212229752617478176727159003060636*x^34 + 38680807563207265438980249456070130*x^33 + 13392516852163747878424136438731053*x^32 + 13392516852163747878424136438731053*x^30 + 22522879771526441803723550949869879*x^29 + 31113824371207190836547101022878634*x^28 - 12936616445156750651495283764374636*x^27 + 22522879771526441803723550949869879*x^26 + 12737464052481102881460945669707673*x^25 + 38680807563207265438980249456070130*x^24 - 12936616445156750651495283764374636*x^23 + 17610434968264643057232099719177790*x^22 + 17610434968264643057232099719177790*x^21 + 31113824371207190836547101022878634*x^20 + 1212229752617478176727159003060636*x^19 + 1212229752617478176727159003060636*x^18 + 31113824371207190836547101022878634*x^17 + 17610434968264643057232099719177790*x^16 + 17610434968264643057232099719177790*x^15 - 12936616445156750651495283764374636*x^14 + 38680807563207265438980249456070130*x^13 + 12737464052481102881460945669707673*x^12 + 22522879771526441803723550949869879*x^11 - 12936616445156750651495283764374636*x^10 + 31113824371207190836547101022878634*x^9 + 22522879771526441803723550949869879*x^8 + 13392516852163747878424136438731053*x^7 + 13392516852163747878424136438731053*x^5 + 38680807563207265438980249456070130*x^4 + 1212229752617478176727159003060636*x^3 + 12737464052481102881460945669707673*x^2 + 46465160155653008000025114267355141, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.133s user 0m0.115s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:03:06 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) b(n)=zp^n+1/zp^n c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))) c(32) Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? Mod(12737464052481102881460945669707673*x^35 + 1212229752617478176727159003060636*x^34 + 38680807563207265438980249456070130*x^33 + 13392516852163747878424136438731053*x^32 + 13392516852163747878424136438731053*x^30 + 22522879771526441803723550949869879*x^29 + 31113824371207190836547101022878634*x^28 - 12936616445156750651495283764374636*x^27 + 22522879771526441803723550949869879*x^26 + 12737464052481102881460945669707673*x^25 + 38680807563207265438980249456070130*x^24 - 12936616445156750651495283764374636*x^23 + 17610434968264643057232099719177790*x^22 + 17610434968264643057232099719177790*x^21 + 31113824371207190836547101022878634*x^20 + 1212229752617478176727159003060636*x^19 + 1212229752617478176727159003060636*x^18 + 31113824371207190836547101022878634*x^17 + 17610434968264643057232099719177790*x^16 + 17610434968264643057232099719177790*x^15 - 12936616445156750651495283764374636*x^14 + 38680807563207265438980249456070130*x^13 + 12737464052481102881460945669707673*x^12 + 22522879771526441803723550949869879*x^11 - 12936616445156750651495283764374636*x^10 + 31113824371207190836547101022878634*x^9 + 22522879771526441803723550949869879*x^8 + 13392516852163747878424136438731053*x^7 + 13392516852163747878424136438731053*x^5 + 38680807563207265438980249456070130*x^4 + 1212229752617478176727159003060636*x^3 + 12737464052481102881460945669707673*x^2 + 46465160155653008000025114267355141, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.050s user 0m0.036s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:03:19 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) b(n)=zp^n+1/zp^n c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))) c(4) Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.041s user 0m0.035s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:03:29 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) b(n)=zp^n+1/zp^n c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))) c(6) Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? Mod(620895279166848325608921724537458204242497018145021577*x^35 + 3011160233140067118829710202241632422944924673822921768*x^34 + 3011160233140067118829710202241632422944924673822921768*x^33 + 2128078179228677514660109466275856284480344231873978717*x^32 + 743898115689077229662291572334822610982201917008296461*x^31 + 3011160233140067118829710202241632422944924673822921768*x^30 + 743898115689077229662291572334822610982201917008296461*x^29 + 5340714852415656298869725116474140435590273348191786920*x^28 + 5340714852415656298869725116474140435590273348191786920*x^25 + 2128078179228677514660109466275856284480344231873978717*x^24 + 743898115689077229662291572334822610982201917008296461*x^23 + 620895279166848325608921724537458204242497018145021577*x^22 + 5340714852415656298869725116474140435590273348191786920*x^21 + 620895279166848325608921724537458204242497018145021577*x^20 + 2128078179228677514660109466275856284480344231873978717*x^19 + 2128078179228677514660109466275856284480344231873978717*x^18 + 620895279166848325608921724537458204242497018145021577*x^17 + 5340714852415656298869725116474140435590273348191786920*x^16 + 620895279166848325608921724537458204242497018145021577*x^15 + 743898115689077229662291572334822610982201917008296461*x^14 + 2128078179228677514660109466275856284480344231873978717*x^13 + 5340714852415656298869725116474140435590273348191786920*x^12 + 5340714852415656298869725116474140435590273348191786920*x^9 + 743898115689077229662291572334822610982201917008296461*x^8 + 3011160233140067118829710202241632422944924673822921768*x^7 + 743898115689077229662291572334822610982201917008296461*x^6 + 2128078179228677514660109466275856284480344231873978717*x^5 + 3011160233140067118829710202241632422944924673822921768*x^4 + 3011160233140067118829710202241632422944924673822921768*x^3 + 620895279166848325608921724537458204242497018145021577*x^2 + 6900151858967388838699082242102387667299485935948702698, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.046s user 0m0.037s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 23:04:42 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 17 23:06:31 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 23:08:38 2005 Input: Factor(96817818241074148177594033335528733) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(9681781824107 ^-------------------- Timing: real 0m0.027s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 23:08:55 2005 Input: Factor(96817818241074148177594033335528733) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(9681781824107 ^-------------------- Timing: real 0m0.023s user 0m0.010s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 23:09:13 2005 Input: Factor(96817818241074148177594033335528733) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(9681781824107 ^-------------------- Timing: real 0m0.016s user 0m0.006s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 23:09:46 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.161s user 0m0.107s sys 0m0.019s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:13:27 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) b(n)=zp^n+1/zp^n c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))) c(4) Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.032s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 23:15:35 2005 Input: mod(13,96817818241074147554367320960850048)^-1 Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,9681781824107 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.023s user 0m0.004s sys 0m0.011s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 23:16:02 2005 Input: Mod(13,96817818241074147554367320960850048)^-1 Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:16:09 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)) b(n)=zp^n+1/zp^n c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))) q=c(4) w=Mod(1-x, sum(n=0, 36, x^n)) (q-9*(1-37))/w^37 Output: ? Mod(x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(15534338931545960708731277351361288230077118991325*x^35 + 21835010423828501738361370570509308139512512949723*x^34 + 17301821718999490880594053722379675970179468399157*x^33 + 3086074884252799797725528323831423079495601517198*x^32 - 17201831622227728404720929353081032923907765742882*x^31 - 38409342297357495796243162452660115601221706913236*x^30 - 55150348035643114865871568710680904484752105180200*x^29 - 63173105820953540986907367179753979560381717775366*x^28 - 60440061657151709668574688313247741799677223364971*x^27 - 47645331706497258011165976897331840478122559199926*x^26 - 28038416177359046508268254404801017079737930240487*x^25 - 6598918107604932265896477275333011123162434196474*x^24 + 11228135081201708762380628661620576645931754143063*x^23 + 20915175013641052670158336668612014605272179526035*x^22 + 20001967060981715870635964841655736276996686444410*x^21 + 8720440302908987252181637654734715420170910588745*x^20 - 10064215993892205278165857602473774493104839358473*x^19 - 31581229364172044275585558080882019845281780946613*x^18 - 50365885660973236805933053338090509758557530893831*x^17 - 61647412419045965424387380525011530615383306749496*x^16 - 62560620371705302223909752351967808943658799831121*x^15 - 52873580439265958316132044344976370984318374448149*x^14 - 35046527250459317287854938408022783215224186108612*x^13 - 13607029180705203045483161278554777258648690064599*x^12 + 5999886348433008457414561213976046139735938894840*x^11 + 18794616299087460114823272629891947461290603059885*x^10 + 21527660462889291433155951496398185221995097470280*x^9 + 13504902677578865312120153027325110146365484875114*x^8 - 3236103060706753757508253230695678737164913391850*x^7 - 24443613735836521149030486330274761414478854562204*x^6 - 44731520242317049351476944007187217417882221822284*x^5 - 58947267077063740434345469405735470308566088704243*x^4 - 63480455781892751292112786253865102477899133254809*x^3 - 57179784289610210262482693034717082568463739296411*x^2 - 41645445358064249553751415683355794338386620305086*x - 20822722679032124776875707841677897169193310152543, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.040s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Thu Mar 17 23:17:22 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 17 23:18:17 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 3439 Killed /usr/bin/gp -q -emacs Timing: real 0m21.566s user 0m20.884s sys 0m0.116s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:18:48 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))); q=c(4); lift(q) w=Mod(1-x, sum(n=0, 36, x^n)) (q-9*(1-37))/w^37 Output: ? ? ? ? ? -8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850 ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(15534338931545960708731277351361288230077118991325*x^35 + 21835010423828501738361370570509308139512512949723*x^34 + 17301821718999490880594053722379675970179468399157*x^33 + 3086074884252799797725528323831423079495601517198*x^32 - 17201831622227728404720929353081032923907765742882*x^31 - 38409342297357495796243162452660115601221706913236*x^30 - 55150348035643114865871568710680904484752105180200*x^29 - 63173105820953540986907367179753979560381717775366*x^28 - 60440061657151709668574688313247741799677223364971*x^27 - 47645331706497258011165976897331840478122559199926*x^26 - 28038416177359046508268254404801017079737930240487*x^25 - 6598918107604932265896477275333011123162434196474*x^24 + 11228135081201708762380628661620576645931754143063*x^23 + 20915175013641052670158336668612014605272179526035*x^22 + 20001967060981715870635964841655736276996686444410*x^21 + 8720440302908987252181637654734715420170910588745*x^20 - 10064215993892205278165857602473774493104839358473*x^19 - 31581229364172044275585558080882019845281780946613*x^18 - 50365885660973236805933053338090509758557530893831*x^17 - 61647412419045965424387380525011530615383306749496*x^16 - 62560620371705302223909752351967808943658799831121*x^15 - 52873580439265958316132044344976370984318374448149*x^14 - 35046527250459317287854938408022783215224186108612*x^13 - 13607029180705203045483161278554777258648690064599*x^12 + 5999886348433008457414561213976046139735938894840*x^11 + 18794616299087460114823272629891947461290603059885*x^10 + 21527660462889291433155951496398185221995097470280*x^9 + 13504902677578865312120153027325110146365484875114*x^8 - 3236103060706753757508253230695678737164913391850*x^7 - 24443613735836521149030486330274761414478854562204*x^6 - 44731520242317049351476944007187217417882221822284*x^5 - 58947267077063740434345469405735470308566088704243*x^4 - 63480455781892751292112786253865102477899133254809*x^3 - 57179784289610210262482693034717082568463739296411*x^2 - 41645445358064249553751415683355794338386620305086*x - 20822722679032124776875707841677897169193310152543, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.046s user 0m0.033s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:19:24 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))); q=c(4); lift(q)*Mod(1, 37) w=Mod(1-x, sum(n=0, 36, x^n)) (q-9*(1-37))/w^37 Output: ? ? ? ? ? Mod(9, 37) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(15534338931545960708731277351361288230077118991325*x^35 + 21835010423828501738361370570509308139512512949723*x^34 + 17301821718999490880594053722379675970179468399157*x^33 + 3086074884252799797725528323831423079495601517198*x^32 - 17201831622227728404720929353081032923907765742882*x^31 - 38409342297357495796243162452660115601221706913236*x^30 - 55150348035643114865871568710680904484752105180200*x^29 - 63173105820953540986907367179753979560381717775366*x^28 - 60440061657151709668574688313247741799677223364971*x^27 - 47645331706497258011165976897331840478122559199926*x^26 - 28038416177359046508268254404801017079737930240487*x^25 - 6598918107604932265896477275333011123162434196474*x^24 + 11228135081201708762380628661620576645931754143063*x^23 + 20915175013641052670158336668612014605272179526035*x^22 + 20001967060981715870635964841655736276996686444410*x^21 + 8720440302908987252181637654734715420170910588745*x^20 - 10064215993892205278165857602473774493104839358473*x^19 - 31581229364172044275585558080882019845281780946613*x^18 - 50365885660973236805933053338090509758557530893831*x^17 - 61647412419045965424387380525011530615383306749496*x^16 - 62560620371705302223909752351967808943658799831121*x^15 - 52873580439265958316132044344976370984318374448149*x^14 - 35046527250459317287854938408022783215224186108612*x^13 - 13607029180705203045483161278554777258648690064599*x^12 + 5999886348433008457414561213976046139735938894840*x^11 + 18794616299087460114823272629891947461290603059885*x^10 + 21527660462889291433155951496398185221995097470280*x^9 + 13504902677578865312120153027325110146365484875114*x^8 - 3236103060706753757508253230695678737164913391850*x^7 - 24443613735836521149030486330274761414478854562204*x^6 - 44731520242317049351476944007187217417882221822284*x^5 - 58947267077063740434345469405735470308566088704243*x^4 - 63480455781892751292112786253865102477899133254809*x^3 - 57179784289610210262482693034717082568463739296411*x^2 - 41645445358064249553751415683355794338386620305086*x - 20822722679032124776875707841677897169193310152543, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.047s user 0m0.039s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:20:08 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))); q=c(4); lift(q)*Mod(1, 37) lift(q)*Mod(1, 37^2) w=Mod(1-x, sum(n=0, 36, x^n)) (q-9*(1-37))/w^37 Output: ? ? ? ? ? Mod(9, 37) ? Mod(407, 1369)*x^35 + Mod(185, 1369)*x^34 + Mod(666, 1369)*x^33 + Mod(1258, 1369)*x^32 + Mod(1258, 1369)*x^30 + Mod(888, 1369)*x^29 + Mod(851, 1369)*x^28 + Mod(444, 1369)*x^27 + Mod(888, 1369)*x^26 + Mod(407, 1369)*x^25 + Mod(666, 1369)*x^24 + Mod(444, 1369)*x^23 + Mod(1295, 1369)*x^22 + Mod(1295, 1369)*x^21 + Mod(851, 1369)*x^20 + Mod(185, 1369)*x^19 + Mod(185, 1369)*x^18 + Mod(851, 1369)*x^17 + Mod(1295, 1369)*x^16 + Mod(1295, 1369)*x^15 + Mod(444, 1369)*x^14 + Mod(666, 1369)*x^13 + Mod(407, 1369)*x^12 + Mod(888, 1369)*x^11 + Mod(444, 1369)*x^10 + Mod(851, 1369)*x^9 + Mod(888, 1369)*x^8 + Mod(1258, 1369)*x^7 + Mod(1258, 1369)*x^5 + Mod(666, 1369)*x^4 + Mod(185, 1369)*x^3 + Mod(407, 1369)*x^2 + Mod(342, 1369) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(15534338931545960708731277351361288230077118991325*x^35 + 21835010423828501738361370570509308139512512949723*x^34 + 17301821718999490880594053722379675970179468399157*x^33 + 3086074884252799797725528323831423079495601517198*x^32 - 17201831622227728404720929353081032923907765742882*x^31 - 38409342297357495796243162452660115601221706913236*x^30 - 55150348035643114865871568710680904484752105180200*x^29 - 63173105820953540986907367179753979560381717775366*x^28 - 60440061657151709668574688313247741799677223364971*x^27 - 47645331706497258011165976897331840478122559199926*x^26 - 28038416177359046508268254404801017079737930240487*x^25 - 6598918107604932265896477275333011123162434196474*x^24 + 11228135081201708762380628661620576645931754143063*x^23 + 20915175013641052670158336668612014605272179526035*x^22 + 20001967060981715870635964841655736276996686444410*x^21 + 8720440302908987252181637654734715420170910588745*x^20 - 10064215993892205278165857602473774493104839358473*x^19 - 31581229364172044275585558080882019845281780946613*x^18 - 50365885660973236805933053338090509758557530893831*x^17 - 61647412419045965424387380525011530615383306749496*x^16 - 62560620371705302223909752351967808943658799831121*x^15 - 52873580439265958316132044344976370984318374448149*x^14 - 35046527250459317287854938408022783215224186108612*x^13 - 13607029180705203045483161278554777258648690064599*x^12 + 5999886348433008457414561213976046139735938894840*x^11 + 18794616299087460114823272629891947461290603059885*x^10 + 21527660462889291433155951496398185221995097470280*x^9 + 13504902677578865312120153027325110146365484875114*x^8 - 3236103060706753757508253230695678737164913391850*x^7 - 24443613735836521149030486330274761414478854562204*x^6 - 44731520242317049351476944007187217417882221822284*x^5 - 58947267077063740434345469405735470308566088704243*x^4 - 63480455781892751292112786253865102477899133254809*x^3 - 57179784289610210262482693034717082568463739296411*x^2 - 41645445358064249553751415683355794338386620305086*x - 20822722679032124776875707841677897169193310152543, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.051s user 0m0.040s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:21:36 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))); q=c(4); lift(q)*Mod(1, 37) w=Mod(1-x, sum(n=0, 36, x^n)) (q-9*(1-37))/w^36 Output: ? ? ? ? ? Mod(9, 37) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9233667439263419679101184132213268320641725032927*x^35 + 20067527636374971566498594199490920399410163541891*x^34 + 29750085766292651791599802749909541120760985873284*x^33 + 35822245438026488911177735028273744233480486251405*x^32 + 36741849606675728100253510450940370907391060161679*x^31 + 32275344669831579778359683609382077113607517258289*x^30 + 23557096716856386829767075820434363305706731586491*x^29 + 12801294767744129390398598484855050469372624580930*x^28 + 2739608980891509051322565935445386908522454826280*x^27 - 4072576597592250794166445141169535168307509968114*x^26 - 5905159138208153533640499778106717726498377052688*x^25 - 2292714257260680319545828585592299539017069348212*x^24 + 5847298999106616800953569344369850270736693608353*x^23 + 16447546884205297508253649178317566558352612072950*x^22 + 26815865689618689327185604538282309086902894846990*x^21 + 34318995228347153239078772608569778143352868938543*x^20 + 37051352301825799706150977829769533582254060579465*x^19 + 34318995228347153239078772608569778143352868938543*x^18 + 26815865689618689327185604538282309086902894846990*x^17 + 16447546884205297508253649178317566558352612072950*x^16 + 5847298999106616800953569344369850270736693608353*x^15 - 2292714257260680319545828585592299539017069348212*x^14 - 5905159138208153533640499778106717726498377052688*x^13 - 4072576597592250794166445141169535168307509968114*x^12 + 2739608980891509051322565935445386908522454826280*x^11 + 12801294767744129390398598484855050469372624580930*x^10 + 23557096716856386829767075820434363305706731586491*x^9 + 32275344669831579778359683609382077113607517258289*x^8 + 36741849606675728100253510450940370907391060161679*x^7 + 35822245438026488911177735028273744233480486251405*x^6 + 29750085766292651791599802749909541120760985873284*x^5 + 20067527636374971566498594199490920399410163541891*x^4 + 9233667439263419679101184132213268320641725032927*x^3 - 5288383747486164068144430490316608939116191161218*x - 5288383747486164068144430490316608939116191161218, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.043s user 0m0.037s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 17 23:21:50 2005 Input: 2947294729472947294396 * 328497239427384288 Output: ? 968178182410742570883554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.004s sys 0m0.011s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:22:06 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))); q=c(4); lift(q)*Mod(1, 37) w=Mod(1-x, sum(n=0, 36, x^n)) (q-9*(1-37))/w^38 Output: ? ? ? ? ? Mod(9, 37) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-20822722679032124776875707841677897169193310152543*x^35 - 57179784289610210262482693034717082568463739296411*x^34 - 99837517392470836777719771446904287877169562398677*x^33 - 137962061790502452435189533010961861016542340950377*x^32 - 161870859353787377009790769176471181265231252620118*x^31 - 165491750410591773381945547665068045510516797029779*x^30 - 147905130792266402362578093054085827078488400269086*x^29 - 113577505435655412273582232185082819762929605241429*x^28 - 71227122293733996063550572847006737371741197618606*x^27 - 31609783315614411171851592375436892741257284406178*x^26 - 4787174288149277937561323319782949432328035358795*x^25 + 2428519210177643793831223243340170478216584729149*x^24 - 11795285361249548717148007323004715567814291226920*x^23 - 43846143121483382256404343826303189382939355522526*x^22 - 85584040814156559703438388336593101157404845201104*x^21 - 126408730554170400350950061019926734603594841798057*x^20 - 155951893536111512380007406516339347192959062539345*x^19 - 166710400221251431878717256755543469869047533333415*x^18 - 155951893536111512380007406516339347192959062539345*x^17 - 126408730554170400350950061019926734603594841798057*x^16 - 85584040814156559703438388336593101157404845201104*x^15 - 43846143121483382256404343826303189382939355522526*x^14 - 11795285361249548717148007323004715567814291226920*x^13 + 2428519210177643793831223243340170478216584729149*x^12 - 4787174288149277937561323319782949432328035358795*x^11 - 31609783315614411171851592375436892741257284406178*x^10 - 71227122293733996063550572847006737371741197618606*x^9 - 113577505435655412273582232185082819762929605241429*x^8 - 147905130792266402362578093054085827078488400269086*x^7 - 165491750410591773381945547665068045510516797029779*x^6 - 161870859353787377009790769176471181265231252620118*x^5 - 137962061790502452435189533010961861016542340950377*x^4 - 99837517392470836777719771446904287877169562398677*x^3 - 57179784289610210262482693034717082568463739296411*x^2 - 20822722679032124776875707841677897169193310152543*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.051s user 0m0.042s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:22:21 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))); q=c(4); lift(q)*Mod(1, 37) w=Mod(1-x, sum(n=0, 36, x^n)) (q-9*(1-37))/w^37 Output: ? ? ? ? ? Mod(9, 37) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(15534338931545960708731277351361288230077118991325*x^35 + 21835010423828501738361370570509308139512512949723*x^34 + 17301821718999490880594053722379675970179468399157*x^33 + 3086074884252799797725528323831423079495601517198*x^32 - 17201831622227728404720929353081032923907765742882*x^31 - 38409342297357495796243162452660115601221706913236*x^30 - 55150348035643114865871568710680904484752105180200*x^29 - 63173105820953540986907367179753979560381717775366*x^28 - 60440061657151709668574688313247741799677223364971*x^27 - 47645331706497258011165976897331840478122559199926*x^26 - 28038416177359046508268254404801017079737930240487*x^25 - 6598918107604932265896477275333011123162434196474*x^24 + 11228135081201708762380628661620576645931754143063*x^23 + 20915175013641052670158336668612014605272179526035*x^22 + 20001967060981715870635964841655736276996686444410*x^21 + 8720440302908987252181637654734715420170910588745*x^20 - 10064215993892205278165857602473774493104839358473*x^19 - 31581229364172044275585558080882019845281780946613*x^18 - 50365885660973236805933053338090509758557530893831*x^17 - 61647412419045965424387380525011530615383306749496*x^16 - 62560620371705302223909752351967808943658799831121*x^15 - 52873580439265958316132044344976370984318374448149*x^14 - 35046527250459317287854938408022783215224186108612*x^13 - 13607029180705203045483161278554777258648690064599*x^12 + 5999886348433008457414561213976046139735938894840*x^11 + 18794616299087460114823272629891947461290603059885*x^10 + 21527660462889291433155951496398185221995097470280*x^9 + 13504902677578865312120153027325110146365484875114*x^8 - 3236103060706753757508253230695678737164913391850*x^7 - 24443613735836521149030486330274761414478854562204*x^6 - 44731520242317049351476944007187217417882221822284*x^5 - 58947267077063740434345469405735470308566088704243*x^4 - 63480455781892751292112786253865102477899133254809*x^3 - 57179784289610210262482693034717082568463739296411*x^2 - 41645445358064249553751415683355794338386620305086*x - 20822722679032124776875707841677897169193310152543, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.067s user 0m0.036s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:22:52 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))); q=c(4); lift(q)*Mod(1, 37) w=Mod(1-x, sum(n=0, 36, x^n)) (q-9)/w^37 Output: ? ? ? ? ? Mod(9, 37) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.037s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:22:59 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))); q=c(4); lift(q)*Mod(1, 37) w=Mod(1-x, sum(n=0, 36, x^n)) (q-9)/w^36 Output: ? ? ? ? ? Mod(9, 37) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.042s user 0m0.036s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 17 23:23:26 2005 Input: Mod(13,968178182410742570883554367320960850048)^(-1) Output: ? Mod(819227692809089867670699849271582257733, 968178182410742570883554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:24:07 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))); q=c(4); lift(q)*Mod(1, 37) w=Mod(1-x, sum(n=0, 36, x^n)) (q-9)/w^36 (q-9)/w^37 Output: ? ? ? ? ? Mod(9, 37) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.049s user 0m0.042s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:32:39 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))); q=c(4); lift(q)*Mod(1, 37) w=Mod(1-x, sum(n=0, 36, x^n)) (q-9)/w^36 (q-9^37)/w^37 Output: ? ? ? ? ? Mod(9, 37) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-58228266845731932088697992918776317114794349293188118697966429*x^35 - 113056673653673081666399095974530113997176677192578716310770420*x^34 - 162907906985845700019948125765374455467592146204320958463909691*x^33 - 206347837623225993104650876052212775773621743636036837705003491*x^32 - 242126777852259568634175022054925762107318823234508388210477876*x^31 - 269215432705080103108496237464105102209420822566160597463620437*x^30 - 286834510901706236745877518074717617346608915813851472118080598*x^29 - 294477143641321577980007385040977527776897649361260886071727384*x^28 - 291923466294829512826640593770183342943809830975012176171925181*x^27 - 279246943509935673278778963478966559368607575550746740294621821*x^26 - 256812255766999738940109693481312691393223658466067193692105476*x^25 - 225264808185595708828957951332327550603914088680748581271159168*x^24 - 185512163394313808749640988423208245352668120106992595455550719*x^23 - 138697932606334226221015826687576738769460910190935740459039918*x^22 - 86168876006991828195189546616712830152632584808110700881742988*x^21 - 29436158915281568717039468972224510744009199147401621766961958*x^20 + 29868121691002278172469536906324677116296361198467092577665236*x^19 + 90037889633772702499484455538332827145410421738330932432017312*x^18 + 149342170240056549388993461416882015005715982084199646776644506*x^17 + 206074887331766808867143539061370334414339367744908725891425536*x^16 + 258603943931109206892969819132234243031167693127733765468722466*x^15 + 305418174719088789421594980867865749614374903043790620465233267*x^14 + 345170819510370689500911943776985054865620871617546606280841716*x^13 + 376718267091774719612063685925970195654930441402865218701788024*x^12 + 399152954834710653950732955923624063630314358487544765304304369*x^11 + 411829477619604493498594586214840847205516613911810201181607729*x^10 + 414383154966096558651961377485635032038604432298058911081409932*x^9 + 406740522226481217417831510519375121608315698750649497127763146*x^8 + 389121444029855083780450229908762606471127605502958622473302985*x^7 + 362032789177034549306129014499583266369025606171306413220160424*x^6 + 326253848948000973776604868496870280035328526572834862714686039*x^5 + 282813918310620680691902118210031959729298929141118983473592239*x^4 + 232962684978448062338353088419187618258883460129376741320452968*x^3 + 178134278170506912760651985363433821376501132229986143707648977*x^2 + 119906011324774980671953992444657504261706782936798025009682548*x + 59953005662387490335976996222328752130853391468399012504841274, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.049s user 0m0.039s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:33:06 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))); q=c(4); lift(q)*Mod(1, 37) w=Mod(1-x, sum(n=0, 36, x^n)) (q-9^37)/w^37 Output: ? ? ? ? ? Mod(9, 37) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-58228266845731932088697992918776317114794349293188118697966429*x^35 - 113056673653673081666399095974530113997176677192578716310770420*x^34 - 162907906985845700019948125765374455467592146204320958463909691*x^33 - 206347837623225993104650876052212775773621743636036837705003491*x^32 - 242126777852259568634175022054925762107318823234508388210477876*x^31 - 269215432705080103108496237464105102209420822566160597463620437*x^30 - 286834510901706236745877518074717617346608915813851472118080598*x^29 - 294477143641321577980007385040977527776897649361260886071727384*x^28 - 291923466294829512826640593770183342943809830975012176171925181*x^27 - 279246943509935673278778963478966559368607575550746740294621821*x^26 - 256812255766999738940109693481312691393223658466067193692105476*x^25 - 225264808185595708828957951332327550603914088680748581271159168*x^24 - 185512163394313808749640988423208245352668120106992595455550719*x^23 - 138697932606334226221015826687576738769460910190935740459039918*x^22 - 86168876006991828195189546616712830152632584808110700881742988*x^21 - 29436158915281568717039468972224510744009199147401621766961958*x^20 + 29868121691002278172469536906324677116296361198467092577665236*x^19 + 90037889633772702499484455538332827145410421738330932432017312*x^18 + 149342170240056549388993461416882015005715982084199646776644506*x^17 + 206074887331766808867143539061370334414339367744908725891425536*x^16 + 258603943931109206892969819132234243031167693127733765468722466*x^15 + 305418174719088789421594980867865749614374903043790620465233267*x^14 + 345170819510370689500911943776985054865620871617546606280841716*x^13 + 376718267091774719612063685925970195654930441402865218701788024*x^12 + 399152954834710653950732955923624063630314358487544765304304369*x^11 + 411829477619604493498594586214840847205516613911810201181607729*x^10 + 414383154966096558651961377485635032038604432298058911081409932*x^9 + 406740522226481217417831510519375121608315698750649497127763146*x^8 + 389121444029855083780450229908762606471127605502958622473302985*x^7 + 362032789177034549306129014499583266369025606171306413220160424*x^6 + 326253848948000973776604868496870280035328526572834862714686039*x^5 + 282813918310620680691902118210031959729298929141118983473592239*x^4 + 232962684978448062338353088419187618258883460129376741320452968*x^3 + 178134278170506912760651985363433821376501132229986143707648977*x^2 + 119906011324774980671953992444657504261706782936798025009682548*x + 59953005662387490335976996222328752130853391468399012504841274, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.040s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 17 23:33:27 2005 Input: Mod(10424944469828754080284344711353162,9681718241074148177594033335528733)^(819227692809089867670699849271582257733) Output: ? Mod(5956040251723121685959807416999103, 9681718241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:34:07 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))); q=c(4); lift(q)*Mod(1, 37) w=Mod(1-x, sum(n=0, 36, x^n)) (q-9^37)/w^37; a=Mod(9, 37^2) a^37 Output: ? ? ? ? ? Mod(9, 37) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? Mod(9, 1369) ? Mod(1045, 1369) ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.038s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:34:19 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))); q=c(4); lift(q)*Mod(1, 37); w=Mod(1-x, sum(n=0, 36, x^n)); (q-9^37)/w^37; a=Mod(9, 37^2) a^37 Output: ? ? ? ? ? ? ? ? Mod(9, 1369) ? Mod(1045, 1369) ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.038s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:34:44 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))); q=c(4); lift(q)*Mod(1, 37); w=Mod(1-x, sum(n=0, 36, x^n)); (q-9^37)/w^37; a=9+O(37^2) a^37 Output: ? ? ? ? ? ? ? ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Errors (if any) and Timing Info: Timing: real 0m0.052s user 0m0.038s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:35:34 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))); q=c(4); lift(q)*Mod(1, 37); w=Mod(1-x, sum(n=0, 36, x^n)); (q-9^37)/w^37; a=9+O(37^2) a^37 9+28*37 Output: ? ? ? ? ? ? ? ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? 1045 ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.038s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:36:09 2005 Input: zp=Mod(x,sum(n=0, 36, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 36, b(n)^(lift(Mod(n^k, 37)))); q=c(4); lift(q)*Mod(1, 37); w=Mod(1-x, sum(n=0, 36, x^n)); (q-9^37)/w^37; a=9+O(37^2) a^37 9+28*37 a*(1-37) Output: ? ? ? ? ? ? ? ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? 1045 ? 9 + 28*37 + O(37^2) ? Errors (if any) and Timing Info: Timing: real 0m0.052s user 0m0.038s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:40:40 2005 Input: Factor(96817818241074148177594033335528733) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(9681781824107 ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:40:46 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.174s user 0m0.106s sys 0m0.012s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:41:12 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:41:30 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.120s user 0m0.104s sys 0m0.016s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:51:07 2005 Input: zp=Mod(x,sum(n=0, 58, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 58, b(n)^(lift(Mod(n^k, 59)))); c(1) q=c(14) lift(q)*Mod(1, 37); w=Mod(1-x, sum(n=0, 36, x^n)); (q-9^37)/w^37; a=9+O(37^2); a^37; 9+28*37; a*(1-37); Output: ? ? ? ? Mod(-1, x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-142088642687402144963513586680203167425602969137769803102752029619486114527598422242590948092899212165984457305892256729625745*x^57 + 15555298980008392991596440895077952538342530202217525832178382508918734553175496727362299934559244332731220920644928439545445*x^56 + 149250814192989265321601185953113727536309915456437905525362894482592349064894562007683903035304436601685705223448978779783993*x^55 - 15511209142151203868161258467532874133921808558639650499752376039736412102507899063451209909533113351604627452721816863948184*x^54 - 140434618753538115266156270829423326243813421655170456256068960457079571083970491748184478812714231178849714652319952684675835*x^53 + 30978452308040846058720148643216849277103825926790077274453451804611833096578713258873591314319884110513174035314306333391159*x^52 + 146775644782544065530930306853323179308140730894703727855406615405024581021708699060258883198412491132676655028353259977134835*x^51 - 30802588423885437102080729530918181042170957147693679357867832604624092666176322588346419476950741323880175212864214337633116*x^50 - 137145323438569944356120846222412649440689723229176805084415523002789822846911680735393946372108674645159595757378260493580680*x^49 + 46094710855577300073048251982795879601112440964041902306798957042069818240632749908407893428950787680157658251395683950720637*x^48 + 142681549932713303345137936559048066911796975097085564680477547374536640142390825967147539662580498985217296015939448776537461*x^47 - 45700874501887039018446438880240915591632903212188586867364635960421036822852348516482433644501372881828655727454425012021831*x^46 - 132258034949527232620637072110267393246072049337738350670425849333339502344606616434069227378083673032156465084991770278987258*x^45 + 60732790168672995910483133000789927845700861528996448987598976134516269932213555212783982014923008907785615515759069941725292*x^44 + 137014920081568751948751049983796619001922739320700928969468535734294565514660683050846734916310349143613810805333537140567093*x^43 - 60037251074118166200774492522300345805083122949174013411345386062772206620059141081895896814672348066023292344447134976926903*x^42 - 125828123553481634444629949474480739815939534471071977074112771112001963104189981472432938449087773262067673830780642961332529*x^41 + 74726824885042284538556560290343409325312745410909063725943981246314193100772249100774155872044527602768073722156354652075768*x^40 + 129839949928318511670632305401819743767137050700497572863461892446189684648221775472168722432361934232901083781425975953747913*x^39 - 73649277242621290503341183747503527782826859441681620046818673141053268232798233873347293000444846407108949588407575478613430*x^38 - 117928429911797197668400703625333457106081095801916655712108946418203504526015789478757003775472328552379634302380296049271395*x^37 + 87918260369579686133734790067721319163442076469876916171634165509891290257169253124320000361261547512904334914312938006256193*x^36 + 121237923893518809404300841642161009729109081750874016766132436314749289313581690830592244432106807398544067033903869850893726*x^35 - 863827329511613615272742590141431345376138950515503158424748948057509078874064210531862147646558676699512467263734[+++] ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.270s user 0m0.266s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:51:26 2005 Input: zp=Mod(x,sum(n=0, 58, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 58, b(n)^(lift(Mod(n^k, 59)))); q=c(14) lift(q)*Mod(1, 37); w=Mod(1-x, sum(n=0, 36, x^n)); (q-9^37)/w^37; a=9+O(37^2); a^37; 9+28*37; a*(1-37); Output: ? ? ? ? Mod(-142088642687402144963513586680203167425602969137769803102752029619486114527598422242590948092899212165984457305892256729625745*x^57 + 15555298980008392991596440895077952538342530202217525832178382508918734553175496727362299934559244332731220920644928439545445*x^56 + 149250814192989265321601185953113727536309915456437905525362894482592349064894562007683903035304436601685705223448978779783993*x^55 - 15511209142151203868161258467532874133921808558639650499752376039736412102507899063451209909533113351604627452721816863948184*x^54 - 140434618753538115266156270829423326243813421655170456256068960457079571083970491748184478812714231178849714652319952684675835*x^53 + 30978452308040846058720148643216849277103825926790077274453451804611833096578713258873591314319884110513174035314306333391159*x^52 + 146775644782544065530930306853323179308140730894703727855406615405024581021708699060258883198412491132676655028353259977134835*x^51 - 30802588423885437102080729530918181042170957147693679357867832604624092666176322588346419476950741323880175212864214337633116*x^50 - 137145323438569944356120846222412649440689723229176805084415523002789822846911680735393946372108674645159595757378260493580680*x^49 + 46094710855577300073048251982795879601112440964041902306798957042069818240632749908407893428950787680157658251395683950720637*x^48 + 142681549932713303345137936559048066911796975097085564680477547374536640142390825967147539662580498985217296015939448776537461*x^47 - 45700874501887039018446438880240915591632903212188586867364635960421036822852348516482433644501372881828655727454425012021831*x^46 - 132258034949527232620637072110267393246072049337738350670425849333339502344606616434069227378083673032156465084991770278987258*x^45 + 60732790168672995910483133000789927845700861528996448987598976134516269932213555212783982014923008907785615515759069941725292*x^44 + 137014920081568751948751049983796619001922739320700928969468535734294565514660683050846734916310349143613810805333537140567093*x^43 - 60037251074118166200774492522300345805083122949174013411345386062772206620059141081895896814672348066023292344447134976926903*x^42 - 125828123553481634444629949474480739815939534471071977074112771112001963104189981472432938449087773262067673830780642961332529*x^41 + 74726824885042284538556560290343409325312745410909063725943981246314193100772249100774155872044527602768073722156354652075768*x^40 + 129839949928318511670632305401819743767137050700497572863461892446189684648221775472168722432361934232901083781425975953747913*x^39 - 73649277242621290503341183747503527782826859441681620046818673141053268232798233873347293000444846407108949588407575478613430*x^38 - 117928429911797197668400703625333457106081095801916655712108946418203504526015789478757003775472328552379634302380296049271395*x^37 + 87918260369579686133734790067721319163442076469876916171634165509891290257169253124320000361261547512904334914312938006256193*x^36 + 121237923893518809404300841642161009729109081750874016766132436314749289313581690830592244432106807398544067033903869850893726*x^35 - 863827329511613615272742590141431345376138950515503158424748948057509078874064210531862147646558676699512467263734[+++] ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.145s user 0m0.139s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:52:46 2005 Input: zp=Mod(x,sum(n=0, 58, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 58, b(n)^(lift(Mod(n^k, 59)))); q=c(14) lift(q)*Mod(1, 59) w=Mod(1-x, sum(n=0, 58, x^n)); Output: ? ? ? ? Mod(-142088642687402144963513586680203167425602969137769803102752029619486114527598422242590948092899212165984457305892256729625745*x^57 + 15555298980008392991596440895077952538342530202217525832178382508918734553175496727362299934559244332731220920644928439545445*x^56 + 149250814192989265321601185953113727536309915456437905525362894482592349064894562007683903035304436601685705223448978779783993*x^55 - 15511209142151203868161258467532874133921808558639650499752376039736412102507899063451209909533113351604627452721816863948184*x^54 - 140434618753538115266156270829423326243813421655170456256068960457079571083970491748184478812714231178849714652319952684675835*x^53 + 30978452308040846058720148643216849277103825926790077274453451804611833096578713258873591314319884110513174035314306333391159*x^52 + 146775644782544065530930306853323179308140730894703727855406615405024581021708699060258883198412491132676655028353259977134835*x^51 - 30802588423885437102080729530918181042170957147693679357867832604624092666176322588346419476950741323880175212864214337633116*x^50 - 137145323438569944356120846222412649440689723229176805084415523002789822846911680735393946372108674645159595757378260493580680*x^49 + 46094710855577300073048251982795879601112440964041902306798957042069818240632749908407893428950787680157658251395683950720637*x^48 + 142681549932713303345137936559048066911796975097085564680477547374536640142390825967147539662580498985217296015939448776537461*x^47 - 45700874501887039018446438880240915591632903212188586867364635960421036822852348516482433644501372881828655727454425012021831*x^46 - 132258034949527232620637072110267393246072049337738350670425849333339502344606616434069227378083673032156465084991770278987258*x^45 + 60732790168672995910483133000789927845700861528996448987598976134516269932213555212783982014923008907785615515759069941725292*x^44 + 137014920081568751948751049983796619001922739320700928969468535734294565514660683050846734916310349143613810805333537140567093*x^43 - 60037251074118166200774492522300345805083122949174013411345386062772206620059141081895896814672348066023292344447134976926903*x^42 - 125828123553481634444629949474480739815939534471071977074112771112001963104189981472432938449087773262067673830780642961332529*x^41 + 74726824885042284538556560290343409325312745410909063725943981246314193100772249100774155872044527602768073722156354652075768*x^40 + 129839949928318511670632305401819743767137050700497572863461892446189684648221775472168722432361934232901083781425975953747913*x^39 - 73649277242621290503341183747503527782826859441681620046818673141053268232798233873347293000444846407108949588407575478613430*x^38 - 117928429911797197668400703625333457106081095801916655712108946418203504526015789478757003775472328552379634302380296049271395*x^37 + 87918260369579686133734790067721319163442076469876916171634165509891290257169253124320000361261547512904334914312938006256193*x^36 + 121237923893518809404300841642161009729109081750874016766132436314749289313581690830592244432106807398544067033903869850893726*x^35 - 863827329511613615272742590141431345376138950515503158424748948057509078874064210531862147646558676699512467263734[+++] ? Mod(22, 59) ? ? Errors (if any) and Timing Info: Timing: real 0m0.138s user 0m0.136s sys 0m0.002s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:53:42 2005 Input: zp=Mod(x,sum(n=0, 58, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 58, b(n)^(lift(Mod(n^k, 59)))); q=c(14) w=Mod(1-x, sum(n=0, 58, x^n)); lift(q)*Mod(1, 59) (q-22)/59 Output: ? ? ? ? Mod(-142088642687402144963513586680203167425602969137769803102752029619486114527598422242590948092899212165984457305892256729625745*x^57 + 15555298980008392991596440895077952538342530202217525832178382508918734553175496727362299934559244332731220920644928439545445*x^56 + 149250814192989265321601185953113727536309915456437905525362894482592349064894562007683903035304436601685705223448978779783993*x^55 - 15511209142151203868161258467532874133921808558639650499752376039736412102507899063451209909533113351604627452721816863948184*x^54 - 140434618753538115266156270829423326243813421655170456256068960457079571083970491748184478812714231178849714652319952684675835*x^53 + 30978452308040846058720148643216849277103825926790077274453451804611833096578713258873591314319884110513174035314306333391159*x^52 + 146775644782544065530930306853323179308140730894703727855406615405024581021708699060258883198412491132676655028353259977134835*x^51 - 30802588423885437102080729530918181042170957147693679357867832604624092666176322588346419476950741323880175212864214337633116*x^50 - 137145323438569944356120846222412649440689723229176805084415523002789822846911680735393946372108674645159595757378260493580680*x^49 + 46094710855577300073048251982795879601112440964041902306798957042069818240632749908407893428950787680157658251395683950720637*x^48 + 142681549932713303345137936559048066911796975097085564680477547374536640142390825967147539662580498985217296015939448776537461*x^47 - 45700874501887039018446438880240915591632903212188586867364635960421036822852348516482433644501372881828655727454425012021831*x^46 - 132258034949527232620637072110267393246072049337738350670425849333339502344606616434069227378083673032156465084991770278987258*x^45 + 60732790168672995910483133000789927845700861528996448987598976134516269932213555212783982014923008907785615515759069941725292*x^44 + 137014920081568751948751049983796619001922739320700928969468535734294565514660683050846734916310349143613810805333537140567093*x^43 - 60037251074118166200774492522300345805083122949174013411345386062772206620059141081895896814672348066023292344447134976926903*x^42 - 125828123553481634444629949474480739815939534471071977074112771112001963104189981472432938449087773262067673830780642961332529*x^41 + 74726824885042284538556560290343409325312745410909063725943981246314193100772249100774155872044527602768073722156354652075768*x^40 + 129839949928318511670632305401819743767137050700497572863461892446189684648221775472168722432361934232901083781425975953747913*x^39 - 73649277242621290503341183747503527782826859441681620046818673141053268232798233873347293000444846407108949588407575478613430*x^38 - 117928429911797197668400703625333457106081095801916655712108946418203504526015789478757003775472328552379634302380296049271395*x^37 + 87918260369579686133734790067721319163442076469876916171634165509891290257169253124320000361261547512904334914312938006256193*x^36 + 121237923893518809404300841642161009729109081750874016766132436314749289313581690830592244432106807398544067033903869850893726*x^35 - 863827329511613615272742590141431345376138950515503158424748948057509078874064210531862147646558676699512467263734[+++] ? ? Mod(22, 59) ? Mod(-2408282079447493982432433672545816397044118120979149205131390332533662958094888512586287255811851053660753513659190792027555*x^57 + 263649135254379542230448150764033093870212376308771624274209873032520924630093164870547456517953293775105439332964888805855*x^56 + 2529674816830326530874596372086673348073049414515896703819710075976141509574484101825150898903465027147215342770321674233627*x^55 - 262901849866969557087478957076828375151217094214231364402582644741295120381489814634766269653103616128891990724098590914376*x^54 - 2380247775483696868917902895413954682098532570426617902645236617916602899728313419460753878181597138624571434785083943808065*x^53 + 525058513695607560317290654969777106391590269945594530075482233976471747399639207777518496852879391703613119242615361582901*x^52 + 2487722792924475686964920455141070835731198828723791997549264667881772559689977950173879376244279510723333136073784067409065*x^51 - 522077769896363340713232703913867475291033171994808124709624281434306655358920721836379991134758327523392800218037531146324*x^50 - 2324497007433388887391878749532417787130334292019945848888398694962539370286638656532100785967943638053552470464038313450520*x^49 + 781266285687750848695733084454167450866312558712574615369473848170674885434453388278099888626284536951824716125350575435943*x^48 + 2418331354791750904154880280661831642572830086391280757296229616517570171904929253680466773942042355681649085015922860619279*x^47 - 774591093252322695227905743732896874434455986647264184192620948481712488522921161296312434652565642064892469956854661220709*x^46 - 2241661609314020891875204612038430394001221175215904248651285581921008514315366380238461480984469034443329916694775767440462*x^45 + 1029369324892762642550561576284575048232217992016888965891508070076546948003619579877694610422423879792976534165407965113988*x^44 + 2322286781043538168622899152267739305117334564757642863889297215835501110417977678827910761293395748196844250937856561704527*x^43 - 1017580526679968918657194788513565183137002083884305312056701458691054349492527814947388081604616068915649022787239575880117*x^42 - 2132680060228502278722541516516622708744737872391050458883267306983084120409999685973439634730301241729960573403061745107331*x^41 + 1266556353983767534551806106615989988564622803574729893660067478751088018657156764419900946983805552589289385121294146645352*x^40 + 2200677117429127316451395006810504131646390689838941912940032075359147197427487719867266481904439563269509894600440270402507*x^39 - 1248292834620699839039681080466161487844523041384434238081672426119546919199970065649954118651607566222185586244196194552770*x^38 - 1998786947657579621498317010598872154340357555964689079866253329122093297051115075911135657211395399192875157667462644902905*x^37 + 1490140006264062476842962543520700324804102991014862985959901110337140512833377171598644073919687245981429405327337932309427*x^36 + 2054880065991844227191539688850186605578120029675830792646312479911004903620028658145631261561132328788882492100065590693114*x^35 - 1464114117816294263174139983290561602332438899178818912584320250944930642159430865308240928214506231694088927565651825863757*x^34 - 18414992443617080502575[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.137s user 0m0.134s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:53:52 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.118s user 0m0.100s sys 0m0.018s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:54:03 2005 Input: zp=Mod(x,sum(n=0, 58, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 58, b(n)^(lift(Mod(n^k, 59)))); q=c(14) w=Mod(1-x, sum(n=0, 58, x^n)); lift(q)*Mod(1, 59) (q-22)/w^58 Output: ? ? ? ? Mod(-142088642687402144963513586680203167425602969137769803102752029619486114527598422242590948092899212165984457305892256729625745*x^57 + 15555298980008392991596440895077952538342530202217525832178382508918734553175496727362299934559244332731220920644928439545445*x^56 + 149250814192989265321601185953113727536309915456437905525362894482592349064894562007683903035304436601685705223448978779783993*x^55 - 15511209142151203868161258467532874133921808558639650499752376039736412102507899063451209909533113351604627452721816863948184*x^54 - 140434618753538115266156270829423326243813421655170456256068960457079571083970491748184478812714231178849714652319952684675835*x^53 + 30978452308040846058720148643216849277103825926790077274453451804611833096578713258873591314319884110513174035314306333391159*x^52 + 146775644782544065530930306853323179308140730894703727855406615405024581021708699060258883198412491132676655028353259977134835*x^51 - 30802588423885437102080729530918181042170957147693679357867832604624092666176322588346419476950741323880175212864214337633116*x^50 - 137145323438569944356120846222412649440689723229176805084415523002789822846911680735393946372108674645159595757378260493580680*x^49 + 46094710855577300073048251982795879601112440964041902306798957042069818240632749908407893428950787680157658251395683950720637*x^48 + 142681549932713303345137936559048066911796975097085564680477547374536640142390825967147539662580498985217296015939448776537461*x^47 - 45700874501887039018446438880240915591632903212188586867364635960421036822852348516482433644501372881828655727454425012021831*x^46 - 132258034949527232620637072110267393246072049337738350670425849333339502344606616434069227378083673032156465084991770278987258*x^45 + 60732790168672995910483133000789927845700861528996448987598976134516269932213555212783982014923008907785615515759069941725292*x^44 + 137014920081568751948751049983796619001922739320700928969468535734294565514660683050846734916310349143613810805333537140567093*x^43 - 60037251074118166200774492522300345805083122949174013411345386062772206620059141081895896814672348066023292344447134976926903*x^42 - 125828123553481634444629949474480739815939534471071977074112771112001963104189981472432938449087773262067673830780642961332529*x^41 + 74726824885042284538556560290343409325312745410909063725943981246314193100772249100774155872044527602768073722156354652075768*x^40 + 129839949928318511670632305401819743767137050700497572863461892446189684648221775472168722432361934232901083781425975953747913*x^39 - 73649277242621290503341183747503527782826859441681620046818673141053268232798233873347293000444846407108949588407575478613430*x^38 - 117928429911797197668400703625333457106081095801916655712108946418203504526015789478757003775472328552379634302380296049271395*x^37 + 87918260369579686133734790067721319163442076469876916171634165509891290257169253124320000361261547512904334914312938006256193*x^36 + 121237923893518809404300841642161009729109081750874016766132436314749289313581690830592244432106807398544067033903869850893726*x^35 - 863827329511613615272742590141431345376138950515503158424748948057509078874064210531862147646558676699512467263734[+++] ? ? Mod(22, 59) ? Mod(10771737091298398390403995202461882953358426394691256064624216976299579813411769161907327234378513465313376214824118*x^57 + 193132892498690875261049248422719075009358579521156350848676495359591020289777344415802567803812931176552534543720956*x^56 + 174510617142367148531935772613762057089788001192681811687861170379911458710584798287445021966384196805522317372122015*x^55 - 5003180396282805809536679423870235310554222914939244900635685527086078614760270555418864763093334308018636788762740*x^54 + 24997825189017971932030440047564513082078324449875163908445163387406228922270954001128591622189020300125151057417128*x^53 + 204340818598556678708428470821483526001305607628308982975702603301577299402221685756970043053874428462733331906242444*x^52 + 165248502200241084875442350975972017043377496867084704975148428054337756302551173791867760480280677293151416219289656*x^51 - 12757158549023799597632651625436558666811099555653989836002679332676719085065384528786045242356032971612853670397974*x^50 + 34233346947470512090800692307441163955838804505241587257098150073462290610311315869998426414681733480176829461548476*x^49 + 207889922038062132010839980365759445586599427023241844972507735501666113174942765765674677730242349153479482607159337*x^48 + 149799649439119177344861981848292255261804754331292318895155021621435047823312342346160763106474127875213594418744353*x^47 - 22617986999679497933665644659505945295590925007398174039957870700418447947164634752250654475144382442758070251986506*x^46 + 43011267052945934651381426924692169088028677411764364807393458067509859893044940636302383312980934304687186496489844*x^45 + 211056276089147653121086976476505090859234330129533891455717048101020263598484828811267513397088499959558572226154800*x^44 + 136787140764076185035175890373241338587431565106467629345322487424977600334458202725317670250957643240469858969405468*x^43 - 25968269479764420479187115780744894212768787479242769037985760375714920952013337340209437785924961354163508688544672*x^42 + 58766108019691707800007665780882781686493566405235920753867509496676366657136421946834864728605776362683534143859596*x^41 + 218867386855179427752984311511131565997159567688774410936593706888826626719329168888420741526531560641948322279762465*x^40 + 127467344710502416699130681220628517307394685840131721727902972744500496707564769848962176239748106353101218394186827*x^39 - 25995639485425460022936190396816900757128725492792461834244514971765166250372048621194033767856268726020585085311456*x^38 + 74809615024789040272116843995973540756138899905948409069380430163458448693095855478952363860403966605499898252580780*x^37 + 223059816687957798486953015448771579493571815780091113770806612804286916780333228623337027724012310474715795418489009*x^36 + 113355967782704515010446890923786067614952960604068259800765527288606514385444739409380051760346615569577453920877115*x^35 - 30746589627366230754299806615322095018490637239876534793966279869677159227246906386056849365568365685047033406006367*x^34 + 84772095574857030094171888532402665566932097440041150151542694284829294758535306118145302388183946824249204316676861*x^33 + 220869564236381618830621053643687691315558066603104120247961411703219442894[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.188s user 0m0.178s sys 0m0.011s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:54:11 2005 Input: 294729472947294396*294729472947294398 Output: ? 86865462223789939810103442587593608 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:54:17 2005 Input: zp=Mod(x,sum(n=0, 58, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 58, b(n)^(lift(Mod(n^k, 59)))); q=c(14) w=Mod(1-x, sum(n=0, 58, x^n)); lift(q)*Mod(1, 59) (q-22)/59 Output: ? ? ? ? Mod(-142088642687402144963513586680203167425602969137769803102752029619486114527598422242590948092899212165984457305892256729625745*x^57 + 15555298980008392991596440895077952538342530202217525832178382508918734553175496727362299934559244332731220920644928439545445*x^56 + 149250814192989265321601185953113727536309915456437905525362894482592349064894562007683903035304436601685705223448978779783993*x^55 - 15511209142151203868161258467532874133921808558639650499752376039736412102507899063451209909533113351604627452721816863948184*x^54 - 140434618753538115266156270829423326243813421655170456256068960457079571083970491748184478812714231178849714652319952684675835*x^53 + 30978452308040846058720148643216849277103825926790077274453451804611833096578713258873591314319884110513174035314306333391159*x^52 + 146775644782544065530930306853323179308140730894703727855406615405024581021708699060258883198412491132676655028353259977134835*x^51 - 30802588423885437102080729530918181042170957147693679357867832604624092666176322588346419476950741323880175212864214337633116*x^50 - 137145323438569944356120846222412649440689723229176805084415523002789822846911680735393946372108674645159595757378260493580680*x^49 + 46094710855577300073048251982795879601112440964041902306798957042069818240632749908407893428950787680157658251395683950720637*x^48 + 142681549932713303345137936559048066911796975097085564680477547374536640142390825967147539662580498985217296015939448776537461*x^47 - 45700874501887039018446438880240915591632903212188586867364635960421036822852348516482433644501372881828655727454425012021831*x^46 - 132258034949527232620637072110267393246072049337738350670425849333339502344606616434069227378083673032156465084991770278987258*x^45 + 60732790168672995910483133000789927845700861528996448987598976134516269932213555212783982014923008907785615515759069941725292*x^44 + 137014920081568751948751049983796619001922739320700928969468535734294565514660683050846734916310349143613810805333537140567093*x^43 - 60037251074118166200774492522300345805083122949174013411345386062772206620059141081895896814672348066023292344447134976926903*x^42 - 125828123553481634444629949474480739815939534471071977074112771112001963104189981472432938449087773262067673830780642961332529*x^41 + 74726824885042284538556560290343409325312745410909063725943981246314193100772249100774155872044527602768073722156354652075768*x^40 + 129839949928318511670632305401819743767137050700497572863461892446189684648221775472168722432361934232901083781425975953747913*x^39 - 73649277242621290503341183747503527782826859441681620046818673141053268232798233873347293000444846407108949588407575478613430*x^38 - 117928429911797197668400703625333457106081095801916655712108946418203504526015789478757003775472328552379634302380296049271395*x^37 + 87918260369579686133734790067721319163442076469876916171634165509891290257169253124320000361261547512904334914312938006256193*x^36 + 121237923893518809404300841642161009729109081750874016766132436314749289313581690830592244432106807398544067033903869850893726*x^35 - 863827329511613615272742590141431345376138950515503158424748948057509078874064210531862147646558676699512467263734[+++] ? ? Mod(22, 59) ? Mod(-2408282079447493982432433672545816397044118120979149205131390332533662958094888512586287255811851053660753513659190792027555*x^57 + 263649135254379542230448150764033093870212376308771624274209873032520924630093164870547456517953293775105439332964888805855*x^56 + 2529674816830326530874596372086673348073049414515896703819710075976141509574484101825150898903465027147215342770321674233627*x^55 - 262901849866969557087478957076828375151217094214231364402582644741295120381489814634766269653103616128891990724098590914376*x^54 - 2380247775483696868917902895413954682098532570426617902645236617916602899728313419460753878181597138624571434785083943808065*x^53 + 525058513695607560317290654969777106391590269945594530075482233976471747399639207777518496852879391703613119242615361582901*x^52 + 2487722792924475686964920455141070835731198828723791997549264667881772559689977950173879376244279510723333136073784067409065*x^51 - 522077769896363340713232703913867475291033171994808124709624281434306655358920721836379991134758327523392800218037531146324*x^50 - 2324497007433388887391878749532417787130334292019945848888398694962539370286638656532100785967943638053552470464038313450520*x^49 + 781266285687750848695733084454167450866312558712574615369473848170674885434453388278099888626284536951824716125350575435943*x^48 + 2418331354791750904154880280661831642572830086391280757296229616517570171904929253680466773942042355681649085015922860619279*x^47 - 774591093252322695227905743732896874434455986647264184192620948481712488522921161296312434652565642064892469956854661220709*x^46 - 2241661609314020891875204612038430394001221175215904248651285581921008514315366380238461480984469034443329916694775767440462*x^45 + 1029369324892762642550561576284575048232217992016888965891508070076546948003619579877694610422423879792976534165407965113988*x^44 + 2322286781043538168622899152267739305117334564757642863889297215835501110417977678827910761293395748196844250937856561704527*x^43 - 1017580526679968918657194788513565183137002083884305312056701458691054349492527814947388081604616068915649022787239575880117*x^42 - 2132680060228502278722541516516622708744737872391050458883267306983084120409999685973439634730301241729960573403061745107331*x^41 + 1266556353983767534551806106615989988564622803574729893660067478751088018657156764419900946983805552589289385121294146645352*x^40 + 2200677117429127316451395006810504131646390689838941912940032075359147197427487719867266481904439563269509894600440270402507*x^39 - 1248292834620699839039681080466161487844523041384434238081672426119546919199970065649954118651607566222185586244196194552770*x^38 - 1998786947657579621498317010598872154340357555964689079866253329122093297051115075911135657211395399192875157667462644902905*x^37 + 1490140006264062476842962543520700324804102991014862985959901110337140512833377171598644073919687245981429405327337932309427*x^36 + 2054880065991844227191539688850186605578120029675830792646312479911004903620028658145631261561132328788882492100065590693114*x^35 - 1464114117816294263174139983290561602332438899178818912584320250944930642159430865308240928214506231694088927565651825863757*x^34 - 18414992443617080502575[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.137s user 0m0.129s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:54:57 2005 Input: Mod(13,86865462223789939810103442587593608)^(-1) Output: ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(13, 86865462223789939810103442587593608). Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:55:11 2005 Input: zp=Mod(x,sum(n=0, 58, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 58, b(n)^(lift(Mod(n^k, 59)))); q=c(14); w=Mod(1-x, sum(n=0, 58, x^n)); lift(q)*Mod(1, 59); a=22+O(59^2) Output: ? ? ? ? ? ? ? 22 + O(59^2) ? Errors (if any) and Timing Info: Timing: real 0m0.138s user 0m0.131s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:55:22 2005 Input: zp=Mod(x,sum(n=0, 58, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 58, b(n)^(lift(Mod(n^k, 59)))); q=c(14); w=Mod(1-x, sum(n=0, 58, x^n)); lift(q)*Mod(1, 59); a=22+O(59^2) a^59 Output: ? ? ? ? ? ? ? 22 + O(59^2) ? 22 + 10*59 + 15*59^2 + O(59^3) ? Errors (if any) and Timing Info: Timing: real 0m0.137s user 0m0.132s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:55:35 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:55:57 2005 Input: zp=Mod(x,sum(n=0, 58, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 58, b(n)^(lift(Mod(n^k, 59)))); q=c(14); w=Mod(1-x, sum(n=0, 58, x^n)); lift(q)*Mod(1, 59); a=22+O(59^2) a^59 (q-22-10*59)/w^59 Output: ? ? ? ? ? ? ? 22 + O(59^2) ? 22 + 10*59 + 15*59^2 + O(59^3) ? Mod(95416059428054331143746855513009803933704121920054159921641297252884157306327287717627695332755209087950159349661255*x^57 + 180060381764810263897089715823557724914049817445417063778658257272476440334083600479732022064193715717711952908456852*x^56 + 82343548694173719779787322913848453838395359844314872851622760228429348169199898145738259341921684405166939962914781*x^55 + 3248990979860902391598405813096200682311480571687221085402353084877981760876898187506756333020546606586776127040061*x^54 + 103668230804198039344881940749976239926569825406680625907678513033845501484583863732476358958251800641054428633558306*x^53 + 174086465043234398556598356215421530778195622876859621920873484790930694635449986979224959624628316713936727818614133*x^52 + 65161705872732050991916740906947808710594137168604798866810630737691827710189746683650732653506763542039586976919844*x^51 - 4670736899454702739778754556014404399079237778425746186698476210865846620842163812669728738066675155200166869679007*x^50 + 103502481077623428001600752582431958201435983697282403570943058689653506218302735133175217947356047432078744943817302*x^49 + 164685193558207247054546915788000598179301301112094976235483266525448154242303274387765436036972227869408226687417871*x^48 + 52211330948199446187453790935250956526405996008907291184613364792475667886466863547929746031744291326641950050196549*x^47 - 2172259062865400013661335400031494801694636402330867788904367744084663362979986269447480296285924438358149371419849*x^46 + 115861787364868429063751164772484254427600410525121466172690232985619305346826506128257435139619053709807833885076662*x^45 + 168266579739976825556116593360801889273275855033411261286932937854358697706761293852478805053130028808767155909264033*x^44 + 52626363078883503578776472397306602347745646823931529752851483984495044955270128326606865999208702084991309626725218*x^43 + 11255281742861649687347437537075067694018203637518060329164026917180983817568883725911015330882744319936532951362745*x^42 + 132639610650680401310281408830829765840491113036814989288784264997577930989361560901949918499083300541695931504456812*x^41 + 169289562059043024654020598562956788087701668551633228456550698034892745717096422675496179285835174940700985212936181*x^40 + 45838234631917928044783142564835026024246222782912977441590422055354894319650447921026273053757433338313744104378171*x^39 + 13786949349469842489399316857216312650555658862835415635320397938341518761862726803287709623172252662529475076257549*x^38 + 135198648262949633656082362767043017341388506275682037391197414063138426652591126130059732716475657007012835815556620*x^37 + 155805092666214924527712374284079280518953728289787788243449077455666995923113560372930219961582754923271190751669075*x^36 + 28161335406311457184506214348317504959086034429750834394274195105970413496943097153780287826074455050393749142803911*x^35 + 10221427051661273317806178937541241277837195745736734515140083780289502305285336157414172252879298751686295021240411*x^34 + 136384076107081835215852841065873140230031954905667429230737517294275711912210531566656611348900476889841439176875603*x^33 + 14702803996027913626542780804648027859680397938568043900082576948036183580975[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.197s user 0m0.191s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:56:07 2005 Input: Mod(13,1002096)^(-1) Output: ? Mod(231253, 1002096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:56:20 2005 Input: zp=Mod(x,sum(n=0, 58, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 58, b(n)^(lift(Mod(n^k, 59)))); q=c(14); w=Mod(1-x, sum(n=0, 58, x^n)); lift(q)*Mod(1, 59); a=22+O(59^2) a^59 (q-22-10*59)/w^60 Output: ? ? ? ? ? ? ? 22 + O(59^2) ? 22 + 10*59 + 15*59^2 + O(59^3) ? Mod(85781915262452698720103588253621231921569281951750557315954535793137983267727574379854365522727879926655187988784225*x^57 + 76147771096851066296460320994232659909434441983446954710267774333391809229127861042081035712700550765360216627907195*x^56 - 18130695405506498880525806575703833083046093510219551752435947145946647837228165057796620828765285025696548291765432*x^55 - 14692328837227519940209541235931054999872171402783867288104171581238012738700488823680514647959089504208300265895988*x^54 + 67840595445364276388295641204593976239385629977279468942448011127021988768150187368667094541748243815860111595848176*x^53 + 49954279903618935763517288708238968234385086522349400350724033886314470551293898016045101106224323101460870951074095*x^52 - 38350269877162764072977479253561330622241254402759664254194915111478240816428514583325492995676113685820668878755813*x^51 - 17730060487442116344790631906887907411266109619613905805051010056032085258890686887121860126454997301205067866891432*x^50 + 72722591674465285115091710902747728909382410110562397697602001947971744629679051305402234134339557780650286991571800*x^49 + 55002025859294555833594546573937002629515708365030551442613479051456221679103890552081381709711390275226730036538723*x^48 - 23901252436459992500848780960442363628216310795313867476915251680853949295471809455829688804532957667526308662094923*x^47 + 9669331877793260031801016357927911766946975147529398654425919319808366085788901376094930686450630932486929276492753*x^46 + 97623506203111358765565940011580638490210893501610823759284822857031012716496462025396776505464435297500266636696827*x^45 + 67543634100695628421918363492717615984179764928239914902549125664549690637397530276993706888573261514347620740404390*x^44 - 14941030376828498414094641614463041367526808153420789068429276396671023801636189195630732641828887367764347180075418*x^43 + 18214521806740696727232474241851588206296826974398238494673775411971914510821256857616766881690290473899531181983589*x^42 + 92741155326331745759988624958397752433847905288630735481464284287928913960979947511560117073535426080618186219405069*x^41 + 45883459938104043169810804381189218514926074203566303508634555083488966239345960989464564097180005465577442703732482*x^40 - 37624186858486282764106205928146337651206312396316367631961607158265796210022887306177249665927289548468354520419474*x^39 + 2319493772048487911214239760639868246116746772521212242402506579517292738054239152650842803043157039873089363986580*x^38 + 74314459685031344141918511157044787517130369861436353923036644434313757243919086729217498702598784303998802276513256*x^37 + 24897726684534409205939736643623002097311145537504873847793766164313313859055534979012131508851007223641154449740861*x^36 - 45125450719227816601669049386835046500073300800532357079700775498215698796330451014063722930003867772974848313143989*x^35 + 12495129136913424933928324518468680462409946721467365841979565188951870974454026212010354766649557103286590532836325*x^34 + 88055617347704850336225733834548671106142032927481188642794017201800351936896264434450548036498138278255483500380139*x^33 + 3745345650307571384047648102229676279767935997356431672801103570066262329241330724764830[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.200s user 0m0.194s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:56:32 2005 Input: zp=Mod(x,sum(n=0, 58, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 58, b(n)^(lift(Mod(n^k, 59)))); q=c(14); w=Mod(1-x, sum(n=0, 58, x^n)); lift(q)*Mod(1, 59); a=22+O(59^2) a^59 (q-22-10*59)/w^72 Output: ? ? ? ? ? ? ? 22 + O(59^2) ? 22 + 10*59 + 15*59^2 + O(59^3) ? Mod(9688474879962899075501613433672556443606882310483927273833262861845554775002680134865331150842839449594021088865894202388/59*x^57 + 21016102345113648011025046637169780758943295858068756716836945060867410287780917613132765690214541008702432241683367510118/59*x^56 + 31958306687156422661187272178233436331476232184761468158705892101890266607527908281659350911147868468258052940992559994069/59*x^55 + 40559253889859405013540005181983483366298523533143347179192700025402002592623588906745225121322233358179190535932763816760/59*x^54 + 45281684357378066094191305787081798139169273378756357705562765562924584545639769497997874651043567947239019987942966080997/59*x^53 + 45281684357378066094191305787081798139169273378756357705562765562924584545639769497997874651043567947239019987942966080997/59*x^52 + 40559253889859405013540005181983483366298523533143347179192700025402002592623588906745225121322233358179190535932763816760/59*x^51 + 31958306687156422661187272178233436331476232184761468158705892101890266607527908281659350911147868468258052940992559994069/59*x^50 + 21016102345113648011025046637169780758943295858068756716836945060867410287780917613132765690214541008702432241683367510118/59*x^49 + 9688474879962899075501613433672556443606882310483927273833262861845554775002680134865331150842839449594021088865894202388/59*x^48 - 6317826273302632612710276901100009402199092143183441815735327429776017691271087123890155942381111365621520360029976773378/59*x^46 - 8135792617951054964038908182841273071600776345218917011199162698781285587539370500891815416804665057964830423825924243859/59*x^45 - 5128843232511470639631106852584767082588706673958590994061115457454216247089656961080487273990587401884789441684981854659/59*x^44 + 2165558928358858851095756843896237916212334433402980693190114232897144045153083238364463366879503717884237277394931844700/59*x^43 + 12443552607758204772620286158249709074320938645590407436182057956768466067274287966898639164151162752743039922430582373384/59*x^42 + 23868182319189761753741124092188528548224472833491593788035237318454024931707787650094885587762792071546907478659615485775/59*x^41 + 34397646730122065540140367070286911316958673811631644978179041060398688021021878818418913099687590017178420461749467148440/59*x^40 + 42149969701417173541627932765559889060488086096277585521723867703196500828367720188861566293368168135433185395395570115456/59*x^39 + 45739449832725719494063354335116694482176797705547423883239003613019048876667739348470127706107026722007240553613965282462/59*x^38 + 44524583276338143579996783145998585075313183915886433908144915521336429165545036711176273337169750319497207640993506597067/59*x^37 + 38722625119794499546008087596364675579207795872664813383061816143089044216623328547901482196587282002106334715214724286919/59*x^36 + 29370510459163535238193556244730468967294951000708176494007317991820101845824002030368024846034749635024288688022248598516/59*x^35 + 18139629930325286563468153019363091431181602168001289978510665566754378078963223943557757040894583540416805433739281214152/59*x^34 + 7037342094233815255161927793110462761340435726498857439424107367028368397047301565471326995928576624451177231563286351483/59*x^33 - 1[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.233s user 0m0.228s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:56:41 2005 Input: zp=Mod(x,sum(n=0, 58, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 58, b(n)^(lift(Mod(n^k, 59)))); q=c(14); w=Mod(1-x, sum(n=0, 58, x^n)); lift(q)*Mod(1, 59); a=22+O(59^2) a^59 (q-22-10*59)/w^71 Output: ? ? ? ? ? ? ? 22 + O(59^2) ? 22 + 10*59 + 15*59^2 + O(59^3) ? Mod(-1639152585187849860021819769824667871729531237100902169170419337176300737775557343402103388528862109514390063951579105342/59*x^57 - 1253729462079875574660612107391099128926054016208784168035684179177301544744310533661254070090488009961599610443298281563/59*x^56 + 1087527677259916723148880429922509408784590962102048253346454938333818789906999509779456940668474559672883493925690379697/59*x^55 + 4966044412444237994850312828574241670736132464870916747463197324322972821986499543612681621121504860534191636855691938151/59*x^54 + 9688474879962899075501613433672556443606882310483927273833262861845554775002680134865331150842839449594021088865894202388/59*x^53 + 14410905347481560156152914038770871216477632156096937800203328399368136728018860726117980680564174038653850540876096466625/59*x^52 + 18289422082665881427854346437422603478429173658865806294320070785357290760098360759951205361017204339515158683806098025079/59*x^51 + 20630679222005673725663838974736212016139818637176638715702209902868411094749670803391916371776166909149641788175086686339/59*x^50 + 21016102345113648011025046637169780758943295858068756716836945060867410287780917613132765690214541008702432241683367510118/59*x^49 + 19376949759925798151003226867345112887213764620967854547666525723691109550005360269730662301685678899188042177731788404776/59*x^48 + 16006301153265531688211890334772565845805974453667369089568590291621572466273767258755487093223950815215541448895870975766/59*x^47 + 11506441224611321426830244715413820113008566512519402469297098130850822671270963511866990625266393141937331152661841672869/59*x^46 + 6681525494523314751093812103416050454594812639223601256695215620518485434552966595054003008028761793513980106724951813188/59*x^45 + 2394072719092569584774749737191551444805841203122355586582033171494194482759939935420380509972748329824994369785980503029/59*x^44 - 589518799436446846022915880680914714501721901703499469158680862025767247118524593668844646428819585264781556169756326296/59*x^43 - 1736154831468657905619224500266263030296651877417259078019916499840004089430819548330915272768789869209846467363138910003/59*x^42 - 840989530969404710897629544425826325127318667656123916310540880099108314311411033458696361081958496037491894223957460277/59*x^41 + 1936151908667791074014047738399578700077470025837986730288436219047741967656838764422677957162261331339256155219791235372/59*x^40 + 6098994748654353123066191864115751021918170701214088912318126952023006726702660975256769738103980863019965930647499035382/59*x^39 + 10903341436350474989568184622790665850470496100144917248927350953528174486125382772159185519780115852104054001486352887783/59*x^38 + 15490433036506543109490308983306465939712270353705547798916362240092939723924388298140122291425307766984894014644676512536/59*x^37 + 19040589540593863383316144785306763055519727182440564162887761013114497145802006652398788501395371816676067116058369890791/59*x^36 + 20919355408801147750227016659039933979720231143190813789329915286911278541863458221675598955983005544201504343148861586752/59*x^35 + 20790762716054370383807838659925185113448048751986359812919821061571564456918602512951761195808846365559649291041889065057/59*x^34 + 1867774[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.230s user 0m0.226s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:56:50 2005 Input: zp=Mod(x,sum(n=0, 58, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 58, b(n)^(lift(Mod(n^k, 59)))); q=c(14); w=Mod(1-x, sum(n=0, 58, x^n)); lift(q)*Mod(1, 59); a=22+O(59^2) a^59 (q-22-10*59)/w^61 Output: ? ? ? ? ? ? ? 22 + O(59^2) ? 22 + 10*59 + 15*59^2 + O(59^3) ? Mod(1675049130208995109659747030412589048562057971054863455197482223537073969226374899096619195606000423338771115618919739/59*x^57 - 1711034740066719005166617646138474586248471693043555971246353164720993074343177090218169174628944068995113860100429797/59*x^56 - 4528704104571936806998029554385612472343045799012062843954669626854035849635345992604331086072276140812595525528034563/59*x^55 - 1783943945438058263387259936006497271881268310854245835363466521706109658012509355097711261569123900957728060694954336/59*x^54 + 757952586167360522744850027326024021673247772964865789832161825124007062797194384596058298266462803129332770611828695/59*x^53 - 1569593414900136674504845773332431527888446424639759422574788607833216305297291771058681084090683158667642697924293950/59*x^52 - 2841846799004658774892618776705941605155108558403510588070024383588696098597256854908722853751917798315062968418745816/59*x^51 + 1095868253956939415072799529666765950119183422414173058124957831525594078798400404604100428598973332487127611046766890/59*x^50 + 3816990952925019389075193842585741535945941861026256955820449648368561078299325830040909371665818596596997730812281117/59*x^49 + 1201407174340562676944529929736214578854437635557938946859413756975302114374636702118796753345785110877401913928464656/59*x^48 - 368663221148821007577801287713479527724931186924000133057299283523540995466117941357385571921186492022204042608400262/59*x^47 + 2716559802811313659632023819365208974901889121054381503278182789183915982193093715633185263152258433700619284074119934/59*x^46 + 3821118352230506427415510884660051229214075558405010437864535772852296352357923433540203548257671632022661572379967246/59*x^45 - 263619383544068630093132545610617393146309187135164708735786552175459428688992926861587069958729627191083043566225808/59*x^44 - 2573644665276115597326568961268367687650857346846456232788702742846817207069072314107596580778551633198821551631165079/59*x^43 - 17074742834239081235238075602459198404717694739766222553893211906152833546162252468764159304646855161953952387795678/59*x^42 + 583317600777054921517792974540886145985827484825601161457836262324578179541758492028465790281626430216744823494092310/59*x^41 - 3213361433267522968661788867591992199049140956148748776751074287126153774929683512056961921450963285200957047831887022/59*x^40 - 4245436439406666406020879295669567042867721363104297228563030813514928813824720311338752007578583184331255051733183721/59*x^39 - 350560284546980613278866115496344072884490960666768083079813767640172868206995061177675081682872677632851019409515016/59*x^38 + 1187638713111153709619240769038492749156678950809343849815920567705380829474179727912544388543581480353407823734196503/59*x^37 - 1521865278096700485094204358814560665791954899960537576445759230382056878690671490014668839303746370243750394961165862/59*x^36 - 1315782022275235518584901790375728740971254515618461678268109210539468427148573154679765402719955373099807391876956922/59*x^35 + 3021668700368200770573319153860128051095128202667810844631718767392331771061298354246613445756273248844479774217458168/59*x^34 + 3959505211499303809131295037683064952374999317156099715152406644781245352794885706834621710129949[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.201s user 0m0.197s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Mar 17 23:56:56 2005 Input: zp=Mod(x,sum(n=0, 58, x^n)); b(n)=zp^n+1/zp^n; c(k)=prod(n=1, 58, b(n)^(lift(Mod(n^k, 59)))); q=c(14); w=Mod(1-x, sum(n=0, 58, x^n)); lift(q)*Mod(1, 59); a=22+O(59^2) a^59 (q-22-10*59)/w^60 Output: ? ? ? ? ? ? ? 22 + O(59^2) ? 22 + 10*59 + 15*59^2 + O(59^3) ? Mod(85781915262452698720103588253621231921569281951750557315954535793137983267727574379854365522727879926655187988784225*x^57 + 76147771096851066296460320994232659909434441983446954710267774333391809229127861042081035712700550765360216627907195*x^56 - 18130695405506498880525806575703833083046093510219551752435947145946647837228165057796620828765285025696548291765432*x^55 - 14692328837227519940209541235931054999872171402783867288104171581238012738700488823680514647959089504208300265895988*x^54 + 67840595445364276388295641204593976239385629977279468942448011127021988768150187368667094541748243815860111595848176*x^53 + 49954279903618935763517288708238968234385086522349400350724033886314470551293898016045101106224323101460870951074095*x^52 - 38350269877162764072977479253561330622241254402759664254194915111478240816428514583325492995676113685820668878755813*x^51 - 17730060487442116344790631906887907411266109619613905805051010056032085258890686887121860126454997301205067866891432*x^50 + 72722591674465285115091710902747728909382410110562397697602001947971744629679051305402234134339557780650286991571800*x^49 + 55002025859294555833594546573937002629515708365030551442613479051456221679103890552081381709711390275226730036538723*x^48 - 23901252436459992500848780960442363628216310795313867476915251680853949295471809455829688804532957667526308662094923*x^47 + 9669331877793260031801016357927911766946975147529398654425919319808366085788901376094930686450630932486929276492753*x^46 + 97623506203111358765565940011580638490210893501610823759284822857031012716496462025396776505464435297500266636696827*x^45 + 67543634100695628421918363492717615984179764928239914902549125664549690637397530276993706888573261514347620740404390*x^44 - 14941030376828498414094641614463041367526808153420789068429276396671023801636189195630732641828887367764347180075418*x^43 + 18214521806740696727232474241851588206296826974398238494673775411971914510821256857616766881690290473899531181983589*x^42 + 92741155326331745759988624958397752433847905288630735481464284287928913960979947511560117073535426080618186219405069*x^41 + 45883459938104043169810804381189218514926074203566303508634555083488966239345960989464564097180005465577442703732482*x^40 - 37624186858486282764106205928146337651206312396316367631961607158265796210022887306177249665927289548468354520419474*x^39 + 2319493772048487911214239760639868246116746772521212242402506579517292738054239152650842803043157039873089363986580*x^38 + 74314459685031344141918511157044787517130369861436353923036644434313757243919086729217498702598784303998802276513256*x^37 + 24897726684534409205939736643623002097311145537504873847793766164313313859055534979012131508851007223641154449740861*x^36 - 45125450719227816601669049386835046500073300800532357079700775498215698796330451014063722930003867772974848313143989*x^35 + 12495129136913424933928324518468680462409946721467365841979565188951870974454026212010354766649557103286590532836325*x^34 + 88055617347704850336225733834548671106142032927481188642794017201800351936896264434450548036498138278255483500380139*x^33 + 3745345650307571384047648102229676279767935997356431672801103570066262329241330724764830[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.199s user 0m0.190s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:57:05 2005 Input: Mod(167366,1022117)^(1002096) Output: ? Mod(635671, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:57:23 2005 Input: Mod(167366,1022117)^(1002096) Output: ? Mod(635671, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:57:47 2005 Input: 167366^1002096 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m5.167s user 0m5.143s sys 0m0.013s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:58:15 2005 Input: Mod(13,1002096)^(-1) Output: ? Mod(231253, 1002096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:58:54 2005 Input: Mod(167366,1022117)^(231253) Output: ? Mod(507959, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:58:57 2005 Input: Mod(167366,1022117)^(231253) Output: ? Mod(507959, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:59:02 2005 Input: Mod(167366,1022117)^(231253) Output: ? Mod(507959, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:59:03 2005 Input: Mod(167366,1022117)^(231253) Output: ? Mod(507959, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:59:04 2005 Input: Mod(167366,1022117)^(231253) Output: ? Mod(507959, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:59:23 2005 Input: Mod(167366^231253,1022117) Output: ? Mod(507959, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.657s user 0m0.651s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:59:26 2005 Input: Mod(167366^231253,1022117) Output: ? Mod(507959, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.663s user 0m0.653s sys 0m0.011s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:59:54 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 17 23:59:55 2005 Input: 167366^231253 Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 4105 Killed /usr/bin/gp -q -emacs Timing: real 0m21.055s user 0m20.986s sys 0m0.016s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Fri Mar 18 00:00:01 2005 Input: 1008*1012 Output: ? 1020096 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Fri Mar 18 00:00:25 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Fri Mar 18 00:01:04 2005 Input: Mod(167366,1022117)^(78469) Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Fri Mar 18 00:02:42 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.120s user 0m0.108s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Fri Mar 18 00:03:08 2005 Input: 294729472947294396*328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Fri Mar 18 00:03:58 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Fri Mar 18 00:05:59 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.121s user 0m0.104s sys 0m0.017s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Fri Mar 18 00:06:19 2005 Input: 294729472947294396*328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Fri Mar 18 00:07:16 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^(52132671360578387144659326671226949) Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Fri Mar 18 00:26:48 2005 Input: Mod(13, 96817818241074147554367320960850048)^-1 Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Fri Mar 18 00:28:46 2005 Input: Mod(10424944469828754080284344711353162, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 00:57:11 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.052s user 0m0.047s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 00:58:16 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=d+O(p^2) Mod(a^2, O(p^2)) Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? Mod(9, 37) ? ? Errors (if any) and Timing Info: *** forbidden division t_POL % t_PADIC. Timing: real 0m0.053s user 0m0.046s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 00:59:25 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=d+O(p^2) a^2 Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? Mod(9, 37) ? Mod(7, 37) ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.046s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 00:59:48 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p lift(d) Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.046s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 01:00:10 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 + O(37^2) ? Errors (if any) and Timing Info: Timing: real 0m0.052s user 0m0.047s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 01:00:18 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) a^2 Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 + O(37^2) ? 7 + 2*37 + O(37^2) ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.049s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 01:00:36 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) a^p Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Errors (if any) and Timing Info: Timing: real 0m0.052s user 0m0.046s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 01:00:57 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) Mod(a, p^2) a^p Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 + O(37^2) ? ? 9 + 28*37 + 34*37^2 + O(37^3) ? Errors (if any) and Timing Info: *** forbidden division t_POL % t_INT. Timing: real 0m0.052s user 0m0.045s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 01:01:28 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) a^p Mod(a^p, p^2) Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? ? Errors (if any) and Timing Info: *** forbidden division t_POL % t_INT. Timing: real 0m0.052s user 0m0.045s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 01:02:03 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) a^p lift(a^p) Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? ? Errors (if any) and Timing Info: *** incorrect type in lift. Timing: real 0m0.053s user 0m0.048s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 01:17:26 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) a^p Mod(a, p^2) Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? ? Errors (if any) and Timing Info: *** forbidden division t_POL % t_INT. Timing: real 0m0.053s user 0m0.048s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 01:17:44 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) a^p Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.047s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 01:19:47 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) a^p (q-9-28*37)/w^p Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Mod(15534338931545960708338121754563884480397627764043*x^35 + 21835010423828501737598015134909666336271507113704*x^34 + 17301821718999490879494104181313772163398536970373*x^33 + 3086074884252799796332273610213937932367257354561*x^32 - 17201831622227728406355762450540517601083390103084*x^31 - 38409342297357495798060897374989371458352920169969*x^30 - 55150348035643114867808267146414371964812683735134*x^29 - 63173105820953540988895668453741306813492012575760*x^28 - 60440061657151709670545747230634507662990485662901*x^27 - 47645331706497258013051444294469368928671916416961*x^26 - 28038416177359046510002243430241589647486610895024*x^25 - 6598918107604932267417458834586238200447677140776*x^24 + 11228135081201708761128055826064851263201009852057*x^23 + 20915175013641052669221852183973776188473941007286*x^22 + 20001967060981715870054155048799564622335741718476*x^21 + 8720440302908987251982885549396904379992071848246*x^20 - 10064215993892205277964188896795905935889133314176*x^19 - 31581229364172044274977624818380280926831700669588*x^18 - 50365885660973236804924699264573091242712905832010*x^17 - 61647412419045965422995968763975751485056575702240*x^16 - 62560620371705302222163665899149963051194774991050*x^15 - 52873580439265958314069869541241038125921843835821*x^14 - 35046527250459317285524354880589948662273156842988*x^13 - 13607029180705203042939570284934597215234223088740*x^12 + 5999886348433008460109630579293182065951082433197*x^11 + 18794616299087460117603933515458320800269651679137*x^10 + 21527660462889291435953854738565119950771178591996*x^9 + 13504902677578865314866453431238185102091849751370*x^8 - 3236103060706753754880916340186815404367913813795*x^7 - 24443613735836521146586051264635669261637443880680*x^6 - 44731520242317049349274087325390124795088091338325*x^5 - 58947267077063740432435917896489959026119370954137*x^4 - 63480455781892751290539828850085853198992341097468*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 41645445358064249552941813715176186862720833983764*x - 20822722679032124776470906857588093431360416991882, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.052s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 01:20:00 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1); (q-d)/w^p; a=lift(d)+O(p^2) a^p (q-9-28*37)/w^p Output: ? 37 ? 32 ? ? ? ? ? ? ? ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Mod(15534338931545960708338121754563884480397627764043*x^35 + 21835010423828501737598015134909666336271507113704*x^34 + 17301821718999490879494104181313772163398536970373*x^33 + 3086074884252799796332273610213937932367257354561*x^32 - 17201831622227728406355762450540517601083390103084*x^31 - 38409342297357495798060897374989371458352920169969*x^30 - 55150348035643114867808267146414371964812683735134*x^29 - 63173105820953540988895668453741306813492012575760*x^28 - 60440061657151709670545747230634507662990485662901*x^27 - 47645331706497258013051444294469368928671916416961*x^26 - 28038416177359046510002243430241589647486610895024*x^25 - 6598918107604932267417458834586238200447677140776*x^24 + 11228135081201708761128055826064851263201009852057*x^23 + 20915175013641052669221852183973776188473941007286*x^22 + 20001967060981715870054155048799564622335741718476*x^21 + 8720440302908987251982885549396904379992071848246*x^20 - 10064215993892205277964188896795905935889133314176*x^19 - 31581229364172044274977624818380280926831700669588*x^18 - 50365885660973236804924699264573091242712905832010*x^17 - 61647412419045965422995968763975751485056575702240*x^16 - 62560620371705302222163665899149963051194774991050*x^15 - 52873580439265958314069869541241038125921843835821*x^14 - 35046527250459317285524354880589948662273156842988*x^13 - 13607029180705203042939570284934597215234223088740*x^12 + 5999886348433008460109630579293182065951082433197*x^11 + 18794616299087460117603933515458320800269651679137*x^10 + 21527660462889291435953854738565119950771178591996*x^9 + 13504902677578865314866453431238185102091849751370*x^8 - 3236103060706753754880916340186815404367913813795*x^7 - 24443613735836521146586051264635669261637443880680*x^6 - 44731520242317049349274087325390124795088091338325*x^5 - 58947267077063740432435917896489959026119370954137*x^4 - 63480455781892751290539828850085853198992341097468*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 41645445358064249552941813715176186862720833983764*x - 20822722679032124776470906857588093431360416991882, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.061s user 0m0.052s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 01:21:26 2005 Input: p=59 j=44 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1); (q-d)/w^p; a=lift(d)+O(p^2) a^p Output: ? 59 ? 44 ? ? ? ? ? ? ? ? 22 + O(59^2) ? 22 + 10*59 + 15*59^2 + O(59^3) ? Errors (if any) and Timing Info: Timing: real 0m0.258s user 0m0.249s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 01:21:34 2005 Input: p=59 j=44 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) a^p Output: ? 59 ? 44 ? ? ? ? ? ? Mod(30589913995013056194895748289084185958932451060104091011293904962432927276381809145293793092271246912138541233154823723303997202804094199062753014040161742787077426193398095170396*x^57 + 76041046371068202028658049294733894695426607930295673385904951279740553531751962020699871651215083012196498096870336022167370691164095339423448103924955223172572981182097367005215*x^56 + 135838417636993723414610617519260887199164588443340106625189199913397851146647282727934268776409462761787678916887602079088262382803659696220566512894648901564095635087780529384587*x^55 + 209304499682529473930368553978909824868104522169979456247622450547804815515318980563399254884887964424764032311328610339155581375145026582371329351342886852404845443962923926106285*x^54 + 295606892442542618753095534754585302884680231241095575120452777974246412610155563169190286908682572206810499553832284707887020356330061289462061697126562660729501297384762614142938*x^53 + 393767755322375779406673718789381499489409336480908337309263486503362130267521743941161157778736402482950868014544506475725776343048465354695953844247231773527213657961057710779614*x^52 + 502674886522509778486936558802012307105910100928467229124217716113799784321172042764822737515490718870964872996038694820447893881231690016621124826123702274264911374083407797549971*x^51 + 621094324729365481957197747024704575839643295891433164838975449979863581675551575658704797402818913102058778162152662910761204406479587746465956954418022251013490336263779212241670*x^50 + 747684330390052573986507589064216461026632745535128523385417289521367123650671366537826330745415685556144099519297957811635926941562455390489035259419735993663635284434198482764823*x^49 + 881010588157635726782210696531651042434786990159423435666893814290044247956380050223467202564940886523838918510115334514053024960862649895149196984670912817027792656476399344988805*x^48 + 1019562458257138710802669613527423817859190945665498605531612661294149966318400839775224071934785315530581627293513898421895967805014266030120715446995081957995565513931350579311663*x^47 + 1161770092637815902410717577714232171948124542446316805048505575989646149021786810253974286388927712897607550332148649584380608605320961053986326843864979824845134518414037049344369*x^46 + 1306022221978846685355841599007910688299381482216747299302003766313790548511872343148479328526400070234094465429841652572423661991368186636174447500174559906450385987423384488545872*x^45 + 1450684412014570901659274876310102912685303982788304697652174304957557290928806918411989109676430093850634340351110356878063771689427775271445593230115423732277939772071542960355089*x^44 + 1594117582327805576812932394015204690528595413088656946329727066157964761724926298987315587562703049120917305014397769447856451197260480843652020732348641103516796526830861736785050*x^43 + 1734696577785914906441201679992466616496275504572414367113207503662849532996998482900708012657321957345424638122588119262593481309215883125835013969012760406062144462377300985928430*x^42 + 187082858219784206214530026388139555692324234805500627373072332167515384092560530089914087849041664494465271885480989574859901307349886410018687532755366334298199364952753937[+++] ? Mod(79190591570902556650034690255632672006004872335062302583406545382214641030145165296730734513021842376331231052746616007585632819101393392386022431500709360317081599608974053141928743/59*x^57 + 156576378216099342984570531362209377040432730057578463797146750371645739350983803853889135233599681184846288172737097415496329803237345227027342435173049177809725631072537618668804122/59*x^56 + 231280548051108875714914396709452749259407432524753321650784903628355687722755603391398577319199833663457925837768363597774087751560056994387381428542186179959625424791767927157425180/59*x^55 + 302456672981428802683487060531449028920661594141658557943305286215679855535248579007181189974413517736843683834418611082693513090076034464696390435782111255084425381930562929065663290/59*x^54 + 369298299071062120371630006102326021259448299668692072608102107015574012449989924450671368449226970212113836980796839080268966608043871288722504435553590291109621100345724470567321218/59*x^53 + 431048083987854662515232059807438160395257038360529736259401938497308115136135911520419876034636540828243248559867350290089265226121791065030265226923832454443662123408997529474816619/59*x^52 + 487006377994737048180273000654497323931386759843218446941561938175824390480497293924622102238712935458080378399755840415607077240983325001489226381613955140122638117198269177680748136/59*x^51 + 536539151260811527899578433940811269818142936223501183006639638307324844235693308698228295238320825421024681945736173428786284321092048682894602448373366066258089945736322170767228590/59*x^50 + 579085177672681521114138457121986371849608854100968928864546632140727533946980931031095446704576351924334445086915782324637006080211146398239133419563412113765375615505733250386898803/59*x^49 + 614162393750570975898969199622830272655042394449458648568213557441181514681736485702094427703618668852853174268023818821336119209760354922586302770758357050456302733333089593045702989/59*x^48 + 641373360620173024668853458783095533157394834365114968447273367780283545082455228035640597265308998924277909128673630092592623556170851971158522580163482554568744566209956084833292237/59*x^47 + 660409767153904397381530641840610199909707440905912853304314766146143338099814743785633111534178507684304824171102926093286394274776403667767422800291482079364087800496980453795832863/59*x^46 + 671055923259175815789332995011103173770772965236642464389859482544968856337674487277379363150253614999677209754252771775393571186163860357968251948004157630015306463519526321026443835/59*x^45 + 673191203733326418003373030925269115167114330120916676314447805714669855005619184328349817280217853232196867346638730281206207947774530738819981976994567955851815289870520689344166130/59*x^44 + 666791414995369291455510503478605715324686267471469001736376067104388615870964741438773194322330320071340672318669835232986078237199685390190714407918467315964498442927273707825144622/59*x^43 + 651929069208931319073582182487341310589504010434300544486328715583283335959339255095252309169152682549537782375566982843148180435662710412801267616210606851174089047453226918496755415/59*x^42 + 62877256269046489624358597362341845222222862799959039941005601824938985454266150990[+++] ? 22 + O(59^2) ? 22 + 10*59 + 15*59^2 + O(59^3) ? Errors (if any) and Timing Info: Timing: real 0m0.257s user 0m0.246s sys 0m0.011s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 01:22:30 2005 Input: p=59 j=44 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1); (q-d)/w^p; a=lift(d)+O(p^2) a^p (q-22-10*59)/w^59 Output: ? 59 ? 44 ? ? ? ? ? ? ? ? 22 + O(59^2) ? 22 + 10*59 + 15*59^2 + O(59^3) ? Mod(95416059428054331143746855513009803933704121920054159921641297252884157306327287717627695332755209087950159349661255*x^57 + 180060381764810263897089715823557724914049817445417063778658257272476440334083600479732022064193715717711952908456852*x^56 + 82343548694173719779787322913848453838395359844314872851622760228429348169199898145738259341921684405166939962914781*x^55 + 3248990979860902391598405813096200682311480571687221085402353084877981760876898187506756333020546606586776127040061*x^54 + 103668230804198039344881940749976239926569825406680625907678513033845501484583863732476358958251800641054428633558306*x^53 + 174086465043234398556598356215421530778195622876859621920873484790930694635449986979224959624628316713936727818614133*x^52 + 65161705872732050991916740906947808710594137168604798866810630737691827710189746683650732653506763542039586976919844*x^51 - 4670736899454702739778754556014404399079237778425746186698476210865846620842163812669728738066675155200166869679007*x^50 + 103502481077623428001600752582431958201435983697282403570943058689653506218302735133175217947356047432078744943817302*x^49 + 164685193558207247054546915788000598179301301112094976235483266525448154242303274387765436036972227869408226687417871*x^48 + 52211330948199446187453790935250956526405996008907291184613364792475667886466863547929746031744291326641950050196549*x^47 - 2172259062865400013661335400031494801694636402330867788904367744084663362979986269447480296285924438358149371419849*x^46 + 115861787364868429063751164772484254427600410525121466172690232985619305346826506128257435139619053709807833885076662*x^45 + 168266579739976825556116593360801889273275855033411261286932937854358697706761293852478805053130028808767155909264033*x^44 + 52626363078883503578776472397306602347745646823931529752851483984495044955270128326606865999208702084991309626725218*x^43 + 11255281742861649687347437537075067694018203637518060329164026917180983817568883725911015330882744319936532951362745*x^42 + 132639610650680401310281408830829765840491113036814989288784264997577930989361560901949918499083300541695931504456812*x^41 + 169289562059043024654020598562956788087701668551633228456550698034892745717096422675496179285835174940700985212936181*x^40 + 45838234631917928044783142564835026024246222782912977441590422055354894319650447921026273053757433338313744104378171*x^39 + 13786949349469842489399316857216312650555658862835415635320397938341518761862726803287709623172252662529475076257549*x^38 + 135198648262949633656082362767043017341388506275682037391197414063138426652591126130059732716475657007012835815556620*x^37 + 155805092666214924527712374284079280518953728289787788243449077455666995923113560372930219961582754923271190751669075*x^36 + 28161335406311457184506214348317504959086034429750834394274195105970413496943097153780287826074455050393749142803911*x^35 + 10221427051661273317806178937541241277837195745736734515140083780289502305285336157414172252879298751686295021240411*x^34 + 136384076107081835215852841065873140230031954905667429230737517294275711912210531566656611348900476889841439176875603*x^33 + 1470280399602791362654278080464802785968039793856804390008257694803618358097[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.313s user 0m0.301s sys 0m0.012s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 01:23:33 2005 Input: p=67 j=58 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) a^p Output: ? 67 ? 58 ? ? ? ? ? ? Mod(206499379518543041796789520074839204703258906955082894578189385721674777768654559794361830483782716317727469352827000878714038497601740379375758077769708292404419971378912573003407566138171854197023326956*x^65 + 513978041550682969738131707421276195763898985635415756237918781217879299788212088488989913902073670530191438697805022902562233772271386349477838030302355263177202336895701994713539622028162856819473593571*x^64 + 919733852558715899868006671473365226421416545195139948011886979463539586126830455124483664473470066030504421669906806717499958987454270990968386427771211975268661378698312490601263378329925958262197207750*x^63 + 1420201015886064602398857297377473761339441248918690981873326576977214582736497521591949987367416393467069203636940024795507180305988786550179256423084538272511467405641897937555465573734688288137046160309*x^62 + 2010981408106509013724438040576464038967283214194691219482446472080371372959708287672873523101320032807565664624713350910504169531567052148684922059047086878279646517280054878759443844245742413585348581118*x^61 + 2686883229890995680619391655997017205191079826612567702946565413348562733455444668685290172760637214463526372232430104171729241072781713299075347440903410418694805389817242137867081069148164623586201606165*x^60 + 3441966631726818876785618974578004212558961060900675971940138939050253461342275401927557336758849276973840094925860974687360009969068365031963921807448989034662992481199274914183575275544262097802602883707*x^59 + 4269595913528712700435525131346893096703406685326219457178375086708290494405196846938071225282084287692214010579909834489859841394300743549678794652168598646100752001147225452208424357693185720114262192973*x^58 + 5162497839409794975703518539819578602115359384750134450157441767263756502965399825906780670865728872891979819044975306947209596043927998360754608755379356242752563563077004937323343757719468038262918627896*x^57 + 6112825555140059125091153636462790120255864795705871214365784986686970010898166332874628218883089581383535649445196271005272620596976668954457987339148769051695489981267608059900439968181844388616676343249*x^56 + 7112227546583490557206524087290937950067350438565551579592311604335634312287904825252886300826152484131125498071258429668007267986700571016969044487338917046509185212146971555224774728362694141311401893391*x^55 + 8151921033104582707363298441716693484521911317007004369185945497984808321690304454578613755551616075915827654023622448284997374175409430084936392425588973541455938165157527560225056538359374211480451894524*x^54 + 9222769150960357319791848766606820426508429948949042357686238757961143023225230878266195896482848411206515524704361772536914034019509611771633218447824471653094457842867450636837904000399284225174853869121*x^53 + 10315361248387464675448420284245635359178098207710991050971131326216859206983942571943311935910414955098384359426692156712002652167716815342154149353359227488031026568131865152103807030841739779652149851417*x^52 + 11420095586748251222103895177145047832692294419299139530738705565306409814902724937085928757148664837898144524472999059447523729057400784195350364507149848871905502030760254005481749542412252336430200895686[+++] ? Mod(783701667684076860683485604551408244257675157734759799424318510173163254980506333629016391723321891728108834074386562566846013241519077789294606850110038408567575987718610882944509319870050989483316623560130/67*x^65 + 1553567876940411337566586311257802261800231968703529044911898331502974299850512811751810540804230341462929927702133716074818185903698838973171037909009506361544055837354834623497790332808844464735432684214208/67*x^64 + 2302833015840592439277617091411985000941725894400715988668276283334539641745208935452064608296113297265515935383767342107192529482475733877050629611089286967478759268501433472796492498003008542811844577005081/67*x^63 + 3024912515403235334669946248974677775029166143607401411575798365883645744455217628587740594499712694569580973206270148623966045471835375509950354570538654173703334943847257418870717171524954493091593987645961/67*x^62 + 3713460715022945866992708414601795277277098737664608915214603995399335622392378628270096337069417687935396170636981729529513077632853204600382951240302028518012642615387861139999010297954781367269728518465388/67*x^61 + 4362426628363886623756656670434580430923965920048324402933598591943113995384584506625030202744951137465398105181512497585355311515757289895715668312455912105735482286448708346066636880260367615042826787090612/67*x^60 + 4966107119645266773838643034034188522433838729400042166260497219421923547223576047452132152893310335824450672316326243172695465605399992893972226884025422016250506313049564005774051768497491574745867903037687/67*x^59 + 5519197023003646769777492167288870484450063496054456675564826420678719820294149929152002203053789325995312220030680120435488358178991490226125250973036378159495661804527823469468261544906077003676410133389448/67*x^58 + 6016835764481299879531797588040036891228610405872359771358193800042427612149508074036167822683211570448042715396212724091513762047092418197591378581451120458774487408169570247114806432810684549912071190020387/67*x^57 + 6454650076924920476843147450423533369144556484828860562621963711808919181431332619329429909458529627692388901594585941092896732353668320096715426644950741999077641637162021799258651720913531180831772265511485/67*x^56 + 6828792432414613376145525761331934675345088701251326990683774627874055445681661808655846210516684517467800847156144353502389480015189961066061348343337812881181619796135702942189831562915398596277771574073932/67*x^55 + 7135974854477596369496174252034850076948251379602194834275408260556731201738878518992919220084654192759124272859756601281479006301600100597219029212796143847633080374640466730934280975985149078293224270776865/67*x^54 + 7373497812943666188786318860991239857742958479097485340964268422364912299166134454165168490186017807400872654114560459813230195473366746570822897770391721028923108505293523267343711507785121995607350617403887/67*x^53 + 7539273947513399109043750598179991133424568830252659302423608935754678971590550318950349756844988855578144948033754783620102968435578680371418078984497519836733355817540014957620081259628420942003952031732910/67*x^52 + 7631846411555515836472192043686941808617311408070782701432861647071312659703132500259164248862312945314662030026552971687[+++] ? 33 + O(67^2) ? 33 + 38*67 + 31*67^2 + O(67^3) ? Errors (if any) and Timing Info: Timing: real 0m0.442s user 0m0.431s sys 0m0.011s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Fri Mar 18 01:24:21 2005 Input: p=67 j=58 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) a^p (q-33-38*67)/w^67 Output: ? 67 ? 58 ? ? ? ? ? ? Mod(206499379518543041796789520074839204703258906955082894578189385721674777768654559794361830483782716317727469352827000878714038497601740379375758077769708292404419971378912573003407566138171854197023326956*x^65 + 513978041550682969738131707421276195763898985635415756237918781217879299788212088488989913902073670530191438697805022902562233772271386349477838030302355263177202336895701994713539622028162856819473593571*x^64 + 919733852558715899868006671473365226421416545195139948011886979463539586126830455124483664473470066030504421669906806717499958987454270990968386427771211975268661378698312490601263378329925958262197207750*x^63 + 1420201015886064602398857297377473761339441248918690981873326576977214582736497521591949987367416393467069203636940024795507180305988786550179256423084538272511467405641897937555465573734688288137046160309*x^62 + 2010981408106509013724438040576464038967283214194691219482446472080371372959708287672873523101320032807565664624713350910504169531567052148684922059047086878279646517280054878759443844245742413585348581118*x^61 + 2686883229890995680619391655997017205191079826612567702946565413348562733455444668685290172760637214463526372232430104171729241072781713299075347440903410418694805389817242137867081069148164623586201606165*x^60 + 3441966631726818876785618974578004212558961060900675971940138939050253461342275401927557336758849276973840094925860974687360009969068365031963921807448989034662992481199274914183575275544262097802602883707*x^59 + 4269595913528712700435525131346893096703406685326219457178375086708290494405196846938071225282084287692214010579909834489859841394300743549678794652168598646100752001147225452208424357693185720114262192973*x^58 + 5162497839409794975703518539819578602115359384750134450157441767263756502965399825906780670865728872891979819044975306947209596043927998360754608755379356242752563563077004937323343757719468038262918627896*x^57 + 6112825555140059125091153636462790120255864795705871214365784986686970010898166332874628218883089581383535649445196271005272620596976668954457987339148769051695489981267608059900439968181844388616676343249*x^56 + 7112227546583490557206524087290937950067350438565551579592311604335634312287904825252886300826152484131125498071258429668007267986700571016969044487338917046509185212146971555224774728362694141311401893391*x^55 + 8151921033104582707363298441716693484521911317007004369185945497984808321690304454578613755551616075915827654023622448284997374175409430084936392425588973541455938165157527560225056538359374211480451894524*x^54 + 9222769150960357319791848766606820426508429948949042357686238757961143023225230878266195896482848411206515524704361772536914034019509611771633218447824471653094457842867450636837904000399284225174853869121*x^53 + 10315361248387464675448420284245635359178098207710991050971131326216859206983942571943311935910414955098384359426692156712002652167716815342154149353359227488031026568131865152103807030841739779652149851417*x^52 + 11420095586748251222103895177145047832692294419299139530738705565306409814902724937085928757148664837898144524472999059447523729057400784195350364507149848871905502030760254005481749542412252336430200895686[+++] ? Mod(783701667684076860683485604551408244257675157734759799424318510173163254980506333629016391723321891728108834074386562566846013241519077789294606850110038408567575987718610882944509319870050989483316623560130/67*x^65 + 1553567876940411337566586311257802261800231968703529044911898331502974299850512811751810540804230341462929927702133716074818185903698838973171037909009506361544055837354834623497790332808844464735432684214208/67*x^64 + 2302833015840592439277617091411985000941725894400715988668276283334539641745208935452064608296113297265515935383767342107192529482475733877050629611089286967478759268501433472796492498003008542811844577005081/67*x^63 + 3024912515403235334669946248974677775029166143607401411575798365883645744455217628587740594499712694569580973206270148623966045471835375509950354570538654173703334943847257418870717171524954493091593987645961/67*x^62 + 3713460715022945866992708414601795277277098737664608915214603995399335622392378628270096337069417687935396170636981729529513077632853204600382951240302028518012642615387861139999010297954781367269728518465388/67*x^61 + 4362426628363886623756656670434580430923965920048324402933598591943113995384584506625030202744951137465398105181512497585355311515757289895715668312455912105735482286448708346066636880260367615042826787090612/67*x^60 + 4966107119645266773838643034034188522433838729400042166260497219421923547223576047452132152893310335824450672316326243172695465605399992893972226884025422016250506313049564005774051768497491574745867903037687/67*x^59 + 5519197023003646769777492167288870484450063496054456675564826420678719820294149929152002203053789325995312220030680120435488358178991490226125250973036378159495661804527823469468261544906077003676410133389448/67*x^58 + 6016835764481299879531797588040036891228610405872359771358193800042427612149508074036167822683211570448042715396212724091513762047092418197591378581451120458774487408169570247114806432810684549912071190020387/67*x^57 + 6454650076924920476843147450423533369144556484828860562621963711808919181431332619329429909458529627692388901594585941092896732353668320096715426644950741999077641637162021799258651720913531180831772265511485/67*x^56 + 6828792432414613376145525761331934675345088701251326990683774627874055445681661808655846210516684517467800847156144353502389480015189961066061348343337812881181619796135702942189831562915398596277771574073932/67*x^55 + 7135974854477596369496174252034850076948251379602194834275408260556731201738878518992919220084654192759124272859756601281479006301600100597219029212796143847633080374640466730934280975985149078293224270776865/67*x^54 + 7373497812943666188786318860991239857742958479097485340964268422364912299166134454165168490186017807400872654114560459813230195473366746570822897770391721028923108505293523267343711507785121995607350617403887/67*x^53 + 7539273947513399109043750598179991133424568830252659302423608935754678971590550318950349756844988855578144948033754783620102968435578680371418078984497519836733355817540014957620081259628420942003952031732910/67*x^52 + 7631846411555515836472192043686941808617311408070782701432861647071312659703132500259164248862312945314662030026552971687[+++] ? 33 + O(67^2) ? 33 + 38*67 + 31*67^2 + O(67^3) ? Mod(-12371305803510284163858263178284441886041864139156157044486207297947009339345809828964219311554417753768240503741389716962361601*x^65 - 19502707931658650619364153157645771309837887172495750390923875543290695831289342393353898644867848166944462553401900950892545466*x^64 - 5462162657936727905862435090182364552614057492133151737252928566169221367793075206887493648935762194699934515377427573471886656*x^63 - 1613822914662127314134126013682305272920729351785218954021182270853885856753847143585317457587940178914625774913557655115671071*x^62 - 16554466908246502129751152814440106976622415757078386041804298973069344543695374823040419396795253704808542581876882831309753829*x^61 - 16909123316439092706415518324326894576681912855418106681601100247332948901384702928018961435152559026613710131850585967048471001*x^60 - 1886702269928514361498501882763877673191575641014634196781883426844377210080653224325396961886322979488517701407965601685912962*x^59 - 5046071153723916045460538468266087533256801054132278408667802025261335690764384297133479656134249485140811259310127208692750566*x^58 - 19328436040520989868143770529244745366482170748686297864568388944697386630622043867657024435758085219754609627529752367377468741*x^57 - 12827080897612336937034055749167906846667115895584355247664134793774306300416497742439041610394140761993226368965585613301926974*x^56 - 65271244654031356190663340105199224363173012521619033604528775695396671759040179361216963246374292427031998947302933761331823*x^55 - 9552742323061924605877934905989148644986876290649139921575652722224889726286043234652700037806998056724948303967732768029461324*x^54 - 20096530759719647964695872499290380612916944001500605696556926017729795658858014337596158679524479245633892017872093713680382707*x^53 - 8143003680980130966561759486856780676262494738985481827688462449302688087426124315155935311946356560104879553705748859281641961*x^52 - 394336109388541373115335677660612123349730414514290877429812656934520037049519506946795045135562324693127664037958542908106911*x^51 - 14159144909034568901333963756310503554394534428661910338114718145171451734930288714010599009507666549506837117178281374129061142*x^50 - 18687755981278188866518950409112150207768542883488993288379996433859550717347302477191465855067111465747143823198702575555060982*x^49 - 3864537857625775833019221593588737120921464500379249082773964424958003180502903979340573041313891205777226644082371177065682244*x^48 - 2804469759903959013421415941528633280244950180562817253088499837621719242379918855521476022498330568060485474194579620289002733*x^47 - 17876044927899590758740126603069987601780681850876251556467352787419632594114696677445904449644149082142156790078483862250223293*x^46 - 15409880942675234813567085111629576954067095941596012156711562732790146167818787776514005403353825425131012220854771116524869529*x^45 - 913908696388622913600456972567536334073025906393083171447777512593993059712797905523143666028064078937993526313665718327165870*x^44 - 6770367016818510659786235220498319287532073389565196246889249965630178220250391313727955721829088349267028641954692239355026159*x^43 - 198972370801371422618781384184302252808864527288754523964027276567172135[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.555s user 0m0.546s sys 0m0.010s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:01:47 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.003s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:02:02 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:04:39 2005 Input: Mod(13,1022117)^13 Output: ? Mod(940431, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:11:51 2005 Input: Mod(13, 1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:14:56 2005 Input: Mod(167366, 1022117)^(78469) Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:20:09 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.120s user 0m0.103s sys 0m0.018s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:25:20 2005 Input: Mod(13,9681784477000000000000000000000000)^(-1) Output: ? Mod(8937031824923076923076923076923077, 9681784477000000000000000000000000) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:25:36 2005 Input: Mod(13,9681784477000000000000000000000000)^(-1) Output: ? Mod(8937031824923076923076923076923077, 9681784477000000000000000000000000) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:29:27 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^(8937031824923076923076923076923077 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...4923076923076923076923077 ^ Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:29:43 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^(8937031824923076923076923076923077) Output: ? Mod(8427537332392310219933739299709752, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:34:57 2005 Input: mod(13,96817844766697240158297704468544444)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,9681784476669 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.014s user 0m0.005s sys 0m0.006s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:35:30 2005 Input: Mod(13,96817844766697240158297704468544444)^(-1) Output: ? Mod(44685159123091033919214325139328205, 96817844766697240158297704468544444) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:38:11 2005 Input: Mod(104249444469828754080284344711353162,968178182410741481775940333355228733)^(44685159123091033919214325139328205) Output: ? Mod(472078811853666464375052041527146909, 968178182410741481775940333355228733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:40:03 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^(44685159123091033919214325139328205) Output: ? Mod(2949398057165111458476462606852211, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:40:51 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.119s user 0m0.103s sys 0m0.017s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:41:53 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:42:44 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^(52132671360578387144659326671226949) Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.002s sys 0m0.012s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:46:22 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 6348 Killed /usr/bin/gp -q -emacs Timing: real 0m21.013s user 0m20.992s sys 0m0.008s '207.172' ************** PARI ***************** Host 207.172.74.6 (207.172.74.6) Time: Fri Mar 18 03:47:11 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 6357 Killed /usr/bin/gp -q -emacs Timing: real 0m21.012s user 0m20.978s sys 0m0.021s '193.204' ************** PARI ***************** Host 193.204.167.87 (193.204.167.87) Time: Fri Mar 18 07:16:22 2005 Input: (z-1/2)*(z-2)^2 Output: ? z^3 - 9/2*z^2 + 6*z - 2 ? Errors (if any) and Timing Info: Timing: real 0m0.130s user 0m0.005s sys 0m0.010s '193.204' ************** PARI ***************** Host 193.204.167.87 (193.204.167.87) Time: Fri Mar 18 07:18:42 2005 Input: (z+1/3)*(z-4/3)*(z-2) Output: ? z^3 - 3*z^2 + 14/9*z + 8/9 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '193.204' ************** PARI ***************** Host 193.204.167.87 (193.204.167.87) Time: Fri Mar 18 07:18:53 2005 Input: (z+1/3)*(z-3)*(z-2) Output: ? z^3 - 14/3*z^2 + 13/3*z + 2 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '193.204' ************** PARI ***************** Host 193.204.167.87 (193.204.167.87) Time: Fri Mar 18 07:19:06 2005 Input: 3*(z+1/3)*(z-3)*(z-2) Output: ? 3*z^3 - 14*z^2 + 13*z + 6 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '213.39.' ************** PARI ***************** Host 213.39.228.62 (213.39.228.62) Time: Fri Mar 18 08:33:35 2005 Input: F:=Group; Order(F : CosetLimit:=1000000); Output: ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,b>:=Group;. *** incorrect type in comparison. *** expected character: ',' instead of: Order(F:CosetLimit:=1000000 ^-------------------- Timing: real 0m0.291s user 0m0.007s sys 0m0.009s '68.191.' ************** PARI ***************** Host 68.191.223.193 (68.191.223.193) Time: Fri Mar 18 09:08:02 2005 Input: /* Code written by Dan Jacobs, (c) 2002. Copied out by LJPK, 2004. Extensions written by LJPK, 2004. */ q=5; p=factor(q)[1,1]; flag=0; /* this is 1 for classic, 0 for extra level structure */ flag_small=0; /* 0 for everything, 1 just for the squares */ /* This allocates the values of x0 and y0 for the homomorphism between D_q and M_2(Q_q) */ if(p%4==1,XX=-1;y0=0); if(p%8==3,XX=-2;y0=1); if(p%8==7,XX=-5;y0=2); /* NB this may not work */ ACC=40; /* Define isomorphisms th: K(i,j) -> M_2(K) and th1: M_2(K) -> K(i,j) */ th(v)=[v[1]+v[2]*x0+v[4]*y0, v[2]*y0-v[3]-v[4]*x0; v[2]*y0+v[3]-v[4]*x0, v[1]-v[2]*x0-v[4]*y0] th1(mm) = [(mm[1,1]+mm[2,2])/2, ((mm[2,2]-mm[1,1])*x0 - (mm[1,2]+mm[2,1])*y0)/2, (mm[2,1]-mm[1,2])/2,((mm[2,2]-mm[1,1])*y0+(mm[1,2]+mm[2,1])*x0)/2] /* Now we use the new coset functions from new_quat_stuff */ r new_quat_stuff.txt unitlist_H = vector(length(unitlist_H), i, th(unitlist_H[i])); /* Choose whether we want small or big space of forms */ if(flag_small==0,clist=findCosetMatrices(),clist=findCosetMatrices_new()); print(clist) /* Inverting the quaternion [q0,q1,q2,q3] */ quatinv(v) = vv = v; N = sum(ii=1,4,v[ii]^2); for(ii=2,4,vv[ii] *= -1/N); vv[1] /= N; vv /* Finding elements d1 of O_D with N(d1)=p and d1 == [0, *; 0, *] mod p */ d1list=[]; bound=floor(sqrt(p)+3); forstep(d0=-bound, bound, 1/2, forstep(d1=-bound, bound, 1/2, forstep(d2=-bound, bound, 1/2, forstep(d3=-bound, bound, 1/2, if(d0^2+d1^2+d2^2+d3^2==p, mm = subst(th([d0,d1,d2,d3]), x0, sqrt(XX+O(p^ACC))); if((mm[1,1]%p == 0) && (mm[2,1]%p == 0), d1list=concat(d1list, [[d0,d1,d2,d3]]))))))) bigd1list=[]; forstep(d0=-bound, bound, 1/2, forstep(d1=-bound, bound, 1/2, forstep(d2=-bound, bound, 1/2, forstep(d3=-bound, bound, 1/2, if(d0^2+d1^2+d2^2+d3^2==p, bigd1list=concat(bigd1list, [[d0,d1,d2,d3]])))))) /* forstep(d0=-2, 2, 1/2, forstep(d1=-2, 2, 1/2, forstep(d2=-2, 2, 1/2, forstep(d3=-2, 2, 1/2, if(d0^2+d1^2+d2^2+d3^2==3, print([d0,d1,d2,d3])))))) */ /* Calculating the units of O_D and their matrix versions */ unitlist=[]; forstep(a=-2, 2, 1/2, forstep(b=-2, 2, 1/2, forstep(cc=-2, 2, 1/2, forstep(d=-2, 2, 1/2, if(a^2+b^2+cc^2+d^2==1, unitlist = concat(unitlist, [[a,b,cc,d]])))))) smallunitlist=[]; forstep(a=-2, 2, 1, forstep(b=-2, 2, 1, forstep(cc=-2, 2, 1, forstep(d=-2, 2, 1, if(a^2+b^2+cc^2+d^2==1, smallunitlist = concat(smallunitlist, [[a,b,cc,d]])))))) /*forstep(a=-2, 2, 1/2, forstep(b=-2, 2, 1/2, forstep(cc=-2, 2, 1/2, forstep(d=-2, 2, 1/2, if(a^2+b^2+cc^2+d^2==1, print([a,b,cc,d])))))) */ matunitlist = vector(length(unitlist), i, th(unitlist[i])); smallmatunitlist = vector(length(smallunitlist), i, th(smallunitlist[i])); /* "test": matrices for integral entries */ test(mm)= MM = mm; temp = matrix(2,2,i,j, valuation(MM[i,j],p)); mmin = vecmin([vecmin(temp[1,]), vecmin(temp[2,])]); mmin >=0 testU0(n)=m=subst(n,x0,sqrt(XX+O(p^ACC)));test(m) testU1(n)=m=subst(n,x0,sqrt(XX+O(p^ACC)));test(m)&&((m[2,1]%q)==0)&&((m[2,2]%q)==1) testUsq(n)=m=subst(n,x0,sqrt(XX+O(p^ACC)));test(m)&&((m[2,1]%q)==0)&&issquare(m[2,2]+O(p^2)) /* Step 1 Factorisation; write c_i v_t^{-1} = du */ fact1list = []; vtp(t) = [p,0; q*t, 1] myc(iii) = clist[iii+1] fact1list = []; /* note: i runs from 0 to length(clist)-1 [cosets] t runs from 0 to **p-1** */ for(t=0,p-1, for(i=0, length(clist)-1, for(j=1, length(bigd1list),u = th(bigd1list[j])*myc(i)*(1/vtp(t)); uu = subst(u, x0, sqrt(XX + O(p^ACC))); if(test(uu), fact1list = concat(fact1list, [[t,i,j,[quatinv(bigd1list[j]), u, vtp(t)]]]); break(1))))) /* Testing the factorisations */ /*print("Testing the factorisations") for(i=1, length(fact1list), mmmm=fact1list[i]; print1(Mod(myc(mmmm[2])*(1/vtp(mmmm[1]))-th(mmmm[4][1])*mmmm[4][2], x0^2+XX) "; "))*/ print("Testing the factorisations") for(i=1, length(fact1list), mmmm=fact1list[i]; print(myc(mmmm[2])*(1/vtp(mmmm[1]))-subst(th(mmmm[4][1])*mmmm[4][2], x0,sqrt(XX+O(p^ACC))))) /*print(subst(th(mmmm[4][1])*mmmm[4][2], x0,sqrt(XX+p^ACC)))))*/ /* Finding alpha & c_i st c_i^{-1} alpha^{-1} u in U_1(q) */ /*D was [-1/2, 1/6, 1/6, -1/6] in the original case --- let's do this in general*/ D = fact1list[1][4][1]; fl=[]; print("debug") mysearch(mlist,myx)=mflag=0;for(i=1,length(mlist),if(mlist[i]==myx,mflag=1));mflag /* changed to matunitlist for q=9 */ /*getFL(start)=output=[];for(aa=0,length(clist)-1,for(bb=1,length(matunitlist),vp=(1/myc(aa))*(1/matunitlist[bb])*start;vvpp=subst(vp,x0,sqrt(XX+O(p^ACC))); vvpp %=q; if(testU1(vvpp),output=([matunitlist[bb],myc(aa),vp]))));output*/ testUstar(vvpp)=temp=0;if(flag_small==0,temp=testU1(vvpp),temp=testUsq(vvpp));temp getFL(start)=output=[];for(aa=0,length(clist)-1,for(bb=1,length(unitlist_H),vp=(1/myc(aa))*(1/unitlist_H[bb])*start;vvpp=subst(vp,x0,sqrt(XX+O(p^ACC))); vvpp %=q; if(testUstar(vvpp),output=([unitlist_H[bb],myc(aa),vp]))));output getFLtest(start)=output=[];for(aa=0,length(clist)-1,for(bb=1,length(matunitlist),vp=(1/myc(aa))*(1/matunitlist[bb])*start;vvpp=subst(vp,x0,sqrt(XX+O(p^ACC))); vvpp %=q; if(testU1(vvpp),output=concat(output,[[matunitlist[bb],myc(aa),vp]]))));output print("debug 1.5") /*for(i=1,length(fact1list), up =fact1list[i][4][2]; for(ii=0, length(clist)-1, for(jj=1, length(matunitlist), vp=(1/myc(ii))*(1/matunitlist[jj])*up; vvpp=subst(vp,x0,sqrt(XX+O(p^ACC))); vvpp %=p; if((vvpp[2,1] ==0) && (vvpp[2,2] == 1), innerthing=subst(th(D)*matunitlist[jj]*myc(ii)*vp,x0,sqrt(XX+O(p^ACC)))*fact1list[i][4][3];bigflag=mysearch(clist,innerthing);if(bigflag,fl=concat(fl, [[D, matunitlist[jj], myc(ii), vp, fact1list[i][4][3]]]);print([i,ii,jj]);break(2))))))*/ for(i=1,length(fact1list),temp=getFL(fact1list[i][4][2]);if(length(temp)!=0,fl=concat(fl,[concat([fact1list[i][4][1],temp[1]],[temp[2],temp[3],fact1list[i][4][3]])]))) print("debug 2") /* Output of the decomposition test */ /* for(i=1, length(f1), print(f1[i])) */ print("debug 3") /* finds the matrices for the generating function */ getNewEpsilonMatrices(a,b)=temp=[]; for(i=1,p,if(fl[length(clist)*(i-1)+a+1][3]==myc(b),temp=concat(temp,[fl[length(clist)*(i-1)+a+1][4]*fl[length(clist)*(i-1)+a+1][5]])));temp /* generating function for the components of the U_p operator */ genfn(matrix1,k)=temp=0; for(i=1,length(matrix1),temp=temp+(matrix1[i][2,1]*x+matrix1[i][2,2])^k/((matrix1[i][2,1]*x+matrix1[i][2,2])*(matrix1[i][2,1]*x+matrix1[i][2,2]-matrix1[i][1,1]*x*y-matrix1[i][1,2]*y)));temp genfn_new(matrix1,k)=temp=[]; for(i=1,length(matrix1),temp=concat(temp, [(matrix1[i][2,1]*x+matrix1[i][2,2])^k/((matrix1[i][2,1]*x+matrix1[i][2,2])*(matrix1[i][2,1]*x+matrix1[i][2,2]-matrix1[i][1,1]*x*y-matrix1[i][1,2]*y))]));temp genfnXX(matrix1,k)=temp=0;for(i=1,length(matrix1),temp=temp+(matrix1[i][2,1]*A+matrix1[i][2,2])^k/((matrix1[i][2,1]*A+matrix1[i][2,2])*(matrix1[i][2,1]*A+matrix1[i][2,2]-matrix1[i][1,1]*A*B-matrix1[i][1,2]*B)));temp print("debug 4"); h_ij_new(i,j,k,acc)=subst(genfn_new(getNewEpsilonMatrices(i,j),k),x0,sqrt(XX+O(p^acc))) h_ij_real(i,j,k,acc)=subst(genfn_new(getNewEpsilonMatrices(i,j),k),x0,sqrt(XX)) my_hm_new(hij,dim)=temp=matrix(dim,dim,i,j,0);for(k=1,length(hij),temp=temp+matrix(dim,dim,i,j,polcoeff(polcoeff(hij[k]+O(x^(dim+1)),i-1,x)+O(y^(dim+1)),j-1,y)));temp my_hm_real(hij,dim)=temp=matrix(dim,dim,i,j,0);for(k=1,length(hij),temp=temp+matrix(dim,dim,i,j,polcoeff(polcoeff(hij[k]+O(x^(dim+1)),i-1,x)+O(y^(dim+1)),j-1,y)));temp /* creating the matrix for the U_p operator */ /* first we make the rows, because it was too hairy to do it all at once */ getRow_new(acc,k,dim,row)=tempm=(my_hm_new(h_ij_new(row,0,k,acc),dim));for(i=1,length(clist)-1,tempm=concat(tempm,my_hm_new(h_ij_new(row,i,k,acc),dim)));mattranspose(tempm) getRow_real(acc,k,dim,row)=tempm=(my_hm_real(h_ij_real(row,0,k,acc),dim));for(i=1,length(clist)-1,tempm=concat(tempm,my_hm_real(h_ij_real(row,i,k,acc),dim)));mattranspose(tempm) /* then we put them together to make the whole matrix */ bigUp_new(acc,k,dim)=tempp=getRow_new(acc,k,dim,length(clist)-1);forstep(i=length(clist)-2,0,-1,print(i);tempp=concat(getRow_new(acc,k,dim,i),tempp));mattranspose(tempp) bigUp_real(acc,k,dim)=tempp=getRow_real(acc,k,dim,length(clist)-1);forstep(i=length(clist)-2,0,-1,print(i);tempp=concat(getRow_real(acc,k,dim,i),tempp));mattranspose(tempp) findSlopes(acc,k,dim)=newtonpoly(matdet(bigUp_new(acc,k,dim)-BIGT*matid(dim*length(clist))),p) charpowerseries(acc,k,dim)=matdet(bigUp_new(acc,k,dim)-BIGT*matid(dim*length(clist))) charpowerseries_real(acc,k,dim)=matdet(bigUp_real(acc,k,dim)-BIGT*matid(dim*length(clist))) getSlopes(acc,k,dim)=newtonpoly(charpowerseries(acc,k,dim),p) getSlopes(100,3,2) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '68.191.' ************** PARI ***************** Host 68.191.223.193 (68.191.223.193) Time: Fri Mar 18 09:08:53 2005 Input: subst(x+1,x,10) Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.005s sys 0m0.007s '68.191.' ************** PARI ***************** Host 68.191.223.193 (68.191.223.193) Time: Fri Mar 18 09:09:10 2005 Input: /* Code written by Dan Jacobs, (c) 2002. Copied out by LJPK, 2004. Extensions written by LJPK, 2004. */ q=5; p=factor(q)[1,1]; flag=0; /* this is 1 for classic, 0 for extra level structure */ flag_small=0; /* 0 for everything, 1 just for the squares */ /* This allocates the values of x0 and y0 for the homomorphism between D_q and M_2(Q_q) */ if(p%4==1,XX=-1;y0=0); if(p%8==3,XX=-2;y0=1); if(p%8==7,XX=-5;y0=2); /* NB this may not work */ ACC=40; /* Define isomorphisms th: K(i,j) -> M_2(K) and th1: M_2(K) -> K(i,j) */ th(v)=[v[1]+v[2]*x0+v[4]*y0, v[2]*y0-v[3]-v[4]*x0; v[2]*y0+v[3]-v[4]*x0, v[1]-v[2]*x0-v[4]*y0] th1(mm) = [(mm[1,1]+mm[2,2])/2, ((mm[2,2]-mm[1,1])*x0 - (mm[1,2]+mm[2,1])*y0)/2, (mm[2,1]-mm[1,2])/2,((mm[2,2]-mm[1,1])*y0+(mm[1,2]+mm[2,1])*x0)/2] /* Now we use the new coset functions from new_quat_stuff */ r new_quat_stuff.txt unitlist_H = vector(length(unitlist_H), i, th(unitlist_H[i])); /* Choose whether we want small or big space of forms */ if(flag_small==0,clist=findCosetMatrices(),clist=findCosetMatrices_new()); print(clist) /* Inverting the quaternion [q0,q1,q2,q3] */ quatinv(v) = vv = v; N = sum(ii=1,4,v[ii]^2); for(ii=2,4,vv[ii] *= -1/N); vv[1] /= N; vv /* Finding elements d1 of O_D with N(d1)=p and d1 == [0, *; 0, *] mod p */ d1list=[]; bound=floor(sqrt(p)+3); forstep(d0=-bound, bound, 1/2, forstep(d1=-bound, bound, 1/2, forstep(d2=-bound, bound, 1/2, forstep(d3=-bound, bound, 1/2, if(d0^2+d1^2+d2^2+d3^2==p, mm = subst(th([d0,d1,d2,d3]), x0, sqrt(XX+O(p^ACC))); if((mm[1,1]%p == 0) && (mm[2,1]%p == 0), d1list=concat(d1list, [[d0,d1,d2,d3]]))))))) bigd1list=[]; forstep(d0=-bound, bound, 1/2, forstep(d1=-bound, bound, 1/2, forstep(d2=-bound, bound, 1/2, forstep(d3=-bound, bound, 1/2, if(d0^2+d1^2+d2^2+d3^2==p, bigd1list=concat(bigd1list, [[d0,d1,d2,d3]])))))) /* forstep(d0=-2, 2, 1/2, forstep(d1=-2, 2, 1/2, forstep(d2=-2, 2, 1/2, forstep(d3=-2, 2, 1/2, if(d0^2+d1^2+d2^2+d3^2==3, print([d0,d1,d2,d3])))))) */ /* Calculating the units of O_D and their matrix versions */ unitlist=[]; forstep(a=-2, 2, 1/2, forstep(b=-2, 2, 1/2, forstep(cc=-2, 2, 1/2, forstep(d=-2, 2, 1/2, if(a^2+b^2+cc^2+d^2==1, unitlist = concat(unitlist, [[a,b,cc,d]])))))) smallunitlist=[]; forstep(a=-2, 2, 1, forstep(b=-2, 2, 1, forstep(cc=-2, 2, 1, forstep(d=-2, 2, 1, if(a^2+b^2+cc^2+d^2==1, smallunitlist = concat(smallunitlist, [[a,b,cc,d]])))))) /*forstep(a=-2, 2, 1/2, forstep(b=-2, 2, 1/2, forstep(cc=-2, 2, 1/2, forstep(d=-2, 2, 1/2, if(a^2+b^2+cc^2+d^2==1, print([a,b,cc,d])))))) */ matunitlist = vector(length(unitlist), i, th(unitlist[i])); smallmatunitlist = vector(length(smallunitlist), i, th(smallunitlist[i])); /* "test": matrices for integral entries */ test(mm)= MM = mm; temp = matrix(2,2,i,j, valuation(MM[i,j],p)); mmin = vecmin([vecmin(temp[1,]), vecmin(temp[2,])]); mmin >=0 testU0(n)=m=subst(n,x0,sqrt(XX+O(p^ACC)));test(m) testU1(n)=m=subst(n,x0,sqrt(XX+O(p^ACC)));test(m)&&((m[2,1]%q)==0)&&((m[2,2]%q)==1) testUsq(n)=m=subst(n,x0,sqrt(XX+O(p^ACC)));test(m)&&((m[2,1]%q)==0)&&issquare(m[2,2]+O(p^2)) /* Step 1 Factorisation; write c_i v_t^{-1} = du */ fact1list = []; vtp(t) = [p,0; q*t, 1] myc(iii) = clist[iii+1] fact1list = []; /* note: i runs from 0 to length(clist)-1 [cosets] t runs from 0 to **p-1** */ for(t=0,p-1, for(i=0, length(clist)-1, for(j=1, length(bigd1list),u = th(bigd1list[j])*myc(i)*(1/vtp(t)); uu = subst(u, x0, sqrt(XX + O(p^ACC))); if(test(uu), fact1list = concat(fact1list, [[t,i,j,[quatinv(bigd1list[j]), u, vtp(t)]]]); break(1))))) /* Testing the factorisations */ /*print("Testing the factorisations") for(i=1, length(fact1list), mmmm=fact1list[i]; print1(Mod(myc(mmmm[2])*(1/vtp(mmmm[1]))-th(mmmm[4][1])*mmmm[4][2], x0^2+XX) "; "))*/ print("Testing the factorisations") for(i=1, length(fact1list), mmmm=fact1list[i]; print(myc(mmmm[2])*(1/vtp(mmmm[1]))-subst(th(mmmm[4][1])*mmmm[4][2], x0,sqrt(XX+O(p^ACC))))) /*print(subst(th(mmmm[4][1])*mmmm[4][2], x0,sqrt(XX+p^ACC)))))*/ /* Finding alpha & c_i st c_i^{-1} alpha^{-1} u in U_1(q) */ /*D was [-1/2, 1/6, 1/6, -1/6] in the original case --- let's do this in general*/ D = fact1list[1][4][1]; fl=[]; print("debug") mysearch(mlist,myx)=mflag=0;for(i=1,length(mlist),if(mlist[i]==myx,mflag=1));mflag /* changed to matunitlist for q=9 */ /*getFL(start)=output=[];for(aa=0,length(clist)-1,for(bb=1,length(matunitlist),vp=(1/myc(aa))*(1/matunitlist[bb])*start;vvpp=subst(vp,x0,sqrt(XX+O(p^ACC))); vvpp %=q; if(testU1(vvpp),output=([matunitlist[bb],myc(aa),vp]))));output*/ testUstar(vvpp)=temp=0;if(flag_small==0,temp=testU1(vvpp),temp=testUsq(vvpp));temp getFL(start)=output=[];for(aa=0,length(clist)-1,for(bb=1,length(unitlist_H),vp=(1/myc(aa))*(1/unitlist_H[bb])*start;vvpp=subst(vp,x0,sqrt(XX+O(p^ACC))); vvpp %=q; if(testUstar(vvpp),output=([unitlist_H[bb],myc(aa),vp]))));output getFLtest(start)=output=[];for(aa=0,length(clist)-1,for(bb=1,length(matunitlist),vp=(1/myc(aa))*(1/matunitlist[bb])*start;vvpp=subst(vp,x0,sqrt(XX+O(p^ACC))); vvpp %=q; if(testU1(vvpp),output=concat(output,[[matunitlist[bb],myc(aa),vp]]))));output print("debug 1.5") /*for(i=1,length(fact1list), up =fact1list[i][4][2]; for(ii=0, length(clist)-1, for(jj=1, length(matunitlist), vp=(1/myc(ii))*(1/matunitlist[jj])*up; vvpp=subst(vp,x0,sqrt(XX+O(p^ACC))); vvpp %=p; if((vvpp[2,1] ==0) && (vvpp[2,2] == 1), innerthing=subst(th(D)*matunitlist[jj]*myc(ii)*vp,x0,sqrt(XX+O(p^ACC)))*fact1list[i][4][3];bigflag=mysearch(clist,innerthing);if(bigflag,fl=concat(fl, [[D, matunitlist[jj], myc(ii), vp, fact1list[i][4][3]]]);print([i,ii,jj]);break(2))))))*/ for(i=1,length(fact1list),temp=getFL(fact1list[i][4][2]);if(length(temp)!=0,fl=concat(fl,[concat([fact1list[i][4][1],temp[1]],[temp[2],temp[3],fact1list[i][4][3]])]))) print("debug 2") /* Output of the decomposition test */ /* for(i=1, length(f1), print(f1[i])) */ print("debug 3") /* finds the matrices for the generating function */ getNewEpsilonMatrices(a,b)=temp=[]; for(i=1,p,if(fl[length(clist)*(i-1)+a+1][3]==myc(b),temp=concat(temp,[fl[length(clist)*(i-1)+a+1][4]*fl[length(clist)*(i-1)+a+1][5]])));temp /* generating function for the components of the U_p operator */ genfn(matrix1,k)=temp=0; for(i=1,length(matrix1),temp=temp+(matrix1[i][2,1]*x+matrix1[i][2,2])^k/((matrix1[i][2,1]*x+matrix1[i][2,2])*(matrix1[i][2,1]*x+matrix1[i][2,2]-matrix1[i][1,1]*x*y-matrix1[i][1,2]*y)));temp genfn_new(matrix1,k)=temp=[]; for(i=1,length(matrix1),temp=concat(temp, [(matrix1[i][2,1]*x+matrix1[i][2,2])^k/((matrix1[i][2,1]*x+matrix1[i][2,2])*(matrix1[i][2,1]*x+matrix1[i][2,2]-matrix1[i][1,1]*x*y-matrix1[i][1,2]*y))]));temp genfnXX(matrix1,k)=temp=0;for(i=1,length(matrix1),temp=temp+(matrix1[i][2,1]*A+matrix1[i][2,2])^k/((matrix1[i][2,1]*A+matrix1[i][2,2])*(matrix1[i][2,1]*A+matrix1[i][2,2]-matrix1[i][1,1]*A*B-matrix1[i][1,2]*B)));temp print("debug 4"); Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '68.191.' ************** PARI ***************** Host 68.191.223.193 (68.191.223.193) Time: Fri Mar 18 09:09:24 2005 Input: /* Code written by Dan Jacobs, (c) 2002. Copied out by LJPK, 2004. Extensions written by LJPK, 2004. */ q=5; p=factor(q)[1,1]; flag=0; /* this is 1 for classic, 0 for extra level structure */ flag_small=0; /* 0 for everything, 1 just for the squares */ /* This allocates the values of x0 and y0 for the homomorphism between D_q and M_2(Q_q) */ if(p%4==1,XX=-1;y0=0); if(p%8==3,XX=-2;y0=1); if(p%8==7,XX=-5;y0=2); /* NB this may not work */ ACC=40; /* Define isomorphisms th: K(i,j) -> M_2(K) and th1: M_2(K) -> K(i,j) */ th(v)=[v[1]+v[2]*x0+v[4]*y0, v[2]*y0-v[3]-v[4]*x0; v[2]*y0+v[3]-v[4]*x0, v[1]-v[2]*x0-v[4]*y0] th1(mm) = [(mm[1,1]+mm[2,2])/2, ((mm[2,2]-mm[1,1])*x0 - (mm[1,2]+mm[2,1])*y0)/2, (mm[2,1]-mm[1,2])/2,((mm[2,2]-mm[1,1])*y0+(mm[1,2]+mm[2,1])*x0)/2] /* Now we use the new coset functions from new_quat_stuff */ r new_quat_stuff.txt unitlist_H = vector(length(unitlist_H), i, th(unitlist_H[i])); /* Choose whether we want small or big space of forms */ if(flag_small==0,clist=findCosetMatrices(),clist=findCosetMatrices_new()); print(clist) /* Inverting the quaternion [q0,q1,q2,q3] */ quatinv(v) = vv = v; N = sum(ii=1,4,v[ii]^2); for(ii=2,4,vv[ii] *= -1/N); vv[1] /= N; vv /* Finding elements d1 of O_D with N(d1)=p and d1 == [0, *; 0, *] mod p */ d1list=[]; bound=floor(sqrt(p)+3); forstep(d0=-bound, bound, 1/2, forstep(d1=-bound, bound, 1/2, forstep(d2=-bound, bound, 1/2, forstep(d3=-bound, bound, 1/2, if(d0^2+d1^2+d2^2+d3^2==p, mm = subst(th([d0,d1,d2,d3]), x0, sqrt(XX+O(p^ACC))); if((mm[1,1]%p == 0) && (mm[2,1]%p == 0), d1list=concat(d1list, [[d0,d1,d2,d3]]))))))) bigd1list=[]; forstep(d0=-bound, bound, 1/2, forstep(d1=-bound, bound, 1/2, forstep(d2=-bound, bound, 1/2, forstep(d3=-bound, bound, 1/2, if(d0^2+d1^2+d2^2+d3^2==p, bigd1list=concat(bigd1list, [[d0,d1,d2,d3]])))))) /* forstep(d0=-2, 2, 1/2, forstep(d1=-2, 2, 1/2, forstep(d2=-2, 2, 1/2, forstep(d3=-2, 2, 1/2, if(d0^2+d1^2+d2^2+d3^2==3, print([d0,d1,d2,d3])))))) */ /* Calculating the units of O_D and their matrix versions */ unitlist=[]; forstep(a=-2, 2, 1/2, forstep(b=-2, 2, 1/2, forstep(cc=-2, 2, 1/2, forstep(d=-2, 2, 1/2, if(a^2+b^2+cc^2+d^2==1, unitlist = concat(unitlist, [[a,b,cc,d]])))))) smallunitlist=[]; forstep(a=-2, 2, 1, forstep(b=-2, 2, 1, forstep(cc=-2, 2, 1, forstep(d=-2, 2, 1, if(a^2+b^2+cc^2+d^2==1, smallunitlist = concat(smallunitlist, [[a,b,cc,d]])))))) /*forstep(a=-2, 2, 1/2, forstep(b=-2, 2, 1/2, forstep(cc=-2, 2, 1/2, forstep(d=-2, 2, 1/2, if(a^2+b^2+cc^2+d^2==1, print([a,b,cc,d])))))) */ matunitlist = vector(length(unitlist), i, th(unitlist[i])); smallmatunitlist = vector(length(smallunitlist), i, th(smallunitlist[i])); /* "test": matrices for integral entries */ test(mm)= MM = mm; temp = matrix(2,2,i,j, valuation(MM[i,j],p)); mmin = vecmin([vecmin(temp[1,]), vecmin(temp[2,])]); mmin >=0 testU0(n)=m=subst(n,x0,sqrt(XX+O(p^ACC)));test(m) testU1(n)=m=subst(n,x0,sqrt(XX+O(p^ACC)));test(m)&&((m[2,1]%q)==0)&&((m[2,2]%q)==1) testUsq(n)=m=subst(n,x0,sqrt(XX+O(p^ACC)));test(m)&&((m[2,1]%q)==0)&&issquare(m[2,2]+O(p^2)) /* Step 1 Factorisation; write c_i v_t^{-1} = du */ fact1list = []; vtp(t) = [p,0; q*t, 1] myc(iii) = clist[iii+1] fact1list = []; /* note: i runs from 0 to length(clist)-1 [cosets] t runs from 0 to **p-1** */ for(t=0,p-1, for(i=0, length(clist)-1, for(j=1, length(bigd1list),u = th(bigd1list[j])*myc(i)*(1/vtp(t)); uu = subst(u, x0, sqrt(XX + O(p^ACC))); if(test(uu), fact1list = concat(fact1list, [[t,i,j,[quatinv(bigd1list[j]), u, vtp(t)]]]); break(1))))) /* Testing the factorisations */ /*print("Testing the factorisations") for(i=1, length(fact1list), mmmm=fact1list[i]; print1(Mod(myc(mmmm[2])*(1/vtp(mmmm[1]))-th(mmmm[4][1])*mmmm[4][2], x0^2+XX) "; "))*/ print("Testing the factorisations") for(i=1, length(fact1list), mmmm=fact1list[i]; print(myc(mmmm[2])*(1/vtp(mmmm[1]))-subst(th(mmmm[4][1])*mmmm[4][2], x0,sqrt(XX+O(p^ACC))))) /*print(subst(th(mmmm[4][1])*mmmm[4][2], x0,sqrt(XX+p^ACC)))))*/ Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '68.191.' ************** PARI ***************** Host 68.191.223.193 (68.191.223.193) Time: Fri Mar 18 09:10:05 2005 Input: /* Code written by Dan Jacobs, (c) 2002. Copied out by LJPK, 2004. Extensions written by LJPK, 2004. */ q=5; p=factor(q)[1,1]; flag=0; /* this is 1 for classic, 0 for extra level structure */ flag_small=0; /* 0 for everything, 1 just for the squares */ /* This allocates the values of x0 and y0 for the homomorphism between D_q and M_2(Q_q) */ if(p%4==1,XX=-1;y0=0); if(p%8==3,XX=-2;y0=1); if(p%8==7,XX=-5;y0=2); /* NB this may not work */ ACC=40; /* Define isomorphisms th: K(i,j) -> M_2(K) and th1: M_2(K) -> K(i,j) */ th(v)=[v[1]+v[2]*x0+v[4]*y0, v[2]*y0-v[3]-v[4]*x0; v[2]*y0+v[3]-v[4]*x0, v[1]-v[2]*x0-v[4]*y0] th1(mm) = [(mm[1,1]+mm[2,2])/2, ((mm[2,2]-mm[1,1])*x0 - (mm[1,2]+mm[2,1])*y0)/2, (mm[2,1]-mm[1,2])/2,((mm[2,2]-mm[1,1])*y0+(mm[1,2]+mm[2,1])*x0)/2] /* Now we use the new coset functions from new_quat_stuff */ r new_quat_stuff.txt unitlist_H = vector(length(unitlist_H), i, th(unitlist_H[i])); /* Choose whether we want small or big space of forms */ if(flag_small==0,clist=findCosetMatrices(),clist=findCosetMatrices_new()); print(clist) /* Inverting the quaternion [q0,q1,q2,q3] */ quatinv(v) = vv = v; N = sum(ii=1,4,v[ii]^2); for(ii=2,4,vv[ii] *= -1/N); vv[1] /= N; vv /* Finding elements d1 of O_D with N(d1)=p and d1 == [0, *; 0, *] mod p */ d1list=[]; bound=floor(sqrt(p)+3); forstep(d0=-bound, bound, 1/2, forstep(d1=-bound, bound, 1/2, forstep(d2=-bound, bound, 1/2, forstep(d3=-bound, bound, 1/2, if(d0^2+d1^2+d2^2+d3^2==p, mm = subst(th([d0,d1,d2,d3]), x0, sqrt(XX+O(p^ACC))); if((mm[1,1]%p == 0) && (mm[2,1]%p == 0), d1list=concat(d1list, [[d0,d1,d2,d3]]))))))) bigd1list=[]; forstep(d0=-bound, bound, 1/2, forstep(d1=-bound, bound, 1/2, forstep(d2=-bound, bound, 1/2, forstep(d3=-bound, bound, 1/2, if(d0^2+d1^2+d2^2+d3^2==p, bigd1list=concat(bigd1list, [[d0,d1,d2,d3]])))))) /* forstep(d0=-2, 2, 1/2, forstep(d1=-2, 2, 1/2, forstep(d2=-2, 2, 1/2, forstep(d3=-2, 2, 1/2, if(d0^2+d1^2+d2^2+d3^2==3, print([d0,d1,d2,d3])))))) */ /* Calculating the units of O_D and their matrix versions */ unitlist=[]; forstep(a=-2, 2, 1/2, forstep(b=-2, 2, 1/2, forstep(cc=-2, 2, 1/2, forstep(d=-2, 2, 1/2, if(a^2+b^2+cc^2+d^2==1, unitlist = concat(unitlist, [[a,b,cc,d]])))))) smallunitlist=[]; forstep(a=-2, 2, 1, forstep(b=-2, 2, 1, forstep(cc=-2, 2, 1, forstep(d=-2, 2, 1, if(a^2+b^2+cc^2+d^2==1, smallunitlist = concat(smallunitlist, [[a,b,cc,d]])))))) /*forstep(a=-2, 2, 1/2, forstep(b=-2, 2, 1/2, forstep(cc=-2, 2, 1/2, forstep(d=-2, 2, 1/2, if(a^2+b^2+cc^2+d^2==1, print([a,b,cc,d])))))) */ matunitlist = vector(length(unitlist), i, th(unitlist[i])); smallmatunitlist = vector(length(smallunitlist), i, th(smallunitlist[i])); /* "test": matrices for integral entries */ test(mm)= MM = mm; temp = matrix(2,2,i,j, valuation(MM[i,j],p)); mmin = vecmin([vecmin(temp[1,]), vecmin(temp[2,])]); mmin >=0 testU0(n)=m=subst(n,x0,sqrt(XX+O(p^ACC)));test(m) testU1(n)=m=subst(n,x0,sqrt(XX+O(p^ACC)));test(m)&&((m[2,1]%q)==0)&&((m[2,2]%q)==1) testUsq(n)=m=subst(n,x0,sqrt(XX+O(p^ACC)));test(m)&&((m[2,1]%q)==0)&&issquare(m[2,2]+O(p^2)) /* Step 1 Factorisation; write c_i v_t^{-1} = du */ fact1list = []; vtp(t) = [p,0; q*t, 1] myc(iii) = clist[iii+1] fact1list = []; /* note: i runs from 0 to length(clist)-1 [cosets] t runs from 0 to **p-1** */ for(t=0,p-1, for(i=0, length(clist)-1, for(j=1, length(bigd1list),u = th(bigd1list[j])*myc(i)*(1/vtp(t)); uu = subst(u, x0, sqrt(XX + O(p^ACC))); if(test(uu), fact1list = concat(fact1list, [[t,i,j,[quatinv(bigd1list[j]), u, vtp(t)]]]); break(1))))) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '68.191.' ************** PARI ***************** Host 68.191.223.193 (68.191.223.193) Time: Fri Mar 18 09:12:29 2005 Input: /* Code written by Dan Jacobs, (c) 2002. Copied out by LJPK, 2004. Extensions written by LJPK, 2004. */ q=5; p=factor(q)[1,1]; flag=0; /* this is 1 for classic, 0 for extra level structure */ flag_small=0; /* 0 for everything, 1 just for the squares */ /* This allocates the values of x0 and y0 for the homomorphism between D_q and M_2(Q_q) */ if(p%4==1,XX=-1;y0=0); if(p%8==3,XX=-2;y0=1); if(p%8==7,XX=-5;y0=2); /* NB this may not work */ ACC=40; /* Define isomorphisms th: K(i,j) -> M_2(K) and th1: M_2(K) -> K(i,j) */ th(v)=[v[1]+v[2]*x0+v[4]*y0, v[2]*y0-v[3]-v[4]*x0; v[2]*y0+v[3]-v[4]*x0, v[1]-v[2]*x0-v[4]*y0] th1(mm) = [(mm[1,1]+mm[2,2])/2, ((mm[2,2]-mm[1,1])*x0 - (mm[1,2]+mm[2,1])*y0)/2, (mm[2,1]-mm[1,2])/2,((mm[2,2]-mm[1,1])*y0+(mm[1,2]+mm[2,1])*x0)/2] /* Now we use the new coset functions from new_quat_stuff */ Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '68.191.' ************** PARI ***************** Host 68.191.223.193 (68.191.223.193) Time: Fri Mar 18 09:12:45 2005 Input: /* Code written by Dan Jacobs, (c) 2002. Copied out by LJPK, 2004. Extensions written by LJPK, 2004. */ q=5; p=factor(q)[1,1]; flag=0; /* this is 1 for classic, 0 for extra level structure */ flag_small=0; /* 0 for everything, 1 just for the squares */ /* This allocates the values of x0 and y0 for the homomorphism between D_q and M_2(Q_q) */ if(p%4==1,XX=-1;y0=0); if(p%8==3,XX=-2;y0=1); if(p%8==7,XX=-5;y0=2); /* NB this may not work */ ACC=40; Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 18 09:15:39 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.006s sys 0m0.007s '161.116' ************** PARI ***************** Host 161.116.84.43 (161.116.84.43) Time: Fri Mar 18 09:58:59 2005 Input: P:=[n:n in Sym(4)|IsEven(n)];P; S:=[n:n in Sym(4)|IsOdd(n)];S; #P; Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: P:=[n:ninSym(4)|IsEven ^-------------------- *** unexpected character: S:=[n:ninSym(4)|IsOdd( ^-------------------- *** unexpected character: #P; ^-- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.110.72 (128.197.110.72) Time: Fri Mar 18 10:22:20 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.110.72 (128.197.110.72) Time: Fri Mar 18 10:23:56 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.110.72 (128.197.110.72) Time: Fri Mar 18 10:36:14 2005 Input: factor(1009) Output: ? [1009 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.110.72 (128.197.110.72) Time: Fri Mar 18 10:36:21 2005 Input: factor(1013) Output: ? [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '128.197' ************** PARI ***************** Host 128.197.110.72 (128.197.110.72) Time: Fri Mar 18 10:36:27 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.110.72 (128.197.110.72) Time: Fri Mar 18 10:40:22 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.110.72 (128.197.110.72) Time: Fri Mar 18 10:45:15 2005 Input: Mod(16,1022117)^78469 Output: ? Mod(703245, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.110.72 (128.197.110.72) Time: Fri Mar 18 10:46:52 2005 Input: Mod(73,1022117)^78469 Output: ? Mod(103745, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.110.72 (128.197.110.72) Time: Fri Mar 18 10:47:06 2005 Input: Mod(66,1022117)^78469 Output: ? Mod(1002067, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.110.72 (128.197.110.72) Time: Fri Mar 18 10:47:56 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.110.72 (128.197.110.72) Time: Fri Mar 18 10:57:48 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.158s user 0m0.105s sys 0m0.014s '128.197' ************** PARI ***************** Host 128.197.110.72 (128.197.110.72) Time: Fri Mar 18 11:10:47 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 18 11:13:16 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 18 11:14:07 2005 Input: 1008*1012 Output: ? 1020096 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 18 11:15:05 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 18 11:16:08 2005 Input: Mod(167366, 1022117)^(78469) Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.88.45 (128.197.88.45) Time: Fri Mar 18 11:17:50 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.119s user 0m0.102s sys 0m0.016s '128.197' ************** PARI ***************** Host 128.197.110.72 (128.197.110.72) Time: Fri Mar 18 11:18:26 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.88.45 (128.197.88.45) Time: Fri Mar 18 11:21:19 2005 Input: 294729472947294396 * 328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.88.45 (128.197.88.45) Time: Fri Mar 18 11:26:12 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Fri Mar 18 11:26:29 2005 Input: Mod(137366,1022117)^78469 Output: ? Mod(935253, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Fri Mar 18 11:26:49 2005 Input: Mod(137366,1022117)^(78469) Output: ? Mod(935253, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Fri Mar 18 11:27:10 2005 Input: Mod(167366,1022117)^(78469) Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.88.45 (128.197.88.45) Time: Fri Mar 18 11:32:21 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.183 (128.197.150.183) Time: Fri Mar 18 11:33:38 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 11310 Killed /usr/bin/gp -q -emacs Timing: real 0m21.003s user 0m20.998s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Fri Mar 18 11:34:44 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.120s user 0m0.110s sys 0m0.010s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Fri Mar 18 11:40:24 2005 Input: Mod(13,294729472947294397*328497239427384289)^(-1) Output: ? Mod(52132671360578387480242941026823164, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Fri Mar 18 11:41:38 2005 Input: Mod(13,294729472947294396*328497239427384288)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.244.172 (128.197.244.172) Time: Fri Mar 18 11:46:37 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^(52132671360578387144659326671226949) Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.183 (128.197.150.183) Time: Fri Mar 18 11:54:35 2005 Input: Mod(167366, 1020096)^78469 Output: ? Mod(845120, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 11:56:30 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 11:57:11 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '128.197' ************** PARI ***************** Host 128.197.150.183 (128.197.150.183) Time: Fri Mar 18 11:57:49 2005 Input: Mod(10424944469828754080284344711353162, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.183 (128.197.150.183) Time: Fri Mar 18 11:59:32 2005 Input: Mod(13, 1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.183 (128.197.150.183) Time: Fri Mar 18 12:00:17 2005 Input: Mod(167366, 1020096)^(78469) Output: ? Mod(845120, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:05:11 2005 Input: Mod(13,102006)^-1 Output: ? Mod(62773, 102006) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Mar 18 12:07:18 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:08:09 2005 Input: Mod(167366,1022117)^62773 Output: ? Mod(174989, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:13:35 2005 Input: factor(33) Output: ? [3 1] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:14:02 2005 Input: Mod(7,20)^-1 Output: ? Mod(3, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:14:35 2005 Input: Mod(14,33)3 Output: ? Mod(14, 33) ? Errors (if any) and Timing Info: *** Warning: unused characters: 3. Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:14:43 2005 Input: Mod(14,33)^3 Output: ? Mod(5, 33) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:15:54 2005 Input: Mod(7,20)^-1 Output: ? Mod(3, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:16:17 2005 Input: Mod(7,33)^3 Output: ? Mod(13, 33) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:17:00 2005 Input: Factor(1022117) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(1022117) ^--------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 12:17:07 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:17:07 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:17:51 2005 Input: Mod(13,1020096)^-1 Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:19:40 2005 Input: Mod(16366,1022117)^78469 Output: ? Mod(613787, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:22:31 2005 Input: Mod(13,1020096)^-1 Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:23:08 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:25:16 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.119s user 0m0.103s sys 0m0.015s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 12:27:56 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:28:01 2005 Input: 294729472947294396 * 328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:28:41 2005 Input: Mod(13,96817818241074147554367320960850048)^1 Output: ? Mod(13, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:28:56 2005 Input: Mod(13,96817818241074147554367320960850048)^-1 Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 18 12:33:06 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.110.72 (128.197.110.72) Time: Fri Mar 18 12:38:11 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13822 Killed /usr/bin/gp -q -emacs Timing: real 0m21.007s user 0m20.993s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 12:49:44 2005 Input: Mod(167366,1022117)^1020097 Output: ? Mod(167366, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 12:51:29 2005 Input: Mod(2,10)^3 Output: ? Mod(8, 10) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 12:51:32 2005 Input: Mod(2,10)^3 Output: ? Mod(8, 10) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 12:52:21 2005 Input: Mod(167366,102117)^3 Output: ? Mod(76295, 102117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 12:52:34 2005 Input: Mod(167366,102117)^1020097 Output: ? Mod(70025, 102117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 12:52:39 2005 Input: Mod(167366,102117)^1020097 Output: ? Mod(70025, 102117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 13:06:40 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 13:06:55 2005 Input: Mod(1/13,1020096)^(-1) Output: ? Mod(13, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 13:07:17 2005 Input: Mod(7,20)^(-1) Output: ? Mod(3, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 13:07:32 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 13:09:22 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 13:15:18 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.118s user 0m0.099s sys 0m0.020s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 13:21:43 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 13:22:25 2005 Input: Mod(13,(1009-1)*(1013-1))^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 13:22:34 2005 Input: Mod(13,(1009-1)*(1013-1))^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 13:24:25 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.120s user 0m0.103s sys 0m0.018s '168.122' ************** PARI ***************** Host 168.122.188.242 (168.122.188.242) Time: Fri Mar 18 13:32:45 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 13:34:04 2005 Input: Mod(13,(294729472947294397 - 1) *(328497239427384289 - 1))^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 13:34:19 2005 Input: Mod(13,(294729472947294397-1)*(328497239427384289-1))^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 13:34:20 2005 Input: Mod(13,(294729472947294397-1)*(328497239427384289-1))^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 13:34:21 2005 Input: Mod(13,(294729472947294397-1)*(328497239427384289-1))^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 13:34:59 2005 Input: Mod(13,(294729472947294397-1)*(328497239427384289-1))^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Mar 18 13:38:52 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.188.242 (168.122.188.242) Time: Fri Mar 18 13:40:07 2005 Input: mod(13,1020096)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.188.242 (168.122.188.242) Time: Fri Mar 18 13:40:14 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.188.242 (168.122.188.242) Time: Fri Mar 18 13:42:29 2005 Input: Mod(167366,1022117)^(78469) Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.188.242 (168.122.188.242) Time: Fri Mar 18 13:43:29 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.119s user 0m0.099s sys 0m0.022s '168.122' ************** PARI ***************** Host 168.122.188.242 (168.122.188.242) Time: Fri Mar 18 13:44:51 2005 Input: 294729472947294396*328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.188.242 (168.122.188.242) Time: Fri Mar 18 13:45:51 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.188.242 (168.122.188.242) Time: Fri Mar 18 13:47:02 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^(52132671360578387144659326671226949) Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.188.242 (168.122.188.242) Time: Fri Mar 18 13:48:44 2005 Input: factor(2179575060383617170819849823956766088165808126850148038256483943383380669273) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 14722 Killed /usr/bin/gp -q -emacs Timing: real 0m21.003s user 0m20.993s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Fri Mar 18 14:04:19 2005 Input: Mod(167366,1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Fri Mar 18 14:07:35 2005 Input: Mod(10424944469828754080284344711353162,96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Fri Mar 18 14:11:26 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.120s user 0m0.101s sys 0m0.019s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Fri Mar 18 14:11:44 2005 Input: 294729472947294396*328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Fri Mar 18 14:12:18 2005 Input: Mod(13,96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Fri Mar 18 14:12:57 2005 Input: Mod(10424944469828754080284344711353162, 96817818241074148177594033335528733)^ 52132671360578387144659326671226949 Output: ? ? 52132671360578387144659326671226949 ? Errors (if any) and Timing Info: *** unexpected character: ...74148177594033335528733)^ ^ Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Fri Mar 18 14:13:15 2005 Input: Mod(10424944469828754080284344711353162, 96817818241074148177594033335528733)^(52132671360578387144659326671226949) Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 18 14:23:34 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 18 14:31:15 2005 Input: mod(13, 1020096)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(13,1020096)^(-1) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 18 14:34:44 2005 Input: Mod(13, 1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 18 14:40:37 2005 Input: Mod(167366, 1022117)^78469 Output: ? Mod(121512, 1022117) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 18 14:43:03 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.118s user 0m0.099s sys 0m0.020s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 18 14:43:52 2005 Input: 294729472947294396*328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 18 14:46:19 2005 Input: Mod(13, 96817818241074147554367320960850048)^(-1) Output: ? Mod(52132671360578387144659326671226949, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 18 14:47:14 2005 Input: Mod(10424944469828754080284344711353162, 96817818241074147554367320960850048)^(52132671360578387144659326671226949) Output: ? Mod(30430901027932430125575860844684416, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 18 14:47:52 2005 Input: Mod(10424944469828754080284344711353162, 96817818241074147554367320960850048)^(52132671360578387144659326671226949) Output: ? Mod(30430901027932430125575860844684416, 96817818241074147554367320960850048) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 18 14:50:22 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.120s user 0m0.103s sys 0m0.016s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 18 14:50:57 2005 Input: 294729472947294396*328497239427384288 Output: ? 96817818241074147554367320960850048 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 18 14:53:39 2005 Input: Mod(10424944469828754080284344711353162, 96817818241074148177594033335528733)^52132671360578387144659326671226949 Output: ? Mod(60518130120, 96817818241074148177594033335528733) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '129.64.' ************** PARI ***************** Host 129.64.99.48 (129.64.99.48) Time: Fri Mar 18 16:23:10 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '201.15.' ************** PARI ***************** Host 201.15.200.180 (201.15.200.180) Time: Fri Mar 18 19:07:46 2005 Input: 01010101 Output: ? 1010101 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Mar 18 20:07:44 2005 Input: 2+1 Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '66.185.' ************** PARI ***************** Host 66.185.84.78 (66.185.84.78) Time: Fri Mar 18 20:28:49 2005 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '219.77.' ************** PARI ***************** Host 219.77.75.4 (219.77.75.4) Time: Fri Mar 18 21:37:36 2005 Input: factorint(10^67-1,1111) Output: ? [3 2] [493121 1] [79863595778924342083 1] [28213380943176667001263153660999177245677 1] ? Errors (if any) and Timing Info: Timing: real 0m11.458s user 0m11.446s sys 0m0.011s '219.77.' ************** PARI ***************** Host 219.77.75.4 (219.77.75.4) Time: Fri Mar 18 21:38:12 2005 Input: factorint(10^67-1,12346) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 21618 Killed /usr/bin/gp -q -emacs Timing: real 0m21.007s user 0m20.979s sys 0m0.021s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:17:01 2005 Input: p:=x^5-5*x^3+x^2+3*x-1; Output: ? ? Errors (if any) and Timing Info: *** unexpected character: p:=x^5-5*x^3+x^2+3*x-1 ^-------------------- Timing: real 0m0.282s user 0m0.007s sys 0m0.004s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:17:21 2005 Input: p=x^5-5*x^3+x^2+3*x-1: Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.064s user 0m0.007s sys 0m0.005s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:17:36 2005 Input: p=x^5-5*x^3+x^2+3*x-1: Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:17:55 2005 Input: p:=x^5-5*x^3+x^2+3*x-1: Output: ? ? Errors (if any) and Timing Info: *** unexpected character: p:=x^5-5*x^3+x^2+3*x-1 ^-------------------- Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:30:53 2005 Input: galoisinit(x^5-5*x^3+x^2+3*x-1): Output: ? ? Errors (if any) and Timing Info: *** galoisinit: field not Galois or Galois group not weakly super solvable. Timing: real 0m0.075s user 0m0.008s sys 0m0.006s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:32:10 2005 Input: galoisinit(x^2-2): Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.046s user 0m0.004s sys 0m0.009s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:32:16 2005 Input: galoisinit(x^2-2): Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:32:27 2005 Input: galoisinit(x^2-2); Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:32:55 2005 Input: galois(x^2-2); Output: ? ? ? Errors (if any) and Timing Info: *** obsolete function: galois(x^2-2); ^-------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: galois(x) ===> polgalois(x) polgalois(x): Galois group of the polynomial x (see manual for group coding). Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:33:18 2005 Input: polgalois(x^2-2); Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:33:23 2005 Input: polgalois(x^2-2); Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:33:35 2005 Input: galois(x^2-2); Output: ? ? ? Errors (if any) and Timing Info: *** obsolete function: galois(x^2-2); ^-------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: galois(x) ===> polgalois(x) polgalois(x): Galois group of the polynomial x (see manual for group coding). Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:34:11 2005 Input: polgalois(x^2-2); Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:34:19 2005 Input: polgalois(x^5-5*x^3+x^2+3*x-1); Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.068s user 0m0.012s sys 0m0.006s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:34:49 2005 Input: polgalois(x^5-5*x^3+x^2+3*x-1), Output: ? [120, -1, 1] ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,. Timing: real 0m0.016s user 0m0.012s sys 0m0.003s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:34:59 2005 Input: polgalois(x^5-5*x^3+x^2+3*x-1): Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.010s sys 0m0.007s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:35:31 2005 Input: (x^5-5*x^3+x^2+3*x-1)^2: Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:35:42 2005 Input: (x^5-5*x^3+x^2+3*x-1)^2; Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:36:38 2005 Input: Galoisinit(x^5-5*x^3+x^2+3*x-1); Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Galoisinit(x^5-5*x^3+x^2+3*x-1); ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:37:22 2005 Input: galoisinit(x^5-5*x^3+x^2+3*x-1); Output: ? ? ? Errors (if any) and Timing Info: *** galoisinit: field not Galois or Galois group not weakly super solvable. Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '193.6.1' ************** PARI ***************** Host 193.6.138.75 (193.6.138.75) Time: Sat Mar 19 12:39:55 2005 Input: polgalois(x^5-5*x^3+x^2+3*x-1); Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.011s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:05:43 2005 Input: 3+4 Output: ? 7 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:16:02 2005 Input: for(n=1,10,print(n^2)) Output: ? 1 4 9 16 25 36 49 64 81 100 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:16:48 2005 Input: for(n=1,10,print(n);print(n^2)) Output: ? 1 1 2 4 3 9 4 16 5 25 6 36 7 49 8 64 9 81 10 100 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:17:19 2005 Input: for(n=1,10,print(n));print(n^2) Output: ? 1 2 3 4 5 6 7 8 9 10 n^2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:18:08 2005 Input: for(n=1,10,print(n^2));print(n) Output: ? 1 4 9 16 25 36 49 64 81 100 n ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:19:54 2005 Input: v=[10,9,8,7,6,5,4,3,2,1] v[1] v[3] Output: ? [10, 9, 8, 7, 6, 5, 4, 3, 2, 1] ? 10 ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:21:20 2005 Input: a=0;for(n=1,10,a=a+v[n];print(a)) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: a=a+v[n];print(a)) ^------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:22:57 2005 Input: a=0 for(n=1,10,a=a+v[n];print(a)) Output: ? 0 ? ? Errors (if any) and Timing Info: *** unexpected character: a=a+v[n];print(a)) ^------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:23:30 2005 Input: m=[1,2;3,4;5,6] Output: ? [1 2] [3 4] [5 6] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:25:04 2005 Input: for(n=1,100,if(issquare(n)<>0,print(n),)) Output: ? 1 4 9 16 25 36 49 64 81 100 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:25:35 2005 Input: for(n=1,100,if(issquare(n)=0,print(n),)) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...or(n=1,100,if(issquare(n)=0,print(n),)) ^-------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:26:14 2005 Input: for(n=1,100,if(issquare(n)<>1,print(n),)) Output: ? 2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 46 47 48 50 51 52 53 54 55 56 57 58 59 60 61 62 63 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:28:54 2005 Input: f=x^2+x+1 subst(f,x,7) Output: ? x^2 + x + 1 ? 57 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:30:45 2005 Input: for(n=1,100,a=lift(mod(n,3));if(a<>0,print(n^2,)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...,3));if(a<>0,print(n^2,)) ^ Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:31:49 2005 Input: for(n=1,100,a=lift(mod(n,3));if(a<>0,print(n^2,))) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: a=lift(mod(n,3));if(a<>0,pr ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.009s sys 0m0.001s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:32:25 2005 Input: for(n=1,100,a=lift(Mod(n,3));if(a<>0,print(n^2,))) Output: ? 1 4 16 25 49 64 100 121 169 196 256 289 361 400 484 529 625 676 784 841 961 1024 1156 1225 1369 1444 1600 1681 1849 1936 2116 2209 2401 2500 2704 2809 3025 3136 3364 3481 3721 3844 4096 4225 4489 4624 4900 5041 5329 5476 5776 5929 6241 6400 6724 6889 7225 7396 7744 7921 8281 8464 8836 9025 9409 9604 10000 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:34:02 2005 Input: 18/19 Output: ? 18/19 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:34:14 2005 Input: 18/19*1.0 Output: ? 0.94736842105263157894736842105263157894 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:34:23 2005 Input: 18/19*1. Output: ? 0.94736842105263157894736842105263157894 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.003s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:34:29 2005 Input: 18/19*1 Output: ? 18/19 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 13:34:35 2005 Input: 18/19*1. Output: ? 0.94736842105263157894736842105263157894 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:33:33 2005 Input: (5,23)^13 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (5,23)^13 ^------- Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:33:49 2005 Input: Mod(5,23)^13 Output: ? Mod(21, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:34:27 2005 Input: Mod(7,7387)^7386 Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:35:05 2005 Input: Mod(7,7392)^7393 Output: ? Mod(4039, 7392) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:44:47 2005 Input: Mod(7,7393)^7392 Output: ? Mod(1, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:45:45 2005 Input: Mod(7,7387)^7386 Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.006s sys 0m0.007s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:47:07 2005 Input: Mod(131769,1147) Output: ? Mod(1011, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.007s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:48:12 2005 Input: Mod(18496,1147) Output: ? Mod(144, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:48:59 2005 Input: Mod(20736,1147) Output: ? Mod(90, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:49:15 2005 Input: Mod(13,12) Output: ? Mod(1, 12) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:49:44 2005 Input: Mod(8100,1147) Output: ? Mod(71, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:50:17 2005 Input: Mod(5041,1147) Output: ? Mod(453, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:51:00 2005 Input: Mod(205209,1147) Output: ? Mod(1043, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:51:45 2005 Input: Mod(10816,1147) Output: ? Mod(493, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:53:08 2005 Input: Mod(243049,1147) Output: ? Mod(1032, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:55:17 2005 Input: Mod(1076376,1147) Output: ? Mod(490, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:55:46 2005 Input: Mod(221970,1147) Output: ? Mod(599, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:56:36 2005 Input: Mod(42529,1147) Output: ? Mod(90, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:56:59 2005 Input: Mod(12960,1147) Output: ? Mod(343, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:57:22 2005 Input: Mod(9604,1147) Output: ? Mod(428, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 16:58:02 2005 Input: Mod(28,1147)^749 Output: ? Mod(289, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:00:46 2005 Input: Mod(346773,1147) Output: ? Mod(379, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:01:31 2005 Input: Mod(10612,1147) Output: ? Mod(289, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:05:12 2005 Input: phi(n)=160 Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:05:30 2005 Input: Phi(n,160) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Phi(n,160) ^---------- Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:27:59 2005 Input: Mod(5764801,7393) Output: ? Mod(5654, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:29:12 2005 Input: Mod(3024121,7393) Output: ? Mod(384, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:29:40 2005 Input: Mod(147456,7393) Output: ? Mod(6989, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:31:14 2005 Input: Mod(163216,7393) Output: ? Mod(570, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:31:38 2005 Input: Mod(324900,7393) Output: ? Mod(7001, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:32:17 2005 Input: Mod(153664,7393) Output: ? Mod(5804, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:33:13 2005 Input: Mod(2524921,7393) Output: ? Mod(3908, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:33:48 2005 Input: Mod(15272464,7393) Output: ? Mod(5919, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:34:21 2005 Input: Mod(35034561,7393) Output: ? Mod(6527, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:34:56 2005 Input: Mod(42601729,7393) Output: ? Mod(3263, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:36:43 2005 Input: Mod(21297601,7393) Output: ? Mod(5761, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.002s sys 0m0.010s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:37:23 2005 Input: Mod(34099359,7393) Output: ? Mod(2843, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:38:17 2005 Input: Mod(19903843,7393) Output: ? Mod(1887, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:38:48 2005 Input: Mod(1075590,7393) Output: ? Mod(3605, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:39:21 2005 Input: Mod(25195345,7393) Output: ? Mod(1, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:47:25 2005 Input: Mod(21297601,7393) Output: ? Mod(5761, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:47:43 2005 Input: Mod(21297601,7387) Output: ? Mod(880, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:48:11 2005 Input: Mod(5208720,7387) Output: ? Mod(885, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:48:52 2005 Input: Mod(6195885,7387) Output: ? Mod(5579, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:49:39 2005 Input: Mod(3180030,7387) Output: ? Mod(3620, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:50:17 2005 Input: Mod(1390080,7387) Output: ? Mod(1324, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:50:40 2005 Input: Mod(7485896,7387) Output: ? Mod(2865, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '155.41.' ************** PARI ***************** Host 155.41.134.192 (155.41.134.192) Time: Sat Mar 19 17:51:12 2005 Input: Mod(140385,7387) Output: ? Mod(32, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:11:05 2005 Input: factor(97) Output: ? [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:11:57 2005 Input: factor(8800) Output: ? [2 5] [5 2] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:16:42 2005 Input: Mod(5,23)^13 Output: ? Mod(21, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:17:13 2005 Input: 28^2 Output: ? 784 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:18:39 2005 Input: Mod(784,1147)^2 Output: ? Mod(1011, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:20:20 2005 Input: Mod(1011,1147)^2 Output: ? Mod(144, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:20:36 2005 Input: Mod(144,1147)^2 Output: ? Mod(90, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:20:52 2005 Input: Mod(90,1147)^2 Output: ? Mod(71, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:21:12 2005 Input: Mod(71,1147)^2 Output: ? Mod(453, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:21:30 2005 Input: Mod(453,1147)^2 Output: ? Mod(1043, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:22:02 2005 Input: Mod(1043,1147)^2 Output: ? Mod(493, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:22:22 2005 Input: Mod(493,1147)^2 Output: ? Mod(1032, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:23:07 2005 Input: 1032*493 Output: ? 508776 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:23:35 2005 Input: Mod(508775,1147) Output: ? Mod(654, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:25:11 2005 Input: Mod(28,1147)^640 Output: ? Mod(490, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:25:36 2005 Input: Mod(28,1147)^704 Output: ? Mod(599, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:27:20 2005 Input: Mod(28,1147)^736 Output: ? Mod(90, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:27:45 2005 Input: Mod(28,1147)^748 Output: ? Mod(379, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:28:05 2005 Input: Mod(28,1147)^749 Output: ? Mod(289, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:29:49 2005 Input: Mod(7,7387)^7386 Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:31:35 2005 Input: Mod(7,7393)^7392 Output: ? Mod(1, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:32:15 2005 Input: factor(7393) Output: ? [7393 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:36:03 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:37:00 2005 Input: 1147 - 31 - 37 + 1 Output: ? 1080 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:37:13 2005 Input: 30*36 Output: ? 1080 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:37:14 2005 Input: 30*36 Output: ? 1080 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:37:18 2005 Input: 30*37 Output: ? 1110 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:38:25 2005 Input: Mod(452,1080)^(-1) Output: ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(4, 1080). Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:41:29 2005 Input: Mod(329,1080)^(-1) Output: ? Mod(929, 1080) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:42:33 2005 Input: 329*929 Output: ? 305641 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:43:44 2005 Input: Mod(452,1147)^(305641) Output: ? Mod(452, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:44:31 2005 Input: Mod(452,1147)^(329) Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:47:19 2005 Input: Mod(452,1147)^(929) Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:47:37 2005 Input: Mod(763,1147)^(329) Output: ? Mod(452, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:51:43 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:52:02 2005 Input: 72*96 Output: ? 6912 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:53:04 2005 Input: Mod(1789,6912)^(-1) Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:54:13 2005 Input: Mod(5192,7081)^(85) Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:54:44 2005 Input: Mod(2604,7081)^(85) Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.225.11 (168.122.225.11) Time: Sat Mar 19 19:55:09 2005 Input: Mod(4222,7081)^(85) Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:12:04 2005 Input: forstep(x=5, 20, [2,4], print(x)) Output: ? 5 7 11 13 17 19 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:14:01 2005 Input: forstep(x=2, 20, 1, print(x)) Output: ? 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:15:00 2005 Input: forstep(x=2, 20, x*2, print(x)) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in gsigne. Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:15:46 2005 Input: forstep(x=2, 20, 1, print(x*2)) Output: ? 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:18:19 2005 Input: forstep(x=2, 20, 1, while(x*2<7,print(x*2)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...1,while(x*2<7,print(x*2)) ^ Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:19:19 2005 Input: forstep(x=2, 20, 1, while(x*2<7,print(x*2))) Output: ? 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 1074 Killed /usr/bin/gp -q -emacs Timing: real 0m21.042s user 0m7.773s sys 0m13.226s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:20:17 2005 Input: forstep(x=2, 20, 1, while(x*2>7,print(x*2))) Output: ? 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 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8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 1086 Killed /usr/bin/gp -q -emacs Timing: real 0m21.296s user 0m8.244s sys 0m12.756s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:22:39 2005 Input: for(x=2,20,while(x*2>7,print(x*2))) Output: ? 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 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8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 1111 Killed /usr/bin/gp -q -emacs Timing: real 0m21.287s user 0m8.513s sys 0m12.488s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:24:41 2005 Input: for(x=2,20,while(x<>1,print(x*2))) Output: ? 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 1134 Killed /usr/bin/gp -q -emacs Timing: real 0m21.070s user 0m10.448s sys 0m10.550s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:30:35 2005 Input: for(x=2,20,if(x<>1,x*2,if(x>7,x-2,))) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:34:21 2005 Input: while(r-1,print(r*2)) Output: ? 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2*r 2* ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 1218 Killed /usr/bin/gp -q -emacs Timing: real 0m21.026s user 0m9.526s sys 0m11.475s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:35:16 2005 Input: for(r=2,20,while(r-1,print(r*2))) Output: ? 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 1230 Killed /usr/bin/gp -q -emacs Timing: real 0m21.242s user 0m9.056s sys 0m11.943s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:36:02 2005 Input: for(r=2,20,until(r-1,print(r*2))) Output: ? 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:37:03 2005 Input: for(r=2,20,until(r-7,print(r*2))) Output: ? 4 6 8 10 12 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 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14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 1256 Killed /usr/bin/gp -q -emacs Timing: real 0m21.253s user 0m9.868s sys 0m11.131s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:40:07 2005 Input: for(r=2,20,until(r-7,print(r-7))) Output: ? -5 -4 -3 -2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 1287 Killed /usr/bin/gp -q -emacs Timing: real 0m21.268s user 0m9.088s sys 0m11.911s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:46:27 2005 Input: forstep(r=2,20,[2],until(r-7,print(r-7))) Output: ? -5 -3 -1 1 3 5 7 9 11 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:48:38 2005 Input: forstep(r=2,20,[2*r],until(r-7,print(r-7))) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in gsigne. Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:48:53 2005 Input: forstep(r=2,20,[2],until(r-7,print(r-7))) Output: ? -5 -3 -1 1 3 5 7 9 11 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 20:49:52 2005 Input: forstep(r=2,20,[2,4,8,16],until(r-7,print(r-7))) Output: ? -5 -3 1 9 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:10:42 2005 Input: for(r=2,20,r=lift(Mod(r,2));print(r-7)) Output: ? -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 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-7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 1553 Killed /usr/bin/gp -q -emacs Timing: real 0m21.155s user 0m11.772s sys 0m9.230s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:12:32 2005 Input: for(n=2,20,r=lift(Mod(r,2))*2;print(r-7)) Output: ? ? Errors (if any) and Timing Info: *** forbidden division t_POL % t_INT. Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:12:58 2005 Input: for(n=2,20,r=lift(Mod(n,2))*2;print(r-7)) Output: ? -7 -5 -7 -5 -7 -5 -7 -5 -7 -5 -7 -5 -7 -5 -7 -5 -7 -5 -7 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:17:19 2005 Input: if(r>=7,r-7,r*2) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:18:13 2005 Input: if(r-6>0,r-7,r*2) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:18:31 2005 Input: if(r>6,r-7,r*2) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:18:57 2005 Input: for(r=2,20,if(r>6,r-7,r*2)) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:19:27 2005 Input: for(r=2,20,if(r>6,print(r-7),print(r*2))) Output: ? 4 6 8 10 12 0 1 2 3 4 5 6 7 8 9 10 11 12 13 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:21:53 2005 Input: for(r=2,20,while(r>6,print(r-7),print(r*2))) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...2,20,while(r>6,print(r-7) *** ,print(r*2))) ^------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:22:12 2005 Input: for(r=2,20,if(r>6,print(r-7),print(r*2))) Output: ? 4 6 8 10 12 0 1 2 3 4 5 6 7 8 9 10 11 12 13 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:27:47 2005 Input: for(r=2,20,while(r>6,print(r-7),print(r*2))) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...2,20,while(r>6,print(r-7) *** ,print(r*2))) ^------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:27:59 2005 Input: for(r=2,20,if(r>6,print(r-7),print(r*2))) Output: ? 4 6 8 10 12 0 1 2 3 4 5 6 7 8 9 10 11 12 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:30:38 2005 Input: if(r>6,print(r-7),print(r*2)) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:30:53 2005 Input: r=2 if(r>6,print(r-7),print(r*2)) Output: ? 2 ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:31:43 2005 Input: r=2 if(r>6,print(r-7),print(r*2)) % Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:31:56 2005 Input: r=2 if(r>6,print(r-7),print(r*2)) Output: ? 2 ? 4 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:32:07 2005 Input: r=2 if(r>6,print(r-7),print(r*2)) Output: ? 2 ? 4 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:32:16 2005 Input: r=2 if(r>6,print(r-7),print(r*2)) Output: ? 2 ? 4 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:32:36 2005 Input: r=2; if(r>6,print(r-7),print(r*2)) Output: ? ? 4 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:35:45 2005 Input: for(x=2,20,if(x>6,print(x-7),print(x*2))) Output: ? 4 6 8 10 12 0 1 2 3 4 5 6 7 8 9 10 11 12 13 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:37:42 2005 Input: forstep(x=2,20,[2,4,8,16],if(x>6,print(x-7),print(x*2))) Output: ? 4 8 1 9 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:41:30 2005 Input: forstep(x=2,20,[2,4,8,16],if(x>4,print(x-5),print(x*2))) Output: ? 4 8 3 11 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sat Mar 19 21:43:53 2005 Input: forstep(x=2,20,[2,4,8,16],if(x>6,print(x-7),print(x*2))) Output: ? 4 8 1 9 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 21:47:21 2005 Input: forstep(x=2,20,2^x,if(x>6,print(x-7),print(x*2))) Output: ? ? ? ? Errors (if any) and Timing Info: *** incorrect type in gsigne. Timing: real 0m0.023s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 21:47:31 2005 Input: forstep(x=1,20,2^x,if(x>6,print(x-7),print(x*2))) Output: ? ? ? ? Errors (if any) and Timing Info: *** incorrect type in gsigne. Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 21:48:05 2005 Input: forstep(x=2,20,[2,4,8,16],if(x>6,print(x-7),print(x*2))) Output: ? 4 8 1 9 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 21:57:02 2005 Input: r=2;p=1 while(r<>1,r*2;p+1) Output: ? 1 ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 2095 Killed /usr/bin/gp -q -emacs Timing: real 0m21.045s user 0m20.993s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:00:03 2005 Input: r=2;p=1 while(r<>1,r*2;print r;while(r>6,r-7;print r);print(p+1)) Output: ? 1 ? 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 2120 Killed /usr/bin/gp -q -emacs Timing: real 0m21.164s user 0m11.593s sys 0m9.408s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:02:04 2005 Input: r=2;p=1 until(r<>1,r*2;print r;until(r>6,r-7;print r);print(p+1)) Output: ? 1 ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 2189 Killed /usr/bin/gp -q -emacs Timing: real 0m21.015s user 0m20.995s sys 0m0.005s '151.204' ************** PARI ***************** Host 151.204.250.33 (151.204.250.33) Time: Sat Mar 19 22:03:19 2005 Input: Mod(329,1147)^(-1) Output: ? Mod(638, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.007s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:03:20 2005 Input: r=2;p=1 while(r<>1,r*2;print r;print(p+1)) Output: ? 1 ? 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 2201 Killed /usr/bin/gp -q -emacs Timing: real 0m21.064s user 0m8.918s sys 0m12.082s '151.204' ************** PARI ***************** Host 151.204.250.33 (151.204.250.33) Time: Sat Mar 19 22:05:37 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:05:45 2005 Input: r=2;p=1 while(r<>1,r*2;print r) Output: ? 1 ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 2232 Killed /usr/bin/gp -q -emacs Timing: real 0m21.025s user 0m20.986s sys 0m0.015s '151.204' ************** PARI ***************** Host 151.204.250.33 (151.204.250.33) Time: Sat Mar 19 22:06:41 2005 Input: Mod(329,1080)^(-1) Output: ? Mod(929, 1080) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:07:03 2005 Input: r=2;p=1 while(r=2,r*2;print r) Output: ? 1 ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 2263 Killed /usr/bin/gp -q -emacs Timing: real 0m21.003s user 0m20.995s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:07:40 2005 Input: for(r=2,10,print(r*2)) Output: ? 4 6 8 10 12 14 16 18 20 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '151.204' ************** PARI ***************** Host 151.204.250.33 (151.204.250.33) Time: Sat Mar 19 22:08:23 2005 Input: Mod(452,1147)^929 Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:08:32 2005 Input: while(r>7,for(r=2,10,print(r*2))) Output: ? ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:10:49 2005 Input: r=2 while(r=1,print(r*2)) Output: ? 2 ? 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 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Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 2317 Killed /usr/bin/gp -q -emacs Timing: real 0m21.532s user 0m8.628s sys 0m12.371s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:12:01 2005 Input: r=2 while(r=2,r*2;print(r*2)) Output: ? 2 ? 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 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4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 2330 Killed /usr/bin/gp -q -emacs Timing: real 0m21.354s user 0m8.494s sys 0m12.506s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:13:20 2005 Input: r=2 while(r>1,r*2;print(r*2)) Output: ? 2 ? 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 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4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 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4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 2345 Killed /usr/bin/gp -q -emacs Timing: real 0m22.248s user 0m8.987s sys 0m12.013s '151.204' ************** PARI ***************** Host 151.204.250.33 (151.204.250.33) Time: Sat Mar 19 22:14:14 2005 Input: Mod(2,1278)^(-1) Output: ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(2, 1278). Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:14:15 2005 Input: r=2 while(r>1,r*2);print(r*2) Output: ? 2 ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 2358 Killed /usr/bin/gp -q -emacs Timing: real 0m21.022s user 0m20.988s sys 0m0.011s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:15:56 2005 Input: r=2 for(m=1,10,2,print(r*m)) Output: ? 2 ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: for(m=1,10,2,print(r*m)) ^------------ Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:16:12 2005 Input: r=2; for(m=1,10,2,print(r*m)) Output: ? ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: for(m=1,10,2,print(r*m)) ^------------ Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:16:33 2005 Input: r=2; for(m=1,10,[2],print(r*m)) Output: ? ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: for(m=1,10,[2],print(r*m)) ^------------ Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:16:49 2005 Input: for(m=1,10,[2],print(r*m)) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: for(m=1,10,[2],print(r*m)) ^------------ Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:16:58 2005 Input: for(m=1,10,[2],print(2*m)) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: for(m=1,10,[2],print(2*m)) ^------------ Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:17:10 2005 Input: forstep(m=1,10,[2],print(2*m)) Output: ? 2 6 10 14 18 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:19:45 2005 Input: forstep(m=1,10,[2],if(2*m>7,print(2*m-7),print(2*m))) Output: ? 2 6 3 7 11 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:21:55 2005 Input: forstep(m=2,10,[2],if(2*m>7,print(2*m-7),print(2*m))) Output: ? 4 1 5 9 13 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:22:13 2005 Input: forstep(m=0,10,[2],if(2*m>7,print(2*m-7),print(2*m))) Output: ? 0 4 1 5 9 13 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:22:57 2005 Input: forstep(m=0,10,[2],if(2*m>5,print(2*m-5),print(2*m))) Output: ? 0 4 3 7 11 15 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:24:53 2005 Input: forstep(m=0,10,[2],if(2*m>9,print(2*m-9),print(2*m))) Output: ? 0 4 8 3 7 11 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:27:33 2005 Input: m=0; forstep(m=0,10,[2],if(2*m>9,print(2*m-9),print(2*m))) Output: ? ? 0 4 8 3 7 11 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:27:58 2005 Input: m=0; if(2*m>9,print(2*m-9),print(2*m))) Output: ? ? 0 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:28:29 2005 Input: m=0; if(2*m>9,print(2*m-9),print(2*m))) Output: ? ? 0 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:28:59 2005 Input: m=1; if(2*m>9,print(2*m-9),print(2*m))) Output: ? ? 2 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:29:53 2005 Input: m=1; if(2*m>9,print(2*m-9),m=2*m);print m)) Output: ? ? printm ? ? Errors (if any) and Timing Info: *** Warning: unused characters: )). Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:30:06 2005 Input: m=1; if(2*m>9,print(2*m-9),m=2*m);print (m))) Output: ? ? 2 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: )). Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:30:42 2005 Input: m=1; if(2*m>9,m=2*m-9),m=2*m);print (m))) Output: ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,m=2*m);print(m))). Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:30:51 2005 Input: m=1; if(2*m>9,m=2*m-9,m=2*m);print (m))) Output: ? ? 2 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: )). Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:31:57 2005 Input: m=1; if(2*m>9,m=2*m-9,m=2*m);print (m))); if(2*M>9,m=2*M-9,m-2*m);print (m))) Output: ? ? 2 ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ));. *** Warning: unused characters: )). *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:32:11 2005 Input: m=1; if(2*m>9,m=2*m-9,m=2*m);print (m))); if(2*m>9,m=2*m-9,m-2*m);print (m))) Output: ? ? 2 ? 2 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ));. *** Warning: unused characters: )). Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:32:27 2005 Input: m=1; if(2*m>9,m=2*m-9,m=2*m);print (m))); if(2*m>9,m=2*m-9,m=2*m);print (m))) Output: ? ? 2 ? 4 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ));. *** Warning: unused characters: )). Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '151.204' ************** PARI ***************** Host 151.204.250.33 (151.204.250.33) Time: Sat Mar 19 22:32:27 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:33:04 2005 Input: m=1; if(2*m>9,m=2*m-9,m=2*m);print (m))); if(2*m>9,m=2*m-9,m=2*m);print (m))); if(2*m>9,m=2*m-9,m=2*m);print (m))); Output: ? ? 2 ? 4 ? 8 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ));. *** Warning: unused characters: ));. *** Warning: unused characters: ));. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:33:32 2005 Input: m=1; if(2*m>9,m=2*m-9,m=2*m);print (m))); if(2*m>9,m=2*m-9,m=2*m);print (m))); if(2*m>9,m=2*m-9,m=2*m);print (m))); if(2*m>9,m=2*m-9,m=2*m);print (m))); if(2*m>9,m=2*m-9,m=2*m);print (m))); if(2*m>9,m=2*m-9,m=2*m);print (m))); Output: ? ? 2 ? 4 ? 8 ? 7 ? 5 ? 1 ? Errors (if any) and Timing Info: *** Warning: unused characters: ));. *** Warning: unused characters: ));. *** Warning: unused characters: ));. *** Warning: unused characters: ));. *** Warning: unused characters: ));. *** Warning: unused characters: ));. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:36:00 2005 Input: while(m>1, if(2*m>9,m=2*m-9,m=2*m);print (m)))) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: while(m>1, ^ *** Warning: unused characters: ))). *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '151.204' ************** PARI ***************** Host 151.204.250.33 (151.204.250.33) Time: Sat Mar 19 22:36:03 2005 Input: Mod(1789,6912)^(-1) Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:36:17 2005 Input: while(m>1,if(2*m>9,m=2*m-9,m=2*m);print (m)))) Output: ? ? Errors (if any) and Timing Info: *** Warning: unused characters: )). *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:36:32 2005 Input: while(m>1,if(2*m>9,m=2*m-9,m=2*m);print (m)) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:36:55 2005 Input: m=2; while(m>1,if(2*m>9,m=2*m-9,m=2*m);print (m)) Output: ? ? 4 8 7 5 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:37:42 2005 Input: m=2;print(m); while(m>1,if(2*m>9,m=2*m-9,m=2*m);print (m)) Output: ? 2 ? 4 8 7 5 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '151.204' ************** PARI ***************** Host 151.204.250.33 (151.204.250.33) Time: Sat Mar 19 22:38:31 2005 Input: Mod(5192,7081)^85 Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:39:13 2005 Input: m=2;r=1;print(m); while(m>1,if(2*m>9,m=2*m-9,m=2*m);r=r+1;print (m)) Output: ? 2 ? 4 8 7 5 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:39:37 2005 Input: m=2;r=1;print(m); while(m>1,if(2*m>9,m=2*m-9,m=2*m);r=r+1;print (m),(r)) Output: ? 2 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...m-9,m=2*m);r=r+1;print(m),(r)) ^----- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:39:53 2005 Input: m=2;r=1;print(m); while(m>1,if(2*m>9,m=2*m-9,m=2*m);r=r+1;print (m,r)) Output: ? 2 ? 42 83 74 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:40:20 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,m=2*m-9,m=2*m);r=r+1;print (m,r)) Output: ? 21 ? 42 83 74 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:42:00 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>7,m=2*m-7,m=2*m);r=r+1;print (m,r)) Output: ? 21 ? 42 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.214 (165.95.7.214) Time: Sat Mar 19 22:42:33 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>5,m=2*m-5,m=2*m);r=r+1;print (m,r)) Output: ? 21 ? 42 33 14 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '151.204' ************** PARI ***************** Host 151.204.250.33 (151.204.250.33) Time: Sat Mar 19 22:51:10 2005 Input: Mod(2604,7081)^85 Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '151.204' ************** PARI ***************** Host 151.204.250.33 (151.204.250.33) Time: Sat Mar 19 22:52:04 2005 Input: Mod(4222,7081)^85 Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sat Mar 19 23:40:52 2005 Input: galois(x^3+1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: galois(x^3+1) ^------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: galois(x) ===> polgalois(x) polgalois(x): Galois group of the polynomial x (see manual for group coding). Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sat Mar 19 23:41:24 2005 Input: polgalois(x^3+1) Output: ? ? Errors (if any) and Timing Info: *** sorry, galois of reducible polynomial is not yet implemented. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sat Mar 19 23:41:41 2005 Input: polgalois(x^3+x+1) Output: ? [6, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.003s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sat Mar 19 23:43:00 2005 Input: polgalois(x) Output: ? [1, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sat Mar 19 23:43:24 2005 Input: polgalois(x^2+x+1) Output: ? [2, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sat Mar 19 23:43:53 2005 Input: polgalois(x^3+x^2-2*x-1) Output: ? [3, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sat Mar 19 23:44:09 2005 Input: polgalois(x^3+2) Output: ? [6, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sat Mar 19 23:45:22 2005 Input: polgalois(x^4+x^3+x^2+x+1) Output: ? [4, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.008s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sat Mar 19 23:45:45 2005 Input: polgalois(x^4+1) Output: ? [4, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.016s sys 0m0.005s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sat Mar 19 23:50:35 2005 Input: polgalois(x^5+20*x+32) Output: ? [10, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.012s sys 0m0.006s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sat Mar 19 23:51:23 2005 Input: polgalois(x^5+2) Output: ? [20, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.012s sys 0m0.004s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sat Mar 19 23:52:34 2005 Input: polgalois(x^5-5*x+12) Output: ? [10, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.017s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:03:12 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,m=2*m-9,m=2*m);r=r+1;print(m,r)) Output: ? 21 ? 42 83 74 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:04:10 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,until(2*m<9,m=m-9,m=2*m);r=r+1;print(m,r)) Output: ? 21 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...f(2*m>9,until(2*m<9,m=m-9 *** ,m=2*m);r=r+1;print( ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:04:21 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,until(2*m<9,m=m-9),m=2*m);r=r+1;print(m,r)) Output: ? 21 ? 42 83 -14 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:24:28 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,until(m<9,m=m-9),m=2*m);r=r+1;print(m,r)) Output: ? 21 ? 42 83 -14 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:27:19 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,until(2*m<9,m=m-9),m=2*m);r=r+1;print(m,r)) Output: ? 21 ? 42 83 -14 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:27:56 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,while(2*m<9,m=m-9),m=2*m);r=r+1;print(m,r)) Output: ? 21 ? 42 83 84 85 86 87 88 89 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 8100 8101 8102 8103 8104 8105 8106 8107 8108 8109 8110 8111 8112 8113 8114 8115 8116 8117 8118 8119 8120 8121 8122 8123 8124 8125 8126 8127 8128 8129 8130 8131 8132 8133 8134 8135 8136 8137 8138 8139 8140 8141 8142 8143 8144 8145 8146 8147 8148 8149 8150 8151 8152 8153 8154 8155 8156 8157 8158 8159 8160 8161 8162 8163 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81800 81801 81802 81803 81804 81805 81806 81807 81808 81809 81810 81811 81812 81813 81814 81815 81816 81817 81818 81819 81820 81821 81822 81823 81824 81825 81826 81827 81828 81829 81830 81831 81832 81833 81834 81835 81836 81837 81838 81839 81840 81841 81842 81843 81844 81845 81846 81847 81848 81849 81850 818 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 4128 Killed /usr/bin/gp -q -emacs Timing: real 0m21.197s user 0m13.831s sys 0m7.169s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:28:17 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,until(2*m<9,m=m-9),m=2*m);r=r+1;print(m,r)) Output: ? 21 ? 42 83 -14 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:28:35 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,until(2*m<9,m=2*m-9),m=2*m);r=r+1;print(m,r)) Output: ? 21 ? 42 83 14 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:29:42 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,until(2*m<9,m=2*m-9;r=r+1),m=2*m);r=r+1;print(m,r)) Output: ? 21 ? 42 83 17 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:30:09 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,until(2*m<9,m=2*m-9),m=2*m);r=r+1;print(m,r)) Output: ? 21 ? 42 83 14 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:30:39 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,until(2*m<9,m=2*m-9;r=r+1),m=2*m);r=r+1;print(m,r)) Output: ? 21 ? 42 83 17 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.001s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:31:28 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,while(2*m<9,m=2*m-9;r=r+1),m=2*m);r=r+1;print(m,r)) Output: ? 21 ? 42 83 84 85 86 87 88 89 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 8100 8101 8102 8103 8104 8105 8106 8107 8108 8109 8110 8111 8112 8113 8114 8115 8116 8117 8118 8119 8120 8121 8122 8123 8124 8125 8126 8127 8128 8129 8130 8131 8132 8133 8134 8135 8136 8137 8138 8139 8140 8141 8142 8143 8144 8145 8146 8147 8148 8149 8150 8151 8152 8153 8154 8155 8156 8157 8158 8159 8160 8161 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Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 4196 Killed /usr/bin/gp -q -emacs Timing: real 0m21.025s user 0m14.002s sys 0m6.998s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:32:08 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,while(2*m<9,m=2*m-9),m=2*m);r=r+1;print(m,r)) Output: ? 21 ? 42 83 84 85 86 87 88 89 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 8100 8101 8102 8103 8104 8105 8106 8107 8108 8109 8110 8111 8112 8113 8114 8115 8116 8117 8118 8119 8120 8121 8122 8123 8124 8125 8126 8127 8128 8129 8130 8131 8132 8133 8134 8135 8136 8137 8138 8139 8140 8141 8142 8143 8144 8145 8146 8147 8148 8149 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81623 81624 81625 81626 81627 81628 81629 81630 81631 81632 81633 81634 81635 81636 81637 81638 81639 81640 81641 81642 81643 81644 81645 81646 81647 81648 81649 81650 81651 81652 81653 81654 81655 81656 81657 81658 81659 81660 81661 81662 81663 81664 81665 81666 81667 81668 81669 81670 81671 81672 81673 81674 81675 81676 81677 81678 81679 81680 81681 81682 81683 81684 81685 81686 81687 81688 81689 81690 81691 81692 81693 81694 81695 81696 81697 81698 81699 81700 81701 81702 81703 81704 81705 81706 81707 81708 81709 81710 81711 81712 81713 81714 81715 81716 81717 81718 81719 81720 81721 81722 81723 81724 81725 81726 81727 81728 81729 81730 81731 81732 81733 81734 81735 81736 81737 81738 81739 81740 81741 81742 81743 81744 81745 81746 81747 81748 81749 81750 81751 81752 81753 81754 81755 81756 81757 81758 81759 81760 81761 81762 81763 81764 81765 81766 81767 81768 81769 81770 81771 81772 81773 81774 81775 81776 81777 81778 81779 81780 81781 81782 81783 81784 81785 81786 81787 81788 81789 81790 81791 81792 81793 81794 81795 81796 81797 81798 81799 81800 81801 81802 81803 81804 81805 81806 81807 81808 81809 81810 81811 81812 81813 81814 81815 81816 81817 81818 81819 81820 81821 81822 81823 81824 81825 81826 81827 81828 81829 81830 81831 81832 81833 81834 81835 81836 81837 81838 81839 81840 81841 81842 81843 81844 81845 81846 81847 81848 81849 81850 818 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 4205 Killed /usr/bin/gp -q -emacs Timing: real 0m21.051s user 0m13.373s sys 0m7.627s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:32:53 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,until(2*m<9,m=2*m-9),m=2*m);r=r+1;print(m,r)) Output: ? 21 ? 42 83 14 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:35:33 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,until(2*m<9,m=2*m-9,r=r+1),m=2*m);r=r+1;print(m,r)) Output: ? 21 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...2*m>9,until(2*m<9,m=2*m-9 *** ,r=r+1),m=2*m);r=r+1 ^-------------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:35:44 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,until(2*m<9,m=2*m-9;r=r+1),m=2*m);r=r+1;print(m,r)) Output: ? 21 ? 42 83 17 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:36:11 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,until(2*m<9,m=2*m-9;r=r+1),m=2*m;r=r+1);print(m,r)) Output: ? 21 ? 42 83 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:37:02 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,until(2*m<9,m=2*m-9;r=r+1;print(m,r)),m=2*m;r=r+1);print(m,r)) Output: ? 21 ? 42 83 74 55 16 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:37:34 2005 Input: m=2;r=1;print(m,r); while(m>1,if(2*m>9,until(2*m<9,m=2*m-9;r=r+1;print(m,r)),m=2*m;r=r+1;print(m,r))) Output: ? 21 ? 42 83 74 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:38:36 2005 Input: m=2;r=1;n=9;print(m,r); while(m>1,if(2*m>n,until(2*m1,if(2*m>n,until(2*m1,if(2*m>n,until(2*m1,if(3*m>n,until(3*m1,if(3*m>n,until(divrem(m,n)[1],m=3*m-n;r=r+1;print(m,r)),m=3*m;r=r+1;print(m,r))) Output: ? 31 ? 92 143 294 745 2096 6147 18298 54749 1640910 4921411 14762912 44287413 132860914 398581415 1195742916 3587227417 10761680918 32285041419 96855122920 290565367421 871696100922 2615088301423 7845264902924 23535794707425 70607384120926 211822152361427 635466457082928 1906399371247429 5719198113740930 17157594341221431 51472783023662932 154418349070987433 463255047212960934 1389765141638881435 4169295424916642936 12507886274749927437 37523658824249780938 112570976472749341439 337712929418248022940 1013138788254744067441 3039416364764232200942 9118249094292696601443 27354747282878089802944 82064241848634269407445 246192725545902808220946 738578176637708424661447 2215734529913125273982948 6647203589739375821947449 19941610769218127465840950 59824832307654382397521451 179474496922963147192562952 538423490768889441577687453 1615270472306668324733060954 4845811416920004974199181455 14537434250760014922597542956 43612302752280044767792627457 130836908256840134303377880958 392510724770520402910133641459 1177532174311561208730400922960 3532596522934683626191202767461 10597789568804050878573608300962 31793368706412152635720824901463 95380106119236457907162474702964 286140318357709373721487424107465 858420955073128121164462272320966 2575262865219384363493386816961467 7725788595658153090480160450882968 23177365786974459271440481352647469 69532097360923377814321444057940970 208596292082770133442964332173821471 625788876248310400328892996521462972 1877366628744931200986678989564387473 5632099886234793602960036968693160974 16896299658704380808880110906079481475 50688898976113142426640332718238442976 152066696928339427279920998154715327477 456200090785018281839762994464145980978 1368600272355054845519288983392437941479 4105800817065164536557866950177313822980 12317402451195493609673600850531941467481 36952207353586480829020802551595824400982 110856622060759442487062407654787473201483 332569866182278327461187222964362419602984 997709598546834982383561668893087258807485 2993128795640504947150685006679261776420986 8979386386921514841452055020037785329261487 26938159160764544524356165060113355987782988 80814477482293633573068495180340067963347489 242443432446880900719205485541020203890040990 727330297340642702157616456623060611670121491 2181990892021928106472849369869181835010362992 6545972676065784319418548109607545505031087493 19637918028197352958255644328822636515093260994 58913754084592058874766932986467909545279781495 176741262253776176624300798959403728635839342996 530223786761328529872902396878211185907518027497 1590671360283985589618707190634633557722554080998 4772014080851956768856121571903900673167662241499 143160422425558703065683647157117020195029867229100 429481267276676109197050941471351060585089601674101 1288443801830028327591152824414053181755268805009102 3865331405490084982773458473242159545265806415014103 11595994216470254948320375419726478635797419245029104 34787982649410764844961126259179435907392257735074105 104363947948232294534883378777538307722176773205209106 313091843844696883604650136332614923166530319615614107 939275531534090650813950408997844769499590958846829108 2817826594602271952441851226993534308498772876540474109 8453479783806815857325553680980602925496318629621409110 25360439351420447571976661042941808776488955888864214111 76081318054261342715929983128825426329466867666592629112 228243954162784028147789949386476278988400602999777874113 684731862488352084443369848159428836965201808999333609114 2054195587465056253330109544478286510895605426998000814115 6162586762395168759990328633434859532686816280994002429116 18487760287185506279970985900304578598060448842982007274117 55463280861556518839912957700913735794181346528946021809118 166389842584669556519738873102741207382544039586838065414119 499169527754008669559216619308223622147632118760514196229120 1497508583262026008677649857924670866442896356281542588674121 4492525749786078026032949573774012599328689068844627766009122 13477577249358234078098848721322037797986067206533883298014123 40432731748074702234296546163966113393958201619601649894029124 121298195244224106702889638491898340181874604858804949682074125 363894585732672320108668915475695020545623814576414849046209126 1091683757198016960326006746427085061636871443729244547138614127 3275051271594050880978020239281255184910614331187733641415829128 9825153814782152642934060717843765554731842993563200924247474129 29475461444346457928802182153531296664195528980689602772742409130 88426384333039373786406546460593889992586586942068808318227214131 265279152999118121359219639381781669977759760826206424954681629132 795837458997354364077658918145345009933279282478619274864044874133 2387512376992063092232976754436035029799837847435857824592134609134 7162537130976189276698930263308105089399513542307573473776403814135 21487611392928567830096790789924315268198540626922720421329211429136 64462834178785703490290372369772945804595621880768161263987634274137 193388502536357110470871117109318837413786865642304483791962902809138 580165507609071331412613351327956512241360596926913451375888708414139 1740496522827213994237840053983869536724081790780740354127666125229140 5221489568481641982713520161951608610172245372342221062382998375674141 15664468705444925948140560485854825830516736117026663187148995127009142 46993406116334777844421681457564477491550208351079989561446985381014143 140980218349004333533265044372693432474650625053239968684340956143029144 422940655047013000599795133118080297423951875159719906053022868429074145 1268821965141039001799385399354240892271855625479159718159068605287209146 3806465895423117005398156198062722676815566876437479154477205815861614147 11419397686269351016194468594188168030446700629312437463431617447584829148 34258193058808053048583405782564504091340101887937312390294852342754474149 102774579176424159145750217347693512274020305663811937170884557028263409150 308323737529272477437250652043080536822060916991435811512653671084790214151 924971212587817432311751956129241610466182750974307434537961013254370629152 2774913637763452296935255868387724831398548252922922303613883039763111874153 8324740913290356890805767605163174494195644758768766910841649119289335609154 24974222739871070672417302815489523482586934276306300732524947357868006814155 74922668219613212017251908446468570447760802828918902197574842073604020429156 224768004658839636051755725339405711343282408486756706592724526220812061274157 674304013976518908155267176018217134029847225460270119778173578662436183809158 2022912041929556724465801528054651402089541676380810359334520735987308551414159 6068736125788670173397404584163954206268625029142431078003562207961925654229160 18206208377366010520192213752491862618805875087427293234010686623885776962674161 54618625132098031560576641257475587856417625262281879702032059871657330888009162 163855875396294094681729923772426763569252875786845639106096179614971992664014163 491567626188882284045189771317280290707758627360536917318288538844915977992029164 1474702878566646852135569313951840872123275882081610751954865616534747933976074165 4424108635699940556406707941855522616369827646244832255864596849604243801928209166 13272325907099821669220123825566567849109482938734496767593790548812731405784614167 39816977721299465007660371476699703547328448816203490302781371646438194217353829168 119450933163898395022981114430099110641985346448610470908344114939314582652061474169 358352799491695185068943343290297331925956039345831412725032344817943747956184409170 1075058398475085555206830029870891995777868118037494238175097034453831243868553214171 3225175195425256665620490089612675987333604354112482714525291103361493731605659629172 9675525586275769996861470268838027962000813062337448143575873310084481194816978874173 29026576758827309990584410806514083886002439187012344430727619930253443584450936609174 87079730276481929971753232419542251658007317561037033292182859790760330753352809814175 261239190829445789915259697258626754974021952683111099876548579372280992260058429429176 783717572488337369745779091775880264922065858049333299629645738116842976780175288274177 2351152717465012109237337275327640794766197574147999898888937214350528930340525864809178 7053458152395036327712011825982922384298592722443999696666811643051586791021577594414179 21160374457185108983136035477948767152895778167331999090000434929154760373064732783229180 63481123371555326949408106433846301458687334501995997270001304787464281119194198349674181 190443370114665980848224319301538904376062003505987991810003914362392843357582595049009182 571330110343997942544672957904616713128186010517963975430011743087178530072747785147014183 1713990331031993827634018873713850139384558031553891926290035229261535590218243355441029184 5141970993095981482902056621141550418153674094661675778870105687784606770654730066323074185 15425912979287944448706169863424651254461022283985027336610317063353820311964190198969209186 46277738937863833346118509590273953763383066851955082009830951190061460935892570596907614187 138833216813591500038355528770821861290149200555865246029492853570184382807677711790722829188 416499650440774500115066586312465583870447601667595738088478560710553148423033135372168474189 1249498951322323500345199758937396751611342805002787214265435682131659445269099406116505409190 3748496853966970501035599276812190254834028415008361642796307046394978335807298218349516214191 11245490561900911503106797830436570764502085245025084928388921139184935007421894655048548629192 33736471685702734509320393491309712293506255735075254785166763417554805022265683965145645874193 101209415057108203527961180473929136880518767205225764355500290252664415066797051895436937609194 303628245171324610583883541421787410641556301615677293066500870757993245200391155686310812814195 910884735513973831751650624265362231924668904847031879199502612273979735601173467058932438429196 2732654206541921495254951872796086695774006714541095637598507836821939206803520401176797315274197 81979626196257644857 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 4430 Killed /usr/bin/gp -q -emacs Timing: real 0m21.036s user 0m20.944s sys 0m0.055s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:52:44 2005 Input: m=3;r=1;n=13;print(m,r); while(m>1,if(3*m>n,until(divrem(m,n)[1]=0,m=3*m-n;r=r+1;print(m,r)),m=3*m;r=r+1;print(m,r))) Output: ? 31 ? ? Errors (if any) and Timing Info: *** unexpected character: ...*m>n,until(divrem(m,n)[1]=0,m=3*m-n;r=r+1;pri ^-------------------- Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 01:54:57 2005 Input: m=3;r=1;n=13;print(m,r); while(m>1,if(3*m>n,until(3*m1,if(3*m>n,while(3*m1,if(3*m>n,until(3*m1,if(3*m>n,until(m1,if(3*m>n,until(3*m<2*n,m=3*m-n;r=r+1;print(m,r)),m=3*m;r=r+1;print(m,r))) Output: ? 31 ? 92 143 294 745 2096 6147 18298 54749 1640910 4921411 14762912 44287413 132860914 398581415 1195742916 3587227417 10761680918 32285041419 96855122920 290565367421 871696100922 2615088301423 7845264902924 23535794707425 70607384120926 211822152361427 635466457082928 1906399371247429 5719198113740930 17157594341221431 51472783023662932 154418349070987433 463255047212960934 1389765141638881435 4169295424916642936 12507886274749927437 37523658824249780938 112570976472749341439 337712929418248022940 1013138788254744067441 3039416364764232200942 9118249094292696601443 27354747282878089802944 82064241848634269407445 246192725545902808220946 738578176637708424661447 2215734529913125273982948 6647203589739375821947449 19941610769218127465840950 59824832307654382397521451 179474496922963147192562952 538423490768889441577687453 1615270472306668324733060954 4845811416920004974199181455 14537434250760014922597542956 43612302752280044767792627457 130836908256840134303377880958 392510724770520402910133641459 1177532174311561208730400922960 3532596522934683626191202767461 10597789568804050878573608300962 31793368706412152635720824901463 95380106119236457907162474702964 286140318357709373721487424107465 858420955073128121164462272320966 2575262865219384363493386816961467 7725788595658153090480160450882968 23177365786974459271440481352647469 69532097360923377814321444057940970 208596292082770133442964332173821471 625788876248310400328892996521462972 1877366628744931200986678989564387473 5632099886234793602960036968693160974 16896299658704380808880110906079481475 50688898976113142426640332718238442976 152066696928339427279920998154715327477 456200090785018281839762994464145980978 1368600272355054845519288983392437941479 4105800817065164536557866950177313822980 12317402451195493609673600850531941467481 36952207353586480829020802551595824400982 110856622060759442487062407654787473201483 332569866182278327461187222964362419602984 997709598546834982383561668893087258807485 2993128795640504947150685006679261776420986 8979386386921514841452055020037785329261487 26938159160764544524356165060113355987782988 80814477482293633573068495180340067963347489 242443432446880900719205485541020203890040990 727330297340642702157616456623060611670121491 2181990892021928106472849369869181835010362992 6545972676065784319418548109607545505031087493 19637918028197352958255644328822636515093260994 58913754084592058874766932986467909545279781495 176741262253776176624300798959403728635839342996 530223786761328529872902396878211185907518027497 1590671360283985589618707190634633557722554080998 4772014080851956768856121571903900673167662241499 143160422425558703065683647157117020195029867229100 429481267276676109197050941471351060585089601674101 1288443801830028327591152824414053181755268805009102 3865331405490084982773458473242159545265806415014103 11595994216470254948320375419726478635797419245029104 34787982649410764844961126259179435907392257735074105 104363947948232294534883378777538307722176773205209106 313091843844696883604650136332614923166530319615614107 939275531534090650813950408997844769499590958846829108 2817826594602271952441851226993534308498772876540474109 8453479783806815857325553680980602925496318629621409110 25360439351420447571976661042941808776488955888864214111 76081318054261342715929983128825426329466867666592629112 228243954162784028147789949386476278988400602999777874113 684731862488352084443369848159428836965201808999333609114 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422940655047013000599795133118080297423951875159719906053022868429074145 1268821965141039001799385399354240892271855625479159718159068605287209146 3806465895423117005398156198062722676815566876437479154477205815861614147 11419397686269351016194468594188168030446700629312437463431617447584829148 34258193058808053048583405782564504091340101887937312390294852342754474149 102774579176424159145750217347693512274020305663811937170884557028263409150 308323737529272477437250652043080536822060916991435811512653671084790214151 924971212587817432311751956129241610466182750974307434537961013254370629152 2774913637763452296935255868387724831398548252922922303613883039763111874153 8324740913290356890805767605163174494195644758768766910841649119289335609154 24974222739871070672417302815489523482586934276306300732524947357868006814155 74922668219613212017251908446468570447760802828918902197574842073604020429156 224768004658839636051755725339405711343282408486756706592724526220812061274157 674304013976518908155267176018217134029847225460270119778173578662436183809158 2022912041929556724465801528054651402089541676380810359334520735987308551414159 6068736125788670173397404584163954206268625029142431078003562207961925654229160 18206208377366010520192213752491862618805875087427293234010686623885776962674161 54618625132098031560576641257475587856417625262281879702032059871657330888009162 163855875396294094681729923772426763569252875786845639106096179614971992664014163 491567626188882284045189771317280290707758627360536917318288538844915977992029164 1474702878566646852135569313951840872123275882081610751954865616534747933976074165 4424108635699940556406707941855522616369827646244832255864596849604243801928209166 13272325907099821669220123825566567849109482938734496767593790548812731405784614167 39816977721299465007660371476699703547328448816203490302781371646438194217353829168 119450933163898395022981114430099110641985346448610470908344114939314582652061474169 358352799491695185068943343290297331925956039345831412725032344817943747956184409170 1075058398475085555206830029870891995777868118037494238175097034453831243868553214171 3225175195425256665620490089612675987333604354112482714525291103361493731605659629172 9675525586275769996861470268838027962000813062337448143575873310084481194816978874173 29026576758827309990584410806514083886002439187012344430727619930253443584450936609174 87079730276481929971753232419542251658007317561037033292182859790760330753352809814175 261239190829445789915259697258626754974021952683111099876548579372280992260058429429176 783717572488337369745779091775880264922065858049333299629645738116842976780175288274177 2351152717465012109237337275327640794766197574147999898888937214350528930340525864809178 7053458152395036327712011825982922384298592722443999696666811643051586791021577594414179 21160374457185108983136035477948767152895778167331999090000434929154760373064732783229180 63481123371555326949408106433846301458687334501995997270001304787464281119194198349674181 190443370114665980848224319301538904376062003505987991810003914362392843357582595049009182 571330110343997942544672957904616713128186010517963975430011743087178530072747785147014183 1713990331031993827634018873713850139384558031553891926290035229261535590218243355441029184 5141970993095981482902056621141550418153674094661675778870105687784606770654730066323074185 15425912979287944448706169863424651254461022283985027336610317063353820311964190198969209186 46277738937863833346118509590273953763383066851955082009830951190061460935892570596907614187 138833216813591500038355528770821861290149200555865246029492853570184382807677711790722829188 416499650440774500115066586312465583870447601667595738088478560710553148423033135372168474189 1249498951322323500345199758937396751611342805002787214265435682131659445269099406116505409190 3748496853966970501035599276812190254834028415008361642796307046394978335807298218349516214191 11245490561900911503106797830436570764502085245025084928388921139184935007421894655048548629192 33736471685702734509320393491309712293506255735075254785166763417554805022265683965145645874193 101209415057108203527961180473929136880518767205225764355500290252664415066797051895436937609194 303628245171324610583883541421787410641556301615677293066500870757993245200391155686310812814195 910884735513973831751650624265362231924668904847031879199502612273979735601173467058932438429196 2732654206541921495254951872796086695774006714541095637598507836821939206803520401176797315274197 81979626196257644857 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 4589 Killed /usr/bin/gp -q -emacs Timing: real 0m21.054s user 0m20.946s sys 0m0.055s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:03:06 2005 Input: m=3;r=1;n=13;print(m,r); while(m>1,if(3*m>n,until(m1,if(3*m>n,while(m>n,m=3*m-n;r=r+1;print(m,r)),m=3*m;r=r+1;print(m,r))) Output: ? 31 ? 92 Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 4651 Killed /usr/bin/gp -q -emacs Timing: real 0m21.016s user 0m20.991s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:08:41 2005 Input: m=3;r=1;n=13;print(m,r); while(m>1,if(3*m>n,while(3*m>n,m=3*m-n;r=r+1;print(m,r)),m=3*m;r=r+1;print(m,r))) Output: ? 31 ? 92 143 294 745 2096 6147 18298 54749 1640910 4921411 14762912 44287413 132860914 398581415 1195742916 3587227417 10761680918 32285041419 96855122920 290565367421 871696100922 2615088301423 7845264902924 23535794707425 70607384120926 211822152361427 635466457082928 1906399371247429 5719198113740930 17157594341221431 51472783023662932 154418349070987433 463255047212960934 1389765141638881435 4169295424916642936 12507886274749927437 37523658824249780938 112570976472749341439 337712929418248022940 1013138788254744067441 3039416364764232200942 9118249094292696601443 27354747282878089802944 82064241848634269407445 246192725545902808220946 738578176637708424661447 2215734529913125273982948 6647203589739375821947449 19941610769218127465840950 59824832307654382397521451 179474496922963147192562952 538423490768889441577687453 1615270472306668324733060954 4845811416920004974199181455 14537434250760014922597542956 43612302752280044767792627457 130836908256840134303377880958 392510724770520402910133641459 1177532174311561208730400922960 3532596522934683626191202767461 10597789568804050878573608300962 31793368706412152635720824901463 95380106119236457907162474702964 286140318357709373721487424107465 858420955073128121164462272320966 2575262865219384363493386816961467 7725788595658153090480160450882968 23177365786974459271440481352647469 69532097360923377814321444057940970 208596292082770133442964332173821471 625788876248310400328892996521462972 1877366628744931200986678989564387473 5632099886234793602960036968693160974 16896299658704380808880110906079481475 50688898976113142426640332718238442976 152066696928339427279920998154715327477 456200090785018281839762994464145980978 1368600272355054845519288983392437941479 4105800817065164536557866950177313822980 12317402451195493609673600850531941467481 36952207353586480829020802551595824400982 110856622060759442487062407654787473201483 332569866182278327461187222964362419602984 997709598546834982383561668893087258807485 2993128795640504947150685006679261776420986 8979386386921514841452055020037785329261487 26938159160764544524356165060113355987782988 80814477482293633573068495180340067963347489 242443432446880900719205485541020203890040990 727330297340642702157616456623060611670121491 2181990892021928106472849369869181835010362992 6545972676065784319418548109607545505031087493 19637918028197352958255644328822636515093260994 58913754084592058874766932986467909545279781495 176741262253776176624300798959403728635839342996 530223786761328529872902396878211185907518027497 1590671360283985589618707190634633557722554080998 4772014080851956768856121571903900673167662241499 143160422425558703065683647157117020195029867229100 429481267276676109197050941471351060585089601674101 1288443801830028327591152824414053181755268805009102 3865331405490084982773458473242159545265806415014103 11595994216470254948320375419726478635797419245029104 34787982649410764844961126259179435907392257735074105 104363947948232294534883378777538307722176773205209106 313091843844696883604650136332614923166530319615614107 939275531534090650813950408997844769499590958846829108 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580165507609071331412613351327956512241360596926913451375888708414139 1740496522827213994237840053983869536724081790780740354127666125229140 5221489568481641982713520161951608610172245372342221062382998375674141 15664468705444925948140560485854825830516736117026663187148995127009142 46993406116334777844421681457564477491550208351079989561446985381014143 140980218349004333533265044372693432474650625053239968684340956143029144 422940655047013000599795133118080297423951875159719906053022868429074145 1268821965141039001799385399354240892271855625479159718159068605287209146 3806465895423117005398156198062722676815566876437479154477205815861614147 11419397686269351016194468594188168030446700629312437463431617447584829148 34258193058808053048583405782564504091340101887937312390294852342754474149 102774579176424159145750217347693512274020305663811937170884557028263409150 308323737529272477437250652043080536822060916991435811512653671084790214151 924971212587817432311751956129241610466182750974307434537961013254370629152 2774913637763452296935255868387724831398548252922922303613883039763111874153 8324740913290356890805767605163174494195644758768766910841649119289335609154 24974222739871070672417302815489523482586934276306300732524947357868006814155 74922668219613212017251908446468570447760802828918902197574842073604020429156 224768004658839636051755725339405711343282408486756706592724526220812061274157 674304013976518908155267176018217134029847225460270119778173578662436183809158 2022912041929556724465801528054651402089541676380810359334520735987308551414159 6068736125788670173397404584163954206268625029142431078003562207961925654229160 18206208377366010520192213752491862618805875087427293234010686623885776962674161 54618625132098031560576641257475587856417625262281879702032059871657330888009162 163855875396294094681729923772426763569252875786845639106096179614971992664014163 491567626188882284045189771317280290707758627360536917318288538844915977992029164 1474702878566646852135569313951840872123275882081610751954865616534747933976074165 4424108635699940556406707941855522616369827646244832255864596849604243801928209166 13272325907099821669220123825566567849109482938734496767593790548812731405784614167 39816977721299465007660371476699703547328448816203490302781371646438194217353829168 119450933163898395022981114430099110641985346448610470908344114939314582652061474169 358352799491695185068943343290297331925956039345831412725032344817943747956184409170 1075058398475085555206830029870891995777868118037494238175097034453831243868553214171 3225175195425256665620490089612675987333604354112482714525291103361493731605659629172 9675525586275769996861470268838027962000813062337448143575873310084481194816978874173 29026576758827309990584410806514083886002439187012344430727619930253443584450936609174 87079730276481929971753232419542251658007317561037033292182859790760330753352809814175 261239190829445789915259697258626754974021952683111099876548579372280992260058429429176 783717572488337369745779091775880264922065858049333299629645738116842976780175288274177 2351152717465012109237337275327640794766197574147999898888937214350528930340525864809178 7053458152395036327712011825982922384298592722443999696666811643051586791021577594414179 21160374457185108983136035477948767152895778167331999090000434929154760373064732783229180 63481123371555326949408106433846301458687334501995997270001304787464281119194198349674181 190443370114665980848224319301538904376062003505987991810003914362392843357582595049009182 571330110343997942544672957904616713128186010517963975430011743087178530072747785147014183 1713990331031993827634018873713850139384558031553891926290035229261535590218243355441029184 5141970993095981482902056621141550418153674094661675778870105687784606770654730066323074185 15425912979287944448706169863424651254461022283985027336610317063353820311964190198969209186 46277738937863833346118509590273953763383066851955082009830951190061460935892570596907614187 138833216813591500038355528770821861290149200555865246029492853570184382807677711790722829188 416499650440774500115066586312465583870447601667595738088478560710553148423033135372168474189 1249498951322323500345199758937396751611342805002787214265435682131659445269099406116505409190 3748496853966970501035599276812190254834028415008361642796307046394978335807298218349516214191 11245490561900911503106797830436570764502085245025084928388921139184935007421894655048548629192 33736471685702734509320393491309712293506255735075254785166763417554805022265683965145645874193 101209415057108203527961180473929136880518767205225764355500290252664415066797051895436937609194 303628245171324610583883541421787410641556301615677293066500870757993245200391155686310812814195 910884735513973831751650624265362231924668904847031879199502612273979735601173467058932438429196 2732654206541921495254951872796086695774006714541095637598507836821939206803520401176797315274197 81979626196257644857 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 4665 Killed /usr/bin/gp -q -emacs Timing: real 0m21.068s user 0m20.944s sys 0m0.056s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:12:39 2005 Input: m=3;r=1;n=13;print(m,r); while(m>1,if(3*m1,if(3*m1,if(3*m1,if(3*m1,if(3*m1,if(3*m1,if(3*m1,if(3*m1,if(3*m1,if(3*m1,if(and(3*m1,if( *** and(3*m1,if(&(3*m1,if(&(3*m1,if(&&(3*m1,if(&&(3*m1,if(gand(3*m1,if( *** gand(3*m1,if(&(3*m1,if(&(3*m1,if(&&(3*m1,if(&&(3*m1,if(and(3*m1,if( *** and(3*m1,if(gand(3*m1,if( *** gand(3*m1,if(3*m1,if(3*mn,m=m-n))) Output: ? 31 ? 22 63 114 55 86 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:32:44 2005 Input: m=3;r=1;n=7;print(m,r); while(m>1,if(3*mn,m=m-n;print(m,r)))) Output: ? 31 ? 63 44 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:33:23 2005 Input: m=3;r=1;n=7;print(m,r); while(m>1,if(3*mn,m=m-n);print(m,r))) Output: ? 31 ? 22 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:33:55 2005 Input: m=3;r=1;n=13;print(m,r); while(m>1,if(3*mn,m=m-n);print(m,r))) Output: ? 31 ? 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:34:45 2005 Input: m=3;r=1;n=15;print(m,r); while(m>1,if(3*mn,m=m-n);print(m,r))) Output: ? 31 ? 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 3157 9158 12159 6160 3161 9162 12163 6164 3165 9166 12167 6168 3169 9170 12171 6172 3173 9174 12175 6176 3177 9178 12179 6180 3181 9182 12183 6184 3185 9186 12187 6188 3189 9190 12191 6192 3193 9194 12195 6196 3197 9198 12199 6200 3201 9202 12203 6204 3205 9206 12207 6208 3209 9210 12211 6212 3213 9214 12215 6216 3217 9218 12219 6220 3221 9222 12223 6224 3225 9226 12227 6228 3229 9230 12231 6232 3233 9234 12235 6236 3237 9238 12239 6240 3241 9242 12243 6244 3245 9246 12247 6248 3249 9250 12251 6252 3253 9254 12255 6256 3257 9258 12259 6260 3261 9262 12263 6264 3265 9266 12267 6268 3269 9270 12271 6272 3273 9274 12275 6276 3277 9278 12279 6280 3281 9282 12283 6284 3285 9286 12287 6288 3289 9290 12291 6292 3293 9294 12295 6296 3297 9298 12299 6300 3301 9302 12303 6304 3305 9306 12307 6308 3309 9310 12311 6312 3313 9314 12315 6316 3317 9318 12319 6320 3321 9322 12323 6324 3325 9326 12327 6328 3329 9330 12331 6332 3333 9334 12335 6336 3337 9338 12339 6340 3341 9342 12343 6344 3345 9346 12347 6348 3349 9350 12351 6352 3353 9354 12355 6356 3357 9358 12359 6360 3361 9362 12363 6364 3365 9366 12367 6368 3369 9370 12371 6372 3373 9374 12375 6376 3377 9378 12379 6380 3381 9382 12383 6384 3385 9386 12387 6388 3389 9390 12391 6392 3393 9394 12395 6396 3397 9398 12399 6400 3401 9402 12403 6404 3405 9406 12407 6408 3409 9410 12411 6412 3413 9414 12415 6416 3417 9418 12419 6420 3421 9422 12423 6424 3425 9426 12427 6428 3429 9430 12431 6432 3433 9434 12435 6436 3437 9438 12439 6440 3441 9442 12443 6444 3445 9446 12447 6448 3449 9450 12451 6452 3453 9454 12455 6456 3457 9458 12459 6460 3461 9462 12463 6464 3465 9466 12467 6468 3469 9470 12471 6472 3473 9474 12475 6476 3477 9478 12479 6480 3481 9482 12483 6484 3485 9486 12487 6488 3489 9490 12491 6492 3493 9494 12495 6496 3497 9498 12499 6500 3501 9502 12503 6504 3505 9506 12507 6508 3509 9510 12511 6512 3513 9514 12515 6516 3517 9518 12519 6520 3521 9522 12523 6524 3525 9526 12527 6528 3529 9530 12531 6532 3533 9534 12535 6536 3537 9538 12539 6540 3541 9542 12543 6544 3545 9546 12547 6548 3549 9550 12551 6552 3553 9554 12555 6556 3557 9558 12559 6560 3561 9562 12563 6564 3565 9566 12567 6568 3569 9570 12571 6572 3573 9574 12575 6576 3577 9578 12579 6580 3581 9582 12583 6584 3585 9586 12587 6588 3589 9590 12591 6592 3593 9594 12595 6596 3597 9598 12599 6600 3601 9602 12603 6604 3605 9606 12607 6608 3609 9610 12611 6612 3613 9614 12615 6616 3617 9618 12619 6620 3621 9622 12623 6624 3625 9626 12627 6628 3629 9630 12631 6632 3633 9634 12635 6636 3637 9638 12639 6640 3641 9642 12643 6644 3645 9646 12647 6648 3649 9650 12651 6652 3653 9654 12655 6656 3657 9658 12659 6660 3661 9662 12663 6664 3665 9666 12667 6668 3669 9670 12671 6672 3673 9674 12675 6676 3677 9678 12679 6680 3681 9682 12683 6684 3685 9686 12687 6688 3689 9690 12691 6692 3693 9694 12695 6696 3697 9698 12699 6700 3701 9702 12703 6704 3705 9706 12707 6708 3709 9710 12711 6712 3713 9714 12715 6716 3717 9718 12719 6720 3721 9722 12723 6724 3725 9726 12727 6728 3729 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31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 317 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 5146 Killed /usr/bin/gp -q -emacs Timing: real 0m21.012s user 0m15.117s sys 0m5.884s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:37:27 2005 Input: m=3;r=1;n=7;print(m,r); while(m>1,if(3*mn,m=m-n);print(m,r))) Output: ? 31 ? 22 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:37:52 2005 Input: m=3;r=1;n=9;print(m,r); while(m>1,if(3*mn,m=m-n);print(m,r))) Output: ? 31 ? 02 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:42:01 2005 Input: m=3;r=1;n=9;print(m,r); while(m>1,if(3*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:42:38 2005 Input: m=3;r=1;n=7;print(m,r); while(m>1,if(3*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 22 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:42:58 2005 Input: m=3;r=1;n=11;print(m,r); while(m>1,if(3*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 53 44 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:43:16 2005 Input: m=3;r=1;n=13;print(m,r); while(m>1,if(3*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:43:51 2005 Input: m=3;r=1;n=15;print(m,r); while(m>1,if(3*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 3157 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121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 317 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 5262 Killed /usr/bin/gp -q -emacs Timing: real 0m21.110s user 0m15.440s sys 0m5.559s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:50:12 2005 Input: m=3;r=1;n=15;print(m,r); while(m>1,while(m<>3,if(3*mn,m=m-n);if(m<>0,print(m,r))))) Output: ? 31 ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 5320 Killed /usr/bin/gp -q -emacs Timing: real 0m21.011s user 0m20.997s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:51:06 2005 Input: m=3;r=1;n=15;print(m,r); while(m>1,if(3*mn,m=m-n);if(m<>0,print(m,r))))) Output: ? 31 ? 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 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61560 31561 91562 121563 61564 31565 91566 121567 61568 31569 91570 121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 317 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** Warning: unused characters: ). /var/www/cgi-bin/calc/gp: line 4: 5332 Killed /usr/bin/gp -q -emacs Timing: real 0m21.230s user 0m15.639s sys 0m5.362s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:55:26 2005 Input: m=3;r=1;n=15;print(m,r); while(m>1,if(3*mn,m=m-n);if(m=0,,if(m<>3,print(m,r)))))) Output: ? 31 ? 92 03 ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:56:24 2005 Input: m=3;r=1;n=15;print(m,r); while(m>1,if(3*mn,m=m-n);if(m=0,,if(m<>3,print(m,r))))))) Output: ? 31 ? 92 03 ? Errors (if any) and Timing Info: *** Warning: unused characters: )). Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:56:36 2005 Input: m=3;r=1;n=15;print(m,r); while(m>1,if(3*mn,m=m-n);if(m=0,,if(m<>3,print(m,r))))) Output: ? 31 ? 92 03 ? Errors (if any) and Timing Info: Timing: real 0m0.043s user 0m0.004s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:57:49 2005 Input: m=3;r=1;n=15;print(m,r); while(m>1,if(3*mn,m=m-n);if(m<>0,print(m,r))))) Output: ? 31 ? 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 3157 9158 12159 6160 3161 9162 12163 6164 3165 9166 12167 6168 3169 9170 12171 6172 3173 9174 12175 6176 3177 9178 12179 6180 3181 9182 12183 6184 3185 9186 12187 6188 3189 9190 12191 6192 3193 9194 12195 6196 3197 9198 12199 6200 3201 9202 12203 6204 3205 9206 12207 6208 3209 9210 12211 6212 3213 9214 12215 6216 3217 9218 12219 6220 3221 9222 12223 6224 3225 9226 12227 6228 3229 9230 12231 6232 3233 9234 12235 6236 3237 9238 12239 6240 3241 9242 12243 6244 3245 9246 12247 6248 3249 9250 12251 6252 3253 9254 12255 6256 3257 9258 12259 6260 3261 9262 12263 6264 3265 9266 12267 6268 3269 9270 12271 6272 3273 9274 12275 6276 3277 9278 12279 6280 3281 9282 12283 6284 3285 9286 12287 6288 3289 9290 12291 6292 3293 9294 12295 6296 3297 9298 12299 6300 3301 9302 12303 6304 3305 9306 12307 6308 3309 9310 12311 6312 3313 9314 12315 6316 3317 9318 12319 6320 3321 9322 12323 6324 3325 9326 12327 6328 3329 9330 12331 6332 3333 9334 12335 6336 3337 9338 12339 6340 3341 9342 12343 6344 3345 9346 12347 6348 3349 9350 12351 6352 3353 9354 12355 6356 3357 9358 12359 6360 3361 9362 12363 6364 3365 9366 12367 6368 3369 9370 12371 6372 3373 9374 12375 6376 3377 9378 12379 6380 3381 9382 12383 6384 3385 9386 12387 6388 3389 9390 12391 6392 3393 9394 12395 6396 3397 9398 12399 6400 3401 9402 12403 6404 3405 9406 12407 6408 3409 9410 12411 6412 3413 9414 12415 6416 3417 9418 12419 6420 3421 9422 12423 6424 3425 9426 12427 6428 3429 9430 12431 6432 3433 9434 12435 6436 3437 9438 12439 6440 3441 9442 12443 6444 3445 9446 12447 6448 3449 9450 12451 6452 3453 9454 12455 6456 3457 9458 12459 6460 3461 9462 12463 6464 3465 9466 12467 6468 3469 9470 12471 6472 3473 9474 12475 6476 3477 9478 12479 6480 3481 9482 12483 6484 3485 9486 12487 6488 3489 9490 12491 6492 3493 9494 12495 6496 3497 9498 12499 6500 3501 9502 12503 6504 3505 9506 12507 6508 3509 9510 12511 6512 3513 9514 12515 6516 3517 9518 12519 6520 3521 9522 12523 6524 3525 9526 12527 6528 3529 9530 12531 6532 3533 9534 12535 6536 3537 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6728 3729 9730 12731 6732 3733 9734 12735 6736 3737 9738 12739 6740 3741 9742 12743 6744 3745 9746 12747 6748 3749 9750 12751 6752 3753 9754 12755 6756 3757 9758 12759 6760 3761 9762 12763 6764 3765 9766 12767 6768 3769 9770 12771 6772 3773 9774 12775 6776 3777 9778 12779 6780 3781 9782 12783 6784 3785 9786 12787 6788 3789 9790 12791 6792 3793 9794 12795 6796 3797 9798 12799 6800 3801 9802 12803 6804 3805 9806 12807 6808 3809 9810 12811 6812 3813 9814 12815 6816 3817 9818 12819 6820 3821 9822 12823 6824 3825 9826 12827 6828 3829 9830 12831 6832 3833 9834 12835 6836 3837 9838 12839 6840 3841 9842 12843 6844 3845 9846 12847 6848 3849 9850 12851 6852 3853 9854 12855 6856 3857 9858 12859 6860 3861 9862 12863 6864 3865 9866 12867 6868 3869 9870 12871 6872 3873 9874 12875 6876 3877 9878 12879 6880 3881 9882 12883 6884 3885 9886 12887 6888 3889 9890 12891 6892 3893 9894 12895 6896 3897 9898 12899 6900 3901 9902 12903 6904 3905 9906 12907 6908 3909 9910 12911 6912 3913 9914 12915 6916 3917 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121091 61092 31093 91094 121095 61096 31097 91098 121099 61100 31101 91102 121103 61104 31105 91106 121107 61108 31109 91110 121111 61112 31113 91114 121115 61116 31117 91118 121119 61120 31121 91122 121123 61124 31125 91126 121127 61128 31129 91130 121131 61132 31133 91134 121135 61136 31137 91138 121139 61140 31141 91142 121143 61144 31145 91146 121147 61148 31149 91150 121151 61152 31153 91154 121155 61156 31157 91158 121159 61160 31161 91162 121163 61164 31165 91166 121167 61168 31169 91170 121171 61172 31173 91174 121175 61176 31177 91178 121179 61180 31181 91182 121183 61184 31185 91186 121187 61188 31189 91190 121191 61192 31193 91194 121195 61196 31197 91198 121199 61200 31201 91202 121203 61204 31205 91206 121207 61208 31209 91210 121211 61212 31213 91214 121215 61216 31217 91218 121219 61220 31221 91222 121223 61224 31225 91226 121227 61228 31229 91230 121231 61232 31233 91234 121235 61236 31237 91238 121239 61240 31241 91242 121243 61244 31245 91246 121247 61248 31249 91250 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121411 61412 31413 91414 121415 61416 31417 91418 121419 61420 31421 91422 121423 61424 31425 91426 121427 61428 31429 91430 121431 61432 31433 91434 121435 61436 31437 91438 121439 61440 31441 91442 121443 61444 31445 91446 121447 61448 31449 91450 121451 61452 31453 91454 121455 61456 31457 91458 121459 61460 31461 91462 121463 61464 31465 91466 121467 61468 31469 91470 121471 61472 31473 91474 121475 61476 31477 91478 121479 61480 31481 91482 121483 61484 31485 91486 121487 61488 31489 91490 121491 61492 31493 91494 121495 61496 31497 91498 121499 61500 31501 91502 121503 61504 31505 91506 121507 61508 31509 91510 121511 61512 31513 91514 121515 61516 31517 91518 121519 61520 31521 91522 121523 61524 31525 91526 121527 61528 31529 91530 121531 61532 31533 91534 121535 61536 31537 91538 121539 61540 31541 91542 121543 61544 31545 91546 121547 61548 31549 91550 121551 61552 31553 91554 121555 61556 31557 91558 121559 61560 31561 91562 121563 61564 31565 91566 121567 61568 31569 91570 121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 317 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** Warning: unused characters: ). /var/www/cgi-bin/calc/gp: line 4: 5414 Killed /usr/bin/gp -q -emacs Timing: real 0m21.022s user 0m15.496s sys 0m5.504s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 02:59:09 2005 Input: m=3;r=1;n=15;print(m,r); while(m>1,if(3*mn,m=m-n);if(m<>0,if(m<>3,print(m,r)))))) Output: ? 31 ? 92 123 64 96 127 68 910 1211 612 914 1215 616 918 1219 620 922 1223 624 926 1227 628 930 1231 632 934 1235 636 938 1239 640 942 1243 644 946 1247 648 950 1251 652 954 1255 656 958 1259 660 962 1263 664 966 1267 668 970 1271 672 974 1275 676 978 1279 680 982 1283 684 986 1287 688 990 1291 692 994 1295 696 998 1299 6100 9102 12103 6104 9106 12107 6108 9110 12111 6112 9114 12115 6116 9118 12119 6120 9122 12123 6124 9126 12127 6128 9130 12131 6132 9134 12135 6136 9138 12139 6140 9142 12143 6144 9146 12147 6148 9150 12151 6152 9154 12155 6156 9158 12159 6160 9162 12163 6164 9166 12167 6168 9170 12171 6172 9174 12175 6176 9178 12179 6180 9182 12183 6184 9186 12187 6188 9190 12191 6192 9194 12195 6196 9198 12199 6200 9202 12203 6204 9206 12207 6208 9210 12211 6212 9214 12215 6216 9218 12219 6220 9222 12223 6224 9226 12227 6228 9230 12231 6232 9234 12235 6236 9238 12239 6240 9242 12243 6244 9246 12247 6248 9250 12251 6252 9254 12255 6256 9258 12259 6260 9262 12263 6264 9266 12267 6268 9270 12271 6272 9274 12275 6276 9278 12279 6280 9282 12283 6284 9286 12287 6288 9290 12291 6292 9294 12295 6296 9298 12299 6300 9302 12303 6304 9306 12307 6308 9310 12311 6312 9314 12315 6316 9318 12319 6320 9322 12323 6324 9326 12327 6328 9330 12331 6332 9334 12335 6336 9338 12339 6340 9342 12343 6344 9346 12347 6348 9350 12351 6352 9354 12355 6356 9358 12359 6360 9362 12363 6364 9366 12367 6368 9370 12371 6372 9374 12375 6376 9378 12379 6380 9382 12383 6384 9386 12387 6388 9390 12391 6392 9394 12395 6396 9398 12399 6400 9402 12403 6404 9406 12407 6408 9410 12411 6412 9414 12415 6416 9418 12419 6420 9422 12423 6424 9426 12427 6428 9430 12431 6432 9434 12435 6436 9438 12439 6440 9442 12443 6444 9446 12447 6448 9450 12451 6452 9454 12455 6456 9458 12459 6460 9462 12463 6464 9466 12467 6468 9470 12471 6472 9474 12475 6476 9478 12479 6480 9482 12483 6484 9486 12487 6488 9490 12491 6492 9494 12495 6496 9498 12499 6500 9502 12503 6504 9506 12507 6508 9510 12511 6512 9514 12515 6516 9518 12519 6520 9522 12523 6524 9526 12527 6528 9530 12531 6532 9534 12535 6536 9538 12539 6540 9542 12543 6544 9546 12547 6548 9550 12551 6552 9554 12555 6556 9558 12559 6560 9562 12563 6564 9566 12567 6568 9570 12571 6572 9574 12575 6576 9578 12579 6580 9582 12583 6584 9586 12587 6588 9590 12591 6592 9594 12595 6596 9598 12599 6600 9602 12603 6604 9606 12607 6608 9610 12611 6612 9614 12615 6616 9618 12619 6620 9622 12623 6624 9626 12627 6628 9630 12631 6632 9634 12635 6636 9638 12639 6640 9642 12643 6644 9646 12647 6648 9650 12651 6652 9654 12655 6656 9658 12659 6660 9662 12663 6664 9666 12667 6668 9670 12671 6672 9674 12675 6676 9678 12679 6680 9682 12683 6684 9686 12687 6688 9690 12691 6692 9694 12695 6696 9698 12699 6700 9702 12703 6704 9706 12707 6708 9710 12711 6712 9714 12715 6716 9718 12719 6720 9722 12723 6724 9726 12727 6728 9730 12731 6732 9734 12735 6736 9738 12739 6740 9742 12743 6744 9746 12747 6748 9750 12751 6752 9754 12755 6756 9758 12759 6760 9762 12763 6764 9766 12767 6768 9770 12771 6772 9774 12775 6776 9778 12779 6780 9782 12783 6784 9786 12787 6788 9790 12791 6792 9794 12795 6796 9798 12799 6800 9802 12803 6804 9806 12807 6808 9810 12811 6812 9814 12815 6816 9818 12819 6820 9822 12823 6824 9826 12827 6828 9830 12831 6832 9834 12835 6836 9838 12839 6840 9842 12843 6844 9846 12847 6848 9850 12851 6852 9854 12855 6856 9858 12859 6860 9862 12863 6864 9866 12867 6868 9870 12871 6872 9874 12875 6876 9878 12879 6880 9882 12883 6884 9886 12887 6888 9890 12891 6892 9894 12895 6896 9898 12899 6900 9902 12903 6904 9906 12907 6908 9910 12911 6912 9914 12915 6916 9918 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121563 61564 91566 121567 61568 91570 121571 61572 91574 121575 61576 91578 121579 61580 91582 121583 61584 91586 121587 61588 91590 121591 61592 91594 121595 61596 91598 121599 61600 91602 121603 61604 91606 121607 61608 91610 121611 61612 91614 121615 61616 91618 121619 61620 91622 121623 61624 91626 121627 61628 91630 121631 61632 91634 121635 61636 91638 121639 61640 91642 121643 61644 91646 121647 61648 91650 121651 61652 91654 121655 61656 91658 121659 61660 91662 121663 61664 91666 121667 61668 91670 121671 61672 91674 121675 61676 91678 121679 61680 91682 121683 61684 91686 121687 61688 91690 121691 61692 91694 121695 61696 91698 121699 61700 91702 121703 61704 91706 121707 61708 91710 121711 61712 91714 121715 61716 91718 121719 61720 91722 121723 61724 91726 121727 61728 91730 121731 61732 91734 121735 61736 91738 121739 61740 91742 121743 61744 91746 121747 61748 91750 121751 61752 91754 121755 61756 91758 121759 61760 91762 121763 61764 91766 121767 61768 91770 121771 61772 91774 121775 61776 91778 121779 61780 91782 121783 61784 91786 121787 61788 91790 121791 61792 91794 121795 61796 91798 121799 61800 91802 121803 61804 91806 121807 61808 91810 121811 61812 91814 121815 61816 91818 121819 61820 91822 121823 61824 91826 121827 61828 91830 121831 61832 91834 121835 61836 91838 121839 61840 91842 121843 61844 91846 121847 61848 91850 121851 61852 91854 121855 61856 91858 121859 61860 91862 121863 61864 91866 121867 61868 91870 121871 61872 91874 121875 61876 91878 121879 61880 91882 121883 61884 91886 121887 61888 91890 121891 61892 91894 121895 61896 91898 121899 61900 91902 121903 61904 91906 121907 61908 91910 121911 61912 91914 121915 61916 91918 121919 61920 91922 121923 61924 91926 121927 61928 91930 121931 61932 91934 121935 61936 91938 121939 61940 91942 121943 61944 91946 121947 61948 91950 121951 61952 91954 121955 61956 91958 121959 61960 91962 121963 61964 91966 121967 61968 91970 121971 61972 91974 121975 61976 91978 121979 61980 91982 121983 61984 91986 121987 61988 91990 121991 61992 91994 121995 61996 91998 121999 62000 92002 122003 62004 92006 122007 62008 92010 122011 62012 92014 122015 62016 92018 122019 62020 92022 122023 62024 92026 122027 62028 92030 122031 62032 92034 122035 62036 92038 122039 62040 92042 122043 62044 92046 122047 62048 92050 122051 62052 92054 122055 62056 92058 122059 62060 92062 122063 62064 92066 122067 62068 92070 122071 62072 92074 122075 62076 92078 122079 62080 92082 122083 62084 92086 122087 62088 92090 122091 62092 92094 122095 62096 92098 122099 62100 92102 122103 62104 92106 122107 62108 92110 122111 62112 92114 122115 62116 92118 122119 62120 92122 122123 62124 92126 122127 62128 92130 122131 62132 92134 122135 62136 92138 122139 62140 92142 122143 62144 92146 122147 62148 92150 122151 62152 92154 122155 62156 92158 122159 62160 92162 122163 62164 92166 122167 62168 92170 122171 62172 92174 122175 62176 92178 122179 62180 92182 122183 62184 92186 122187 62188 92190 122191 62192 92194 122195 62196 92198 122199 62200 92202 122203 62204 92206 122207 62208 92210 122211 62212 92214 122215 62216 92218 122219 62220 92222 122223 62224 92226 122227 62228 92230 122231 62232 92234 122235 62236 92238 122239 62240 92242 122243 62244 92246 122247 62248 92250 122251 62252 92254 122255 62256 92258 122259 62260 92262 122263 62264 92266 122267 62268 92270 122271 62272 92274 122275 62276 92278 12227 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** Warning: unused characters: ). /var/www/cgi-bin/calc/gp: line 4: 5430 Killed /usr/bin/gp -q -emacs Timing: real 0m21.227s user 0m16.798s sys 0m4.202s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:00:19 2005 Input: m=3;r=1;n=15;print(m,r); while(m>1,if(3*mn,m=m-n);if(m<>0,print(m,r)))))) Output: ? 31 ? 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 3157 9158 12159 6160 3161 9162 12163 6164 3165 9166 12167 6168 3169 9170 12171 6172 3173 9174 12175 6176 3177 9178 12179 6180 3181 9182 12183 6184 3185 9186 12187 6188 3189 9190 12191 6192 3193 9194 12195 6196 3197 9198 12199 6200 3201 9202 12203 6204 3205 9206 12207 6208 3209 9210 12211 6212 3213 9214 12215 6216 3217 9218 12219 6220 3221 9222 12223 6224 3225 9226 12227 6228 3229 9230 12231 6232 3233 9234 12235 6236 3237 9238 12239 6240 3241 9242 12243 6244 3245 9246 12247 6248 3249 9250 12251 6252 3253 9254 12255 6256 3257 9258 12259 6260 3261 9262 12263 6264 3265 9266 12267 6268 3269 9270 12271 6272 3273 9274 12275 6276 3277 9278 12279 6280 3281 9282 12283 6284 3285 9286 12287 6288 3289 9290 12291 6292 3293 9294 12295 6296 3297 9298 12299 6300 3301 9302 12303 6304 3305 9306 12307 6308 3309 9310 12311 6312 3313 9314 12315 6316 3317 9318 12319 6320 3321 9322 12323 6324 3325 9326 12327 6328 3329 9330 12331 6332 3333 9334 12335 6336 3337 9338 12339 6340 3341 9342 12343 6344 3345 9346 12347 6348 3349 9350 12351 6352 3353 9354 12355 6356 3357 9358 12359 6360 3361 9362 12363 6364 3365 9366 12367 6368 3369 9370 12371 6372 3373 9374 12375 6376 3377 9378 12379 6380 3381 9382 12383 6384 3385 9386 12387 6388 3389 9390 12391 6392 3393 9394 12395 6396 3397 9398 12399 6400 3401 9402 12403 6404 3405 9406 12407 6408 3409 9410 12411 6412 3413 9414 12415 6416 3417 9418 12419 6420 3421 9422 12423 6424 3425 9426 12427 6428 3429 9430 12431 6432 3433 9434 12435 6436 3437 9438 12439 6440 3441 9442 12443 6444 3445 9446 12447 6448 3449 9450 12451 6452 3453 9454 12455 6456 3457 9458 12459 6460 3461 9462 12463 6464 3465 9466 12467 6468 3469 9470 12471 6472 3473 9474 12475 6476 3477 9478 12479 6480 3481 9482 12483 6484 3485 9486 12487 6488 3489 9490 12491 6492 3493 9494 12495 6496 3497 9498 12499 6500 3501 9502 12503 6504 3505 9506 12507 6508 3509 9510 12511 6512 3513 9514 12515 6516 3517 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6708 3709 9710 12711 6712 3713 9714 12715 6716 3717 9718 12719 6720 3721 9722 12723 6724 3725 9726 12727 6728 3729 9730 12731 6732 3733 9734 12735 6736 3737 9738 12739 6740 3741 9742 12743 6744 3745 9746 12747 6748 3749 9750 12751 6752 3753 9754 12755 6756 3757 9758 12759 6760 3761 9762 12763 6764 3765 9766 12767 6768 3769 9770 12771 6772 3773 9774 12775 6776 3777 9778 12779 6780 3781 9782 12783 6784 3785 9786 12787 6788 3789 9790 12791 6792 3793 9794 12795 6796 3797 9798 12799 6800 3801 9802 12803 6804 3805 9806 12807 6808 3809 9810 12811 6812 3813 9814 12815 6816 3817 9818 12819 6820 3821 9822 12823 6824 3825 9826 12827 6828 3829 9830 12831 6832 3833 9834 12835 6836 3837 9838 12839 6840 3841 9842 12843 6844 3845 9846 12847 6848 3849 9850 12851 6852 3853 9854 12855 6856 3857 9858 12859 6860 3861 9862 12863 6864 3865 9866 12867 6868 3869 9870 12871 6872 3873 9874 12875 6876 3877 9878 12879 6880 3881 9882 12883 6884 3885 9886 12887 6888 3889 9890 12891 6892 3893 9894 12895 6896 3897 9898 12899 6900 3901 9902 12903 6904 3905 9906 12907 6908 3909 9910 12911 6912 3913 9914 12915 6916 3917 9918 12919 6920 3921 9922 12923 6924 3925 9926 12927 6928 3929 9930 12931 6932 3933 9934 12935 6936 3937 9938 12939 6940 3941 9942 12943 6944 3945 9946 12947 6948 3949 9950 12951 6952 3953 9954 12955 6956 3957 9958 12959 6960 3961 9962 12963 6964 3965 9966 12967 6968 3969 9970 12971 6972 3973 9974 12975 6976 3977 9978 12979 6980 3981 9982 12983 6984 3985 9986 12987 6988 3989 9990 12991 6992 3993 9994 12995 6996 3997 9998 12999 61000 31001 91002 121003 61004 31005 91006 121007 61008 31009 91010 121011 61012 31013 91014 121015 61016 31017 91018 121019 61020 31021 91022 121023 61024 31025 91026 121027 61028 31029 91030 121031 61032 31033 91034 121035 61036 31037 91038 121039 61040 31041 91042 121043 61044 31045 91046 121047 61048 31049 91050 121051 61052 31053 91054 121055 61056 31057 91058 121059 61060 31061 91062 121063 61064 31065 91066 121067 61068 31069 91070 121071 61072 31073 91074 121075 61076 31077 91078 121079 61080 31081 91082 121083 61084 31085 91086 121087 61088 31089 91090 121091 61092 31093 91094 121095 61096 31097 91098 121099 61100 31101 91102 121103 61104 31105 91106 121107 61108 31109 91110 121111 61112 31113 91114 121115 61116 31117 91118 121119 61120 31121 91122 121123 61124 31125 91126 121127 61128 31129 91130 121131 61132 31133 91134 121135 61136 31137 91138 121139 61140 31141 91142 121143 61144 31145 91146 121147 61148 31149 91150 121151 61152 31153 91154 121155 61156 31157 91158 121159 61160 31161 91162 121163 61164 31165 91166 121167 61168 31169 91170 121171 61172 31173 91174 121175 61176 31177 91178 121179 61180 31181 91182 121183 61184 31185 91186 121187 61188 31189 91190 121191 61192 31193 91194 121195 61196 31197 91198 121199 61200 31201 91202 121203 61204 31205 91206 121207 61208 31209 91210 121211 61212 31213 91214 121215 61216 31217 91218 121219 61220 31221 91222 121223 61224 31225 91226 121227 61228 31229 91230 121231 61232 31233 91234 121235 61236 31237 91238 121239 61240 31241 91242 121243 61244 31245 91246 121247 61248 31249 91250 121251 61252 31253 91254 121255 61256 31257 91258 121259 61260 31261 91262 121263 61264 31265 91266 121267 61268 31269 91270 121271 61272 31273 91274 121275 61276 31277 91278 121279 61280 31281 91282 121283 61284 31285 91286 121287 61288 31289 91290 121291 61292 31293 91294 121295 61296 31297 91298 121299 61300 31301 91302 121303 61304 31305 91306 121307 61308 31309 91310 121311 61312 31313 91314 121315 61316 31317 91318 121319 61320 31321 91322 121323 61324 31325 91326 121327 61328 31329 91330 121331 61332 31333 91334 121335 61336 31337 91338 121339 61340 31341 91342 121343 61344 31345 91346 121347 61348 31349 91350 121351 61352 31353 91354 121355 61356 31357 91358 121359 61360 31361 91362 121363 61364 31365 91366 121367 61368 31369 91370 121371 61372 31373 91374 121375 61376 31377 91378 121379 61380 31381 91382 121383 61384 31385 91386 121387 61388 31389 91390 121391 61392 31393 91394 121395 61396 31397 91398 121399 61400 31401 91402 121403 61404 31405 91406 121407 61408 31409 91410 121411 61412 31413 91414 121415 61416 31417 91418 121419 61420 31421 91422 121423 61424 31425 91426 121427 61428 31429 91430 121431 61432 31433 91434 121435 61436 31437 91438 121439 61440 31441 91442 121443 61444 31445 91446 121447 61448 31449 91450 121451 61452 31453 91454 121455 61456 31457 91458 121459 61460 31461 91462 121463 61464 31465 91466 121467 61468 31469 91470 121471 61472 31473 91474 121475 61476 31477 91478 121479 61480 31481 91482 121483 61484 31485 91486 121487 61488 31489 91490 121491 61492 31493 91494 121495 61496 31497 91498 121499 61500 31501 91502 121503 61504 31505 91506 121507 61508 31509 91510 121511 61512 31513 91514 121515 61516 31517 91518 121519 61520 31521 91522 121523 61524 31525 91526 121527 61528 31529 91530 121531 61532 31533 91534 121535 61536 31537 91538 121539 61540 31541 91542 121543 61544 31545 91546 121547 61548 31549 91550 121551 61552 31553 91554 121555 61556 31557 91558 121559 61560 31561 91562 121563 61564 31565 91566 121567 61568 31569 91570 121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 317 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** Warning: unused characters: )). /var/www/cgi-bin/calc/gp: line 4: 5448 Killed /usr/bin/gp -q -emacs Timing: real 0m21.009s user 0m15.531s sys 0m5.470s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:04:26 2005 Input: m=3;a=3;r=1;n=15;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))))) Output: ? 31 ? 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 3157 9158 12159 6160 3161 9162 12163 6164 3165 9166 12167 6168 3169 9170 12171 6172 3173 9174 12175 6176 3177 9178 12179 6180 3181 9182 12183 6184 3185 9186 12187 6188 3189 9190 12191 6192 3193 9194 12195 6196 3197 9198 12199 6200 3201 9202 12203 6204 3205 9206 12207 6208 3209 9210 12211 6212 3213 9214 12215 6216 3217 9218 12219 6220 3221 9222 12223 6224 3225 9226 12227 6228 3229 9230 12231 6232 3233 9234 12235 6236 3237 9238 12239 6240 3241 9242 12243 6244 3245 9246 12247 6248 3249 9250 12251 6252 3253 9254 12255 6256 3257 9258 12259 6260 3261 9262 12263 6264 3265 9266 12267 6268 3269 9270 12271 6272 3273 9274 12275 6276 3277 9278 12279 6280 3281 9282 12283 6284 3285 9286 12287 6288 3289 9290 12291 6292 3293 9294 12295 6296 3297 9298 12299 6300 3301 9302 12303 6304 3305 9306 12307 6308 3309 9310 12311 6312 3313 9314 12315 6316 3317 9318 12319 6320 3321 9322 12323 6324 3325 9326 12327 6328 3329 9330 12331 6332 3333 9334 12335 6336 3337 9338 12339 6340 3341 9342 12343 6344 3345 9346 12347 6348 3349 9350 12351 6352 3353 9354 12355 6356 3357 9358 12359 6360 3361 9362 12363 6364 3365 9366 12367 6368 3369 9370 12371 6372 3373 9374 12375 6376 3377 9378 12379 6380 3381 9382 12383 6384 3385 9386 12387 6388 3389 9390 12391 6392 3393 9394 12395 6396 3397 9398 12399 6400 3401 9402 12403 6404 3405 9406 12407 6408 3409 9410 12411 6412 3413 9414 12415 6416 3417 9418 12419 6420 3421 9422 12423 6424 3425 9426 12427 6428 3429 9430 12431 6432 3433 9434 12435 6436 3437 9438 12439 6440 3441 9442 12443 6444 3445 9446 12447 6448 3449 9450 12451 6452 3453 9454 12455 6456 3457 9458 12459 6460 3461 9462 12463 6464 3465 9466 12467 6468 3469 9470 12471 6472 3473 9474 12475 6476 3477 9478 12479 6480 3481 9482 12483 6484 3485 9486 12487 6488 3489 9490 12491 6492 3493 9494 12495 6496 3497 9498 12499 6500 3501 9502 12503 6504 3505 9506 12507 6508 3509 9510 12511 6512 3513 9514 12515 6516 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12707 6708 3709 9710 12711 6712 3713 9714 12715 6716 3717 9718 12719 6720 3721 9722 12723 6724 3725 9726 12727 6728 3729 9730 12731 6732 3733 9734 12735 6736 3737 9738 12739 6740 3741 9742 12743 6744 3745 9746 12747 6748 3749 9750 12751 6752 3753 9754 12755 6756 3757 9758 12759 6760 3761 9762 12763 6764 3765 9766 12767 6768 3769 9770 12771 6772 3773 9774 12775 6776 3777 9778 12779 6780 3781 9782 12783 6784 3785 9786 12787 6788 3789 9790 12791 6792 3793 9794 12795 6796 3797 9798 12799 6800 3801 9802 12803 6804 3805 9806 12807 6808 3809 9810 12811 6812 3813 9814 12815 6816 3817 9818 12819 6820 3821 9822 12823 6824 3825 9826 12827 6828 3829 9830 12831 6832 3833 9834 12835 6836 3837 9838 12839 6840 3841 9842 12843 6844 3845 9846 12847 6848 3849 9850 12851 6852 3853 9854 12855 6856 3857 9858 12859 6860 3861 9862 12863 6864 3865 9866 12867 6868 3869 9870 12871 6872 3873 9874 12875 6876 3877 9878 12879 6880 3881 9882 12883 6884 3885 9886 12887 6888 3889 9890 12891 6892 3893 9894 12895 6896 3897 9898 12899 6900 3901 9902 12903 6904 3905 9906 12907 6908 3909 9910 12911 6912 3913 9914 12915 6916 3917 9918 12919 6920 3921 9922 12923 6924 3925 9926 12927 6928 3929 9930 12931 6932 3933 9934 12935 6936 3937 9938 12939 6940 3941 9942 12943 6944 3945 9946 12947 6948 3949 9950 12951 6952 3953 9954 12955 6956 3957 9958 12959 6960 3961 9962 12963 6964 3965 9966 12967 6968 3969 9970 12971 6972 3973 9974 12975 6976 3977 9978 12979 6980 3981 9982 12983 6984 3985 9986 12987 6988 3989 9990 12991 6992 3993 9994 12995 6996 3997 9998 12999 61000 31001 91002 121003 61004 31005 91006 121007 61008 31009 91010 121011 61012 31013 91014 121015 61016 31017 91018 121019 61020 31021 91022 121023 61024 31025 91026 121027 61028 31029 91030 121031 61032 31033 91034 121035 61036 31037 91038 121039 61040 31041 91042 121043 61044 31045 91046 121047 61048 31049 91050 121051 61052 31053 91054 121055 61056 31057 91058 121059 61060 31061 91062 121063 61064 31065 91066 121067 61068 31069 91070 121071 61072 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31233 91234 121235 61236 31237 91238 121239 61240 31241 91242 121243 61244 31245 91246 121247 61248 31249 91250 121251 61252 31253 91254 121255 61256 31257 91258 121259 61260 31261 91262 121263 61264 31265 91266 121267 61268 31269 91270 121271 61272 31273 91274 121275 61276 31277 91278 121279 61280 31281 91282 121283 61284 31285 91286 121287 61288 31289 91290 121291 61292 31293 91294 121295 61296 31297 91298 121299 61300 31301 91302 121303 61304 31305 91306 121307 61308 31309 91310 121311 61312 31313 91314 121315 61316 31317 91318 121319 61320 31321 91322 121323 61324 31325 91326 121327 61328 31329 91330 121331 61332 31333 91334 121335 61336 31337 91338 121339 61340 31341 91342 121343 61344 31345 91346 121347 61348 31349 91350 121351 61352 31353 91354 121355 61356 31357 91358 121359 61360 31361 91362 121363 61364 31365 91366 121367 61368 31369 91370 121371 61372 31373 91374 121375 61376 31377 91378 121379 61380 31381 91382 121383 61384 31385 91386 121387 61388 31389 91390 121391 61392 31393 91394 121395 61396 31397 91398 121399 61400 31401 91402 121403 61404 31405 91406 121407 61408 31409 91410 121411 61412 31413 91414 121415 61416 31417 91418 121419 61420 31421 91422 121423 61424 31425 91426 121427 61428 31429 91430 121431 61432 31433 91434 121435 61436 31437 91438 121439 61440 31441 91442 121443 61444 31445 91446 121447 61448 31449 91450 121451 61452 31453 91454 121455 61456 31457 91458 121459 61460 31461 91462 121463 61464 31465 91466 121467 61468 31469 91470 121471 61472 31473 91474 121475 61476 31477 91478 121479 61480 31481 91482 121483 61484 31485 91486 121487 61488 31489 91490 121491 61492 31493 91494 121495 61496 31497 91498 121499 61500 31501 91502 121503 61504 31505 91506 121507 61508 31509 91510 121511 61512 31513 91514 121515 61516 31517 91518 121519 61520 31521 91522 121523 61524 31525 91526 121527 61528 31529 91530 121531 61532 31533 91534 121535 61536 31537 91538 121539 61540 31541 91542 121543 61544 31545 91546 121547 61548 31549 91550 121551 61552 31553 91554 121555 61556 31557 91558 121559 61560 31561 91562 121563 61564 31565 91566 121567 61568 31569 91570 121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 317 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** Warning: unused characters: )). /var/www/cgi-bin/calc/gp: line 4: 5507 Killed /usr/bin/gp -q -emacs Timing: real 0m21.240s user 0m15.974s sys 0m5.027s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:05:41 2005 Input: m=3;a=2;r=1;n=3;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))))) Output: ? 31 ? 32 33 34 35 36 37 38 39 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 3100 3101 3102 3103 3104 3105 3106 3107 3108 3109 3110 3111 3112 3113 3114 3115 3116 3117 3118 3119 3120 3121 3122 3123 3124 3125 3126 3127 3128 3129 3130 3131 3132 3133 3134 3135 3136 3137 3138 3139 3140 3141 3142 3143 3144 3145 3146 3147 3148 3149 3150 3151 3152 3153 3154 3155 3156 3157 3158 3159 3160 3161 3162 3163 3164 3165 3166 3167 3168 3169 3170 3171 3172 3173 3174 3175 3176 3177 3178 3179 3180 3181 3182 3183 3184 3185 3186 3187 3188 3189 3190 3191 3192 3193 3194 3195 3196 3197 3198 3199 3200 3201 3202 3203 3204 3205 3206 3207 3208 3209 3210 3211 3212 3213 3214 3215 3216 3217 3218 3219 3220 3221 3222 3223 3224 3225 3226 3227 3228 3229 3230 3231 3232 3233 3234 3235 3236 3237 3238 3239 3240 3241 3242 3243 3244 3245 3246 3247 3248 3249 3250 3251 3252 3253 3254 3255 3256 3257 3258 3259 3260 3261 3262 3263 3264 3265 3266 3267 3268 3269 3270 3271 3272 3273 3274 3275 3276 3277 3278 3279 3280 3281 3282 3283 3284 3285 3286 3287 3288 3289 3290 3291 3292 3293 3294 3295 3296 3297 3298 3299 3300 3301 3302 3303 3304 3305 3306 3307 3308 3309 3310 3311 3312 3313 3314 3315 3316 3317 3318 3319 3320 3321 3322 3323 3324 3325 3326 3327 3328 3329 3330 3331 3332 3333 3334 3335 3336 3337 3338 3339 3340 3341 3342 3343 3344 3345 3346 3347 3348 3349 3350 3351 3352 3353 3354 3355 3356 3357 3358 3359 3360 3361 3362 3363 3364 3365 3366 3367 3368 3369 3370 3371 3372 3373 3374 3375 3376 3377 3378 3379 3380 3381 3382 3383 3384 3385 3386 3387 3388 3389 3390 3391 3392 3393 3394 3395 3396 3397 3398 3399 3400 3401 3402 3403 3404 3405 3406 3407 3408 3409 3410 3411 3412 3413 3414 3415 3416 3417 3418 3419 3420 3421 3422 3423 3424 3425 3426 3427 3428 3429 3430 3431 3432 3433 3434 3435 3436 3437 3438 3439 3440 3441 3442 3443 3444 3445 3446 3447 3448 3449 3450 3451 3452 3453 3454 3455 3456 3457 3458 3459 3460 3461 3462 3463 3464 3465 3466 3467 3468 3469 3470 3471 3472 3473 3474 3475 3476 3477 3478 3479 3480 3481 3482 3483 3484 3485 3486 3487 3488 3489 3490 3491 3492 3493 3494 3495 3496 3497 3498 3499 3500 3501 3502 3503 3504 3505 3506 3507 3508 3509 3510 3511 3512 3513 3514 3515 3516 3517 3518 3519 3520 3521 3522 3523 3524 3525 3526 3527 3528 3529 3530 3531 3532 3533 3534 3535 3536 3537 3538 3539 3540 3541 3542 3543 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31452 31453 31454 31455 31456 31457 31458 31459 31460 31461 31462 31463 31464 31465 31466 31467 31468 31469 31470 31471 31472 31473 31474 31475 31476 31477 31478 31479 31480 31481 31482 31483 31484 31485 31486 31487 31488 31489 31490 31491 31492 31493 31494 31495 31496 31497 31498 31499 31500 31501 31502 31503 31504 31505 31506 31507 31508 31509 31510 31511 31512 31513 31514 31515 31516 31517 31518 31519 31520 31521 31522 31523 31524 31525 31526 31527 31528 31529 31530 31531 31532 31533 31534 31535 31536 31537 31538 31539 31540 31541 31542 31543 31544 31545 31546 31547 31548 31549 31550 31551 31552 31553 31554 31555 31556 31557 31558 31559 31560 31561 31562 31563 31564 31565 31566 31567 31568 31569 31570 31571 31572 31573 31574 31575 31576 31577 31578 31579 31580 31581 31582 31583 31584 31585 31586 31587 31588 31589 31590 31591 31592 31593 31594 31595 31596 31597 31598 31599 31600 31601 31602 31603 31604 31605 31606 31607 31608 31609 31610 31611 31612 31613 31614 31615 31616 31617 31618 31619 31620 31621 31622 31623 31624 31625 31626 31627 31628 31629 31630 31631 31632 31633 31634 31635 31636 31637 31638 31639 31640 31641 31642 31643 31644 31645 31646 31647 31648 31649 31650 31651 31652 31653 31654 31655 31656 31657 31658 31659 31660 31661 31662 31663 31664 31665 31666 31667 31668 31669 31670 31671 31672 31673 31674 31675 31676 31677 31678 31679 31680 31681 31682 31683 31684 31685 31686 31687 31688 31689 31690 31691 31692 31693 31694 31695 31696 31697 31698 31699 31700 31701 31702 31703 31704 31705 31706 31707 31708 31709 31710 31711 31712 31713 31714 31715 31716 31717 31718 31719 31720 31721 31722 31723 31724 31725 31726 31727 31728 31729 31730 31731 31732 31733 31734 31735 31736 31737 31738 31739 31740 31741 31742 31743 31744 31745 31746 31747 31748 31749 31750 31751 31752 31753 31754 31755 31756 31757 31758 31759 31760 31761 31762 31763 31764 31765 31766 31767 31768 31769 31770 31771 31772 31773 31774 31775 31776 31777 31778 31779 31780 31781 31782 31783 31784 31785 31786 31787 31788 31789 31790 31791 31792 31793 31794 31795 31796 31797 31798 31799 31800 31801 31802 31803 31804 31805 31806 31807 31808 31809 31810 31811 31812 31813 31814 31815 31816 31817 31818 31819 31820 31821 31822 31823 31824 31825 31826 31827 31828 31829 31830 31831 31832 31833 31834 31835 31836 31837 31838 31839 31840 31841 31842 31843 31844 31845 31846 31847 31848 31849 31850 318 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** Warning: unused characters: )). /var/www/cgi-bin/calc/gp: line 4: 5558 Killed /usr/bin/gp -q -emacs Timing: real 0m21.011s user 0m16.006s sys 0m4.993s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:06:24 2005 Input: m=2;a=2;r=1;n=3;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))))) Output: ? 21 ? 12 ? Errors (if any) and Timing Info: *** Warning: unused characters: )). Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:06:55 2005 Input: m=a=2;r=1;n=3;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))))) Output: ? 21 ? 12 ? Errors (if any) and Timing Info: *** Warning: unused characters: )). Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:07:34 2005 Input: m=a=2;r=1;n=5;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))))) Output: ? 21 ? 42 33 14 ? Errors (if any) and Timing Info: *** Warning: unused characters: )). Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:07:48 2005 Input: m=a=2;r=1;n=5;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 ? 42 33 14 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:08:05 2005 Input: m=a=2;r=1;n=7;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 ? 42 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:08:20 2005 Input: m=a=2;r=1;n=9;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 ? 42 83 74 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:09:02 2005 Input: m=a=2;r=1;n=11;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 ? 42 83 54 105 96 77 38 69 110 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:09:32 2005 Input: m=a=2;r=1;n=13;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 ? 42 83 34 65 126 117 98 59 1010 711 112 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:09:46 2005 Input: m=a=2;r=1;n=15;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 ? 42 83 14 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:10:20 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 3157 9158 12159 6160 3161 9162 12163 6164 3165 9166 12167 6168 3169 9170 12171 6172 3173 9174 12175 6176 3177 9178 12179 6180 3181 9182 12183 6184 3185 9186 12187 6188 3189 9190 12191 6192 3193 9194 12195 6196 3197 9198 12199 6200 3201 9202 12203 6204 3205 9206 12207 6208 3209 9210 12211 6212 3213 9214 12215 6216 3217 9218 12219 6220 3221 9222 12223 6224 3225 9226 12227 6228 3229 9230 12231 6232 3233 9234 12235 6236 3237 9238 12239 6240 3241 9242 12243 6244 3245 9246 12247 6248 3249 9250 12251 6252 3253 9254 12255 6256 3257 9258 12259 6260 3261 9262 12263 6264 3265 9266 12267 6268 3269 9270 12271 6272 3273 9274 12275 6276 3277 9278 12279 6280 3281 9282 12283 6284 3285 9286 12287 6288 3289 9290 12291 6292 3293 9294 12295 6296 3297 9298 12299 6300 3301 9302 12303 6304 3305 9306 12307 6308 3309 9310 12311 6312 3313 9314 12315 6316 3317 9318 12319 6320 3321 9322 12323 6324 3325 9326 12327 6328 3329 9330 12331 6332 3333 9334 12335 6336 3337 9338 12339 6340 3341 9342 12343 6344 3345 9346 12347 6348 3349 9350 12351 6352 3353 9354 12355 6356 3357 9358 12359 6360 3361 9362 12363 6364 3365 9366 12367 6368 3369 9370 12371 6372 3373 9374 12375 6376 3377 9378 12379 6380 3381 9382 12383 6384 3385 9386 12387 6388 3389 9390 12391 6392 3393 9394 12395 6396 3397 9398 12399 6400 3401 9402 12403 6404 3405 9406 12407 6408 3409 9410 12411 6412 3413 9414 12415 6416 3417 9418 12419 6420 3421 9422 12423 6424 3425 9426 12427 6428 3429 9430 12431 6432 3433 9434 12435 6436 3437 9438 12439 6440 3441 9442 12443 6444 3445 9446 12447 6448 3449 9450 12451 6452 3453 9454 12455 6456 3457 9458 12459 6460 3461 9462 12463 6464 3465 9466 12467 6468 3469 9470 12471 6472 3473 9474 12475 6476 3477 9478 12479 6480 3481 9482 12483 6484 3485 9486 12487 6488 3489 9490 12491 6492 3493 9494 12495 6496 3497 9498 12499 6500 3501 9502 12503 6504 3505 9506 12507 6508 3509 9510 12511 6512 3513 9514 12515 6516 3517 9518 12519 6520 3521 9522 12523 6524 3525 9526 12527 6528 3529 9530 12531 6532 3533 9534 12535 6536 3537 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6728 3729 9730 12731 6732 3733 9734 12735 6736 3737 9738 12739 6740 3741 9742 12743 6744 3745 9746 12747 6748 3749 9750 12751 6752 3753 9754 12755 6756 3757 9758 12759 6760 3761 9762 12763 6764 3765 9766 12767 6768 3769 9770 12771 6772 3773 9774 12775 6776 3777 9778 12779 6780 3781 9782 12783 6784 3785 9786 12787 6788 3789 9790 12791 6792 3793 9794 12795 6796 3797 9798 12799 6800 3801 9802 12803 6804 3805 9806 12807 6808 3809 9810 12811 6812 3813 9814 12815 6816 3817 9818 12819 6820 3821 9822 12823 6824 3825 9826 12827 6828 3829 9830 12831 6832 3833 9834 12835 6836 3837 9838 12839 6840 3841 9842 12843 6844 3845 9846 12847 6848 3849 9850 12851 6852 3853 9854 12855 6856 3857 9858 12859 6860 3861 9862 12863 6864 3865 9866 12867 6868 3869 9870 12871 6872 3873 9874 12875 6876 3877 9878 12879 6880 3881 9882 12883 6884 3885 9886 12887 6888 3889 9890 12891 6892 3893 9894 12895 6896 3897 9898 12899 6900 3901 9902 12903 6904 3905 9906 12907 6908 3909 9910 12911 6912 3913 9914 12915 6916 3917 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121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 317 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 5667 Killed /usr/bin/gp -q -emacs Timing: real 0m21.023s user 0m15.657s sys 0m5.343s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:10:34 2005 Input: m=a=3;r=1;n=13;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:10:44 2005 Input: m=a=3;r=1;n=11;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 53 44 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:10:55 2005 Input: m=a=3;r=1;n=9;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:11:05 2005 Input: m=a=3;r=1;n=7;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 22 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:11:27 2005 Input: m=a=3;r=1;n=2047;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 273 814 2435 7296 1407 4208 12609 173310 110511 126812 175713 117714 148415 35816 107417 117518 147819 34020 102021 101322 99223 92924 74025 17326 51927 155728 57729 173130 109931 125032 170333 101534 99835 94736 79437 33538 100539 96840 85741 52442 157243 62244 186645 150446 41847 125448 171549 105150 110651 127152 176653 120454 156555 60156 180357 131558 189859 160060 70661 7162 21363 63964 191765 165766 87767 58468 175269 116270 143971 22372 66973 200774 192775 168776 96777 85478 51579 154580 54181 162382 77583 27884 83485 45586 136587 188 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.003s sys 0m0.011s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:13:08 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 3157 9158 12159 6160 3161 9162 12163 6164 3165 9166 12167 6168 3169 9170 12171 6172 3173 9174 12175 6176 3177 9178 12179 6180 3181 9182 12183 6184 3185 9186 12187 6188 3189 9190 12191 6192 3193 9194 12195 6196 3197 9198 12199 6200 3201 9202 12203 6204 3205 9206 12207 6208 3209 9210 12211 6212 3213 9214 12215 6216 3217 9218 12219 6220 3221 9222 12223 6224 3225 9226 12227 6228 3229 9230 12231 6232 3233 9234 12235 6236 3237 9238 12239 6240 3241 9242 12243 6244 3245 9246 12247 6248 3249 9250 12251 6252 3253 9254 12255 6256 3257 9258 12259 6260 3261 9262 12263 6264 3265 9266 12267 6268 3269 9270 12271 6272 3273 9274 12275 6276 3277 9278 12279 6280 3281 9282 12283 6284 3285 9286 12287 6288 3289 9290 12291 6292 3293 9294 12295 6296 3297 9298 12299 6300 3301 9302 12303 6304 3305 9306 12307 6308 3309 9310 12311 6312 3313 9314 12315 6316 3317 9318 12319 6320 3321 9322 12323 6324 3325 9326 12327 6328 3329 9330 12331 6332 3333 9334 12335 6336 3337 9338 12339 6340 3341 9342 12343 6344 3345 9346 12347 6348 3349 9350 12351 6352 3353 9354 12355 6356 3357 9358 12359 6360 3361 9362 12363 6364 3365 9366 12367 6368 3369 9370 12371 6372 3373 9374 12375 6376 3377 9378 12379 6380 3381 9382 12383 6384 3385 9386 12387 6388 3389 9390 12391 6392 3393 9394 12395 6396 3397 9398 12399 6400 3401 9402 12403 6404 3405 9406 12407 6408 3409 9410 12411 6412 3413 9414 12415 6416 3417 9418 12419 6420 3421 9422 12423 6424 3425 9426 12427 6428 3429 9430 12431 6432 3433 9434 12435 6436 3437 9438 12439 6440 3441 9442 12443 6444 3445 9446 12447 6448 3449 9450 12451 6452 3453 9454 12455 6456 3457 9458 12459 6460 3461 9462 12463 6464 3465 9466 12467 6468 3469 9470 12471 6472 3473 9474 12475 6476 3477 9478 12479 6480 3481 9482 12483 6484 3485 9486 12487 6488 3489 9490 12491 6492 3493 9494 12495 6496 3497 9498 12499 6500 3501 9502 12503 6504 3505 9506 12507 6508 3509 9510 12511 6512 3513 9514 12515 6516 3517 9518 12519 6520 3521 9522 12523 6524 3525 9526 12527 6528 3529 9530 12531 6532 3533 9534 12535 6536 3537 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6728 3729 9730 12731 6732 3733 9734 12735 6736 3737 9738 12739 6740 3741 9742 12743 6744 3745 9746 12747 6748 3749 9750 12751 6752 3753 9754 12755 6756 3757 9758 12759 6760 3761 9762 12763 6764 3765 9766 12767 6768 3769 9770 12771 6772 3773 9774 12775 6776 3777 9778 12779 6780 3781 9782 12783 6784 3785 9786 12787 6788 3789 9790 12791 6792 3793 9794 12795 6796 3797 9798 12799 6800 3801 9802 12803 6804 3805 9806 12807 6808 3809 9810 12811 6812 3813 9814 12815 6816 3817 9818 12819 6820 3821 9822 12823 6824 3825 9826 12827 6828 3829 9830 12831 6832 3833 9834 12835 6836 3837 9838 12839 6840 3841 9842 12843 6844 3845 9846 12847 6848 3849 9850 12851 6852 3853 9854 12855 6856 3857 9858 12859 6860 3861 9862 12863 6864 3865 9866 12867 6868 3869 9870 12871 6872 3873 9874 12875 6876 3877 9878 12879 6880 3881 9882 12883 6884 3885 9886 12887 6888 3889 9890 12891 6892 3893 9894 12895 6896 3897 9898 12899 6900 3901 9902 12903 6904 3905 9906 12907 6908 3909 9910 12911 6912 3913 9914 12915 6916 3917 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121091 61092 31093 91094 121095 61096 31097 91098 121099 61100 31101 91102 121103 61104 31105 91106 121107 61108 31109 91110 121111 61112 31113 91114 121115 61116 31117 91118 121119 61120 31121 91122 121123 61124 31125 91126 121127 61128 31129 91130 121131 61132 31133 91134 121135 61136 31137 91138 121139 61140 31141 91142 121143 61144 31145 91146 121147 61148 31149 91150 121151 61152 31153 91154 121155 61156 31157 91158 121159 61160 31161 91162 121163 61164 31165 91166 121167 61168 31169 91170 121171 61172 31173 91174 121175 61176 31177 91178 121179 61180 31181 91182 121183 61184 31185 91186 121187 61188 31189 91190 121191 61192 31193 91194 121195 61196 31197 91198 121199 61200 31201 91202 121203 61204 31205 91206 121207 61208 31209 91210 121211 61212 31213 91214 121215 61216 31217 91218 121219 61220 31221 91222 121223 61224 31225 91226 121227 61228 31229 91230 121231 61232 31233 91234 121235 61236 31237 91238 121239 61240 31241 91242 121243 61244 31245 91246 121247 61248 31249 91250 121251 61252 31253 91254 121255 61256 31257 91258 121259 61260 31261 91262 121263 61264 31265 91266 121267 61268 31269 91270 121271 61272 31273 91274 121275 61276 31277 91278 121279 61280 31281 91282 121283 61284 31285 91286 121287 61288 31289 91290 121291 61292 31293 91294 121295 61296 31297 91298 121299 61300 31301 91302 121303 61304 31305 91306 121307 61308 31309 91310 121311 61312 31313 91314 121315 61316 31317 91318 121319 61320 31321 91322 121323 61324 31325 91326 121327 61328 31329 91330 121331 61332 31333 91334 121335 61336 31337 91338 121339 61340 31341 91342 121343 61344 31345 91346 121347 61348 31349 91350 121351 61352 31353 91354 121355 61356 31357 91358 121359 61360 31361 91362 121363 61364 31365 91366 121367 61368 31369 91370 121371 61372 31373 91374 121375 61376 31377 91378 121379 61380 31381 91382 121383 61384 31385 91386 121387 61388 31389 91390 121391 61392 31393 91394 121395 61396 31397 91398 121399 61400 31401 91402 121403 61404 31405 91406 121407 61408 31409 91410 121411 61412 31413 91414 121415 61416 31417 91418 121419 61420 31421 91422 121423 61424 31425 91426 121427 61428 31429 91430 121431 61432 31433 91434 121435 61436 31437 91438 121439 61440 31441 91442 121443 61444 31445 91446 121447 61448 31449 91450 121451 61452 31453 91454 121455 61456 31457 91458 121459 61460 31461 91462 121463 61464 31465 91466 121467 61468 31469 91470 121471 61472 31473 91474 121475 61476 31477 91478 121479 61480 31481 91482 121483 61484 31485 91486 121487 61488 31489 91490 121491 61492 31493 91494 121495 61496 31497 91498 121499 61500 31501 91502 121503 61504 31505 91506 121507 61508 31509 91510 121511 61512 31513 91514 121515 61516 31517 91518 121519 61520 31521 91522 121523 61524 31525 91526 121527 61528 31529 91530 121531 61532 31533 91534 121535 61536 31537 91538 121539 61540 31541 91542 121543 61544 31545 91546 121547 61548 31549 91550 121551 61552 31553 91554 121555 61556 31557 91558 121559 61560 31561 91562 121563 61564 31565 91566 121567 61568 31569 91570 121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 317 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 5725 Killed /usr/bin/gp -q -emacs Timing: real 0m21.007s user 0m15.635s sys 0m5.365s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:18:50 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,if(m+r=a+r,if(a*mn,m=m-n);if(m<>0,print(m,r))),m=0) Output: ? 31 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...if(m<>0,print(m,r))),m=0) ^ Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:19:24 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,if(m+r=a+r,if(a*mn,m=m-n);if(m<>0,print(m,r))),m=0)) Output: ? 31 ? 95 129 613 317 921 1225 629 333 937 1241 645 349 953 1257 661 365 969 1273 677 381 985 1289 693 397 9101 12105 6109 3113 9117 12121 6125 3129 9133 12137 6141 3145 9149 12153 6157 3161 9165 12169 6173 3177 9181 12185 6189 3193 9197 12201 6205 3209 9213 12217 6221 3225 9229 12233 6237 3241 9245 12249 6253 3257 9261 12265 6269 3273 9277 12281 6285 3289 9293 12297 6301 3305 9309 12313 6317 3321 9325 12329 6333 3337 9341 12345 6349 3353 9357 12361 6365 3369 9373 12377 6381 3385 9389 12393 6397 3401 9405 12409 6413 3417 9421 12425 6429 3433 9437 12441 6445 3449 9453 12457 6461 3465 9469 12473 6477 3481 9485 12489 6493 3497 9501 12505 6509 3513 9517 12521 6525 3529 9533 12537 6541 3545 9549 12553 6557 3561 9565 12569 6573 3577 9581 12585 6589 3593 9597 12601 6605 3609 9613 12617 6621 3625 9629 12633 6637 3641 9645 12649 6653 3657 9661 12665 6669 3673 9677 12681 6685 3689 9693 12697 6701 3705 9709 12713 6717 3721 9725 12729 6733 3737 9741 12745 6749 3753 9757 12761 6765 3769 9773 12777 6781 3785 9789 12793 6797 3801 9805 12809 6813 3817 9821 12825 6829 3833 9837 12841 6845 3849 9853 12857 6861 3865 9869 12873 6877 3881 9885 12889 6893 3897 9901 12905 6909 3913 9917 12921 6925 3929 9933 12937 6941 3945 9949 12953 6957 3961 9965 12969 6973 3977 9981 12985 6989 3993 9997 121001 61005 31009 91013 121017 61021 31025 91029 121033 61037 31041 91045 121049 61053 31057 91061 121065 61069 31073 91077 121081 61085 31089 91093 121097 61101 31105 91109 121113 61117 31121 91125 121129 61133 31137 91141 121145 61149 31153 91157 121161 61165 31169 91173 121177 61181 31185 91189 121193 61197 31201 91205 121209 61213 31217 91221 121225 61229 31233 91237 121241 61245 31249 91253 121257 61261 31265 91269 121273 61277 31281 91285 121289 61293 31297 91301 121305 61309 31313 91317 121321 61325 31329 91333 121337 61341 31345 91349 121353 61357 31361 91365 121369 61373 31377 91381 121385 61389 31393 91397 121401 61405 31409 91413 121417 61421 31425 91429 121433 61437 31441 91445 121449 61453 31457 91461 121465 61469 31473 91477 121481 61485 31489 91493 121497 61501 31505 91509 121513 61517 31521 91525 121529 61533 31537 91541 121545 61549 31553 91557 121561 61565 31569 91573 121577 61581 31585 91589 121593 61597 31601 91605 121609 61613 31617 91621 121625 61629 31633 91637 121641 61645 31649 91653 121657 61661 31665 91669 121673 61677 31681 91685 121689 61693 31697 91701 121705 61709 31713 91717 121721 61725 31729 91733 121737 61741 31745 91749 121753 61757 31761 91765 121769 61773 31777 91781 121785 61789 31793 91797 121801 61805 31809 91813 121817 61821 31825 91829 121833 61837 31841 91845 121849 61853 31857 91861 121865 61869 31873 91877 121881 61885 31889 91893 121897 61901 31905 91909 121913 61917 31921 91925 121929 61933 31937 91941 121945 61949 31953 91957 121961 61965 31969 91973 121977 61981 31985 91989 121993 61997 32001 92005 122009 62013 32017 92021 122025 62029 32033 92037 122041 62045 32049 92053 122057 62061 32065 92069 122073 62077 32081 92085 122089 62093 32097 92101 122105 62109 32113 92117 122121 62125 32129 92133 122137 62141 32145 92149 122153 62157 32161 92165 122169 62173 32177 92181 122185 62189 32193 92197 122201 62205 32209 92213 122217 62221 32225 92229 122233 62237 32241 92245 122249 62253 32257 92261 122265 62269 32273 92277 122281 62285 32289 92293 122297 62301 32305 92309 122313 62317 32321 92325 122329 62333 32337 92341 122345 62349 32353 92357 122361 62365 32369 92373 122377 62381 32385 92389 122393 62397 32401 92405 122409 62413 32417 92421 122425 62429 32433 92437 122441 62445 32449 92453 122457 62461 32465 92469 122473 62477 32481 92485 122489 62493 32497 92501 122505 62509 32513 92517 122521 62525 32529 92533 122537 62541 32545 92549 122553 62557 32561 92565 122569 62573 32577 92581 122585 62589 32593 92597 122601 62605 32609 92613 122617 62621 32625 92629 122633 62637 32641 92645 122649 62653 32657 92661 122665 62669 32673 92677 122681 62685 32689 92693 122697 62701 32705 92709 122713 62717 32721 92725 122729 62733 32737 92741 122745 62749 32753 92757 122761 62765 32769 92773 122777 62781 32785 92789 122793 62797 32801 92805 122809 62813 32817 92821 122825 62829 32833 92837 122841 62845 32849 92853 122857 62861 32865 92869 122873 62877 32881 92885 122889 62893 32897 92901 122905 62909 32913 92917 122921 62925 32929 92933 122937 62941 32945 92949 122953 62957 32961 92965 122969 62973 32977 92981 122985 62989 32993 92997 123001 63005 33009 93013 123017 63021 33025 93029 123033 63037 33041 93045 123049 63053 33057 93061 123065 63069 33073 93077 123081 63085 33089 93093 123097 63101 33105 93109 123113 63117 33121 93125 123129 63133 33137 93141 123145 63149 33153 93157 123161 63165 33169 93173 123177 63181 33185 93189 123193 63197 33201 93205 123209 63213 33217 93221 123225 63229 33233 93237 123241 63245 33249 93253 123257 63261 33265 93269 123273 63277 33281 93285 123289 63293 33297 93301 123305 63309 33313 93317 123321 63325 33329 93333 123337 63341 33345 93349 123353 63357 33361 93365 123369 63373 33377 93381 123385 63389 33393 93397 123401 63405 33409 93413 123417 63421 33425 93429 123433 63437 33441 93445 123449 63453 33457 93461 123465 63469 33473 93477 123481 63485 33489 93493 123497 63501 33505 93509 123513 63517 33521 93525 123529 63533 33537 93541 123545 63549 33553 93557 123561 63565 33569 93573 123577 63581 33585 93589 123593 63597 33601 93605 123609 63613 33617 93621 123625 63629 33633 93637 123641 63645 33649 93653 123657 63661 33665 93669 123673 63677 33681 93685 123689 63693 33697 93701 123705 63709 33713 93717 123721 63725 33729 93733 123737 63741 33745 93749 123753 63757 33761 93765 123769 63773 33777 93781 123785 63789 33793 93797 123801 63805 33809 93813 123817 63821 33825 93829 123833 63837 33841 93845 123849 63853 33857 93861 123865 63869 33873 93877 123881 63885 33889 93893 123897 63901 33905 93909 123913 63917 33921 93925 123929 63933 33937 93941 123945 63949 33953 93957 123961 63965 33969 93973 123977 63981 33985 93989 123993 63997 34001 94005 124009 64013 34017 94021 124025 64029 34033 94037 124041 64045 34049 94053 124057 64061 34065 94069 124073 64077 34081 94085 124089 64093 34097 94101 124105 64109 34113 94117 124121 64125 34129 94133 124137 64141 34145 94149 124153 64157 34161 94165 124169 64173 34177 94181 124185 64189 34193 94197 124201 64205 34209 94213 124217 64221 34225 94229 124233 64237 34241 94245 124249 64253 34257 94261 124265 64269 34273 94277 124281 64285 34289 94293 124297 64301 34305 94309 124313 64317 34321 94325 124329 64333 34337 94341 124345 64349 34353 94357 124361 64365 34369 94373 124377 64381 34385 94389 124393 64397 34401 94405 124409 64413 34417 94421 124425 64429 34433 94437 124441 64445 34449 94453 124457 64461 34465 94469 124473 64477 34481 94485 124489 64493 34497 94501 124505 64509 34513 94517 124521 64525 34529 94533 124537 64541 34545 94549 124553 64557 34561 94565 124569 64573 34577 94581 124585 64589 34593 94597 124601 64605 34609 94613 124617 64621 34625 94629 124633 64637 34641 94645 124649 64653 34657 94661 124665 64669 34673 94677 124681 64685 34689 94693 124697 64701 34705 94709 124713 64717 34721 94725 124729 64733 34737 94741 124745 64749 34753 94757 124761 64765 34769 94773 124777 64781 34785 94789 124793 64797 34801 94805 124809 64813 34817 94821 124825 64829 34833 94837 124841 64845 34849 94853 124857 64861 34865 94869 124873 64877 34881 94885 124889 64893 34897 94901 124905 64909 34913 94917 124921 64925 34929 94933 124937 64941 34945 94949 124953 64957 34961 94965 124969 64973 34977 94981 124985 64989 34993 94997 125001 65005 35009 95013 125017 65021 35025 95029 125033 65037 35041 95045 125049 65053 35057 95061 125065 65069 35073 95077 125081 65085 35089 95093 125097 65101 35105 95109 125113 65117 35121 95125 125129 65133 35137 95141 125145 65149 35153 95157 125161 65165 35169 95173 125177 65181 35185 95189 125193 65197 35201 95205 125209 65213 35217 95221 125225 65229 35233 95237 125241 65245 35249 95253 125257 65261 35265 95269 125273 65277 35281 95285 125289 65293 35297 95301 125305 65309 35313 95317 125321 65325 35329 95333 125337 65341 35345 95349 125353 65357 35361 95365 125369 65373 35377 95381 125385 65389 35393 95397 125401 65405 35409 95413 125417 65421 35425 95429 125433 65437 35441 95445 125449 65453 35457 95461 125465 65469 35473 95477 125481 65485 35489 95493 125497 65501 35505 95509 125513 65517 35521 95525 125529 65533 35537 95541 125545 65549 35553 95557 125561 65565 35569 95573 125577 65581 35585 95589 125593 65597 35601 95605 125609 65613 35617 95621 125625 65629 35633 95637 125641 65645 35649 95653 125657 65661 35665 95669 125673 65677 35681 95685 125689 65693 35697 95701 125705 65709 35713 95717 125721 65725 35729 95733 125737 65741 35745 95749 125753 65757 35761 95765 125769 65773 35777 95781 125785 65789 35793 95797 125801 65805 35809 95813 125817 65821 35825 95829 125833 65837 35841 95845 125849 65853 35857 95861 125865 65869 35873 95877 125881 65885 35889 95893 125897 65901 35905 95909 125913 65917 35921 95925 125929 65933 35937 95941 125945 65949 35953 95957 125961 65965 35969 95973 125977 65981 35985 95989 125993 65997 36001 96005 126009 66013 36017 96021 126025 66029 36033 96037 126041 66045 36049 96053 126057 66061 36065 96069 126073 66077 36081 96085 126089 66093 36097 96101 126105 66109 36113 96117 126121 66125 36129 96133 126137 66141 36145 96149 126153 66157 36161 96165 126169 66173 36177 96181 126185 66189 36193 96197 126201 66205 36209 96213 126217 66221 36225 96229 126233 66237 36241 96245 126249 66253 36257 96261 126265 66269 36273 96277 126281 66285 36289 96293 126297 66301 36305 96309 126313 66317 36321 96325 126329 66333 36337 96341 126345 66349 36353 96357 126361 66365 36369 96373 126377 66381 36385 96389 126393 66397 36401 96405 126409 66413 36417 96421 126425 66429 36433 96437 126441 66445 36449 96453 126457 66461 36465 96469 126473 66477 36481 96485 126489 66493 36497 96501 126505 66509 36513 96517 126521 66525 36529 96533 126537 66541 36545 96549 126553 66557 36561 96565 126569 66573 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 5805 Killed /usr/bin/gp -q -emacs Timing: real 0m21.037s user 0m16.001s sys 0m4.999s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:20:37 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,if(r>1,if(a*mn,m=m-n);if(m<>0,print(m,r))),m=0)) Output: ? 31 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:28:56 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,if(m+r>=a+1,if(a*mn,m=m-n);if(m<>0,print(m,r))),m=0)) Output: ? 31 ? 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 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61568 31569 91570 121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 317 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 5908 Killed /usr/bin/gp -q -emacs Timing: real 0m23.128s user 0m17.739s sys 0m3.261s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:29:25 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,if(m+r>a+1,if(a*mn,m=m-n);if(m<>0,print(m,r))),m=0)) Output: ? 31 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:30:31 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,if(m+r>=a+1,if(a*mn,m=m-n);if(m<>0,print(m,r))),m=0)) Output: ? 31 ? 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 3157 9158 12159 6160 3161 9162 12163 6164 3165 9166 12167 6168 3169 9170 12171 6172 3173 9174 12175 6176 3177 9178 12179 6180 3181 9182 12183 6184 3185 9186 12187 6188 3189 9190 12191 6192 3193 9194 12195 6196 3197 9198 12199 6200 3201 9202 12203 6204 3205 9206 12207 6208 3209 9210 12211 6212 3213 9214 12215 6216 3217 9218 12219 6220 3221 9222 12223 6224 3225 9226 12227 6228 3229 9230 12231 6232 3233 9234 12235 6236 3237 9238 12239 6240 3241 9242 12243 6244 3245 9246 12247 6248 3249 9250 12251 6252 3253 9254 12255 6256 3257 9258 12259 6260 3261 9262 12263 6264 3265 9266 12267 6268 3269 9270 12271 6272 3273 9274 12275 6276 3277 9278 12279 6280 3281 9282 12283 6284 3285 9286 12287 6288 3289 9290 12291 6292 3293 9294 12295 6296 3297 9298 12299 6300 3301 9302 12303 6304 3305 9306 12307 6308 3309 9310 12311 6312 3313 9314 12315 6316 3317 9318 12319 6320 3321 9322 12323 6324 3325 9326 12327 6328 3329 9330 12331 6332 3333 9334 12335 6336 3337 9338 12339 6340 3341 9342 12343 6344 3345 9346 12347 6348 3349 9350 12351 6352 3353 9354 12355 6356 3357 9358 12359 6360 3361 9362 12363 6364 3365 9366 12367 6368 3369 9370 12371 6372 3373 9374 12375 6376 3377 9378 12379 6380 3381 9382 12383 6384 3385 9386 12387 6388 3389 9390 12391 6392 3393 9394 12395 6396 3397 9398 12399 6400 3401 9402 12403 6404 3405 9406 12407 6408 3409 9410 12411 6412 3413 9414 12415 6416 3417 9418 12419 6420 3421 9422 12423 6424 3425 9426 12427 6428 3429 9430 12431 6432 3433 9434 12435 6436 3437 9438 12439 6440 3441 9442 12443 6444 3445 9446 12447 6448 3449 9450 12451 6452 3453 9454 12455 6456 3457 9458 12459 6460 3461 9462 12463 6464 3465 9466 12467 6468 3469 9470 12471 6472 3473 9474 12475 6476 3477 9478 12479 6480 3481 9482 12483 6484 3485 9486 12487 6488 3489 9490 12491 6492 3493 9494 12495 6496 3497 9498 12499 6500 3501 9502 12503 6504 3505 9506 12507 6508 3509 9510 12511 6512 3513 9514 12515 6516 3517 9518 12519 6520 3521 9522 12523 6524 3525 9526 12527 6528 3529 9530 12531 6532 3533 9534 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61248 31249 91250 121251 61252 31253 91254 121255 61256 31257 91258 121259 61260 31261 91262 121263 61264 31265 91266 121267 61268 31269 91270 121271 61272 31273 91274 121275 61276 31277 91278 121279 61280 31281 91282 121283 61284 31285 91286 121287 61288 31289 91290 121291 61292 31293 91294 121295 61296 31297 91298 121299 61300 31301 91302 121303 61304 31305 91306 121307 61308 31309 91310 121311 61312 31313 91314 121315 61316 31317 91318 121319 61320 31321 91322 121323 61324 31325 91326 121327 61328 31329 91330 121331 61332 31333 91334 121335 61336 31337 91338 121339 61340 31341 91342 121343 61344 31345 91346 121347 61348 31349 91350 121351 61352 31353 91354 121355 61356 31357 91358 121359 61360 31361 91362 121363 61364 31365 91366 121367 61368 31369 91370 121371 61372 31373 91374 121375 61376 31377 91378 121379 61380 31381 91382 121383 61384 31385 91386 121387 61388 31389 91390 121391 61392 31393 91394 121395 61396 31397 91398 121399 61400 31401 91402 121403 61404 31405 91406 121407 61408 31409 91410 121411 61412 31413 91414 121415 61416 31417 91418 121419 61420 31421 91422 121423 61424 31425 91426 121427 61428 31429 91430 121431 61432 31433 91434 121435 61436 31437 91438 121439 61440 31441 91442 121443 61444 31445 91446 121447 61448 31449 91450 121451 61452 31453 91454 121455 61456 31457 91458 121459 61460 31461 91462 121463 61464 31465 91466 121467 61468 31469 91470 121471 61472 31473 91474 121475 61476 31477 91478 121479 61480 31481 91482 121483 61484 31485 91486 121487 61488 31489 91490 121491 61492 31493 91494 121495 61496 31497 91498 121499 61500 31501 91502 121503 61504 31505 91506 121507 61508 31509 91510 121511 61512 31513 91514 121515 61516 31517 91518 121519 61520 31521 91522 121523 61524 31525 91526 121527 61528 31529 91530 121531 61532 31533 91534 121535 61536 31537 91538 121539 61540 31541 91542 121543 61544 31545 91546 121547 61548 31549 91550 121551 61552 31553 91554 121555 61556 31557 91558 121559 61560 31561 91562 121563 61564 31565 91566 121567 61568 31569 91570 121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 317 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 5937 Killed /usr/bin/gp -q -emacs Timing: real 0m21.009s user 0m16.230s sys 0m4.770s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:31:13 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,if(m+r>=a,if(a*mn,m=m-n);if(m<>0,print(m,r))),m=0)) Output: ? 31 ? 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 3157 9158 12159 6160 3161 9162 12163 6164 3165 9166 12167 6168 3169 9170 12171 6172 3173 9174 12175 6176 3177 9178 12179 6180 3181 9182 12183 6184 3185 9186 12187 6188 3189 9190 12191 6192 3193 9194 12195 6196 3197 9198 12199 6200 3201 9202 12203 6204 3205 9206 12207 6208 3209 9210 12211 6212 3213 9214 12215 6216 3217 9218 12219 6220 3221 9222 12223 6224 3225 9226 12227 6228 3229 9230 12231 6232 3233 9234 12235 6236 3237 9238 12239 6240 3241 9242 12243 6244 3245 9246 12247 6248 3249 9250 12251 6252 3253 9254 12255 6256 3257 9258 12259 6260 3261 9262 12263 6264 3265 9266 12267 6268 3269 9270 12271 6272 3273 9274 12275 6276 3277 9278 12279 6280 3281 9282 12283 6284 3285 9286 12287 6288 3289 9290 12291 6292 3293 9294 12295 6296 3297 9298 12299 6300 3301 9302 12303 6304 3305 9306 12307 6308 3309 9310 12311 6312 3313 9314 12315 6316 3317 9318 12319 6320 3321 9322 12323 6324 3325 9326 12327 6328 3329 9330 12331 6332 3333 9334 12335 6336 3337 9338 12339 6340 3341 9342 12343 6344 3345 9346 12347 6348 3349 9350 12351 6352 3353 9354 12355 6356 3357 9358 12359 6360 3361 9362 12363 6364 3365 9366 12367 6368 3369 9370 12371 6372 3373 9374 12375 6376 3377 9378 12379 6380 3381 9382 12383 6384 3385 9386 12387 6388 3389 9390 12391 6392 3393 9394 12395 6396 3397 9398 12399 6400 3401 9402 12403 6404 3405 9406 12407 6408 3409 9410 12411 6412 3413 9414 12415 6416 3417 9418 12419 6420 3421 9422 12423 6424 3425 9426 12427 6428 3429 9430 12431 6432 3433 9434 12435 6436 3437 9438 12439 6440 3441 9442 12443 6444 3445 9446 12447 6448 3449 9450 12451 6452 3453 9454 12455 6456 3457 9458 12459 6460 3461 9462 12463 6464 3465 9466 12467 6468 3469 9470 12471 6472 3473 9474 12475 6476 3477 9478 12479 6480 3481 9482 12483 6484 3485 9486 12487 6488 3489 9490 12491 6492 3493 9494 12495 6496 3497 9498 12499 6500 3501 9502 12503 6504 3505 9506 12507 6508 3509 9510 12511 6512 3513 9514 12515 6516 3517 9518 12519 6520 3521 9522 12523 6524 3525 9526 12527 6528 3529 9530 12531 6532 3533 9534 12535 6536 3537 9538 12539 6540 3541 9542 12543 6544 3545 9546 12547 6548 3549 9550 12551 6552 3553 9554 12555 6556 3557 9558 12559 6560 3561 9562 12563 6564 3565 9566 12567 6568 3569 9570 12571 6572 3573 9574 12575 6576 3577 9578 12579 6580 3581 9582 12583 6584 3585 9586 12587 6588 3589 9590 12591 6592 3593 9594 12595 6596 3597 9598 12599 6600 3601 9602 12603 6604 3605 9606 12607 6608 3609 9610 12611 6612 3613 9614 12615 6616 3617 9618 12619 6620 3621 9622 12623 6624 3625 9626 12627 6628 3629 9630 12631 6632 3633 9634 12635 6636 3637 9638 12639 6640 3641 9642 12643 6644 3645 9646 12647 6648 3649 9650 12651 6652 3653 9654 12655 6656 3657 9658 12659 6660 3661 9662 12663 6664 3665 9666 12667 6668 3669 9670 12671 6672 3673 9674 12675 6676 3677 9678 12679 6680 3681 9682 12683 6684 3685 9686 12687 6688 3689 9690 12691 6692 3693 9694 12695 6696 3697 9698 12699 6700 3701 9702 12703 6704 3705 9706 12707 6708 3709 9710 12711 6712 3713 9714 12715 6716 3717 9718 12719 6720 3721 9722 12723 6724 3725 9726 12727 6728 3729 9730 12731 6732 3733 9734 12735 6736 3737 9738 12739 6740 3741 9742 12743 6744 3745 9746 12747 6748 3749 9750 12751 6752 3753 9754 12755 6756 3757 9758 12759 6760 3761 9762 12763 6764 3765 9766 12767 6768 3769 9770 12771 6772 3773 9774 12775 6776 3777 9778 12779 6780 3781 9782 12783 6784 3785 9786 12787 6788 3789 9790 12791 6792 3793 9794 12795 6796 3797 9798 12799 6800 3801 9802 12803 6804 3805 9806 12807 6808 3809 9810 12811 6812 3813 9814 12815 6816 3817 9818 12819 6820 3821 9822 12823 6824 3825 9826 12827 6828 3829 9830 12831 6832 3833 9834 12835 6836 3837 9838 12839 6840 3841 9842 12843 6844 3845 9846 12847 6848 3849 9850 12851 6852 3853 9854 12855 6856 3857 9858 12859 6860 3861 9862 12863 6864 3865 9866 12867 6868 3869 9870 12871 6872 3873 9874 12875 6876 3877 9878 12879 6880 3881 9882 12883 6884 3885 9886 12887 6888 3889 9890 12891 6892 3893 9894 12895 6896 3897 9898 12899 6900 3901 9902 12903 6904 3905 9906 12907 6908 3909 9910 12911 6912 3913 9914 12915 6916 3917 9918 12919 6920 3921 9922 12923 6924 3925 9926 12927 6928 3929 9930 12931 6932 3933 9934 12935 6936 3937 9938 12939 6940 3941 9942 12943 6944 3945 9946 12947 6948 3949 9950 12951 6952 3953 9954 12955 6956 3957 9958 12959 6960 3961 9962 12963 6964 3965 9966 12967 6968 3969 9970 12971 6972 3973 9974 12975 6976 3977 9978 12979 6980 3981 9982 12983 6984 3985 9986 12987 6988 3989 9990 12991 6992 3993 9994 12995 6996 3997 9998 12999 61000 31001 91002 121003 61004 31005 91006 121007 61008 31009 91010 121011 61012 31013 91014 121015 61016 31017 91018 121019 61020 31021 91022 121023 61024 31025 91026 121027 61028 31029 91030 121031 61032 31033 91034 121035 61036 31037 91038 121039 61040 31041 91042 121043 61044 31045 91046 121047 61048 31049 91050 121051 61052 31053 91054 121055 61056 31057 91058 121059 61060 31061 91062 121063 61064 31065 91066 121067 61068 31069 91070 121071 61072 31073 91074 121075 61076 31077 91078 121079 61080 31081 91082 121083 61084 31085 91086 121087 61088 31089 91090 121091 61092 31093 91094 121095 61096 31097 91098 121099 61100 31101 91102 121103 61104 31105 91106 121107 61108 31109 91110 121111 61112 31113 91114 121115 61116 31117 91118 121119 61120 31121 91122 121123 61124 31125 91126 121127 61128 31129 91130 121131 61132 31133 91134 121135 61136 31137 91138 121139 61140 31141 91142 121143 61144 31145 91146 121147 61148 31149 91150 121151 61152 31153 91154 121155 61156 31157 91158 121159 61160 31161 91162 121163 61164 31165 91166 121167 61168 31169 91170 121171 61172 31173 91174 121175 61176 31177 91178 121179 61180 31181 91182 121183 61184 31185 91186 121187 61188 31189 91190 121191 61192 31193 91194 121195 61196 31197 91198 121199 61200 31201 91202 121203 61204 31205 91206 121207 61208 31209 91210 121211 61212 31213 91214 121215 61216 31217 91218 121219 61220 31221 91222 121223 61224 31225 91226 121227 61228 31229 91230 121231 61232 31233 91234 121235 61236 31237 91238 121239 61240 31241 91242 121243 61244 31245 91246 121247 61248 31249 91250 121251 61252 31253 91254 121255 61256 31257 91258 121259 61260 31261 91262 121263 61264 31265 91266 121267 61268 31269 91270 121271 61272 31273 91274 121275 61276 31277 91278 121279 61280 31281 91282 121283 61284 31285 91286 121287 61288 31289 91290 121291 61292 31293 91294 121295 61296 31297 91298 121299 61300 31301 91302 121303 61304 31305 91306 121307 61308 31309 91310 121311 61312 31313 91314 121315 61316 31317 91318 121319 61320 31321 91322 121323 61324 31325 91326 121327 61328 31329 91330 121331 61332 31333 91334 121335 61336 31337 91338 121339 61340 31341 91342 121343 61344 31345 91346 121347 61348 31349 91350 121351 61352 31353 91354 121355 61356 31357 91358 121359 61360 31361 91362 121363 61364 31365 91366 121367 61368 31369 91370 121371 61372 31373 91374 121375 61376 31377 91378 121379 61380 31381 91382 121383 61384 31385 91386 121387 61388 31389 91390 121391 61392 31393 91394 121395 61396 31397 91398 121399 61400 31401 91402 121403 61404 31405 91406 121407 61408 31409 91410 121411 61412 31413 91414 121415 61416 31417 91418 121419 61420 31421 91422 121423 61424 31425 91426 121427 61428 31429 91430 121431 61432 31433 91434 121435 61436 31437 91438 121439 61440 31441 91442 121443 61444 31445 91446 121447 61448 31449 91450 121451 61452 31453 91454 121455 61456 31457 91458 121459 61460 31461 91462 121463 61464 31465 91466 121467 61468 31469 91470 121471 61472 31473 91474 121475 61476 31477 91478 121479 61480 31481 91482 121483 61484 31485 91486 121487 61488 31489 91490 121491 61492 31493 91494 121495 61496 31497 91498 121499 61500 31501 91502 121503 61504 31505 91506 121507 61508 31509 91510 121511 61512 31513 91514 121515 61516 31517 91518 121519 61520 31521 91522 121523 61524 31525 91526 121527 61528 31529 91530 121531 61532 31533 91534 121535 61536 31537 91538 121539 61540 31541 91542 121543 61544 31545 91546 121547 61548 31549 91550 121551 61552 31553 91554 121555 61556 31557 91558 121559 61560 31561 91562 121563 61564 31565 91566 121567 61568 31569 91570 121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 317 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 5949 Killed /usr/bin/gp -q -emacs Timing: real 0m21.011s user 0m16.277s sys 0m4.723s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:31:41 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,if(m+r>=a,if(a*mn,m=m-n);if(m<>0,print(m,r)))),m=0) Output: ? 31 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...-n);if(m<>0,print(m,r)))),m=0) ^----- Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:31:57 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,if(m+r>=a,if(a*mn,m=m-n);if(m<>0,print(m,r)))),m=0)) Output: ? 31 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...-n);if(m<>0,print(m,r)))),m=0)) ^------ Timing: real 0m0.012s user 0m0.009s sys 0m0.001s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:32:32 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,if(m+r>=a,if(a*mn,m=m-n);if(m<>0,print(m,r))),m=0)) Output: ? 31 ? 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 3157 9158 12159 6160 3161 9162 12163 6164 3165 9166 12167 6168 3169 9170 12171 6172 3173 9174 12175 6176 3177 9178 12179 6180 3181 9182 12183 6184 3185 9186 12187 6188 3189 9190 12191 6192 3193 9194 12195 6196 3197 9198 12199 6200 3201 9202 12203 6204 3205 9206 12207 6208 3209 9210 12211 6212 3213 9214 12215 6216 3217 9218 12219 6220 3221 9222 12223 6224 3225 9226 12227 6228 3229 9230 12231 6232 3233 9234 12235 6236 3237 9238 12239 6240 3241 9242 12243 6244 3245 9246 12247 6248 3249 9250 12251 6252 3253 9254 12255 6256 3257 9258 12259 6260 3261 9262 12263 6264 3265 9266 12267 6268 3269 9270 12271 6272 3273 9274 12275 6276 3277 9278 12279 6280 3281 9282 12283 6284 3285 9286 12287 6288 3289 9290 12291 6292 3293 9294 12295 6296 3297 9298 12299 6300 3301 9302 12303 6304 3305 9306 12307 6308 3309 9310 12311 6312 3313 9314 12315 6316 3317 9318 12319 6320 3321 9322 12323 6324 3325 9326 12327 6328 3329 9330 12331 6332 3333 9334 12335 6336 3337 9338 12339 6340 3341 9342 12343 6344 3345 9346 12347 6348 3349 9350 12351 6352 3353 9354 12355 6356 3357 9358 12359 6360 3361 9362 12363 6364 3365 9366 12367 6368 3369 9370 12371 6372 3373 9374 12375 6376 3377 9378 12379 6380 3381 9382 12383 6384 3385 9386 12387 6388 3389 9390 12391 6392 3393 9394 12395 6396 3397 9398 12399 6400 3401 9402 12403 6404 3405 9406 12407 6408 3409 9410 12411 6412 3413 9414 12415 6416 3417 9418 12419 6420 3421 9422 12423 6424 3425 9426 12427 6428 3429 9430 12431 6432 3433 9434 12435 6436 3437 9438 12439 6440 3441 9442 12443 6444 3445 9446 12447 6448 3449 9450 12451 6452 3453 9454 12455 6456 3457 9458 12459 6460 3461 9462 12463 6464 3465 9466 12467 6468 3469 9470 12471 6472 3473 9474 12475 6476 3477 9478 12479 6480 3481 9482 12483 6484 3485 9486 12487 6488 3489 9490 12491 6492 3493 9494 12495 6496 3497 9498 12499 6500 3501 9502 12503 6504 3505 9506 12507 6508 3509 9510 12511 6512 3513 9514 12515 6516 3517 9518 12519 6520 3521 9522 12523 6524 3525 9526 12527 6528 3529 9530 12531 6532 3533 9534 12535 6536 3537 9538 12539 6540 3541 9542 12543 6544 3545 9546 12547 6548 3549 9550 12551 6552 3553 9554 12555 6556 3557 9558 12559 6560 3561 9562 12563 6564 3565 9566 12567 6568 3569 9570 12571 6572 3573 9574 12575 6576 3577 9578 12579 6580 3581 9582 12583 6584 3585 9586 12587 6588 3589 9590 12591 6592 3593 9594 12595 6596 3597 9598 12599 6600 3601 9602 12603 6604 3605 9606 12607 6608 3609 9610 12611 6612 3613 9614 12615 6616 3617 9618 12619 6620 3621 9622 12623 6624 3625 9626 12627 6628 3629 9630 12631 6632 3633 9634 12635 6636 3637 9638 12639 6640 3641 9642 12643 6644 3645 9646 12647 6648 3649 9650 12651 6652 3653 9654 12655 6656 3657 9658 12659 6660 3661 9662 12663 6664 3665 9666 12667 6668 3669 9670 12671 6672 3673 9674 12675 6676 3677 9678 12679 6680 3681 9682 12683 6684 3685 9686 12687 6688 3689 9690 12691 6692 3693 9694 12695 6696 3697 9698 12699 6700 3701 9702 12703 6704 3705 9706 12707 6708 3709 9710 12711 6712 3713 9714 12715 6716 3717 9718 12719 6720 3721 9722 12723 6724 3725 9726 12727 6728 3729 9730 12731 6732 3733 9734 12735 6736 3737 9738 12739 6740 3741 9742 12743 6744 3745 9746 12747 6748 3749 9750 12751 6752 3753 9754 12755 6756 3757 9758 12759 6760 3761 9762 12763 6764 3765 9766 12767 6768 3769 9770 12771 6772 3773 9774 12775 6776 3777 9778 12779 6780 3781 9782 12783 6784 3785 9786 12787 6788 3789 9790 12791 6792 3793 9794 12795 6796 3797 9798 12799 6800 3801 9802 12803 6804 3805 9806 12807 6808 3809 9810 12811 6812 3813 9814 12815 6816 3817 9818 12819 6820 3821 9822 12823 6824 3825 9826 12827 6828 3829 9830 12831 6832 3833 9834 12835 6836 3837 9838 12839 6840 3841 9842 12843 6844 3845 9846 12847 6848 3849 9850 12851 6852 3853 9854 12855 6856 3857 9858 12859 6860 3861 9862 12863 6864 3865 9866 12867 6868 3869 9870 12871 6872 3873 9874 12875 6876 3877 9878 12879 6880 3881 9882 12883 6884 3885 9886 12887 6888 3889 9890 12891 6892 3893 9894 12895 6896 3897 9898 12899 6900 3901 9902 12903 6904 3905 9906 12907 6908 3909 9910 12911 6912 3913 9914 12915 6916 3917 9918 12919 6920 3921 9922 12923 6924 3925 9926 12927 6928 3929 9930 12931 6932 3933 9934 12935 6936 3937 9938 12939 6940 3941 9942 12943 6944 3945 9946 12947 6948 3949 9950 12951 6952 3953 9954 12955 6956 3957 9958 12959 6960 3961 9962 12963 6964 3965 9966 12967 6968 3969 9970 12971 6972 3973 9974 12975 6976 3977 9978 12979 6980 3981 9982 12983 6984 3985 9986 12987 6988 3989 9990 12991 6992 3993 9994 12995 6996 3997 9998 12999 61000 31001 91002 121003 61004 31005 91006 121007 61008 31009 91010 121011 61012 31013 91014 121015 61016 31017 91018 121019 61020 31021 91022 121023 61024 31025 91026 121027 61028 31029 91030 121031 61032 31033 91034 121035 61036 31037 91038 121039 61040 31041 91042 121043 61044 31045 91046 121047 61048 31049 91050 121051 61052 31053 91054 121055 61056 31057 91058 121059 61060 31061 91062 121063 61064 31065 91066 121067 61068 31069 91070 121071 61072 31073 91074 121075 61076 31077 91078 121079 61080 31081 91082 121083 61084 31085 91086 121087 61088 31089 91090 121091 61092 31093 91094 121095 61096 31097 91098 121099 61100 31101 91102 121103 61104 31105 91106 121107 61108 31109 91110 121111 61112 31113 91114 121115 61116 31117 91118 121119 61120 31121 91122 121123 61124 31125 91126 121127 61128 31129 91130 121131 61132 31133 91134 121135 61136 31137 91138 121139 61140 31141 91142 121143 61144 31145 91146 121147 61148 31149 91150 121151 61152 31153 91154 121155 61156 31157 91158 121159 61160 31161 91162 121163 61164 31165 91166 121167 61168 31169 91170 121171 61172 31173 91174 121175 61176 31177 91178 121179 61180 31181 91182 121183 61184 31185 91186 121187 61188 31189 91190 121191 61192 31193 91194 121195 61196 31197 91198 121199 61200 31201 91202 121203 61204 31205 91206 121207 61208 31209 91210 121211 61212 31213 91214 121215 61216 31217 91218 121219 61220 31221 91222 121223 61224 31225 91226 121227 61228 31229 91230 121231 61232 31233 91234 121235 61236 31237 91238 121239 61240 31241 91242 121243 61244 31245 91246 121247 61248 31249 91250 121251 61252 31253 91254 121255 61256 31257 91258 121259 61260 31261 91262 121263 61264 31265 91266 121267 61268 31269 91270 121271 61272 31273 91274 121275 61276 31277 91278 121279 61280 31281 91282 121283 61284 31285 91286 121287 61288 31289 91290 121291 61292 31293 91294 121295 61296 31297 91298 121299 61300 31301 91302 121303 61304 31305 91306 121307 61308 31309 91310 121311 61312 31313 91314 121315 61316 31317 91318 121319 61320 31321 91322 121323 61324 31325 91326 121327 61328 31329 91330 121331 61332 31333 91334 121335 61336 31337 91338 121339 61340 31341 91342 121343 61344 31345 91346 121347 61348 31349 91350 121351 61352 31353 91354 121355 61356 31357 91358 121359 61360 31361 91362 121363 61364 31365 91366 121367 61368 31369 91370 121371 61372 31373 91374 121375 61376 31377 91378 121379 61380 31381 91382 121383 61384 31385 91386 121387 61388 31389 91390 121391 61392 31393 91394 121395 61396 31397 91398 121399 61400 31401 91402 121403 61404 31405 91406 121407 61408 31409 91410 121411 61412 31413 91414 121415 61416 31417 91418 121419 61420 31421 91422 121423 61424 31425 91426 121427 61428 31429 91430 121431 61432 31433 91434 121435 61436 31437 91438 121439 61440 31441 91442 121443 61444 31445 91446 121447 61448 31449 91450 121451 61452 31453 91454 121455 61456 31457 91458 121459 61460 31461 91462 121463 61464 31465 91466 121467 61468 31469 91470 121471 61472 31473 91474 121475 61476 31477 91478 121479 61480 31481 91482 121483 61484 31485 91486 121487 61488 31489 91490 121491 61492 31493 91494 121495 61496 31497 91498 121499 61500 31501 91502 121503 61504 31505 91506 121507 61508 31509 91510 121511 61512 31513 91514 121515 61516 31517 91518 121519 61520 31521 91522 121523 61524 31525 91526 121527 61528 31529 91530 121531 61532 31533 91534 121535 61536 31537 91538 121539 61540 31541 91542 121543 61544 31545 91546 121547 61548 31549 91550 121551 61552 31553 91554 121555 61556 31557 91558 121559 61560 31561 91562 121563 61564 31565 91566 121567 61568 31569 91570 121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 317 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 5978 Killed /usr/bin/gp -q -emacs Timing: real 0m21.091s user 0m16.030s sys 0m4.969s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:35:24 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 3157 9158 12159 6160 3161 9162 12163 6164 3165 9166 12167 6168 3169 9170 12171 6172 3173 9174 12175 6176 3177 9178 12179 6180 3181 9182 12183 6184 3185 9186 12187 6188 3189 9190 12191 6192 3193 9194 12195 6196 3197 9198 12199 6200 3201 9202 12203 6204 3205 9206 12207 6208 3209 9210 12211 6212 3213 9214 12215 6216 3217 9218 12219 6220 3221 9222 12223 6224 3225 9226 12227 6228 3229 9230 12231 6232 3233 9234 12235 6236 3237 9238 12239 6240 3241 9242 12243 6244 3245 9246 12247 6248 3249 9250 12251 6252 3253 9254 12255 6256 3257 9258 12259 6260 3261 9262 12263 6264 3265 9266 12267 6268 3269 9270 12271 6272 3273 9274 12275 6276 3277 9278 12279 6280 3281 9282 12283 6284 3285 9286 12287 6288 3289 9290 12291 6292 3293 9294 12295 6296 3297 9298 12299 6300 3301 9302 12303 6304 3305 9306 12307 6308 3309 9310 12311 6312 3313 9314 12315 6316 3317 9318 12319 6320 3321 9322 12323 6324 3325 9326 12327 6328 3329 9330 12331 6332 3333 9334 12335 6336 3337 9338 12339 6340 3341 9342 12343 6344 3345 9346 12347 6348 3349 9350 12351 6352 3353 9354 12355 6356 3357 9358 12359 6360 3361 9362 12363 6364 3365 9366 12367 6368 3369 9370 12371 6372 3373 9374 12375 6376 3377 9378 12379 6380 3381 9382 12383 6384 3385 9386 12387 6388 3389 9390 12391 6392 3393 9394 12395 6396 3397 9398 12399 6400 3401 9402 12403 6404 3405 9406 12407 6408 3409 9410 12411 6412 3413 9414 12415 6416 3417 9418 12419 6420 3421 9422 12423 6424 3425 9426 12427 6428 3429 9430 12431 6432 3433 9434 12435 6436 3437 9438 12439 6440 3441 9442 12443 6444 3445 9446 12447 6448 3449 9450 12451 6452 3453 9454 12455 6456 3457 9458 12459 6460 3461 9462 12463 6464 3465 9466 12467 6468 3469 9470 12471 6472 3473 9474 12475 6476 3477 9478 12479 6480 3481 9482 12483 6484 3485 9486 12487 6488 3489 9490 12491 6492 3493 9494 12495 6496 3497 9498 12499 6500 3501 9502 12503 6504 3505 9506 12507 6508 3509 9510 12511 6512 3513 9514 12515 6516 3517 9518 12519 6520 3521 9522 12523 6524 3525 9526 12527 6528 3529 9530 12531 6532 3533 9534 12535 6536 3537 9538 12539 6540 3541 9542 12543 6544 3545 9546 12547 6548 3549 9550 12551 6552 3553 9554 12555 6556 3557 9558 12559 6560 3561 9562 12563 6564 3565 9566 12567 6568 3569 9570 12571 6572 3573 9574 12575 6576 3577 9578 12579 6580 3581 9582 12583 6584 3585 9586 12587 6588 3589 9590 12591 6592 3593 9594 12595 6596 3597 9598 12599 6600 3601 9602 12603 6604 3605 9606 12607 6608 3609 9610 12611 6612 3613 9614 12615 6616 3617 9618 12619 6620 3621 9622 12623 6624 3625 9626 12627 6628 3629 9630 12631 6632 3633 9634 12635 6636 3637 9638 12639 6640 3641 9642 12643 6644 3645 9646 12647 6648 3649 9650 12651 6652 3653 9654 12655 6656 3657 9658 12659 6660 3661 9662 12663 6664 3665 9666 12667 6668 3669 9670 12671 6672 3673 9674 12675 6676 3677 9678 12679 6680 3681 9682 12683 6684 3685 9686 12687 6688 3689 9690 12691 6692 3693 9694 12695 6696 3697 9698 12699 6700 3701 9702 12703 6704 3705 9706 12707 6708 3709 9710 12711 6712 3713 9714 12715 6716 3717 9718 12719 6720 3721 9722 12723 6724 3725 9726 12727 6728 3729 9730 12731 6732 3733 9734 12735 6736 3737 9738 12739 6740 3741 9742 12743 6744 3745 9746 12747 6748 3749 9750 12751 6752 3753 9754 12755 6756 3757 9758 12759 6760 3761 9762 12763 6764 3765 9766 12767 6768 3769 9770 12771 6772 3773 9774 12775 6776 3777 9778 12779 6780 3781 9782 12783 6784 3785 9786 12787 6788 3789 9790 12791 6792 3793 9794 12795 6796 3797 9798 12799 6800 3801 9802 12803 6804 3805 9806 12807 6808 3809 9810 12811 6812 3813 9814 12815 6816 3817 9818 12819 6820 3821 9822 12823 6824 3825 9826 12827 6828 3829 9830 12831 6832 3833 9834 12835 6836 3837 9838 12839 6840 3841 9842 12843 6844 3845 9846 12847 6848 3849 9850 12851 6852 3853 9854 12855 6856 3857 9858 12859 6860 3861 9862 12863 6864 3865 9866 12867 6868 3869 9870 12871 6872 3873 9874 12875 6876 3877 9878 12879 6880 3881 9882 12883 6884 3885 9886 12887 6888 3889 9890 12891 6892 3893 9894 12895 6896 3897 9898 12899 6900 3901 9902 12903 6904 3905 9906 12907 6908 3909 9910 12911 6912 3913 9914 12915 6916 3917 9918 12919 6920 3921 9922 12923 6924 3925 9926 12927 6928 3929 9930 12931 6932 3933 9934 12935 6936 3937 9938 12939 6940 3941 9942 12943 6944 3945 9946 12947 6948 3949 9950 12951 6952 3953 9954 12955 6956 3957 9958 12959 6960 3961 9962 12963 6964 3965 9966 12967 6968 3969 9970 12971 6972 3973 9974 12975 6976 3977 9978 12979 6980 3981 9982 12983 6984 3985 9986 12987 6988 3989 9990 12991 6992 3993 9994 12995 6996 3997 9998 12999 61000 31001 91002 121003 61004 31005 91006 121007 61008 31009 91010 121011 61012 31013 91014 121015 61016 31017 91018 121019 61020 31021 91022 121023 61024 31025 91026 121027 61028 31029 91030 121031 61032 31033 91034 121035 61036 31037 91038 121039 61040 31041 91042 121043 61044 31045 91046 121047 61048 31049 91050 121051 61052 31053 91054 121055 61056 31057 91058 121059 61060 31061 91062 121063 61064 31065 91066 121067 61068 31069 91070 121071 61072 31073 91074 121075 61076 31077 91078 121079 61080 31081 91082 121083 61084 31085 91086 121087 61088 31089 91090 121091 61092 31093 91094 121095 61096 31097 91098 121099 61100 31101 91102 121103 61104 31105 91106 121107 61108 31109 91110 121111 61112 31113 91114 121115 61116 31117 91118 121119 61120 31121 91122 121123 61124 31125 91126 121127 61128 31129 91130 121131 61132 31133 91134 121135 61136 31137 91138 121139 61140 31141 91142 121143 61144 31145 91146 121147 61148 31149 91150 121151 61152 31153 91154 121155 61156 31157 91158 121159 61160 31161 91162 121163 61164 31165 91166 121167 61168 31169 91170 121171 61172 31173 91174 121175 61176 31177 91178 121179 61180 31181 91182 121183 61184 31185 91186 121187 61188 31189 91190 121191 61192 31193 91194 121195 61196 31197 91198 121199 61200 31201 91202 121203 61204 31205 91206 121207 61208 31209 91210 121211 61212 31213 91214 121215 61216 31217 91218 121219 61220 31221 91222 121223 61224 31225 91226 121227 61228 31229 91230 121231 61232 31233 91234 121235 61236 31237 91238 121239 61240 31241 91242 121243 61244 31245 91246 121247 61248 31249 91250 121251 61252 31253 91254 121255 61256 31257 91258 121259 61260 31261 91262 121263 61264 31265 91266 121267 61268 31269 91270 121271 61272 31273 91274 121275 61276 31277 91278 121279 61280 31281 91282 121283 61284 31285 91286 121287 61288 31289 91290 121291 61292 31293 91294 121295 61296 31297 91298 121299 61300 31301 91302 121303 61304 31305 91306 121307 61308 31309 91310 121311 61312 31313 91314 121315 61316 31317 91318 121319 61320 31321 91322 121323 61324 31325 91326 121327 61328 31329 91330 121331 61332 31333 91334 121335 61336 31337 91338 121339 61340 31341 91342 121343 61344 31345 91346 121347 61348 31349 91350 121351 61352 31353 91354 121355 61356 31357 91358 121359 61360 31361 91362 121363 61364 31365 91366 121367 61368 31369 91370 121371 61372 31373 91374 121375 61376 31377 91378 121379 61380 31381 91382 121383 61384 31385 91386 121387 61388 31389 91390 121391 61392 31393 91394 121395 61396 31397 91398 121399 61400 31401 91402 121403 61404 31405 91406 121407 61408 31409 91410 121411 61412 31413 91414 121415 61416 31417 91418 121419 61420 31421 91422 121423 61424 31425 91426 121427 61428 31429 91430 121431 61432 31433 91434 121435 61436 31437 91438 121439 61440 31441 91442 121443 61444 31445 91446 121447 61448 31449 91450 121451 61452 31453 91454 121455 61456 31457 91458 121459 61460 31461 91462 121463 61464 31465 91466 121467 61468 31469 91470 121471 61472 31473 91474 121475 61476 31477 91478 121479 61480 31481 91482 121483 61484 31485 91486 121487 61488 31489 91490 121491 61492 31493 91494 121495 61496 31497 91498 121499 61500 31501 91502 121503 61504 31505 91506 121507 61508 31509 91510 121511 61512 31513 91514 121515 61516 31517 91518 121519 61520 31521 91522 121523 61524 31525 91526 121527 61528 31529 91530 121531 61532 31533 91534 121535 61536 31537 91538 121539 61540 31541 91542 121543 61544 31545 91546 121547 61548 31549 91550 121551 61552 31553 91554 121555 61556 31557 91558 121559 61560 31561 91562 121563 61564 31565 91566 121567 61568 31569 91570 121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 317 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 6015 Killed /usr/bin/gp -q -emacs Timing: real 0m21.156s user 0m15.907s sys 0m5.093s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:35:31 2005 Input: m=a=3;r=1;n=13;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:35:41 2005 Input: m=a=3;r=1;n=11;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 53 44 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:35:54 2005 Input: m=a=3;r=1;n=9;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:36:02 2005 Input: m=a=3;r=1;n=7;print(m,r); while(m>1,if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 22 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:38:55 2005 Input: m=a=3;r=1;n=7;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 22 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:39:11 2005 Input: m=a=3;r=1;n=9;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:39:24 2005 Input: m=a=3;r=1;n=11;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 53 44 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:39:38 2005 Input: m=a=3;r=1;n=13;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:40:08 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 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91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 317 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 6114 Killed /usr/bin/gp -q -emacs Timing: real 0m21.115s user 0m15.945s sys 0m5.055s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:46:28 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,r=r+1;if(m+2<>a+r,if(a*mn,m=m-n);if(m<>0,print(m,r))),m=0)) Output: ? 31 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:46:41 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,r=r+1;if(m+2<>a+r,if(a*mn,m=m-n);if(m<>0,print(m,r)))),m=0) Output: ? 31 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...-n);if(m<>0,print(m,r)))),m=0) ^----- Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:46:53 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,r=r+1;if(m+2<>a+r,if(a*mn,m=m-n);if(m<>0,print(m,r)))),m=0)) Output: ? 31 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...-n);if(m<>0,print(m,r)))),m=0)) ^------ Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:47:00 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,r=r+1;if(m+2<>a+r,if(a*mn,m=m-n);if(m<>0,print(m,r))),m=0)) Output: ? 31 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:47:22 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,r=r+1;if(m+2n,m=m-n);if(m<>0,print(m,r))),m=0)) Output: ? 31 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:47:41 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,r=r+1;if(m+2<=a+r,if(a*mn,m=m-n);if(m<>0,print(m,r))),m=0)) Output: ? 31 ? 92 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:48:58 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,r=r+1;if(m<>a,if(a*mn,m=m-n);if(m<>0,print(m,r))),m=0)) Output: ? 31 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:49:32 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,r=r+1;if(m+2<>a+r,if(a*mn,m=m-n);if(m<>0,print(m,r))),m=0)) Output: ? 31 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:49:49 2005 Input: m=a=3;r=1;n=15;print(m,r); while(m>1,r=r+1;if(m+2=a+r,if(a*mn,m=m-n);if(m<>0,print(m,r))),m=0)) Output: ? 31 ? ? Errors (if any) and Timing Info: *** unexpected character: while(m>1,r=r+1;if(m+2=a+r,if(a*m1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 3157 9158 12159 6160 3161 9162 12163 6164 3165 9166 12167 6168 3169 9170 12171 6172 3173 9174 12175 6176 3177 9178 12179 6180 3181 9182 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3753 9754 12755 6756 3757 9758 12759 6760 3761 9762 12763 6764 3765 9766 12767 6768 3769 9770 12771 6772 3773 9774 12775 6776 3777 9778 12779 6780 3781 9782 12783 6784 3785 9786 12787 6788 3789 9790 12791 6792 3793 9794 12795 6796 3797 9798 12799 6800 3801 9802 12803 6804 3805 9806 12807 6808 3809 9810 12811 6812 3813 9814 12815 6816 3817 9818 12819 6820 3821 9822 12823 6824 3825 9826 12827 6828 3829 9830 12831 6832 3833 9834 12835 6836 3837 9838 12839 6840 3841 9842 12843 6844 3845 9846 12847 6848 3849 9850 12851 6852 3853 9854 12855 6856 3857 9858 12859 6860 3861 9862 12863 6864 3865 9866 12867 6868 3869 9870 12871 6872 3873 9874 12875 6876 3877 9878 12879 6880 3881 9882 12883 6884 3885 9886 12887 6888 3889 9890 12891 6892 3893 9894 12895 6896 3897 9898 12899 6900 3901 9902 12903 6904 3905 9906 12907 6908 3909 9910 12911 6912 3913 9914 12915 6916 3917 9918 12919 6920 3921 9922 12923 6924 3925 9926 12927 6928 3929 9930 12931 6932 3933 9934 12935 6936 3937 9938 12939 6940 3941 9942 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61272 31273 91274 121275 61276 31277 91278 121279 61280 31281 91282 121283 61284 31285 91286 121287 61288 31289 91290 121291 61292 31293 91294 121295 61296 31297 91298 121299 61300 31301 91302 121303 61304 31305 91306 121307 61308 31309 91310 121311 61312 31313 91314 121315 61316 31317 91318 121319 61320 31321 91322 121323 61324 31325 91326 121327 61328 31329 91330 121331 61332 31333 91334 121335 61336 31337 91338 121339 61340 31341 91342 121343 61344 31345 91346 121347 61348 31349 91350 121351 61352 31353 91354 121355 61356 31357 91358 121359 61360 31361 91362 121363 61364 31365 91366 121367 61368 31369 91370 121371 61372 31373 91374 121375 61376 31377 91378 121379 61380 31381 91382 121383 61384 31385 91386 121387 61388 31389 91390 121391 61392 31393 91394 121395 61396 31397 91398 121399 61400 31401 91402 121403 61404 31405 91406 121407 61408 31409 91410 121411 61412 31413 91414 121415 61416 31417 91418 121419 61420 31421 91422 121423 61424 31425 91426 121427 61428 31429 91430 121431 61432 31433 91434 121435 61436 31437 91438 121439 61440 31441 91442 121443 61444 31445 91446 121447 61448 31449 91450 121451 61452 31453 91454 121455 61456 31457 91458 121459 61460 31461 91462 121463 61464 31465 91466 121467 61468 31469 91470 121471 61472 31473 91474 121475 61476 31477 91478 121479 61480 31481 91482 121483 61484 31485 91486 121487 61488 31489 91490 121491 61492 31493 91494 121495 61496 31497 91498 121499 61500 31501 91502 121503 61504 31505 91506 121507 61508 31509 91510 121511 61512 31513 91514 121515 61516 31517 91518 121519 61520 31521 91522 121523 61524 31525 91526 121527 61528 31529 91530 121531 61532 31533 91534 121535 61536 31537 91538 121539 61540 31541 91542 121543 61544 31545 91546 121547 61548 31549 91550 121551 61552 31553 91554 121555 61556 31557 91558 121559 61560 31561 91562 121563 61564 31565 91566 121567 61568 31569 91570 121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 317 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 6285 Killed /usr/bin/gp -q -emacs Timing: real 0m21.282s user 0m15.826s sys 0m5.175s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:51:39 2005 Input: m=a=3;r=1;n=13;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:51:49 2005 Input: m=a=3;r=1;n=11;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 53 44 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:52:56 2005 Input: m=a=3;r=1;n=341;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 92 273 814 2435 476 1417 828 2469 5610 16811 16312 14813 10314 30915 24516 5317 15918 13619 6720 20121 26222 10423 31224 25425 8026 24027 3828 11429 130 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 03:53:33 2005 Input: m=a=3;r=1;n=7;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 22 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '139.168' ************** PARI ***************** Host 139.168.223.35 (139.168.223.35) Time: Sun Mar 20 05:40:28 2005 Input: factor(1079007) Output: ? [3 1] [17 1] [21157 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '139.168' ************** PARI ***************** Host 139.168.223.35 (139.168.223.35) Time: Sun Mar 20 05:41:00 2005 Input: factor(22) Output: ? [2 1] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.223.35 (139.168.223.35) Time: Sun Mar 20 05:41:33 2005 Input: factor(1079007) Output: ? [3 1] [17 1] [21157 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.223.35 (139.168.223.35) Time: Sun Mar 20 05:42:20 2005 Input: factor(210283) Output: ? [210283 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.223.35 (139.168.223.35) Time: Sun Mar 20 05:42:54 2005 Input: factor(83393192) Output: ? [2 3] [71 1] [146819 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.223.35 (139.168.223.35) Time: Sun Mar 20 05:44:23 2005 Input: factor(5152) Output: ? [2 5] [7 1] [23 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '139.168' ************** PARI ***************** Host 139.168.223.35 (139.168.223.35) Time: Sun Mar 20 05:46:09 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.223.35 (139.168.223.35) Time: Sun Mar 20 05:46:34 2005 Input: evalf(Pi) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '139.168' ************** PARI ***************** Host 139.168.223.35 (139.168.223.35) Time: Sun Mar 20 05:48:14 2005 Input: lcm(22,37,5152) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: lcm(22,37,5152) ^------ Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '139.168' ************** PARI ***************** Host 139.168.223.35 (139.168.223.35) Time: Sun Mar 20 05:51:06 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 06:13:08 2005 Input: polgalois(x^5+20*x+32) Output: ? [10, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.011s sys 0m0.005s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sun Mar 20 06:16:32 2005 Input: polgalois(x^5+20*x+16) Output: ? [60, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sun Mar 20 06:17:34 2005 Input: polgalois(x^5+10*x+20) Output: ? [120, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sun Mar 20 06:19:02 2005 Input: polgalois(x^5-x^4-x^2+x-1) Output: ? [120, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.011s sys 0m0.004s '217.228' ************** PARI ***************** Host 217.228.68.224 (217.228.68.224) Time: Sun Mar 20 06:19:15 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sun Mar 20 06:24:55 2005 Input: polgalois(31*x^6-42*x^5+3*x^4+9*x^2-6*x+1) Output: ? [12, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.019s sys 0m0.007s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 06:27:00 2005 Input: polgalois(10*x^6+70*x^3-603*x^2+1225) Output: ? [720, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.023s sys 0m0.007s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sun Mar 20 06:31:12 2005 Input: polgalois(x^4-x-10) Output: ? [24, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.011s sys 0m0.004s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sun Mar 20 06:34:47 2005 Input: polgalois(x^4+(x-2)^4-34) Output: ? ? Errors (if any) and Timing Info: *** sorry, galois of reducible polynomial is not yet implemented. Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '129.120' ************** PARI ***************** Host 129.120.202.73 (129.120.202.73) Time: Sun Mar 20 14:17:57 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.200s user 0m0.006s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:43:25 2005 Input: m=a=3;r=1;n=7;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n); if(m<>0),print(m,r)))) Output: ? 31 ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...r),m=a*m-n;if(m>n,m=m-n); ^ *** expected character: ',' instead of: if(m<>0),print(m,r)))) ^--------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:44:09 2005 Input: m=a=3;r=1;n=7;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n); if(m<>0,print(m,r)))) Output: ? 31 ? ? 31 ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...r),m=a*m-n;if(m>n,m=m-n); ^ *** Warning: unused characters: )). Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:45:55 2005 Input: m=a=3;r=1;n=7;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 22 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:46:07 2005 Input: m=a=3;r=1;n=7;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n); if(m<>0,print(m,r)))) Output: ? 31 ? ? 31 ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...r),m=a*m-n;if(m>n,m=m-n); ^ *** Warning: unused characters: )). Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:46:17 2005 Input: m=a=3;r=1;n=7;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 22 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:46:31 2005 Input: m=a=3;r=1;n=7;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n); if(m<>0,print(m,r)))) Output: ? 31 ? ? 31 ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...r),m=a*m-n;if(m>n,m=m-n); ^ *** Warning: unused characters: )). Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:46:40 2005 Input: m=a=3;r=1;n=7;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? 22 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:48:19 2005 Input: m=a=3;r=1;n=9;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:48:32 2005 Input: m=a=2;r=1;n=9;print(m,r); while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 ? 42 83 74 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:51:28 2005 Input: m=a=2;r=1;n=9;print(m,r); while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:52:38 2005 Input: m=a=2;r=1;n=9;print(m,r);m=a*m; while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 ? 82 73 54 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:53:23 2005 Input: m=a=2;r=1;n=9;print(m,r);m=a*m;print(m,r+1); while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 42 ? 82 73 54 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:54:07 2005 Input: m=a=2;r=1;n=9;print(m,r);m=a*m;print(m,r+1);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 42 82 73 54 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:54:58 2005 Input: m=a=2;r=1;n=9;print(m,r);m=a*m;print(m,r=r+1);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 42 83 74 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:55:21 2005 Input: m=a=2;r=1;n=9;print(m,r);print(m=a*m,r=r+1);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 42 83 74 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:56:21 2005 Input: m=a=3;r=1;n=9;print(m,r);print(m=a*m,r=r+1);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 92 93 94 95 96 97 98 99 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 9100 9101 9102 9103 9104 9105 9106 9107 9108 9109 9110 9111 9112 9113 9114 9115 9116 9117 9118 9119 9120 9121 9122 9123 9124 9125 9126 9127 9128 9129 9130 9131 9132 9133 9134 9135 9136 9137 9138 9139 9140 9141 9142 9143 9144 9145 9146 9147 9148 9149 9150 9151 9152 9153 9154 9155 9156 9157 9158 9159 9160 9161 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Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13433 Killed /usr/bin/gp -q -emacs Timing: real 0m21.218s user 0m15.662s sys 0m5.338s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 14:59:05 2005 Input: m=a=3;r=1;n=15;print(m,r);print(m=a*m,r=r+1);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 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61396 31397 91398 121399 61400 31401 91402 121403 61404 31405 91406 121407 61408 31409 91410 121411 61412 31413 91414 121415 61416 31417 91418 121419 61420 31421 91422 121423 61424 31425 91426 121427 61428 31429 91430 121431 61432 31433 91434 121435 61436 31437 91438 121439 61440 31441 91442 121443 61444 31445 91446 121447 61448 31449 91450 121451 61452 31453 91454 121455 61456 31457 91458 121459 61460 31461 91462 121463 61464 31465 91466 121467 61468 31469 91470 121471 61472 31473 91474 121475 61476 31477 91478 121479 61480 31481 91482 121483 61484 31485 91486 121487 61488 31489 91490 121491 61492 31493 91494 121495 61496 31497 91498 121499 61500 31501 91502 121503 61504 31505 91506 121507 61508 31509 91510 121511 61512 31513 91514 121515 61516 31517 91518 121519 61520 31521 91522 121523 61524 31525 91526 121527 61528 31529 91530 121531 61532 31533 91534 121535 61536 31537 91538 121539 61540 31541 91542 121543 61544 31545 91546 121547 61548 31549 91550 121551 61552 31553 91554 121555 61556 31557 91558 121559 61560 31561 91562 121563 61564 31565 91566 121567 61568 31569 91570 121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 31777 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13463 Killed /usr/bin/gp -q -emacs Timing: real 0m21.035s user 0m15.460s sys 0m5.540s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:02:24 2005 Input: m=a=3;r=1;n=15;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 92 123 64 35 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:03:14 2005 Input: m=a=3;r=1;n=15;print(m,r);print(m=a*m,r=r+1);while(m>=a,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 3157 9158 12159 6160 3161 9162 12163 6164 3165 9166 12167 6168 3169 9170 12171 6172 3173 9174 12175 6176 3177 9178 12179 6180 3181 9182 12183 6184 3185 9186 12187 6188 3189 9190 12191 6192 3193 9194 12195 6196 3197 9198 12199 6200 3201 9202 12203 6204 3205 9206 12207 6208 3209 9210 12211 6212 3213 9214 12215 6216 3217 9218 12219 6220 3221 9222 12223 6224 3225 9226 12227 6228 3229 9230 12231 6232 3233 9234 12235 6236 3237 9238 12239 6240 3241 9242 12243 6244 3245 9246 12247 6248 3249 9250 12251 6252 3253 9254 12255 6256 3257 9258 12259 6260 3261 9262 12263 6264 3265 9266 12267 6268 3269 9270 12271 6272 3273 9274 12275 6276 3277 9278 12279 6280 3281 9282 12283 6284 3285 9286 12287 6288 3289 9290 12291 6292 3293 9294 12295 6296 3297 9298 12299 6300 3301 9302 12303 6304 3305 9306 12307 6308 3309 9310 12311 6312 3313 9314 12315 6316 3317 9318 12319 6320 3321 9322 12323 6324 3325 9326 12327 6328 3329 9330 12331 6332 3333 9334 12335 6336 3337 9338 12339 6340 3341 9342 12343 6344 3345 9346 12347 6348 3349 9350 12351 6352 3353 9354 12355 6356 3357 9358 12359 6360 3361 9362 12363 6364 3365 9366 12367 6368 3369 9370 12371 6372 3373 9374 12375 6376 3377 9378 12379 6380 3381 9382 12383 6384 3385 9386 12387 6388 3389 9390 12391 6392 3393 9394 12395 6396 3397 9398 12399 6400 3401 9402 12403 6404 3405 9406 12407 6408 3409 9410 12411 6412 3413 9414 12415 6416 3417 9418 12419 6420 3421 9422 12423 6424 3425 9426 12427 6428 3429 9430 12431 6432 3433 9434 12435 6436 3437 9438 12439 6440 3441 9442 12443 6444 3445 9446 12447 6448 3449 9450 12451 6452 3453 9454 12455 6456 3457 9458 12459 6460 3461 9462 12463 6464 3465 9466 12467 6468 3469 9470 12471 6472 3473 9474 12475 6476 3477 9478 12479 6480 3481 9482 12483 6484 3485 9486 12487 6488 3489 9490 12491 6492 3493 9494 12495 6496 3497 9498 12499 6500 3501 9502 12503 6504 3505 9506 12507 6508 3509 9510 12511 6512 3513 9514 12515 6516 3517 9518 12519 6520 3521 9522 12523 6524 3525 9526 12527 6528 3529 9530 12531 6532 3533 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121087 61088 31089 91090 121091 61092 31093 91094 121095 61096 31097 91098 121099 61100 31101 91102 121103 61104 31105 91106 121107 61108 31109 91110 121111 61112 31113 91114 121115 61116 31117 91118 121119 61120 31121 91122 121123 61124 31125 91126 121127 61128 31129 91130 121131 61132 31133 91134 121135 61136 31137 91138 121139 61140 31141 91142 121143 61144 31145 91146 121147 61148 31149 91150 121151 61152 31153 91154 121155 61156 31157 91158 121159 61160 31161 91162 121163 61164 31165 91166 121167 61168 31169 91170 121171 61172 31173 91174 121175 61176 31177 91178 121179 61180 31181 91182 121183 61184 31185 91186 121187 61188 31189 91190 121191 61192 31193 91194 121195 61196 31197 91198 121199 61200 31201 91202 121203 61204 31205 91206 121207 61208 31209 91210 121211 61212 31213 91214 121215 61216 31217 91218 121219 61220 31221 91222 121223 61224 31225 91226 121227 61228 31229 91230 121231 61232 31233 91234 121235 61236 31237 91238 121239 61240 31241 91242 121243 61244 31245 91246 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121407 61408 31409 91410 121411 61412 31413 91414 121415 61416 31417 91418 121419 61420 31421 91422 121423 61424 31425 91426 121427 61428 31429 91430 121431 61432 31433 91434 121435 61436 31437 91438 121439 61440 31441 91442 121443 61444 31445 91446 121447 61448 31449 91450 121451 61452 31453 91454 121455 61456 31457 91458 121459 61460 31461 91462 121463 61464 31465 91466 121467 61468 31469 91470 121471 61472 31473 91474 121475 61476 31477 91478 121479 61480 31481 91482 121483 61484 31485 91486 121487 61488 31489 91490 121491 61492 31493 91494 121495 61496 31497 91498 121499 61500 31501 91502 121503 61504 31505 91506 121507 61508 31509 91510 121511 61512 31513 91514 121515 61516 31517 91518 121519 61520 31521 91522 121523 61524 31525 91526 121527 61528 31529 91530 121531 61532 31533 91534 121535 61536 31537 91538 121539 61540 31541 91542 121543 61544 31545 91546 121547 61548 31549 91550 121551 61552 31553 91554 121555 61556 31557 91558 121559 61560 31561 91562 121563 61564 31565 91566 121567 61568 31569 91570 121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 31777 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13511 Killed /usr/bin/gp -q -emacs Timing: real 0m21.079s user 0m15.324s sys 0m5.676s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:03:30 2005 Input: m=a=3;r=1;n=15;print(m,r);print(m=a*m,r=r+1);while(m>a+1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 92 123 64 35 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:05:05 2005 Input: m=a=3;r=1;n=15;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 92 123 64 35 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:06:06 2005 Input: m=a=3;r=1;n=15;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 123 64 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:06:26 2005 Input: m=a=3;r=1;n=13;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:06:38 2005 Input: m=a=3;r=1;n=11;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 53 44 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:07:11 2005 Input: m=a=3;r=1;n=9;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 93 94 95 96 97 98 99 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 9100 9101 9102 9103 9104 9105 9106 9107 9108 9109 9110 9111 9112 9113 9114 9115 9116 9117 9118 9119 9120 9121 9122 9123 9124 9125 9126 9127 9128 9129 9130 9131 9132 9133 9134 9135 9136 9137 9138 9139 9140 9141 9142 9143 9144 9145 9146 9147 9148 9149 9150 9151 9152 9153 9154 9155 9156 9157 9158 9159 9160 9161 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Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13582 Killed /usr/bin/gp -q -emacs Timing: real 0m21.055s user 0m15.500s sys 0m5.501s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:07:21 2005 Input: m=a=2;r=1;n=9;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 83 74 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:07:32 2005 Input: m=a=2;r=1;n=7;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:07:41 2005 Input: m=a=2;r=1;n=11;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 83 54 105 96 77 38 69 110 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:07:58 2005 Input: m=a=2;r=1;n=13;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 83 34 65 126 117 98 59 1010 711 112 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:08:18 2005 Input: m=a=2;r=1;n=15;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 83 14 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:08:54 2005 Input: m=a=3;r=1;n=9;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 93 94 95 96 97 98 99 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 9100 9101 9102 9103 9104 9105 9106 9107 9108 9109 9110 9111 9112 9113 9114 9115 9116 9117 9118 9119 9120 9121 9122 9123 9124 9125 9126 9127 9128 9129 9130 9131 9132 9133 9134 9135 9136 9137 9138 9139 9140 9141 9142 9143 9144 9145 9146 9147 9148 9149 9150 9151 9152 9153 9154 9155 9156 9157 9158 9159 9160 9161 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91633 91634 91635 91636 91637 91638 91639 91640 91641 91642 91643 91644 91645 91646 91647 91648 91649 91650 91651 91652 91653 91654 91655 91656 91657 91658 91659 91660 91661 91662 91663 91664 91665 91666 91667 91668 91669 91670 91671 91672 91673 91674 91675 91676 91677 91678 91679 91680 91681 91682 91683 91684 91685 91686 91687 91688 91689 91690 91691 91692 91693 91694 91695 91696 91697 91698 91699 91700 91701 91702 91703 91704 91705 91706 91707 91708 91709 91710 91711 91712 91713 91714 91715 91716 91717 91718 91719 91720 91721 91722 91723 91724 91725 91726 91727 91728 91729 91730 91731 91732 91733 91734 91735 91736 91737 91738 91739 91740 91741 91742 91743 91744 91745 91746 91747 91748 91749 91750 91751 91752 91753 91754 91755 91756 91757 91758 91759 91760 91761 91762 91763 91764 91765 91766 91767 91768 91769 91770 91771 91772 91773 91774 91775 91776 91777 91778 91779 91780 91781 91782 91783 91784 91785 91786 91787 91788 91789 91790 91791 91792 91793 91794 91795 91796 91797 91798 91799 91800 91801 91802 91803 91804 91805 91806 91807 91808 91809 91810 91811 91812 91813 91814 91815 91816 91817 91818 91819 91820 91821 91822 91823 91824 91825 91826 91827 91828 91829 91830 91831 91832 91833 91834 91835 91836 91837 91838 91839 91840 91841 91842 91843 91844 91845 91846 91847 91848 91849 91850 91851 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13638 Killed /usr/bin/gp -q -emacs Timing: real 0m21.003s user 0m15.152s sys 0m5.848s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:11:19 2005 Input: m=a=3;r=1;n=9;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:12:45 2005 Input: m=a=10;r=1;n=3;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 101 1002 9943 99344 993345 9933346 99333347 993333348 9933333349 993333333410 9933333333411 99333333333412 993333333333413 9933333333333414 99333333333333415 993333333333333416 9933333333333333417 99333333333333333418 993333333333333333419 9933333333333333333420 99333333333333333333421 993333333333333333333422 9933333333333333333333423 99333333333333333333333424 993333333333333333333333425 9933333333333333333333333426 99333333333333333333333333427 993333333333333333333333333428 9933333333333333333333333333429 99333333333333333333333333333430 993333333333333333333333333333431 9933333333333333333333333333333432 99333333333333333333333333333333433 993333333333333333333333333333333434 9933333333333333333333333333333333435 99333333333333333333333333333333333436 993333333333333333333333333333333333437 9933333333333333333333333333333333333438 99333333333333333333333333333333333333439 993333333333333333333333333333333333333440 9933333333333333333333333333333333333333441 99333333333333333333333333333333333333333442 993333333333333333333333333333333333333333443 9933333333333333333333333333333333333333333444 99333333333333333333333333333333333333333333445 993333333333333333333333333333333333333333333446 9933333333333333333333333333333333333333333333447 99333333333333333333333333333333333333333333333448 993333333333333333333333333333333333333333333333449 9933333333333333333333333333333333333333333333333450 99333333333333333333333333333333333333333333333333451 993333333333333333333333333333333333333333333333333452 9933333333333333333333333333333333333333333333333333453 99333333333333333333333333333333333333333333333333333454 993333333333333333333333333333333333333333333333333333455 9933333333333333333333333333333333333333333333333333333456 99333333333333333333333333333333333333333333333333333333457 993333333333333333333333333333333333333333333333333333333458 9933333333333333333333333333333333333333333333333333333333459 99333333333333333333333333333333333333333333333333333333333460 993333333333333333333333333333333333333333333333333333333333461 9933333333333333333333333333333333333333333333333333333333333462 99333333333333333333333333333333333333333333333333333333333333463 993333333333333333333333333333333333333333333333333333333333333464 9933333333333333333333333333333333333333333333333333333333333333465 99333333333333333333333333333333333333333333333333333333333333333466 993333333333333333333333333333333333333333333333333333333333333333467 9933333333333333333333333333333333333333333333333333333333333333333468 99333333333333333333333333333333333333333333333333333333333333333333469 993333333333333333333333333333333333333333333333333333333333333333333470 9933333333333333333333333333333333333333333333333333333333333333333333471 99333333333333333333333333333333333333333333333333333333333333333333333472 993333333333333333333333333333333333333333333333333333333333333333333333473 9933333333333333333333333333333333333333333333333333333333333333333333333474 99333333333333333333333333333333333333333333333333333333333333333333333333475 993333333333333333333333333333333333333333333333333333333333333333333333333476 9933333333333333333333333333333333333333333333333333333333333333333333333333477 99333333333333333333333333333333333333333333333333333333333333333333333333333478 993333333333333333333333333333333333333333333333333333333333333333333333333333479 9933333333333333333333333333333333333333333333333333333333333333333333333333333480 99333333333333333333333333333333333333333333333333333333333333333333333333333333481 993333333333333333333333333333333333333333333333333333333333333333333333333333333482 9933333333333333333333333333333333333333333333333333333333333333333333333333333333483 99333333333333333333333333333333333333333333333333333333333333333333333333333333333484 993333333333333333333333333333333333333333333333333333333333333333333333333333333333485 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333486 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333487 993333333333333333333333333333333333333333333333333333333333333333333333333333333333333488 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333489 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333490 993333333333333333333333333333333333333333333333333333333333333333333333333333333333333333491 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333492 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333493 993333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333494 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333495 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333496 993333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333497 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333498 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333499 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334100 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334101 993333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334102 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334103 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334104 993333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334105 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334106 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334107 993333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334108 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334109 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334110 993333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334111 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334112 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334113 993333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334114 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334115 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334116 993333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334117 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334118 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334119 993333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334120 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334121 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334122 993333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334123 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334124 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334125 993333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334126 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334127 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334128 993333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334129 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334130 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334131 993333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334132 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334133 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334134 993333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334135 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334136 99333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334137 9933333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13681 Killed /usr/bin/gp -q -emacs Timing: real 0m21.044s user 0m20.965s sys 0m0.037s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:13:05 2005 Input: m=a=2;r=1;n=3;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:14:13 2005 Input: m=a=3;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 133 254 615 1696 4937 14658 43819 1312910 3937311 11810512 35430113 106288914 318865315 956594516 2869782117 8609344918 25828033319 77484098520 232452294121 697356880922 2092070641323 6276211922524 18828635766125 56485907296926 169457721889327 508373165666528 1525119496998129 4575358490992930 13726075472977331 41178226418930532 123534679256790133 370604037770368934 1111812113311105335 3335436339933314536 10006309019799942137 30018927059399824938 90056781178199473339 270170343534598418540 810511030603795254141 2431533091811385760942 7294599275434157281343 21883797826302471842544 65651393478907415526145 196954180436722246576946 590862541310166739729347 1772587623930500219186548 5317762871791500657558149 15953288615374501972672950 47859865846123505918017351 143579597538370517754050552 430738792615111553262150153 1292216377845334659786448954 3876649133536003979359345355 11629947400608011938078034556 34889842201824035814234102157 104669526605472107442702304958 314008579816416322328106913359 942025739449248966984320738560 2826077218347746900952962214161 8478231655043240702858886640962 25434694965129722108576659921363 76304084895389166325729979762564 228912254686167498977189939286165 686736764058502496931569817856966 2060210292175507490794709453569367 6180630876526522472384128360706568 18541892629579567417152385082118169 55625677888738702251457155246352970 166877033666216106754371465739057371 500631100998648320263114397217170572 1501893302995944960789343191651510173 4505679908987834882368029574954528974 13517039726963504647104088724863585375 40551119180890513941312266174590754576 121653357542671541823936798523772262177 364960072628014625471810395571316784978 1094880217884043876415431186713950353379 3284640653652131629246293560141851058580 9853921960956394887738880680425553174181 29561765882869184663216642041276659520982 88685297648607553989649926123829978561383 266055892945822661968949778371489935682584 798167678837467985906849335114469807046185 2394503036512403957720548005343409421136986 7183509109537211873161644016030228263409387 21550527328611635619484932048090684790226588 64651581985834906858454796144272054370678189 193954745957504720575364388432816163112032990 581864237872514161726093165298448489336097391 1745592713617542485178279495895345468008290592 5236778140852627455534838487686036404024870193 15710334422557882366604515463058109212074608994 47131003267673647099813546389174327636223825395 141393009803020941299440639167522982908671474596 424179029409062823898321917502568948726014422197 1272537088227188471694965752507706846178043264998 3817611264681565415084897257523120538534129793399 114528337940446962452546917725693616156023893785100 343585013821340887357640753177080848468071681341101 1030755041464022662072922259531242545404215044009102 3092265124392067986218766778593727636212645132013103 9276795373176203958656300335781182908637935396025104 27830386119528611875968901007343548725913806188061105 83491158358585835627906703022030646177741418564169106 250473475075757506883720109066091938533224255692493107 751420425227272520651160327198275815599672767077465108 2254261275681817561953480981594827446799018301232381109 6762783827045452685860442944784482340397054903697129110 20288351481136358057581328834353447021191164711091373111 60865054443409074172743986503060341063573494133274105112 182595163330227222518231959509181023190720482399822301113 547785489990681667554695878527543069572161447199466889114 1643356469972045002664087635582629208716484341598400653115 4930069409916135007992262906747887626149453024795201945116 14790208229748405023976788720243662878448359074385605821117 44370624689245215071930366160730988635345077223156817449118 133111874067735645215791098482192965906035231669470452333119 399335622203206935647373295446578897718105695008411356985120 1198006866609620806942119886339736693154317085025234070941121 3594020599828862420826359659019210079462951255075702212809122 10782061799486587262479078977057630238388853765227106638413123 32346185398459761787437236931172890715166561295681319915225124 97038556195379285362311710793518672145499683887043959745661125 291115668586137856086935132380556016436499051661131879236969126 873347005758413568260805397141668049309497154983395637710893127 2620041017275240704782416191425004147928491464950186913132665128 7860123051825722114347248574275012443785474394850560739397981129 23580369155477166343041745722825037331356423184551682218193929130 70741107466431499029125237168475111994069269553655046654581773131 212223322399294497087375711505425335982207808660965139963745305132 636669967197883491262127134516276007946623425982895419891235901133 1910009901593650473786381403548828023839870277948686259673707689134 5730029704780951421359144210646484071519610833846058779021123053135 17190089114342854264077432631939452214558832501538176337063369145136 51570267343028562792232297895818356643676497504614529011190107421137 154710802029085688376696893687455069931029492513843587033570322249138 464132406087257065130090681062365209793088477541530761100710966733139 1392397218261771195390272043187095629379265432624592283302132900185140 4177191654785313586170816129561286888137796297873776849906398700541141 12531574964355940758512448388683860664413388893621330549719196101609142 37594724893067822275537345166051581993240166680863991649157588304813143 112784174679203466826612035498154745979720500042591974947472764914425144 338352524037610400479836106494464237939161500127775924842418294743261145 1015057572112831201439508319483392713817484500383327774527254884229769146 3045172716338493604318524958450178141452453501149983323581764652689293147 9135518149015480812955574875350534424357360503449949970745293958067865148 27406554447046442438866724626051603273072081510349849912235881874203581149 82219663341139327316600173878154809819216244531049549736707645622610729150 246658990023417981949800521634464429457648733593148649210122936867832173151 739976970070253945849401564903393288372946200779445947630368810603496505152 2219930910210761837548204694710179865118838602338337842891106431810489501153 6659792730632285512644614084130539595356515807015013528673319295431468489154 19979378191896856537933842252391618786069547421045040586019957886294405453155 59938134575690569613801526757174856358208642263135121758059873658883216345156 179814403727071708841404580271524569074625926789405365274179620976649649021157 539443211181215126524213740814573707223877780368216095822538862929948947049158 1618329633543645379572641222443721121671633341104648287467616588789846841133159 4854988900630936138717923667331163365014900023313944862402849766369540523385160 14564966701892808416153771001993490095044700069941834587208549299108621570141161 43694900105678425248461313005980470285134100209825503761625647897325864710409162 131084700317035275745383939017941410855402300629476511284876943691977594131213163 393254100951105827236151817053824232566206901888429533854630831075932782393625164 1179762302853317481708455451161472697698620705665288601563892493227798347180861165 3539286908559952445125366353484418093095862116995865804691677479683395041542569166 10617860725679857335376099060453254279287586350987597414075032439050185124627693167 31853582177039572006128297181359762837862759052962792242225097317150555373883065168 95560746531118716018384891544079288513588277158888376726675291951451666121649181169 286682239593356148055154674632237865540764831476665130180025875854354998364947529170 860046718780068444165464023896713596622294494429995390540077627563064995094842573171 2580140156340205332496392071690140789866883483289986171620232882689194985284527705172 7740420469020615997489176215070422369600650449869958514860698648067584955853583101173 23221261407061847992467528645211267108801951349609875544582095944202754867560749289174 69663784221185543977402585935633801326405854048829626633746287832608264602682247853175 208991352663556631932207757806901403979217562146488879901238863497824793808046743545176 626974057990669895796623273420704211937652686439466639703716590493474381424140230621177 1880922173972009687389869820262112635812958059318399919111149771480423144272420691849178 5642766521916029062169609460786337907438874177955199757333449314441269432817262075533179 16928299565748087186508828382359013722316622533865599272000347943323808298451786226585180 50784898697244261559526485147077041166949867601596797816001043829971424895355358679741181 152354696091732784678579455441231123500849602804790393448003131489914274686066076039209182 457064088275198354035738366323693370502548808414371180344009394469742824058198228117613183 1371192264825595062107215098971080111507646425243113541032028183409228472174594684352825184 4113576794476785186321645296913240334522939275729340623096084550227685416523784053058461185 12340730383430355558964935890739721003568817827188021869288253650683056249571352159175369186 37022191150291066676894807672219163010706453481564065607864760952049168748714056477526093187 111066573450873200030684423016657489032119360444692196823594282856147506246142169432578265188 333199720352619600092053269049972467096358081334076590470782848568442518738426508297734781189 999599161057858800276159807149917401289074244002229771412348545705327556215279524893204329190 2998797483173576400828479421449752203867222732006689314237045637115982668645838574679612973191 8996392449520729202485438264349256611601668196020067942711136911347948005937515724038838905192 26989177348562187607456314793047769834805004588060203828133410734043844017812547172116516701193 80967532045686562822368944379143309504415013764180611484400232202131532053437641516349550089194 242902596137059688467106833137429928513245041292541834453200696606394596160312924549048650253195 728707788411179065401320499412289785539735123877625503359602089819183788480938773647145950745196 2186123365233537196203961498236869356619205371632876510078806269457551365442816320941437852221197 65583700957006115886118844947106080698576 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13706 Killed /usr/bin/gp -q -emacs Timing: real 0m21.028s user 0m20.944s sys 0m0.058s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:15:02 2005 Input: m=a=3;r=1;n=9;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:15:30 2005 Input: m=a=3;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 133 254 615 1696 4937 14658 43819 1312910 3937311 11810512 35430113 106288914 318865315 956594516 2869782117 8609344918 25828033319 77484098520 232452294121 697356880922 2092070641323 6276211922524 18828635766125 56485907296926 169457721889327 508373165666528 1525119496998129 4575358490992930 13726075472977331 41178226418930532 123534679256790133 370604037770368934 1111812113311105335 3335436339933314536 10006309019799942137 30018927059399824938 90056781178199473339 270170343534598418540 810511030603795254141 2431533091811385760942 7294599275434157281343 21883797826302471842544 65651393478907415526145 196954180436722246576946 590862541310166739729347 1772587623930500219186548 5317762871791500657558149 15953288615374501972672950 47859865846123505918017351 143579597538370517754050552 430738792615111553262150153 1292216377845334659786448954 3876649133536003979359345355 11629947400608011938078034556 34889842201824035814234102157 104669526605472107442702304958 314008579816416322328106913359 942025739449248966984320738560 2826077218347746900952962214161 8478231655043240702858886640962 25434694965129722108576659921363 76304084895389166325729979762564 228912254686167498977189939286165 686736764058502496931569817856966 2060210292175507490794709453569367 6180630876526522472384128360706568 18541892629579567417152385082118169 55625677888738702251457155246352970 166877033666216106754371465739057371 500631100998648320263114397217170572 1501893302995944960789343191651510173 4505679908987834882368029574954528974 13517039726963504647104088724863585375 40551119180890513941312266174590754576 121653357542671541823936798523772262177 364960072628014625471810395571316784978 1094880217884043876415431186713950353379 3284640653652131629246293560141851058580 9853921960956394887738880680425553174181 29561765882869184663216642041276659520982 88685297648607553989649926123829978561383 266055892945822661968949778371489935682584 798167678837467985906849335114469807046185 2394503036512403957720548005343409421136986 7183509109537211873161644016030228263409387 21550527328611635619484932048090684790226588 64651581985834906858454796144272054370678189 193954745957504720575364388432816163112032990 581864237872514161726093165298448489336097391 1745592713617542485178279495895345468008290592 5236778140852627455534838487686036404024870193 15710334422557882366604515463058109212074608994 47131003267673647099813546389174327636223825395 141393009803020941299440639167522982908671474596 424179029409062823898321917502568948726014422197 1272537088227188471694965752507706846178043264998 3817611264681565415084897257523120538534129793399 114528337940446962452546917725693616156023893785100 343585013821340887357640753177080848468071681341101 1030755041464022662072922259531242545404215044009102 3092265124392067986218766778593727636212645132013103 9276795373176203958656300335781182908637935396025104 27830386119528611875968901007343548725913806188061105 83491158358585835627906703022030646177741418564169106 250473475075757506883720109066091938533224255692493107 751420425227272520651160327198275815599672767077465108 2254261275681817561953480981594827446799018301232381109 6762783827045452685860442944784482340397054903697129110 20288351481136358057581328834353447021191164711091373111 60865054443409074172743986503060341063573494133274105112 182595163330227222518231959509181023190720482399822301113 547785489990681667554695878527543069572161447199466889114 1643356469972045002664087635582629208716484341598400653115 4930069409916135007992262906747887626149453024795201945116 14790208229748405023976788720243662878448359074385605821117 44370624689245215071930366160730988635345077223156817449118 133111874067735645215791098482192965906035231669470452333119 399335622203206935647373295446578897718105695008411356985120 1198006866609620806942119886339736693154317085025234070941121 3594020599828862420826359659019210079462951255075702212809122 10782061799486587262479078977057630238388853765227106638413123 32346185398459761787437236931172890715166561295681319915225124 97038556195379285362311710793518672145499683887043959745661125 291115668586137856086935132380556016436499051661131879236969126 873347005758413568260805397141668049309497154983395637710893127 2620041017275240704782416191425004147928491464950186913132665128 7860123051825722114347248574275012443785474394850560739397981129 23580369155477166343041745722825037331356423184551682218193929130 70741107466431499029125237168475111994069269553655046654581773131 212223322399294497087375711505425335982207808660965139963745305132 636669967197883491262127134516276007946623425982895419891235901133 1910009901593650473786381403548828023839870277948686259673707689134 5730029704780951421359144210646484071519610833846058779021123053135 17190089114342854264077432631939452214558832501538176337063369145136 51570267343028562792232297895818356643676497504614529011190107421137 154710802029085688376696893687455069931029492513843587033570322249138 464132406087257065130090681062365209793088477541530761100710966733139 1392397218261771195390272043187095629379265432624592283302132900185140 4177191654785313586170816129561286888137796297873776849906398700541141 12531574964355940758512448388683860664413388893621330549719196101609142 37594724893067822275537345166051581993240166680863991649157588304813143 112784174679203466826612035498154745979720500042591974947472764914425144 338352524037610400479836106494464237939161500127775924842418294743261145 1015057572112831201439508319483392713817484500383327774527254884229769146 3045172716338493604318524958450178141452453501149983323581764652689293147 9135518149015480812955574875350534424357360503449949970745293958067865148 27406554447046442438866724626051603273072081510349849912235881874203581149 82219663341139327316600173878154809819216244531049549736707645622610729150 246658990023417981949800521634464429457648733593148649210122936867832173151 739976970070253945849401564903393288372946200779445947630368810603496505152 2219930910210761837548204694710179865118838602338337842891106431810489501153 6659792730632285512644614084130539595356515807015013528673319295431468489154 19979378191896856537933842252391618786069547421045040586019957886294405453155 59938134575690569613801526757174856358208642263135121758059873658883216345156 179814403727071708841404580271524569074625926789405365274179620976649649021157 539443211181215126524213740814573707223877780368216095822538862929948947049158 1618329633543645379572641222443721121671633341104648287467616588789846841133159 4854988900630936138717923667331163365014900023313944862402849766369540523385160 14564966701892808416153771001993490095044700069941834587208549299108621570141161 43694900105678425248461313005980470285134100209825503761625647897325864710409162 131084700317035275745383939017941410855402300629476511284876943691977594131213163 393254100951105827236151817053824232566206901888429533854630831075932782393625164 1179762302853317481708455451161472697698620705665288601563892493227798347180861165 3539286908559952445125366353484418093095862116995865804691677479683395041542569166 10617860725679857335376099060453254279287586350987597414075032439050185124627693167 31853582177039572006128297181359762837862759052962792242225097317150555373883065168 95560746531118716018384891544079288513588277158888376726675291951451666121649181169 286682239593356148055154674632237865540764831476665130180025875854354998364947529170 860046718780068444165464023896713596622294494429995390540077627563064995094842573171 2580140156340205332496392071690140789866883483289986171620232882689194985284527705172 7740420469020615997489176215070422369600650449869958514860698648067584955853583101173 23221261407061847992467528645211267108801951349609875544582095944202754867560749289174 69663784221185543977402585935633801326405854048829626633746287832608264602682247853175 208991352663556631932207757806901403979217562146488879901238863497824793808046743545176 626974057990669895796623273420704211937652686439466639703716590493474381424140230621177 1880922173972009687389869820262112635812958059318399919111149771480423144272420691849178 5642766521916029062169609460786337907438874177955199757333449314441269432817262075533179 16928299565748087186508828382359013722316622533865599272000347943323808298451786226585180 50784898697244261559526485147077041166949867601596797816001043829971424895355358679741181 152354696091732784678579455441231123500849602804790393448003131489914274686066076039209182 457064088275198354035738366323693370502548808414371180344009394469742824058198228117613183 1371192264825595062107215098971080111507646425243113541032028183409228472174594684352825184 4113576794476785186321645296913240334522939275729340623096084550227685416523784053058461185 12340730383430355558964935890739721003568817827188021869288253650683056249571352159175369186 37022191150291066676894807672219163010706453481564065607864760952049168748714056477526093187 111066573450873200030684423016657489032119360444692196823594282856147506246142169432578265188 333199720352619600092053269049972467096358081334076590470782848568442518738426508297734781189 999599161057858800276159807149917401289074244002229771412348545705327556215279524893204329190 2998797483173576400828479421449752203867222732006689314237045637115982668645838574679612973191 8996392449520729202485438264349256611601668196020067942711136911347948005937515724038838905192 26989177348562187607456314793047769834805004588060203828133410734043844017812547172116516701193 80967532045686562822368944379143309504415013764180611484400232202131532053437641516349550089194 242902596137059688467106833137429928513245041292541834453200696606394596160312924549048650253195 728707788411179065401320499412289785539735123877625503359602089819183788480938773647145950745196 2186123365233537196203961498236869356619205371632876510078806269457551365442816320941437852221197 65583700957006115886118844947106080698576 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13725 Killed /usr/bin/gp -q -emacs Timing: real 0m21.028s user 0m20.935s sys 0m0.066s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:20:22 2005 Input: m=a=3;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 23 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:21:56 2005 Input: m=a=3;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 133 254 615 1696 4937 14658 43819 1312910 3937311 11810512 35430113 106288914 318865315 956594516 2869782117 8609344918 25828033319 77484098520 232452294121 697356880922 2092070641323 6276211922524 18828635766125 56485907296926 169457721889327 508373165666528 1525119496998129 4575358490992930 13726075472977331 41178226418930532 123534679256790133 370604037770368934 1111812113311105335 3335436339933314536 10006309019799942137 30018927059399824938 90056781178199473339 270170343534598418540 810511030603795254141 2431533091811385760942 7294599275434157281343 21883797826302471842544 65651393478907415526145 196954180436722246576946 590862541310166739729347 1772587623930500219186548 5317762871791500657558149 15953288615374501972672950 47859865846123505918017351 143579597538370517754050552 430738792615111553262150153 1292216377845334659786448954 3876649133536003979359345355 11629947400608011938078034556 34889842201824035814234102157 104669526605472107442702304958 314008579816416322328106913359 942025739449248966984320738560 2826077218347746900952962214161 8478231655043240702858886640962 25434694965129722108576659921363 76304084895389166325729979762564 228912254686167498977189939286165 686736764058502496931569817856966 2060210292175507490794709453569367 6180630876526522472384128360706568 18541892629579567417152385082118169 55625677888738702251457155246352970 166877033666216106754371465739057371 500631100998648320263114397217170572 1501893302995944960789343191651510173 4505679908987834882368029574954528974 13517039726963504647104088724863585375 40551119180890513941312266174590754576 121653357542671541823936798523772262177 364960072628014625471810395571316784978 1094880217884043876415431186713950353379 3284640653652131629246293560141851058580 9853921960956394887738880680425553174181 29561765882869184663216642041276659520982 88685297648607553989649926123829978561383 266055892945822661968949778371489935682584 798167678837467985906849335114469807046185 2394503036512403957720548005343409421136986 7183509109537211873161644016030228263409387 21550527328611635619484932048090684790226588 64651581985834906858454796144272054370678189 193954745957504720575364388432816163112032990 581864237872514161726093165298448489336097391 1745592713617542485178279495895345468008290592 5236778140852627455534838487686036404024870193 15710334422557882366604515463058109212074608994 47131003267673647099813546389174327636223825395 141393009803020941299440639167522982908671474596 424179029409062823898321917502568948726014422197 1272537088227188471694965752507706846178043264998 3817611264681565415084897257523120538534129793399 114528337940446962452546917725693616156023893785100 343585013821340887357640753177080848468071681341101 1030755041464022662072922259531242545404215044009102 3092265124392067986218766778593727636212645132013103 9276795373176203958656300335781182908637935396025104 27830386119528611875968901007343548725913806188061105 83491158358585835627906703022030646177741418564169106 250473475075757506883720109066091938533224255692493107 751420425227272520651160327198275815599672767077465108 2254261275681817561953480981594827446799018301232381109 6762783827045452685860442944784482340397054903697129110 20288351481136358057581328834353447021191164711091373111 60865054443409074172743986503060341063573494133274105112 182595163330227222518231959509181023190720482399822301113 547785489990681667554695878527543069572161447199466889114 1643356469972045002664087635582629208716484341598400653115 4930069409916135007992262906747887626149453024795201945116 14790208229748405023976788720243662878448359074385605821117 44370624689245215071930366160730988635345077223156817449118 133111874067735645215791098482192965906035231669470452333119 399335622203206935647373295446578897718105695008411356985120 1198006866609620806942119886339736693154317085025234070941121 3594020599828862420826359659019210079462951255075702212809122 10782061799486587262479078977057630238388853765227106638413123 32346185398459761787437236931172890715166561295681319915225124 97038556195379285362311710793518672145499683887043959745661125 291115668586137856086935132380556016436499051661131879236969126 873347005758413568260805397141668049309497154983395637710893127 2620041017275240704782416191425004147928491464950186913132665128 7860123051825722114347248574275012443785474394850560739397981129 23580369155477166343041745722825037331356423184551682218193929130 70741107466431499029125237168475111994069269553655046654581773131 212223322399294497087375711505425335982207808660965139963745305132 636669967197883491262127134516276007946623425982895419891235901133 1910009901593650473786381403548828023839870277948686259673707689134 5730029704780951421359144210646484071519610833846058779021123053135 17190089114342854264077432631939452214558832501538176337063369145136 51570267343028562792232297895818356643676497504614529011190107421137 154710802029085688376696893687455069931029492513843587033570322249138 464132406087257065130090681062365209793088477541530761100710966733139 1392397218261771195390272043187095629379265432624592283302132900185140 4177191654785313586170816129561286888137796297873776849906398700541141 12531574964355940758512448388683860664413388893621330549719196101609142 37594724893067822275537345166051581993240166680863991649157588304813143 112784174679203466826612035498154745979720500042591974947472764914425144 338352524037610400479836106494464237939161500127775924842418294743261145 1015057572112831201439508319483392713817484500383327774527254884229769146 3045172716338493604318524958450178141452453501149983323581764652689293147 9135518149015480812955574875350534424357360503449949970745293958067865148 27406554447046442438866724626051603273072081510349849912235881874203581149 82219663341139327316600173878154809819216244531049549736707645622610729150 246658990023417981949800521634464429457648733593148649210122936867832173151 739976970070253945849401564903393288372946200779445947630368810603496505152 2219930910210761837548204694710179865118838602338337842891106431810489501153 6659792730632285512644614084130539595356515807015013528673319295431468489154 19979378191896856537933842252391618786069547421045040586019957886294405453155 59938134575690569613801526757174856358208642263135121758059873658883216345156 179814403727071708841404580271524569074625926789405365274179620976649649021157 539443211181215126524213740814573707223877780368216095822538862929948947049158 1618329633543645379572641222443721121671633341104648287467616588789846841133159 4854988900630936138717923667331163365014900023313944862402849766369540523385160 14564966701892808416153771001993490095044700069941834587208549299108621570141161 43694900105678425248461313005980470285134100209825503761625647897325864710409162 131084700317035275745383939017941410855402300629476511284876943691977594131213163 393254100951105827236151817053824232566206901888429533854630831075932782393625164 1179762302853317481708455451161472697698620705665288601563892493227798347180861165 3539286908559952445125366353484418093095862116995865804691677479683395041542569166 10617860725679857335376099060453254279287586350987597414075032439050185124627693167 31853582177039572006128297181359762837862759052962792242225097317150555373883065168 95560746531118716018384891544079288513588277158888376726675291951451666121649181169 286682239593356148055154674632237865540764831476665130180025875854354998364947529170 860046718780068444165464023896713596622294494429995390540077627563064995094842573171 2580140156340205332496392071690140789866883483289986171620232882689194985284527705172 7740420469020615997489176215070422369600650449869958514860698648067584955853583101173 23221261407061847992467528645211267108801951349609875544582095944202754867560749289174 69663784221185543977402585935633801326405854048829626633746287832608264602682247853175 208991352663556631932207757806901403979217562146488879901238863497824793808046743545176 626974057990669895796623273420704211937652686439466639703716590493474381424140230621177 1880922173972009687389869820262112635812958059318399919111149771480423144272420691849178 5642766521916029062169609460786337907438874177955199757333449314441269432817262075533179 16928299565748087186508828382359013722316622533865599272000347943323808298451786226585180 50784898697244261559526485147077041166949867601596797816001043829971424895355358679741181 152354696091732784678579455441231123500849602804790393448003131489914274686066076039209182 457064088275198354035738366323693370502548808414371180344009394469742824058198228117613183 1371192264825595062107215098971080111507646425243113541032028183409228472174594684352825184 4113576794476785186321645296913240334522939275729340623096084550227685416523784053058461185 12340730383430355558964935890739721003568817827188021869288253650683056249571352159175369186 37022191150291066676894807672219163010706453481564065607864760952049168748714056477526093187 111066573450873200030684423016657489032119360444692196823594282856147506246142169432578265188 333199720352619600092053269049972467096358081334076590470782848568442518738426508297734781189 999599161057858800276159807149917401289074244002229771412348545705327556215279524893204329190 2998797483173576400828479421449752203867222732006689314237045637115982668645838574679612973191 8996392449520729202485438264349256611601668196020067942711136911347948005937515724038838905192 26989177348562187607456314793047769834805004588060203828133410734043844017812547172116516701193 80967532045686562822368944379143309504415013764180611484400232202131532053437641516349550089194 242902596137059688467106833137429928513245041292541834453200696606394596160312924549048650253195 728707788411179065401320499412289785539735123877625503359602089819183788480938773647145950745196 2186123365233537196203961498236869356619205371632876510078806269457551365442816320941437852221197 65583700957006115886118844947106080698576 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13795 Killed /usr/bin/gp -q -emacs Timing: real 0m21.040s user 0m20.931s sys 0m0.071s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:22:13 2005 Input: m=a=3;r=1;n=7;print(m,r);if(n<>a*m,print(m,r=r+1));while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 32 23 64 45 56 17 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:22:49 2005 Input: m=a=3;r=1;n=7;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 22 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:23:17 2005 Input: m=a=3;r=1;n=9;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 02 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:25:16 2005 Input: m=a=3;r=1;n=9;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(lift(Mod(m,a)<>0,print(m,r)))) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...t(Mod(m,a)<>0,print(m,r)))) ^-- Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:27:06 2005 Input: m=a=3;r=1;n=9;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(divrem(m,a)[2]<>0,print(m,r)))) Output: ? 31 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:27:38 2005 Input: m=a=3;r=1;n=7;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(divrem(m,a)[2]<>0,print(m,r)))) Output: ? 31 22 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:27:52 2005 Input: m=a=3;r=1;n=9;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(divrem(m,a)[2]<>0,print(m,r)))) Output: ? 31 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:28:14 2005 Input: m=a=3;r=1;n=11;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(divrem(m,a)[2]<>0,print(m,r)))) Output: ? 31 92 53 44 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:28:25 2005 Input: m=a=3;r=1;n=13;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(divrem(m,a)[2]<>0,print(m,r)))) Output: ? 31 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:28:55 2005 Input: m=a=3;r=1;n=15;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(divrem(m,a)[2]<>0,print(m,r)))) Output: ? 31 92 96 910 914 918 922 926 930 934 938 942 946 950 954 958 962 966 970 974 978 982 986 990 994 998 9102 9106 9110 9114 9118 9122 9126 9130 9134 9138 9142 9146 9150 9154 9158 9162 9166 9170 9174 9178 9182 9186 9190 9194 9198 9202 9206 9210 9214 9218 9222 9226 9230 9234 9238 9242 9246 9250 9254 9258 9262 9266 9270 9274 9278 9282 9286 9290 9294 9298 9302 9306 9310 9314 9318 9322 9326 9330 9334 9338 9342 9346 9350 9354 9358 9362 9366 9370 9374 9378 9382 9386 9390 9394 9398 9402 9406 9410 9414 9418 9422 9426 9430 9434 9438 9442 9446 9450 9454 9458 9462 9466 9470 9474 9478 9482 9486 9490 9494 9498 9502 9506 9510 9514 9518 9522 9526 9530 9534 9538 9542 9546 9550 9554 9558 9562 9566 9570 9574 9578 9582 9586 9590 9594 9598 9602 9606 9610 9614 9618 9622 9626 9630 9634 9638 9642 9646 9650 9654 9658 9662 9666 9670 9674 9678 9682 9686 9690 9694 9698 9702 9706 9710 9714 9718 9722 9726 9730 9734 9738 9742 9746 9750 9754 9758 9762 9766 9770 9774 9778 9782 9786 9790 9794 9798 9802 9806 9810 9814 9818 9822 9826 9830 9834 9838 9842 9846 9850 9854 9858 9862 9866 9870 9874 9878 9882 9886 9890 9894 9898 9902 9906 9910 9914 9918 9922 9926 9930 9934 9938 9942 9946 9950 9954 9958 9962 9966 9970 9974 9978 9982 9986 9990 9994 9998 91002 91006 91010 91014 91018 91022 91026 91030 91034 91038 91042 91046 91050 91054 91058 91062 91066 91070 91074 91078 91082 91086 91090 91094 91098 91102 91106 91110 91114 91118 91122 91126 91130 91134 91138 91142 91146 91150 91154 91158 91162 91166 91170 91174 91178 91182 91186 91190 91194 91198 91202 91206 91210 91214 91218 91222 91226 91230 91234 91238 91242 91246 91250 91254 91258 91262 91266 91270 91274 91278 91282 91286 91290 91294 91298 91302 91306 91310 91314 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96630 96634 96638 96642 96646 96650 96654 96658 96662 96666 96670 96674 96678 96682 96686 96690 96694 96698 96702 96706 96710 96714 96718 96722 96726 96730 96734 96738 96742 96746 96750 96754 96758 96762 96766 96770 96774 96778 96782 96786 96790 96794 96798 96802 96806 96810 96814 96818 96822 96826 96830 96834 96838 96842 96846 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13916 Killed /usr/bin/gp -q -emacs Timing: real 0m21.163s user 0m19.290s sys 0m1.710s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:29:45 2005 Input: m=a=3;r=1;n=15;print(m,r);while(m>a,r=r+1;if(a*mn,m=m-n);if(divrem(m,a)[2]<>0,print(m,r)))) Output: ? 31 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:29:59 2005 Input: m=a=3;r=1;n=13;print(m,r);while(m>a,r=r+1;if(a*mn,m=m-n);if(divrem(m,a)[2]<>0,print(m,r)))) Output: ? 31 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:30:11 2005 Input: m=a=3;r=1;n=13;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(divrem(m,a)[2]<>0,print(m,r)))) Output: ? 31 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:30:56 2005 Input: m=a=3;r=1;n=15;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(divrem(m,a)[2]<>0,print(m,r)))) Output: ? 31 92 96 910 914 918 922 926 930 934 938 942 946 950 954 958 962 966 970 974 978 982 986 990 994 998 9102 9106 9110 9114 9118 9122 9126 9130 9134 9138 9142 9146 9150 9154 9158 9162 9166 9170 9174 9178 9182 9186 9190 9194 9198 9202 9206 9210 9214 9218 9222 9226 9230 9234 9238 9242 9246 9250 9254 9258 9262 9266 9270 9274 9278 9282 9286 9290 9294 9298 9302 9306 9310 9314 9318 9322 9326 9330 9334 9338 9342 9346 9350 9354 9358 9362 9366 9370 9374 9378 9382 9386 9390 9394 9398 9402 9406 9410 9414 9418 9422 9426 9430 9434 9438 9442 9446 9450 9454 9458 9462 9466 9470 9474 9478 9482 9486 9490 9494 9498 9502 9506 9510 9514 9518 9522 9526 9530 9534 9538 9542 9546 9550 9554 9558 9562 9566 9570 9574 9578 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95966 95970 95974 95978 95982 95986 95990 95994 95998 96002 96006 96010 96014 96018 96022 96026 96030 96034 96038 96042 96046 96050 96054 96058 96062 96066 96070 96074 96078 96082 96086 96090 96094 96098 96102 96106 96110 96114 96118 96122 96126 96130 96134 96138 96142 96146 96150 96154 96158 96162 96166 96170 96174 96178 96182 96186 96190 96194 96198 96202 96206 96210 96214 96218 96222 96226 96230 96234 96238 96242 96246 96250 96254 96258 96262 96266 96270 96274 96278 96282 96286 96290 96294 96298 96302 96306 96310 96314 96318 96322 96326 96330 96334 96338 96342 96346 96350 96354 96358 96362 96366 96370 96374 96378 96382 96386 96390 96394 96398 96402 96406 96410 96414 96418 96422 96426 96430 96434 96438 96442 96446 96450 96454 96458 96462 96466 96470 96474 96478 96482 96486 96490 96494 96498 96502 96506 96510 96514 96518 96522 96526 96530 96534 96538 96542 96546 96550 96554 96558 96562 96566 96570 96574 96578 96582 96586 96590 96594 96598 96602 96606 96610 96614 96618 96622 96626 96630 96634 96638 96642 96646 96650 96654 96658 96662 96666 96670 96674 96678 96682 96686 96690 96694 96698 96702 96706 96710 96714 96718 96722 96726 96730 96734 96738 96742 96746 96750 96754 96758 96762 96766 96770 96774 96778 96782 96786 96790 96794 96798 96802 96806 96810 96814 96818 96822 96826 96830 96834 96838 96842 96846 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13959 Killed /usr/bin/gp -q -emacs Timing: real 0m21.005s user 0m19.396s sys 0m1.603s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:33:41 2005 Input: m=a=3;r=1;n=15;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 3157 9158 12159 6160 3161 9162 12163 6164 3165 9166 12167 6168 3169 9170 12171 6172 3173 9174 12175 6176 3177 9178 12179 6180 3181 9182 12183 6184 3185 9186 12187 6188 3189 9190 12191 6192 3193 9194 12195 6196 3197 9198 12199 6200 3201 9202 12203 6204 3205 9206 12207 6208 3209 9210 12211 6212 3213 9214 12215 6216 3217 9218 12219 6220 3221 9222 12223 6224 3225 9226 12227 6228 3229 9230 12231 6232 3233 9234 12235 6236 3237 9238 12239 6240 3241 9242 12243 6244 3245 9246 12247 6248 3249 9250 12251 6252 3253 9254 12255 6256 3257 9258 12259 6260 3261 9262 12263 6264 3265 9266 12267 6268 3269 9270 12271 6272 3273 9274 12275 6276 3277 9278 12279 6280 3281 9282 12283 6284 3285 9286 12287 6288 3289 9290 12291 6292 3293 9294 12295 6296 3297 9298 12299 6300 3301 9302 12303 6304 3305 9306 12307 6308 3309 9310 12311 6312 3313 9314 12315 6316 3317 9318 12319 6320 3321 9322 12323 6324 3325 9326 12327 6328 3329 9330 12331 6332 3333 9334 12335 6336 3337 9338 12339 6340 3341 9342 12343 6344 3345 9346 12347 6348 3349 9350 12351 6352 3353 9354 12355 6356 3357 9358 12359 6360 3361 9362 12363 6364 3365 9366 12367 6368 3369 9370 12371 6372 3373 9374 12375 6376 3377 9378 12379 6380 3381 9382 12383 6384 3385 9386 12387 6388 3389 9390 12391 6392 3393 9394 12395 6396 3397 9398 12399 6400 3401 9402 12403 6404 3405 9406 12407 6408 3409 9410 12411 6412 3413 9414 12415 6416 3417 9418 12419 6420 3421 9422 12423 6424 3425 9426 12427 6428 3429 9430 12431 6432 3433 9434 12435 6436 3437 9438 12439 6440 3441 9442 12443 6444 3445 9446 12447 6448 3449 9450 12451 6452 3453 9454 12455 6456 3457 9458 12459 6460 3461 9462 12463 6464 3465 9466 12467 6468 3469 9470 12471 6472 3473 9474 12475 6476 3477 9478 12479 6480 3481 9482 12483 6484 3485 9486 12487 6488 3489 9490 12491 6492 3493 9494 12495 6496 3497 9498 12499 6500 3501 9502 12503 6504 3505 9506 12507 6508 3509 9510 12511 6512 3513 9514 12515 6516 3517 9518 12519 6520 3521 9522 12523 6524 3525 9526 12527 6528 3529 9530 12531 6532 3533 9534 12535 6536 3537 9538 12539 6540 3541 9542 12543 6544 3545 9546 12547 6548 3549 9550 12551 6552 3553 9554 12555 6556 3557 9558 12559 6560 3561 9562 12563 6564 3565 9566 12567 6568 3569 9570 12571 6572 3573 9574 12575 6576 3577 9578 12579 6580 3581 9582 12583 6584 3585 9586 12587 6588 3589 9590 12591 6592 3593 9594 12595 6596 3597 9598 12599 6600 3601 9602 12603 6604 3605 9606 12607 6608 3609 9610 12611 6612 3613 9614 12615 6616 3617 9618 12619 6620 3621 9622 12623 6624 3625 9626 12627 6628 3629 9630 12631 6632 3633 9634 12635 6636 3637 9638 12639 6640 3641 9642 12643 6644 3645 9646 12647 6648 3649 9650 12651 6652 3653 9654 12655 6656 3657 9658 12659 6660 3661 9662 12663 6664 3665 9666 12667 6668 3669 9670 12671 6672 3673 9674 12675 6676 3677 9678 12679 6680 3681 9682 12683 6684 3685 9686 12687 6688 3689 9690 12691 6692 3693 9694 12695 6696 3697 9698 12699 6700 3701 9702 12703 6704 3705 9706 12707 6708 3709 9710 12711 6712 3713 9714 12715 6716 3717 9718 12719 6720 3721 9722 12723 6724 3725 9726 12727 6728 3729 9730 12731 6732 3733 9734 12735 6736 3737 9738 12739 6740 3741 9742 12743 6744 3745 9746 12747 6748 3749 9750 12751 6752 3753 9754 12755 6756 3757 9758 12759 6760 3761 9762 12763 6764 3765 9766 12767 6768 3769 9770 12771 6772 3773 9774 12775 6776 3777 9778 12779 6780 3781 9782 12783 6784 3785 9786 12787 6788 3789 9790 12791 6792 3793 9794 12795 6796 3797 9798 12799 6800 3801 9802 12803 6804 3805 9806 12807 6808 3809 9810 12811 6812 3813 9814 12815 6816 3817 9818 12819 6820 3821 9822 12823 6824 3825 9826 12827 6828 3829 9830 12831 6832 3833 9834 12835 6836 3837 9838 12839 6840 3841 9842 12843 6844 3845 9846 12847 6848 3849 9850 12851 6852 3853 9854 12855 6856 3857 9858 12859 6860 3861 9862 12863 6864 3865 9866 12867 6868 3869 9870 12871 6872 3873 9874 12875 6876 3877 9878 12879 6880 3881 9882 12883 6884 3885 9886 12887 6888 3889 9890 12891 6892 3893 9894 12895 6896 3897 9898 12899 6900 3901 9902 12903 6904 3905 9906 12907 6908 3909 9910 12911 6912 3913 9914 12915 6916 3917 9918 12919 6920 3921 9922 12923 6924 3925 9926 12927 6928 3929 9930 12931 6932 3933 9934 12935 6936 3937 9938 12939 6940 3941 9942 12943 6944 3945 9946 12947 6948 3949 9950 12951 6952 3953 9954 12955 6956 3957 9958 12959 6960 3961 9962 12963 6964 3965 9966 12967 6968 3969 9970 12971 6972 3973 9974 12975 6976 3977 9978 12979 6980 3981 9982 12983 6984 3985 9986 12987 6988 3989 9990 12991 6992 3993 9994 12995 6996 3997 9998 12999 61000 31001 91002 121003 61004 31005 91006 121007 61008 31009 91010 121011 61012 31013 91014 121015 61016 31017 91018 121019 61020 31021 91022 121023 61024 31025 91026 121027 61028 31029 91030 121031 61032 31033 91034 121035 61036 31037 91038 121039 61040 31041 91042 121043 61044 31045 91046 121047 61048 31049 91050 121051 61052 31053 91054 121055 61056 31057 91058 121059 61060 31061 91062 121063 61064 31065 91066 121067 61068 31069 91070 121071 61072 31073 91074 121075 61076 31077 91078 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121399 61400 31401 91402 121403 61404 31405 91406 121407 61408 31409 91410 121411 61412 31413 91414 121415 61416 31417 91418 121419 61420 31421 91422 121423 61424 31425 91426 121427 61428 31429 91430 121431 61432 31433 91434 121435 61436 31437 91438 121439 61440 31441 91442 121443 61444 31445 91446 121447 61448 31449 91450 121451 61452 31453 91454 121455 61456 31457 91458 121459 61460 31461 91462 121463 61464 31465 91466 121467 61468 31469 91470 121471 61472 31473 91474 121475 61476 31477 91478 121479 61480 31481 91482 121483 61484 31485 91486 121487 61488 31489 91490 121491 61492 31493 91494 121495 61496 31497 91498 121499 61500 31501 91502 121503 61504 31505 91506 121507 61508 31509 91510 121511 61512 31513 91514 121515 61516 31517 91518 121519 61520 31521 91522 121523 61524 31525 91526 121527 61528 31529 91530 121531 61532 31533 91534 121535 61536 31537 91538 121539 61540 31541 91542 121543 61544 31545 91546 121547 61548 31549 91550 121551 61552 31553 91554 121555 61556 31557 91558 121559 61560 31561 91562 121563 61564 31565 91566 121567 61568 31569 91570 121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 31777 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13987 Killed /usr/bin/gp -q -emacs Timing: real 0m21.091s user 0m15.655s sys 0m5.344s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:33:59 2005 Input: m=a=3;r=1;n=15;print(m,r);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:34:28 2005 Input: m=a=3;r=1;n=15;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 3157 9158 12159 6160 3161 9162 12163 6164 3165 9166 12167 6168 3169 9170 12171 6172 3173 9174 12175 6176 3177 9178 12179 6180 3181 9182 12183 6184 3185 9186 12187 6188 3189 9190 12191 6192 3193 9194 12195 6196 3197 9198 12199 6200 3201 9202 12203 6204 3205 9206 12207 6208 3209 9210 12211 6212 3213 9214 12215 6216 3217 9218 12219 6220 3221 9222 12223 6224 3225 9226 12227 6228 3229 9230 12231 6232 3233 9234 12235 6236 3237 9238 12239 6240 3241 9242 12243 6244 3245 9246 12247 6248 3249 9250 12251 6252 3253 9254 12255 6256 3257 9258 12259 6260 3261 9262 12263 6264 3265 9266 12267 6268 3269 9270 12271 6272 3273 9274 12275 6276 3277 9278 12279 6280 3281 9282 12283 6284 3285 9286 12287 6288 3289 9290 12291 6292 3293 9294 12295 6296 3297 9298 12299 6300 3301 9302 12303 6304 3305 9306 12307 6308 3309 9310 12311 6312 3313 9314 12315 6316 3317 9318 12319 6320 3321 9322 12323 6324 3325 9326 12327 6328 3329 9330 12331 6332 3333 9334 12335 6336 3337 9338 12339 6340 3341 9342 12343 6344 3345 9346 12347 6348 3349 9350 12351 6352 3353 9354 12355 6356 3357 9358 12359 6360 3361 9362 12363 6364 3365 9366 12367 6368 3369 9370 12371 6372 3373 9374 12375 6376 3377 9378 12379 6380 3381 9382 12383 6384 3385 9386 12387 6388 3389 9390 12391 6392 3393 9394 12395 6396 3397 9398 12399 6400 3401 9402 12403 6404 3405 9406 12407 6408 3409 9410 12411 6412 3413 9414 12415 6416 3417 9418 12419 6420 3421 9422 12423 6424 3425 9426 12427 6428 3429 9430 12431 6432 3433 9434 12435 6436 3437 9438 12439 6440 3441 9442 12443 6444 3445 9446 12447 6448 3449 9450 12451 6452 3453 9454 12455 6456 3457 9458 12459 6460 3461 9462 12463 6464 3465 9466 12467 6468 3469 9470 12471 6472 3473 9474 12475 6476 3477 9478 12479 6480 3481 9482 12483 6484 3485 9486 12487 6488 3489 9490 12491 6492 3493 9494 12495 6496 3497 9498 12499 6500 3501 9502 12503 6504 3505 9506 12507 6508 3509 9510 12511 6512 3513 9514 12515 6516 3517 9518 12519 6520 3521 9522 12523 6524 3525 9526 12527 6528 3529 9530 12531 6532 3533 9534 12535 6536 3537 9538 12539 6540 3541 9542 12543 6544 3545 9546 12547 6548 3549 9550 12551 6552 3553 9554 12555 6556 3557 9558 12559 6560 3561 9562 12563 6564 3565 9566 12567 6568 3569 9570 12571 6572 3573 9574 12575 6576 3577 9578 12579 6580 3581 9582 12583 6584 3585 9586 12587 6588 3589 9590 12591 6592 3593 9594 12595 6596 3597 9598 12599 6600 3601 9602 12603 6604 3605 9606 12607 6608 3609 9610 12611 6612 3613 9614 12615 6616 3617 9618 12619 6620 3621 9622 12623 6624 3625 9626 12627 6628 3629 9630 12631 6632 3633 9634 12635 6636 3637 9638 12639 6640 3641 9642 12643 6644 3645 9646 12647 6648 3649 9650 12651 6652 3653 9654 12655 6656 3657 9658 12659 6660 3661 9662 12663 6664 3665 9666 12667 6668 3669 9670 12671 6672 3673 9674 12675 6676 3677 9678 12679 6680 3681 9682 12683 6684 3685 9686 12687 6688 3689 9690 12691 6692 3693 9694 12695 6696 3697 9698 12699 6700 3701 9702 12703 6704 3705 9706 12707 6708 3709 9710 12711 6712 3713 9714 12715 6716 3717 9718 12719 6720 3721 9722 12723 6724 3725 9726 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91410 121411 61412 31413 91414 121415 61416 31417 91418 121419 61420 31421 91422 121423 61424 31425 91426 121427 61428 31429 91430 121431 61432 31433 91434 121435 61436 31437 91438 121439 61440 31441 91442 121443 61444 31445 91446 121447 61448 31449 91450 121451 61452 31453 91454 121455 61456 31457 91458 121459 61460 31461 91462 121463 61464 31465 91466 121467 61468 31469 91470 121471 61472 31473 91474 121475 61476 31477 91478 121479 61480 31481 91482 121483 61484 31485 91486 121487 61488 31489 91490 121491 61492 31493 91494 121495 61496 31497 91498 121499 61500 31501 91502 121503 61504 31505 91506 121507 61508 31509 91510 121511 61512 31513 91514 121515 61516 31517 91518 121519 61520 31521 91522 121523 61524 31525 91526 121527 61528 31529 91530 121531 61532 31533 91534 121535 61536 31537 91538 121539 61540 31541 91542 121543 61544 31545 91546 121547 61548 31549 91550 121551 61552 31553 91554 121555 61556 31557 91558 121559 61560 31561 91562 121563 61564 31565 91566 121567 61568 31569 91570 121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 31777 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 14005 Killed /usr/bin/gp -q -emacs Timing: real 0m21.099s user 0m15.426s sys 0m5.573s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:34:59 2005 Input: m=a=3;r=1;n=15;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 123 64 96 127 68 910 1211 612 914 1215 616 918 1219 620 922 1223 624 926 1227 628 930 1231 632 934 1235 636 938 1239 640 942 1243 644 946 1247 648 950 1251 652 954 1255 656 958 1259 660 962 1263 664 966 1267 668 970 1271 672 974 1275 676 978 1279 680 982 1283 684 986 1287 688 990 1291 692 994 1295 696 998 1299 6100 9102 12103 6104 9106 12107 6108 9110 12111 6112 9114 12115 6116 9118 12119 6120 9122 12123 6124 9126 12127 6128 9130 12131 6132 9134 12135 6136 9138 12139 6140 9142 12143 6144 9146 12147 6148 9150 12151 6152 9154 12155 6156 9158 12159 6160 9162 12163 6164 9166 12167 6168 9170 12171 6172 9174 12175 6176 9178 12179 6180 9182 12183 6184 9186 12187 6188 9190 12191 6192 9194 12195 6196 9198 12199 6200 9202 12203 6204 9206 12207 6208 9210 12211 6212 9214 12215 6216 9218 12219 6220 9222 12223 6224 9226 12227 6228 9230 12231 6232 9234 12235 6236 9238 12239 6240 9242 12243 6244 9246 12247 6248 9250 12251 6252 9254 12255 6256 9258 12259 6260 9262 12263 6264 9266 12267 6268 9270 12271 6272 9274 12275 6276 9278 12279 6280 9282 12283 6284 9286 12287 6288 9290 12291 6292 9294 12295 6296 9298 12299 6300 9302 12303 6304 9306 12307 6308 9310 12311 6312 9314 12315 6316 9318 12319 6320 9322 12323 6324 9326 12327 6328 9330 12331 6332 9334 12335 6336 9338 12339 6340 9342 12343 6344 9346 12347 6348 9350 12351 6352 9354 12355 6356 9358 12359 6360 9362 12363 6364 9366 12367 6368 9370 12371 6372 9374 12375 6376 9378 12379 6380 9382 12383 6384 9386 12387 6388 9390 12391 6392 9394 12395 6396 9398 12399 6400 9402 12403 6404 9406 12407 6408 9410 12411 6412 9414 12415 6416 9418 12419 6420 9422 12423 6424 9426 12427 6428 9430 12431 6432 9434 12435 6436 9438 12439 6440 9442 12443 6444 9446 12447 6448 9450 12451 6452 9454 12455 6456 9458 12459 6460 9462 12463 6464 9466 12467 6468 9470 12471 6472 9474 12475 6476 9478 12479 6480 9482 12483 6484 9486 12487 6488 9490 12491 6492 9494 12495 6496 9498 12499 6500 9502 12503 6504 9506 12507 6508 9510 12511 6512 9514 12515 6516 9518 12519 6520 9522 12523 6524 9526 12527 6528 9530 12531 6532 9534 12535 6536 9538 12539 6540 9542 12543 6544 9546 12547 6548 9550 12551 6552 9554 12555 6556 9558 12559 6560 9562 12563 6564 9566 12567 6568 9570 12571 6572 9574 12575 6576 9578 12579 6580 9582 12583 6584 9586 12587 6588 9590 12591 6592 9594 12595 6596 9598 12599 6600 9602 12603 6604 9606 12607 6608 9610 12611 6612 9614 12615 6616 9618 12619 6620 9622 12623 6624 9626 12627 6628 9630 12631 6632 9634 12635 6636 9638 12639 6640 9642 12643 6644 9646 12647 6648 9650 12651 6652 9654 12655 6656 9658 12659 6660 9662 12663 6664 9666 12667 6668 9670 12671 6672 9674 12675 6676 9678 12679 6680 9682 12683 6684 9686 12687 6688 9690 12691 6692 9694 12695 6696 9698 12699 6700 9702 12703 6704 9706 12707 6708 9710 12711 6712 9714 12715 6716 9718 12719 6720 9722 12723 6724 9726 12727 6728 9730 12731 6732 9734 12735 6736 9738 12739 6740 9742 12743 6744 9746 12747 6748 9750 12751 6752 9754 12755 6756 9758 12759 6760 9762 12763 6764 9766 12767 6768 9770 12771 6772 9774 12775 6776 9778 12779 6780 9782 12783 6784 9786 12787 6788 9790 12791 6792 9794 12795 6796 9798 12799 6800 9802 12803 6804 9806 12807 6808 9810 12811 6812 9814 12815 6816 9818 12819 6820 9822 12823 6824 9826 12827 6828 9830 12831 6832 9834 12835 6836 9838 12839 6840 9842 12843 6844 9846 12847 6848 9850 12851 6852 9854 12855 6856 9858 12859 6860 9862 12863 6864 9866 12867 6868 9870 12871 6872 9874 12875 6876 9878 12879 6880 9882 12883 6884 9886 12887 6888 9890 12891 6892 9894 12895 6896 9898 12899 6900 9902 12903 6904 9906 12907 6908 9910 12911 6912 9914 12915 6916 9918 12919 6920 9922 12923 6924 9926 12927 6928 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91994 121995 61996 91998 121999 62000 92002 122003 62004 92006 122007 62008 92010 122011 62012 92014 122015 62016 92018 122019 62020 92022 122023 62024 92026 122027 62028 92030 122031 62032 92034 122035 62036 92038 122039 62040 92042 122043 62044 92046 122047 62048 92050 122051 62052 92054 122055 62056 92058 122059 62060 92062 122063 62064 92066 122067 62068 92070 122071 62072 92074 122075 62076 92078 122079 62080 92082 122083 62084 92086 122087 62088 92090 122091 62092 92094 122095 62096 92098 122099 62100 92102 122103 62104 92106 122107 62108 92110 122111 62112 92114 122115 62116 92118 122119 62120 92122 122123 62124 92126 122127 62128 92130 122131 62132 92134 122135 62136 92138 122139 62140 92142 122143 62144 92146 122147 62148 92150 122151 62152 92154 122155 62156 92158 122159 62160 92162 122163 62164 92166 122167 62168 92170 122171 62172 92174 122175 62176 92178 122179 62180 92182 122183 62184 92186 122187 62188 92190 122191 62192 92194 122195 62196 92198 122199 62200 92202 122203 62204 92206 122207 62208 92210 122211 62212 92214 122215 62216 92218 122219 62220 92222 122223 62224 92226 122227 62228 92230 122231 62232 92234 122235 62236 92238 122239 62240 92242 122243 62244 92246 122247 62248 92250 122251 62252 92254 122255 62256 92258 122259 62260 92262 122263 62264 92266 122267 62268 92270 122271 62272 92274 122275 62276 92278 122279 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 14017 Killed /usr/bin/gp -q -emacs Timing: real 0m21.007s user 0m16.364s sys 0m4.635s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:35:49 2005 Input: m=a=3;r=1;n=15;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 3157 9158 12159 6160 3161 9162 12163 6164 3165 9166 12167 6168 3169 9170 12171 6172 3173 9174 12175 6176 3177 9178 12179 6180 3181 9182 12183 6184 3185 9186 12187 6188 3189 9190 12191 6192 3193 9194 12195 6196 3197 9198 12199 6200 3201 9202 12203 6204 3205 9206 12207 6208 3209 9210 12211 6212 3213 9214 12215 6216 3217 9218 12219 6220 3221 9222 12223 6224 3225 9226 12227 6228 3229 9230 12231 6232 3233 9234 12235 6236 3237 9238 12239 6240 3241 9242 12243 6244 3245 9246 12247 6248 3249 9250 12251 6252 3253 9254 12255 6256 3257 9258 12259 6260 3261 9262 12263 6264 3265 9266 12267 6268 3269 9270 12271 6272 3273 9274 12275 6276 3277 9278 12279 6280 3281 9282 12283 6284 3285 9286 12287 6288 3289 9290 12291 6292 3293 9294 12295 6296 3297 9298 12299 6300 3301 9302 12303 6304 3305 9306 12307 6308 3309 9310 12311 6312 3313 9314 12315 6316 3317 9318 12319 6320 3321 9322 12323 6324 3325 9326 12327 6328 3329 9330 12331 6332 3333 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121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 31777 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 14030 Killed /usr/bin/gp -q -emacs Timing: real 0m21.009s user 0m15.427s sys 0m5.573s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:35:58 2005 Input: m=a=3;r=1;n=13;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:36:07 2005 Input: m=a=3;r=1;n=11;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 92 53 44 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:36:14 2005 Input: m=a=3;r=1;n=9;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.001s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:36:20 2005 Input: m=a=3;r=1;n=7;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 22 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:36:27 2005 Input: m=a=2;r=1;n=7;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 42 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:36:35 2005 Input: m=a=2;r=1;n=9;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 42 83 74 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:36:43 2005 Input: m=a=2;r=1;n=11;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 42 83 54 105 96 77 38 69 110 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:36:54 2005 Input: m=a=2;r=1;n=13;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 42 83 34 65 126 117 98 59 1010 711 112 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:37:04 2005 Input: m=a=2;r=1;n=15;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 21 42 83 14 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:37:34 2005 Input: m=a=3;r=1;n=15;print(m,r);while(m>1,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 92 123 64 35 96 127 68 39 910 1211 612 313 914 1215 616 317 918 1219 620 321 922 1223 624 325 926 1227 628 329 930 1231 632 333 934 1235 636 337 938 1239 640 341 942 1243 644 345 946 1247 648 349 950 1251 652 353 954 1255 656 357 958 1259 660 361 962 1263 664 365 966 1267 668 369 970 1271 672 373 974 1275 676 377 978 1279 680 381 982 1283 684 385 986 1287 688 389 990 1291 692 393 994 1295 696 397 998 1299 6100 3101 9102 12103 6104 3105 9106 12107 6108 3109 9110 12111 6112 3113 9114 12115 6116 3117 9118 12119 6120 3121 9122 12123 6124 3125 9126 12127 6128 3129 9130 12131 6132 3133 9134 12135 6136 3137 9138 12139 6140 3141 9142 12143 6144 3145 9146 12147 6148 3149 9150 12151 6152 3153 9154 12155 6156 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91570 121571 61572 31573 91574 121575 61576 31577 91578 121579 61580 31581 91582 121583 61584 31585 91586 121587 61588 31589 91590 121591 61592 31593 91594 121595 61596 31597 91598 121599 61600 31601 91602 121603 61604 31605 91606 121607 61608 31609 91610 121611 61612 31613 91614 121615 61616 31617 91618 121619 61620 31621 91622 121623 61624 31625 91626 121627 61628 31629 91630 121631 61632 31633 91634 121635 61636 31637 91638 121639 61640 31641 91642 121643 61644 31645 91646 121647 61648 31649 91650 121651 61652 31653 91654 121655 61656 31657 91658 121659 61660 31661 91662 121663 61664 31665 91666 121667 61668 31669 91670 121671 61672 31673 91674 121675 61676 31677 91678 121679 61680 31681 91682 121683 61684 31685 91686 121687 61688 31689 91690 121691 61692 31693 91694 121695 61696 31697 91698 121699 61700 31701 91702 121703 61704 31705 91706 121707 61708 31709 91710 121711 61712 31713 91714 121715 61716 31717 91718 121719 61720 31721 91722 121723 61724 31725 91726 121727 61728 31729 91730 121731 61732 31733 91734 121735 61736 31737 91738 121739 61740 31741 91742 121743 61744 31745 91746 121747 61748 31749 91750 121751 61752 31753 91754 121755 61756 31757 91758 121759 61760 31761 91762 121763 61764 31765 91766 121767 61768 31769 91770 121771 61772 31773 91774 121775 61776 31777 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 14105 Killed /usr/bin/gp -q -emacs Timing: real 0m21.172s user 0m15.519s sys 0m5.480s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:39:26 2005 Input: m=a=3;r=1;n=15;print(m,r);print(a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 92 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:40:19 2005 Input: m=a=3;r=1;n=15;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 92 123 64 35 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:41:06 2005 Input: m=a=3;r=1;n=15;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 123 64 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:41:18 2005 Input: m=a=3;r=1;n=13;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:41:25 2005 Input: m=a=3;r=1;n=11;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 53 44 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:41:55 2005 Input: m=a=3;r=1;n=7;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 133 254 615 1696 4937 14658 43819 1312910 3937311 11810512 35430113 106288914 318865315 956594516 2869782117 8609344918 25828033319 77484098520 232452294121 697356880922 2092070641323 6276211922524 18828635766125 56485907296926 169457721889327 508373165666528 1525119496998129 4575358490992930 13726075472977331 41178226418930532 123534679256790133 370604037770368934 1111812113311105335 3335436339933314536 10006309019799942137 30018927059399824938 90056781178199473339 270170343534598418540 810511030603795254141 2431533091811385760942 7294599275434157281343 21883797826302471842544 65651393478907415526145 196954180436722246576946 590862541310166739729347 1772587623930500219186548 5317762871791500657558149 15953288615374501972672950 47859865846123505918017351 143579597538370517754050552 430738792615111553262150153 1292216377845334659786448954 3876649133536003979359345355 11629947400608011938078034556 34889842201824035814234102157 104669526605472107442702304958 314008579816416322328106913359 942025739449248966984320738560 2826077218347746900952962214161 8478231655043240702858886640962 25434694965129722108576659921363 76304084895389166325729979762564 228912254686167498977189939286165 686736764058502496931569817856966 2060210292175507490794709453569367 6180630876526522472384128360706568 18541892629579567417152385082118169 55625677888738702251457155246352970 166877033666216106754371465739057371 500631100998648320263114397217170572 1501893302995944960789343191651510173 4505679908987834882368029574954528974 13517039726963504647104088724863585375 40551119180890513941312266174590754576 121653357542671541823936798523772262177 364960072628014625471810395571316784978 1094880217884043876415431186713950353379 3284640653652131629246293560141851058580 9853921960956394887738880680425553174181 29561765882869184663216642041276659520982 88685297648607553989649926123829978561383 266055892945822661968949778371489935682584 798167678837467985906849335114469807046185 2394503036512403957720548005343409421136986 7183509109537211873161644016030228263409387 21550527328611635619484932048090684790226588 64651581985834906858454796144272054370678189 193954745957504720575364388432816163112032990 581864237872514161726093165298448489336097391 1745592713617542485178279495895345468008290592 5236778140852627455534838487686036404024870193 15710334422557882366604515463058109212074608994 47131003267673647099813546389174327636223825395 141393009803020941299440639167522982908671474596 424179029409062823898321917502568948726014422197 1272537088227188471694965752507706846178043264998 3817611264681565415084897257523120538534129793399 114528337940446962452546917725693616156023893785100 343585013821340887357640753177080848468071681341101 1030755041464022662072922259531242545404215044009102 3092265124392067986218766778593727636212645132013103 9276795373176203958656300335781182908637935396025104 27830386119528611875968901007343548725913806188061105 83491158358585835627906703022030646177741418564169106 250473475075757506883720109066091938533224255692493107 751420425227272520651160327198275815599672767077465108 2254261275681817561953480981594827446799018301232381109 6762783827045452685860442944784482340397054903697129110 20288351481136358057581328834353447021191164711091373111 60865054443409074172743986503060341063573494133274105112 182595163330227222518231959509181023190720482399822301113 547785489990681667554695878527543069572161447199466889114 1643356469972045002664087635582629208716484341598400653115 4930069409916135007992262906747887626149453024795201945116 14790208229748405023976788720243662878448359074385605821117 44370624689245215071930366160730988635345077223156817449118 133111874067735645215791098482192965906035231669470452333119 399335622203206935647373295446578897718105695008411356985120 1198006866609620806942119886339736693154317085025234070941121 3594020599828862420826359659019210079462951255075702212809122 10782061799486587262479078977057630238388853765227106638413123 32346185398459761787437236931172890715166561295681319915225124 97038556195379285362311710793518672145499683887043959745661125 291115668586137856086935132380556016436499051661131879236969126 873347005758413568260805397141668049309497154983395637710893127 2620041017275240704782416191425004147928491464950186913132665128 7860123051825722114347248574275012443785474394850560739397981129 23580369155477166343041745722825037331356423184551682218193929130 70741107466431499029125237168475111994069269553655046654581773131 212223322399294497087375711505425335982207808660965139963745305132 636669967197883491262127134516276007946623425982895419891235901133 1910009901593650473786381403548828023839870277948686259673707689134 5730029704780951421359144210646484071519610833846058779021123053135 17190089114342854264077432631939452214558832501538176337063369145136 51570267343028562792232297895818356643676497504614529011190107421137 154710802029085688376696893687455069931029492513843587033570322249138 464132406087257065130090681062365209793088477541530761100710966733139 1392397218261771195390272043187095629379265432624592283302132900185140 4177191654785313586170816129561286888137796297873776849906398700541141 12531574964355940758512448388683860664413388893621330549719196101609142 37594724893067822275537345166051581993240166680863991649157588304813143 112784174679203466826612035498154745979720500042591974947472764914425144 338352524037610400479836106494464237939161500127775924842418294743261145 1015057572112831201439508319483392713817484500383327774527254884229769146 3045172716338493604318524958450178141452453501149983323581764652689293147 9135518149015480812955574875350534424357360503449949970745293958067865148 27406554447046442438866724626051603273072081510349849912235881874203581149 82219663341139327316600173878154809819216244531049549736707645622610729150 246658990023417981949800521634464429457648733593148649210122936867832173151 739976970070253945849401564903393288372946200779445947630368810603496505152 2219930910210761837548204694710179865118838602338337842891106431810489501153 6659792730632285512644614084130539595356515807015013528673319295431468489154 19979378191896856537933842252391618786069547421045040586019957886294405453155 59938134575690569613801526757174856358208642263135121758059873658883216345156 179814403727071708841404580271524569074625926789405365274179620976649649021157 539443211181215126524213740814573707223877780368216095822538862929948947049158 1618329633543645379572641222443721121671633341104648287467616588789846841133159 4854988900630936138717923667331163365014900023313944862402849766369540523385160 14564966701892808416153771001993490095044700069941834587208549299108621570141161 43694900105678425248461313005980470285134100209825503761625647897325864710409162 131084700317035275745383939017941410855402300629476511284876943691977594131213163 393254100951105827236151817053824232566206901888429533854630831075932782393625164 1179762302853317481708455451161472697698620705665288601563892493227798347180861165 3539286908559952445125366353484418093095862116995865804691677479683395041542569166 10617860725679857335376099060453254279287586350987597414075032439050185124627693167 31853582177039572006128297181359762837862759052962792242225097317150555373883065168 95560746531118716018384891544079288513588277158888376726675291951451666121649181169 286682239593356148055154674632237865540764831476665130180025875854354998364947529170 860046718780068444165464023896713596622294494429995390540077627563064995094842573171 2580140156340205332496392071690140789866883483289986171620232882689194985284527705172 7740420469020615997489176215070422369600650449869958514860698648067584955853583101173 23221261407061847992467528645211267108801951349609875544582095944202754867560749289174 69663784221185543977402585935633801326405854048829626633746287832608264602682247853175 208991352663556631932207757806901403979217562146488879901238863497824793808046743545176 626974057990669895796623273420704211937652686439466639703716590493474381424140230621177 1880922173972009687389869820262112635812958059318399919111149771480423144272420691849178 5642766521916029062169609460786337907438874177955199757333449314441269432817262075533179 16928299565748087186508828382359013722316622533865599272000347943323808298451786226585180 50784898697244261559526485147077041166949867601596797816001043829971424895355358679741181 152354696091732784678579455441231123500849602804790393448003131489914274686066076039209182 457064088275198354035738366323693370502548808414371180344009394469742824058198228117613183 1371192264825595062107215098971080111507646425243113541032028183409228472174594684352825184 4113576794476785186321645296913240334522939275729340623096084550227685416523784053058461185 12340730383430355558964935890739721003568817827188021869288253650683056249571352159175369186 37022191150291066676894807672219163010706453481564065607864760952049168748714056477526093187 111066573450873200030684423016657489032119360444692196823594282856147506246142169432578265188 333199720352619600092053269049972467096358081334076590470782848568442518738426508297734781189 999599161057858800276159807149917401289074244002229771412348545705327556215279524893204329190 2998797483173576400828479421449752203867222732006689314237045637115982668645838574679612973191 8996392449520729202485438264349256611601668196020067942711136911347948005937515724038838905192 26989177348562187607456314793047769834805004588060203828133410734043844017812547172116516701193 80967532045686562822368944379143309504415013764180611484400232202131532053437641516349550089194 242902596137059688467106833137429928513245041292541834453200696606394596160312924549048650253195 728707788411179065401320499412289785539735123877625503359602089819183788480938773647145950745196 2186123365233537196203961498236869356619205371632876510078806269457551365442816320941437852221197 65583700957006115886118844947106080698576 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 14188 Killed /usr/bin/gp -q -emacs Timing: real 0m21.056s user 0m20.946s sys 0m0.055s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:43:37 2005 Input: m=a=3;r=1;n=7;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>0,print(m,r)))) Output: ? 31 92 133 254 615 1696 4937 14658 43819 1312910 3937311 11810512 35430113 106288914 318865315 956594516 2869782117 8609344918 25828033319 77484098520 232452294121 697356880922 2092070641323 6276211922524 18828635766125 56485907296926 169457721889327 508373165666528 1525119496998129 4575358490992930 13726075472977331 41178226418930532 123534679256790133 370604037770368934 1111812113311105335 3335436339933314536 10006309019799942137 30018927059399824938 90056781178199473339 270170343534598418540 810511030603795254141 2431533091811385760942 7294599275434157281343 21883797826302471842544 65651393478907415526145 196954180436722246576946 590862541310166739729347 1772587623930500219186548 5317762871791500657558149 15953288615374501972672950 47859865846123505918017351 143579597538370517754050552 430738792615111553262150153 1292216377845334659786448954 3876649133536003979359345355 11629947400608011938078034556 34889842201824035814234102157 104669526605472107442702304958 314008579816416322328106913359 942025739449248966984320738560 2826077218347746900952962214161 8478231655043240702858886640962 25434694965129722108576659921363 76304084895389166325729979762564 228912254686167498977189939286165 686736764058502496931569817856966 2060210292175507490794709453569367 6180630876526522472384128360706568 18541892629579567417152385082118169 55625677888738702251457155246352970 166877033666216106754371465739057371 500631100998648320263114397217170572 1501893302995944960789343191651510173 4505679908987834882368029574954528974 13517039726963504647104088724863585375 40551119180890513941312266174590754576 121653357542671541823936798523772262177 364960072628014625471810395571316784978 1094880217884043876415431186713950353379 3284640653652131629246293560141851058580 9853921960956394887738880680425553174181 29561765882869184663216642041276659520982 88685297648607553989649926123829978561383 266055892945822661968949778371489935682584 798167678837467985906849335114469807046185 2394503036512403957720548005343409421136986 7183509109537211873161644016030228263409387 21550527328611635619484932048090684790226588 64651581985834906858454796144272054370678189 193954745957504720575364388432816163112032990 581864237872514161726093165298448489336097391 1745592713617542485178279495895345468008290592 5236778140852627455534838487686036404024870193 15710334422557882366604515463058109212074608994 47131003267673647099813546389174327636223825395 141393009803020941299440639167522982908671474596 424179029409062823898321917502568948726014422197 1272537088227188471694965752507706846178043264998 3817611264681565415084897257523120538534129793399 114528337940446962452546917725693616156023893785100 343585013821340887357640753177080848468071681341101 1030755041464022662072922259531242545404215044009102 3092265124392067986218766778593727636212645132013103 9276795373176203958656300335781182908637935396025104 27830386119528611875968901007343548725913806188061105 83491158358585835627906703022030646177741418564169106 250473475075757506883720109066091938533224255692493107 751420425227272520651160327198275815599672767077465108 2254261275681817561953480981594827446799018301232381109 6762783827045452685860442944784482340397054903697129110 20288351481136358057581328834353447021191164711091373111 60865054443409074172743986503060341063573494133274105112 182595163330227222518231959509181023190720482399822301113 547785489990681667554695878527543069572161447199466889114 1643356469972045002664087635582629208716484341598400653115 4930069409916135007992262906747887626149453024795201945116 14790208229748405023976788720243662878448359074385605821117 44370624689245215071930366160730988635345077223156817449118 133111874067735645215791098482192965906035231669470452333119 399335622203206935647373295446578897718105695008411356985120 1198006866609620806942119886339736693154317085025234070941121 3594020599828862420826359659019210079462951255075702212809122 10782061799486587262479078977057630238388853765227106638413123 32346185398459761787437236931172890715166561295681319915225124 97038556195379285362311710793518672145499683887043959745661125 291115668586137856086935132380556016436499051661131879236969126 873347005758413568260805397141668049309497154983395637710893127 2620041017275240704782416191425004147928491464950186913132665128 7860123051825722114347248574275012443785474394850560739397981129 23580369155477166343041745722825037331356423184551682218193929130 70741107466431499029125237168475111994069269553655046654581773131 212223322399294497087375711505425335982207808660965139963745305132 636669967197883491262127134516276007946623425982895419891235901133 1910009901593650473786381403548828023839870277948686259673707689134 5730029704780951421359144210646484071519610833846058779021123053135 17190089114342854264077432631939452214558832501538176337063369145136 51570267343028562792232297895818356643676497504614529011190107421137 154710802029085688376696893687455069931029492513843587033570322249138 464132406087257065130090681062365209793088477541530761100710966733139 1392397218261771195390272043187095629379265432624592283302132900185140 4177191654785313586170816129561286888137796297873776849906398700541141 12531574964355940758512448388683860664413388893621330549719196101609142 37594724893067822275537345166051581993240166680863991649157588304813143 112784174679203466826612035498154745979720500042591974947472764914425144 338352524037610400479836106494464237939161500127775924842418294743261145 1015057572112831201439508319483392713817484500383327774527254884229769146 3045172716338493604318524958450178141452453501149983323581764652689293147 9135518149015480812955574875350534424357360503449949970745293958067865148 27406554447046442438866724626051603273072081510349849912235881874203581149 82219663341139327316600173878154809819216244531049549736707645622610729150 246658990023417981949800521634464429457648733593148649210122936867832173151 739976970070253945849401564903393288372946200779445947630368810603496505152 2219930910210761837548204694710179865118838602338337842891106431810489501153 6659792730632285512644614084130539595356515807015013528673319295431468489154 19979378191896856537933842252391618786069547421045040586019957886294405453155 59938134575690569613801526757174856358208642263135121758059873658883216345156 179814403727071708841404580271524569074625926789405365274179620976649649021157 539443211181215126524213740814573707223877780368216095822538862929948947049158 1618329633543645379572641222443721121671633341104648287467616588789846841133159 4854988900630936138717923667331163365014900023313944862402849766369540523385160 14564966701892808416153771001993490095044700069941834587208549299108621570141161 43694900105678425248461313005980470285134100209825503761625647897325864710409162 131084700317035275745383939017941410855402300629476511284876943691977594131213163 393254100951105827236151817053824232566206901888429533854630831075932782393625164 1179762302853317481708455451161472697698620705665288601563892493227798347180861165 3539286908559952445125366353484418093095862116995865804691677479683395041542569166 10617860725679857335376099060453254279287586350987597414075032439050185124627693167 31853582177039572006128297181359762837862759052962792242225097317150555373883065168 95560746531118716018384891544079288513588277158888376726675291951451666121649181169 286682239593356148055154674632237865540764831476665130180025875854354998364947529170 860046718780068444165464023896713596622294494429995390540077627563064995094842573171 2580140156340205332496392071690140789866883483289986171620232882689194985284527705172 7740420469020615997489176215070422369600650449869958514860698648067584955853583101173 23221261407061847992467528645211267108801951349609875544582095944202754867560749289174 69663784221185543977402585935633801326405854048829626633746287832608264602682247853175 208991352663556631932207757806901403979217562146488879901238863497824793808046743545176 626974057990669895796623273420704211937652686439466639703716590493474381424140230621177 1880922173972009687389869820262112635812958059318399919111149771480423144272420691849178 5642766521916029062169609460786337907438874177955199757333449314441269432817262075533179 16928299565748087186508828382359013722316622533865599272000347943323808298451786226585180 50784898697244261559526485147077041166949867601596797816001043829971424895355358679741181 152354696091732784678579455441231123500849602804790393448003131489914274686066076039209182 457064088275198354035738366323693370502548808414371180344009394469742824058198228117613183 1371192264825595062107215098971080111507646425243113541032028183409228472174594684352825184 4113576794476785186321645296913240334522939275729340623096084550227685416523784053058461185 12340730383430355558964935890739721003568817827188021869288253650683056249571352159175369186 37022191150291066676894807672219163010706453481564065607864760952049168748714056477526093187 111066573450873200030684423016657489032119360444692196823594282856147506246142169432578265188 333199720352619600092053269049972467096358081334076590470782848568442518738426508297734781189 999599161057858800276159807149917401289074244002229771412348545705327556215279524893204329190 2998797483173576400828479421449752203867222732006689314237045637115982668645838574679612973191 8996392449520729202485438264349256611601668196020067942711136911347948005937515724038838905192 26989177348562187607456314793047769834805004588060203828133410734043844017812547172116516701193 80967532045686562822368944379143309504415013764180611484400232202131532053437641516349550089194 242902596137059688467106833137429928513245041292541834453200696606394596160312924549048650253195 728707788411179065401320499412289785539735123877625503359602089819183788480938773647145950745196 2186123365233537196203961498236869356619205371632876510078806269457551365442816320941437852221197 65583700957006115886118844947106080698576 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 14203 Killed /usr/bin/gp -q -emacs Timing: real 0m21.044s user 0m20.939s sys 0m0.061s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:44:08 2005 Input: m=a=3;r=1;n=7;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 133 254 615 1696 4937 14658 43819 1312910 3937311 11810512 35430113 106288914 318865315 956594516 2869782117 8609344918 25828033319 77484098520 232452294121 697356880922 2092070641323 6276211922524 18828635766125 56485907296926 169457721889327 508373165666528 1525119496998129 4575358490992930 13726075472977331 41178226418930532 123534679256790133 370604037770368934 1111812113311105335 3335436339933314536 10006309019799942137 30018927059399824938 90056781178199473339 270170343534598418540 810511030603795254141 2431533091811385760942 7294599275434157281343 21883797826302471842544 65651393478907415526145 196954180436722246576946 590862541310166739729347 1772587623930500219186548 5317762871791500657558149 15953288615374501972672950 47859865846123505918017351 143579597538370517754050552 430738792615111553262150153 1292216377845334659786448954 3876649133536003979359345355 11629947400608011938078034556 34889842201824035814234102157 104669526605472107442702304958 314008579816416322328106913359 942025739449248966984320738560 2826077218347746900952962214161 8478231655043240702858886640962 25434694965129722108576659921363 76304084895389166325729979762564 228912254686167498977189939286165 686736764058502496931569817856966 2060210292175507490794709453569367 6180630876526522472384128360706568 18541892629579567417152385082118169 55625677888738702251457155246352970 166877033666216106754371465739057371 500631100998648320263114397217170572 1501893302995944960789343191651510173 4505679908987834882368029574954528974 13517039726963504647104088724863585375 40551119180890513941312266174590754576 121653357542671541823936798523772262177 364960072628014625471810395571316784978 1094880217884043876415431186713950353379 3284640653652131629246293560141851058580 9853921960956394887738880680425553174181 29561765882869184663216642041276659520982 88685297648607553989649926123829978561383 266055892945822661968949778371489935682584 798167678837467985906849335114469807046185 2394503036512403957720548005343409421136986 7183509109537211873161644016030228263409387 21550527328611635619484932048090684790226588 64651581985834906858454796144272054370678189 193954745957504720575364388432816163112032990 581864237872514161726093165298448489336097391 1745592713617542485178279495895345468008290592 5236778140852627455534838487686036404024870193 15710334422557882366604515463058109212074608994 47131003267673647099813546389174327636223825395 141393009803020941299440639167522982908671474596 424179029409062823898321917502568948726014422197 1272537088227188471694965752507706846178043264998 3817611264681565415084897257523120538534129793399 114528337940446962452546917725693616156023893785100 343585013821340887357640753177080848468071681341101 1030755041464022662072922259531242545404215044009102 3092265124392067986218766778593727636212645132013103 9276795373176203958656300335781182908637935396025104 27830386119528611875968901007343548725913806188061105 83491158358585835627906703022030646177741418564169106 250473475075757506883720109066091938533224255692493107 751420425227272520651160327198275815599672767077465108 2254261275681817561953480981594827446799018301232381109 6762783827045452685860442944784482340397054903697129110 20288351481136358057581328834353447021191164711091373111 60865054443409074172743986503060341063573494133274105112 182595163330227222518231959509181023190720482399822301113 547785489990681667554695878527543069572161447199466889114 1643356469972045002664087635582629208716484341598400653115 4930069409916135007992262906747887626149453024795201945116 14790208229748405023976788720243662878448359074385605821117 44370624689245215071930366160730988635345077223156817449118 133111874067735645215791098482192965906035231669470452333119 399335622203206935647373295446578897718105695008411356985120 1198006866609620806942119886339736693154317085025234070941121 3594020599828862420826359659019210079462951255075702212809122 10782061799486587262479078977057630238388853765227106638413123 32346185398459761787437236931172890715166561295681319915225124 97038556195379285362311710793518672145499683887043959745661125 291115668586137856086935132380556016436499051661131879236969126 873347005758413568260805397141668049309497154983395637710893127 2620041017275240704782416191425004147928491464950186913132665128 7860123051825722114347248574275012443785474394850560739397981129 23580369155477166343041745722825037331356423184551682218193929130 70741107466431499029125237168475111994069269553655046654581773131 212223322399294497087375711505425335982207808660965139963745305132 636669967197883491262127134516276007946623425982895419891235901133 1910009901593650473786381403548828023839870277948686259673707689134 5730029704780951421359144210646484071519610833846058779021123053135 17190089114342854264077432631939452214558832501538176337063369145136 51570267343028562792232297895818356643676497504614529011190107421137 154710802029085688376696893687455069931029492513843587033570322249138 464132406087257065130090681062365209793088477541530761100710966733139 1392397218261771195390272043187095629379265432624592283302132900185140 4177191654785313586170816129561286888137796297873776849906398700541141 12531574964355940758512448388683860664413388893621330549719196101609142 37594724893067822275537345166051581993240166680863991649157588304813143 112784174679203466826612035498154745979720500042591974947472764914425144 338352524037610400479836106494464237939161500127775924842418294743261145 1015057572112831201439508319483392713817484500383327774527254884229769146 3045172716338493604318524958450178141452453501149983323581764652689293147 9135518149015480812955574875350534424357360503449949970745293958067865148 27406554447046442438866724626051603273072081510349849912235881874203581149 82219663341139327316600173878154809819216244531049549736707645622610729150 246658990023417981949800521634464429457648733593148649210122936867832173151 739976970070253945849401564903393288372946200779445947630368810603496505152 2219930910210761837548204694710179865118838602338337842891106431810489501153 6659792730632285512644614084130539595356515807015013528673319295431468489154 19979378191896856537933842252391618786069547421045040586019957886294405453155 59938134575690569613801526757174856358208642263135121758059873658883216345156 179814403727071708841404580271524569074625926789405365274179620976649649021157 539443211181215126524213740814573707223877780368216095822538862929948947049158 1618329633543645379572641222443721121671633341104648287467616588789846841133159 4854988900630936138717923667331163365014900023313944862402849766369540523385160 14564966701892808416153771001993490095044700069941834587208549299108621570141161 43694900105678425248461313005980470285134100209825503761625647897325864710409162 131084700317035275745383939017941410855402300629476511284876943691977594131213163 393254100951105827236151817053824232566206901888429533854630831075932782393625164 1179762302853317481708455451161472697698620705665288601563892493227798347180861165 3539286908559952445125366353484418093095862116995865804691677479683395041542569166 10617860725679857335376099060453254279287586350987597414075032439050185124627693167 31853582177039572006128297181359762837862759052962792242225097317150555373883065168 95560746531118716018384891544079288513588277158888376726675291951451666121649181169 286682239593356148055154674632237865540764831476665130180025875854354998364947529170 860046718780068444165464023896713596622294494429995390540077627563064995094842573171 2580140156340205332496392071690140789866883483289986171620232882689194985284527705172 7740420469020615997489176215070422369600650449869958514860698648067584955853583101173 23221261407061847992467528645211267108801951349609875544582095944202754867560749289174 69663784221185543977402585935633801326405854048829626633746287832608264602682247853175 208991352663556631932207757806901403979217562146488879901238863497824793808046743545176 626974057990669895796623273420704211937652686439466639703716590493474381424140230621177 1880922173972009687389869820262112635812958059318399919111149771480423144272420691849178 5642766521916029062169609460786337907438874177955199757333449314441269432817262075533179 16928299565748087186508828382359013722316622533865599272000347943323808298451786226585180 50784898697244261559526485147077041166949867601596797816001043829971424895355358679741181 152354696091732784678579455441231123500849602804790393448003131489914274686066076039209182 457064088275198354035738366323693370502548808414371180344009394469742824058198228117613183 1371192264825595062107215098971080111507646425243113541032028183409228472174594684352825184 4113576794476785186321645296913240334522939275729340623096084550227685416523784053058461185 12340730383430355558964935890739721003568817827188021869288253650683056249571352159175369186 37022191150291066676894807672219163010706453481564065607864760952049168748714056477526093187 111066573450873200030684423016657489032119360444692196823594282856147506246142169432578265188 333199720352619600092053269049972467096358081334076590470782848568442518738426508297734781189 999599161057858800276159807149917401289074244002229771412348545705327556215279524893204329190 2998797483173576400828479421449752203867222732006689314237045637115982668645838574679612973191 8996392449520729202485438264349256611601668196020067942711136911347948005937515724038838905192 26989177348562187607456314793047769834805004588060203828133410734043844017812547172116516701193 80967532045686562822368944379143309504415013764180611484400232202131532053437641516349550089194 242902596137059688467106833137429928513245041292541834453200696606394596160312924549048650253195 728707788411179065401320499412289785539735123877625503359602089819183788480938773647145950745196 2186123365233537196203961498236869356619205371632876510078806269457551365442816320941437852221197 65583700957006115886118844947106080698576 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 14215 Killed /usr/bin/gp -q -emacs Timing: real 0m21.024s user 0m20.954s sys 0m0.047s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:44:38 2005 Input: m=a=3;r=1;n=7;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:45:44 2005 Input: m=a=3;r=1;n=9;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 93 94 95 96 97 98 99 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 9100 9101 9102 9103 9104 9105 9106 9107 9108 9109 9110 9111 9112 9113 9114 9115 9116 9117 9118 9119 9120 9121 9122 9123 9124 9125 9126 9127 9128 9129 9130 9131 9132 9133 9134 9135 9136 9137 9138 9139 9140 9141 9142 9143 9144 9145 9146 9147 9148 9149 9150 9151 9152 9153 9154 9155 9156 9157 9158 9159 9160 9161 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Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 14237 Killed /usr/bin/gp -q -emacs Timing: real 0m21.005s user 0m16.135s sys 0m4.864s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:46:02 2005 Input: m=a=3;r=1;n=11;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 53 44 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:46:14 2005 Input: m=a=3;r=1;n=13;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:46:21 2005 Input: m=a=3;r=1;n=15;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 123 64 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:46:55 2005 Input: m=a=3;r=1;n=9;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 93 94 95 96 97 98 99 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 9100 9101 9102 9103 9104 9105 9106 9107 9108 9109 9110 9111 9112 9113 9114 9115 9116 9117 9118 9119 9120 9121 9122 9123 9124 9125 9126 9127 9128 9129 9130 9131 9132 9133 9134 9135 9136 9137 9138 9139 9140 9141 9142 9143 9144 9145 9146 9147 9148 9149 9150 9151 9152 9153 9154 9155 9156 9157 9158 9159 9160 9161 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Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 14273 Killed /usr/bin/gp -q -emacs Timing: real 0m21.005s user 0m16.099s sys 0m4.901s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:49:02 2005 Input: m=a=3;r=1;n=9;print(m,r);print(m=a*m,r=r+1);while(divrem(m,a)[2]<>0,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:50:20 2005 Input: m=a=3;r=1;n=9;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(divrem(m,a)[2]<>0,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:50:28 2005 Input: m=a=3;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(divrem(m,a)[2]<>0,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:51:02 2005 Input: m=a=3;r=1;n=7;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:51:22 2005 Input: m=a=3;r=1;n=11;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 53 44 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:51:30 2005 Input: m=a=3;r=1;n=13;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.011s sys 0m0.002s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:51:35 2005 Input: m=a=3;r=1;n=15;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 123 64 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 15:52:09 2005 Input: m=a=3;r=1;n=9;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 93 94 95 96 97 98 99 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 9100 9101 9102 9103 9104 9105 9106 9107 9108 9109 9110 9111 9112 9113 9114 9115 9116 9117 9118 9119 9120 9121 9122 9123 9124 9125 9126 9127 9128 9129 9130 9131 9132 9133 9134 9135 9136 9137 9138 9139 9140 9141 9142 9143 9144 9145 9146 9147 9148 9149 9150 9151 9152 9153 9154 9155 9156 9157 9158 9159 9160 9161 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91799 91800 91801 91802 91803 91804 91805 91806 91807 91808 91809 91810 91811 91812 91813 91814 91815 91816 91817 91818 91819 91820 91821 91822 91823 91824 91825 91826 91827 91828 91829 91830 91831 91832 91833 91834 91835 91836 91837 91838 91839 91840 91841 91842 91843 91844 91845 91846 91847 91848 91849 91850 91851 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 14364 Killed /usr/bin/gp -q -emacs Timing: real 0m21.007s user 0m16.177s sys 0m4.822s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 17:01:17 2005 Input: ?polgalois Output: ? polgalois(x): Galois group of the polynomial x (see manual for group coding). ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 17:03:53 2005 Input: polgalois(x^5-x+1) Output: ? [120, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.170s user 0m0.010s sys 0m0.010s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 17:04:45 2005 Input: polgalois(x^5+20*x+16) Output: ? [60, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 17:05:23 2005 Input: polgalois(x^5+2) Output: ? [20, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.010s sys 0m0.006s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 17:05:48 2005 Input: polgalois(x^5-5*x+12) Output: ? [10, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.018s sys 0m0.006s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 17:06:52 2005 Input: polgalois(x^5+x^4-4*x^3-3*x^2+3*x+1) Output: ? [5, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.011s sys 0m0.004s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 17:09:10 2005 Input: polgalois(x^5-16*x+2) Output: ? [120, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.006s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 17:11:46 2005 Input: polgalois(x^5+20*x+32) Output: ? [10, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.011s sys 0m0.006s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 17:14:14 2005 Input: polgalois(x^5+2*x^4+3*x^3+3*x^2+2*x+1) Output: ? ? Errors (if any) and Timing Info: *** sorry, galois of reducible polynomial is not yet implemented. Timing: real 0m0.044s user 0m0.007s sys 0m0.007s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 17:14:29 2005 Input: polgalois(x^5+2*x^4+7*x^3+7*x^2+2*x+1) Output: ? ? Errors (if any) and Timing Info: *** sorry, galois of reducible polynomial is not yet implemented. Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 17:19:34 2005 Input: polgalois(10*x^6+70*x^3-603*x^2+1225) Output: ? [720, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.020s sys 0m0.005s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sun Mar 20 17:22:01 2005 Input: polgalois(x^5-x^4-x^2+x-1) Output: ? [120, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.006s sys 0m0.011s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 18:00:06 2005 Input: polgalois(x^3-x-4) Output: ? [6, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 18:00:31 2005 Input: polgalois(x^4-3*x^3+20*x^2+44*x+54) Output: ? [24, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.011s sys 0m0.004s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 18:01:15 2005 Input: polgalois(x^4+2*x^3+7*x^2-11) Output: ? [24, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.012s sys 0m0.005s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 18:01:38 2005 Input: polgalois(x^4-x-10) Output: ? [24, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 18:02:32 2005 Input: polgalois(x^4+5*x^3+3*x^2-5*x-9) Output: ? [24, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.011s sys 0m0.004s '58.8.0.' ************** PARI ***************** Host 58.8.0.253 (58.8.0.253) Time: Sun Mar 20 18:05:13 2005 Input: factor(2*x^4+16*x^3+x^2-74*x+56) Output: ? [x^2 + 6*x - 8 1] [2*x^2 + 4*x - 7 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Sun Mar 20 18:08:44 2005 Input: polgalois(10000*X^4 - 20379*X^3 - 154245*X^2 + 156696*X + 354936) Output: ? [24, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.013s sys 0m0.006s '151.205' ************** PARI ***************** Host 151.205.160.94 (151.205.160.94) Time: Sun Mar 20 18:52:19 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 18:57:55 2005 Input: m=a=3;r=1;n=9;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 93 94 95 96 97 98 99 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 9100 9101 9102 9103 9104 9105 9106 9107 9108 9109 9110 9111 9112 9113 9114 9115 9116 9117 9118 9119 9120 9121 9122 9123 9124 9125 9126 9127 9128 9129 9130 9131 9132 9133 9134 9135 9136 9137 9138 9139 9140 9141 9142 9143 9144 9145 9146 9147 9148 9149 9150 9151 9152 9153 9154 9155 9156 9157 9158 9159 9160 9161 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91799 91800 91801 91802 91803 91804 91805 91806 91807 91808 91809 91810 91811 91812 91813 91814 91815 91816 91817 91818 91819 91820 91821 91822 91823 91824 91825 91826 91827 91828 91829 91830 91831 91832 91833 91834 91835 91836 91837 91838 91839 91840 91841 91842 91843 91844 91845 91846 91847 91848 91849 91850 91851 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 17303 Killed /usr/bin/gp -q -emacs Timing: real 0m21.029s user 0m15.877s sys 0m5.122s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 18:58:17 2005 Input: m=a=3;r=1;n=7;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 18:58:32 2005 Input: m=a=3;r=1;n=11;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 53 44 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 18:58:41 2005 Input: m=a=3;r=1;n=13;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 18:58:48 2005 Input: m=a=3;r=1;n=15;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 123 64 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 18:59:24 2005 Input: m=a=3;r=1;n=9;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*mn,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 93 94 95 96 97 98 99 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 9100 9101 9102 9103 9104 9105 9106 9107 9108 9109 9110 9111 9112 9113 9114 9115 9116 9117 9118 9119 9120 9121 9122 9123 9124 9125 9126 9127 9128 9129 9130 9131 9132 9133 9134 9135 9136 9137 9138 9139 9140 9141 9142 9143 9144 9145 9146 9147 9148 9149 9150 9151 9152 9153 9154 9155 9156 9157 9158 9159 9160 9161 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91799 91800 91801 91802 91803 91804 91805 91806 91807 91808 91809 91810 91811 91812 91813 91814 91815 91816 91817 91818 91819 91820 91821 91822 91823 91824 91825 91826 91827 91828 91829 91830 91831 91832 91833 91834 91835 91836 91837 91838 91839 91840 91841 91842 91843 91844 91845 91846 91847 91848 91849 91850 91851 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 17346 Killed /usr/bin/gp -q -emacs Timing: real 0m21.051s user 0m16.440s sys 0m4.560s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:00:24 2005 Input: m=a=3;r=1;n=9;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 03 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:01:20 2005 Input: m=a=3;r=1;n=7;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:01:35 2005 Input: m=a=3;r=1;n=11;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 53 44 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:01:41 2005 Input: m=a=3;r=1;n=13;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:01:48 2005 Input: m=a=3;r=1;n=15;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 123 64 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:01:57 2005 Input: m=a=3;r=1;n=9;print(m,r);print(m=a*m,r=r+1);while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 03 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:03:33 2005 Input: m=a=3;r=1;n=9;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:03:52 2005 Input: m=a=3;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:04:09 2005 Input: m=a=3;r=1;n=11;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 53 44 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:04:16 2005 Input: m=a=3;r=1;n=13;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:04:23 2005 Input: m=a=3;r=1;n=15;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 123 64 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:04:35 2005 Input: m=a=3;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:07:04 2005 Input: m=a=3;r=1;n=7;print(m,r);while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:08:33 2005 Input: m=a=3;r=1;n=7;print(m,r);m=a*m;r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:14:24 2005 Input: m=a=2;r=1;n=7;print(m,r);m=a*m;r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 13 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:15:43 2005 Input: m=a=2;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));m=a*m;r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:16:48 2005 Input: m=a=2;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));m=a*m;r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n); if(m<>a,print(m,r)))) Output: ? ? mr ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...=a*m-n;while(m>=n,m=m-n); ^ *** Warning: unused characters: )). Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:17:08 2005 Input: m=a=2;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));m=a*m;r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.001s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:17:32 2005 Input: m=a=2;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:17:55 2005 Input: m=a=2;r=1;n=5;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 33 14 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:18:07 2005 Input: m=a=2;r=1;n=3;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:22:14 2005 Input: m=a=2;r=1;n=3;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(r)))) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:22:54 2005 Input: m=a=2;r=1;n=3;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(r)))) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:24:13 2005 Input: m=a=2;r=1;n=3;m=a*m;r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(r)))) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:24:29 2005 Input: m=a=2;r=1;n=7;m=a*m;r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(r)))) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:24:50 2005 Input: m=a=2;r=1;n=9;m=a*m;r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(r)))) Output: ? 3 4 5 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:25:39 2005 Input: m=a=2;r=1;n=9;m=a*m;r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 83 74 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:25:53 2005 Input: m=a=2;r=1;n=7;m=a*m;r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:26:10 2005 Input: m=a=2;r=1;n=3;m=a*m;r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:27:03 2005 Input: m=a=2;r=1;n=3;print(m,r);if(n<>a*m,print(m=a*m;r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...,r);if(n<>a*m,print(m=a*m;r=r+1));while(m>a,r ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:28:39 2005 Input: m=a=2;r=1;n=3;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.002s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:29:30 2005 Input: m=a=2;r=1;n=5;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 33 14 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:29:36 2005 Input: m=a=2;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:29:44 2005 Input: m=a=2;r=1;n=9;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 83 74 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:29:56 2005 Input: m=a=2;r=1;n=11;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 83 54 105 96 77 38 69 110 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:30:08 2005 Input: m=a=2;r=1;n=13;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 83 34 65 126 117 98 59 1010 711 112 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:30:19 2005 Input: m=a=2;r=1;n=15;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 21 42 83 14 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:30:33 2005 Input: m=a=3;r=1;n=15;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 123 64 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:30:44 2005 Input: m=a=3;r=1;n=13;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:30:50 2005 Input: m=a=3;r=1;n=11;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 53 44 15 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:31:01 2005 Input: m=a=3;r=1;n=9;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:31:12 2005 Input: m=a=3;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:31:29 2005 Input: m=a=10;r=1;n=3;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 101 1002 13 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:32:11 2005 Input: m=a=10;r=1;n=5;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 101 1002 03 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:32:22 2005 Input: m=a=10;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 101 1002 63 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:32:41 2005 Input: m=a=10;r=1;n=5;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 101 1002 03 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:33:10 2005 Input: m=a=5;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 51 252 63 24 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:41:31 2005 Input: m=a=5;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>1,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 51 252 63 24 35 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:42:33 2005 Input: m=a=3;r=1;n=15;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>1,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 123 64 96 127 68 910 1211 612 914 1215 616 918 1219 620 922 1223 624 926 1227 628 930 1231 632 934 1235 636 938 1239 640 942 1243 644 946 1247 648 950 1251 652 954 1255 656 958 1259 660 962 1263 664 966 1267 668 970 1271 672 974 1275 676 978 1279 680 982 1283 684 986 1287 688 990 1291 692 994 1295 696 998 1299 6100 9102 12103 6104 9106 12107 6108 9110 12111 6112 9114 12115 6116 9118 12119 6120 9122 12123 6124 9126 12127 6128 9130 12131 6132 9134 12135 6136 9138 12139 6140 9142 12143 6144 9146 12147 6148 9150 12151 6152 9154 12155 6156 9158 12159 6160 9162 12163 6164 9166 12167 6168 9170 12171 6172 9174 12175 6176 9178 12179 6180 9182 12183 6184 9186 12187 6188 9190 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62212 92214 122215 62216 92218 122219 62220 92222 122223 62224 92226 122227 62228 92230 122231 62232 92234 122235 62236 92238 122239 62240 92242 122243 62244 92246 122247 62248 92250 122251 62252 92254 122255 62256 92258 122259 62260 92262 122263 62264 92266 122267 62268 92270 122271 62272 92274 122275 62276 92278 122279 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 17993 Killed /usr/bin/gp -q -emacs Timing: real 0m21.227s user 0m16.627s sys 0m4.372s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:44:03 2005 Input: m=a=5;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>1,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 51 252 63 24 35 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:44:17 2005 Input: m=a=5;r=1;n=9;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>1,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 51 252 83 44 25 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:44:26 2005 Input: m=a=5;r=1;n=11;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>1,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 51 252 43 94 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:44:33 2005 Input: m=a=5;r=1;n=13;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>1,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 51 252 83 14 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.011s sys 0m0.001s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:45:01 2005 Input: m=a=5;r=1;n=15;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>1,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 51 252 104 106 108 1010 1012 1014 1016 1018 1020 1022 1024 1026 1028 1030 1032 1034 1036 1038 1040 1042 1044 1046 1048 1050 1052 1054 1056 1058 1060 1062 1064 1066 1068 1070 1072 1074 1076 1078 1080 1082 1084 1086 1088 1090 1092 1094 1096 1098 10100 10102 10104 10106 10108 10110 10112 10114 10116 10118 10120 10122 10124 10126 10128 10130 10132 10134 10136 10138 10140 10142 10144 10146 10148 10150 10152 10154 10156 10158 10160 10162 10164 10166 10168 10170 10172 10174 10176 10178 10180 10182 10184 10186 10188 10190 10192 10194 10196 10198 10200 10202 10204 10206 10208 10210 10212 10214 10216 10218 10220 10222 10224 10226 10228 10230 10232 10234 10236 10238 10240 10242 10244 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102066 102068 102070 102072 102074 102076 102078 102080 102082 102084 102086 102088 102090 102092 102094 102096 102098 102100 102102 102104 102106 102108 102110 102112 102114 102116 102118 102120 102122 102124 102126 102128 102130 102132 102134 102136 102138 102140 102142 102144 102146 102148 102150 102152 102154 102156 102158 102160 102162 102164 102166 102168 102170 102172 102174 102176 102178 102180 102182 102184 102186 102188 102190 102192 102194 102196 102198 102200 102202 102204 102206 102208 102210 102212 102214 102216 102218 102220 102222 102224 102226 102228 102230 102232 102234 102236 102238 102240 102242 102244 102246 102248 102250 102252 102254 102256 102258 102260 102262 102264 102266 102268 102270 102272 102274 102276 102278 102280 102282 102284 102286 102288 102290 102292 102294 102296 102298 102300 102302 102304 102306 102308 102310 102312 102314 102316 102318 102320 102322 102324 102326 102328 102330 102332 102334 102336 102338 102340 102342 102344 102346 102348 102350 102352 102354 102356 102358 102360 102362 102364 102366 102368 102370 102372 102374 102376 102378 102380 102382 102384 102386 102388 102390 102392 102394 102396 102398 102400 102402 102404 102406 102408 102410 102412 102414 102416 102418 102420 102422 102424 102426 102428 102430 102432 102434 102436 102438 102440 102442 102444 102446 102448 102450 102452 102454 102456 102458 102460 102462 102464 102466 102468 102470 102472 102474 102476 102478 102480 102482 102484 102486 102488 102490 102492 102494 102496 102498 102500 102502 102504 102506 102508 102510 102512 102514 102516 102518 102520 102522 102524 102526 102528 102530 102532 102534 102536 102538 102540 102542 102544 102546 102548 102550 102552 102554 102556 102558 102560 102562 102564 102566 102568 102570 102572 102574 102576 102578 102580 102582 102584 102586 102588 102590 102592 102594 102596 102598 102600 102602 102604 102606 102608 102610 102612 102614 102616 102618 102620 102622 102624 102626 102628 102630 102632 102634 102636 102638 102640 102642 102644 102646 102648 102650 102652 102654 102656 102658 102660 102662 102664 102666 102668 102670 102672 102674 102676 102678 102680 102682 102684 102686 102688 102690 102692 102694 102696 102698 102700 102702 102704 102706 102708 102710 102712 102714 102716 102718 102720 102722 102724 102726 102728 102730 102732 102734 102736 102738 102740 102742 102744 102746 102748 102750 102752 102754 102756 102758 102760 102762 102764 102766 102768 102770 102772 102774 102776 102778 102780 102782 102784 102786 102788 102790 102792 102794 102796 102798 102800 102802 102804 102806 102808 102810 102812 102814 102816 102818 102820 102822 102824 102826 102828 102830 102832 102834 102836 102838 102840 102842 102844 102846 102848 102850 102852 102854 102856 102858 102860 102862 102864 102866 102868 102870 102872 102874 102876 102878 102880 102882 102884 102886 102888 102890 102892 102894 102896 102898 102900 102902 102904 102906 102908 102910 102912 102914 102916 102918 102920 102922 102924 102926 102928 102930 102932 102934 102936 102938 102940 102942 102944 102946 102948 102950 102952 102954 102956 102958 102960 102962 102964 102966 102968 102970 102972 102974 102976 102978 102980 102982 102984 102986 102988 102990 102992 102994 102996 102998 103000 103002 103004 103006 103008 103010 103012 10301 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 18044 Killed /usr/bin/gp -q -emacs Timing: real 0m21.101s user 0m18.421s sys 0m2.579s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Sun Mar 20 19:45:16 2005 Input: m=a=5;r=1;n=15;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 51 252 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '58.8.0.' ************** PARI ***************** Host 58.8.0.250 (58.8.0.250) Time: Sun Mar 20 20:14:13 2005 Input: polgalois(X^6 - 3*X^5 - 16*X^4 + 146*X^3 + 144*X^2 - 243*X - 729) Output: ? [24, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m4.350s user 0m0.024s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 20:53:57 2005 Input: lcm(22,5152) Output: ? 56672 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 20:56:38 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 20:58:03 2005 Input: factor(83393192) Output: ? [2 3] [71 1] [146819 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:02:41 2005 Input: isprime(1079003) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:02:53 2005 Input: isprime(1079001) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:03:04 2005 Input: isprime(1079999) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:03:16 2005 Input: isprime(1078999) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:03:29 2005 Input: isprime(1078997) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:03:36 2005 Input: isprime(1078993) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:04:06 2005 Input: isprime(83393191) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:04:12 2005 Input: isprime(83393189) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:04:23 2005 Input: isprime(83393187) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:04:29 2005 Input: isprime(83393185) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:04:34 2005 Input: isprime(83393183) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:04:38 2005 Input: isprime(83393181) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:04:45 2005 Input: isprime(83393179) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:05:43 2005 Input: lcm(814,190624) Output: ? 2096864 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:08:45 2005 Input: lcm(20,30) Output: ? 60 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:09:11 2005 Input: lcm(20,40) Output: ? 40 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Mar 20 21:09:26 2005 Input: lcm(60,40) Output: ? 120 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '137.219' ************** PARI ***************** Host 137.219.16.124 (137.219.16.124) Time: Sun Mar 20 23:31:37 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '155.207' ************** PARI ***************** Host 155.207.120.6 (155.207.120.6) Time: Mon Mar 21 03:45:35 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '137.222' ************** PARI ***************** Host 137.222.92.186 (137.222.92.186) Time: Mon Mar 21 07:08:00 2005 Input: factor(28847515606604057311273627054818790089037287985892228129358683688705867482899) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 24699 Killed /usr/bin/gp -q -emacs Timing: real 0m21.424s user 0m20.917s sys 0m0.083s '137.222' ************** PARI ***************** Host 137.222.92.186 (137.222.92.186) Time: Mon Mar 21 07:08:37 2005 Input: isprime(28847515606604057311273627054818790089037287985892228129358683688705867482899) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.007s '137.222' ************** PARI ***************** Host 137.222.92.186 (137.222.92.186) Time: Mon Mar 21 07:08:41 2005 Input: isprime(28847515606604057311273627054818790089037287985892228129358683688705867482899) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '137.222' ************** PARI ***************** Host 137.222.92.186 (137.222.92.186) Time: Mon Mar 21 07:08:42 2005 Input: isprime(28847515606604057311273627054818790089037287985892228129358683688705867482899) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.008s '137.222' ************** PARI ***************** Host 137.222.92.186 (137.222.92.186) Time: Mon Mar 21 07:08:45 2005 Input: isprime(28847515606604057311273627054818790089037287985892228129358683688705867482899) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '137.222' ************** PARI ***************** Host 137.222.92.186 (137.222.92.186) Time: Mon Mar 21 07:09:05 2005 Input: factor(28) Output: ? [2 2] [7 1] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.008s sys 0m0.004s '137.222' ************** PARI ***************** Host 137.222.92.186 (137.222.92.186) Time: Mon Mar 21 07:09:14 2005 Input: factor(2) Output: ? [2 1] ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.006s sys 0m0.005s '137.222' ************** PARI ***************** Host 137.222.92.186 (137.222.92.186) Time: Mon Mar 21 07:09:18 2005 Input: factor(28847515606604057311273627054818790089037287985892228129358683688705867482899) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 24746 Killed /usr/bin/gp -q -emacs Timing: real 0m21.070s user 0m20.955s sys 0m0.045s '137.222' ************** PARI ***************** Host 137.222.92.186 (137.222.92.186) Time: Mon Mar 21 07:09:21 2005 Input: isprime(2) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '137.222' ************** PARI ***************** Host 137.222.92.186 (137.222.92.186) Time: Mon Mar 21 07:09:30 2005 Input: isprime(3) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.010s '192.91.' ************** PARI ***************** Host 192.91.247.213 (192.91.247.213) Time: Mon Mar 21 09:27:30 2005 Input: bezout(30,43) Output: ? [-10, 7, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.042s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.251.56 (128.197.251.56) Time: Mon Mar 21 10:40:10 2005 Input: factor(1734251) Output: ? [1171 1] [1481 1] ? Errors (if any) and Timing Info: Timing: real 0m0.098s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.251.56 (128.197.251.56) Time: Mon Mar 21 10:40:31 2005 Input: factor(52633) Output: ? [7 1] [73 1] [103 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '147.197' ************** PARI ***************** Host 147.197.236.200 (147.197.236.200) Time: Mon Mar 21 11:42:11 2005 Input: 1 +1 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.005s sys 0m0.006s '147.197' ************** PARI ***************** Host 147.197.236.200 (147.197.236.200) Time: Mon Mar 21 11:42:17 2005 Input: 1 + 1 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '193.136' ************** PARI ***************** Host 193.136.173.40 (193.136.173.40) Time: Mon Mar 21 12:43:09 2005 Input: Pi Output: ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.006s sys 0m0.008s '140.177' ************** PARI ***************** Host 140.177.203.1 (140.177.203.1) Time: Mon Mar 21 19:27:04 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:05:45 2005 Input: factor(7393) Output: ? [7393 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:06:51 2005 Input: Mod(3263*866*1474*570*6989*384*5654*2401*7, 7393) Output: ? Mod(5200, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:07:22 2005 Input: Mod(7, 7393)^2 Output: ? Mod(49, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.007s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:07:28 2005 Input: Mod(7, 7393)^4 Output: ? Mod(2401, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:07:35 2005 Input: Mod(7, 7393)^8 Output: ? Mod(5654, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:07:42 2005 Input: Mod(7, 7393)^16 Output: ? Mod(384, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:07:48 2005 Input: Mod(7, 7393)^32 Output: ? Mod(6989, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:07:56 2005 Input: Mod(7, 7393)^64 Output: ? Mod(570, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:08:03 2005 Input: Mod(7, 7393)^128 Output: ? Mod(7001, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:08:23 2005 Input: Mod(7, 7393)^128 Output: ? Mod(7001, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:08:31 2005 Input: Mod(7, 7393)^256 Output: ? Mod(5804, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:08:40 2005 Input: Mod(7, 7393)^512 Output: ? Mod(3908, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:08:49 2005 Input: Mod(7, 7393)^1024 Output: ? Mod(5919, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:09:01 2005 Input: Mod(7, 7393)^2048 Output: ? Mod(6527, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:09:07 2005 Input: Mod(7, 7393)^4196 Output: ? Mod(947, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:10:35 2005 Input: Mod(7, 7387)^7386 Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:11:18 2005 Input: Mod(5654*384*6989*570*5919*6527*947, 7393) Output: ? Mod(428, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:11:44 2005 Input: Mod(2401*5654*384*6989*570*5919*6527*947, 7393) Output: ? Mod(1, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:12:16 2005 Input: Mod(7, 7387)^8 Output: ? Mod(2941, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:12:23 2005 Input: Mod(7, 7387)^16 Output: ? Mod(6691, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:12:38 2005 Input: Mod(7, 7387)^32 Output: ? Mod(4261, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:12:52 2005 Input: Mod(7, 7387)^64 Output: ? Mod(6262, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:13:02 2005 Input: Mod(7, 7387)^128 Output: ? Mod(2448, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:13:12 2005 Input: Mod(7, 7387)^256 Output: ? Mod(1847, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:13:20 2005 Input: Mod(7, 7387)^512 Output: ? Mod(6002, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.006s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:13:31 2005 Input: Mod(7, 7387)^1024 Output: ? Mod(4992, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:13:44 2005 Input: Mod(7, 7387)^2048 Output: ? Mod(3713, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:13:56 2005 Input: Mod(7, 7387)^4196 Output: ? Mod(3277, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:14:50 2005 Input: Mod(49*2401*2941*6691*4261*6262*2448*1847*6002*4992*3713*3277, 7387) Output: ? Mod(6925, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:15:37 2005 Input: Mod(7, 7387)^7386 Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:16:38 2005 Input: Mod(7, 7387)^1 Output: ? Mod(7, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:16:42 2005 Input: Mod(7, 7387)^2 Output: ? Mod(49, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:16:46 2005 Input: Mod(7, 7387)^4 Output: ? Mod(2401, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:16:53 2005 Input: Mod(7, 7387)^16 Output: ? Mod(6691, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '212.149' ************** PARI ***************** Host 212.149.214.44 (212.149.214.44) Time: Mon Mar 21 20:16:57 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:16:59 2005 Input: Mod(7, 7387)^32 Output: ? Mod(4261, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:17:07 2005 Input: Mod(7, 7387)^64 Output: ? Mod(6262, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:17:14 2005 Input: Mod(7, 7387)^1024 Output: ? Mod(4992, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:17:22 2005 Input: Mod(7, 7387)^2048 Output: ? Mod(3713, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:17:35 2005 Input: Mod(7, 7387)^4196 Output: ? Mod(3277, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.18 (128.197.60.18) Time: Mon Mar 21 20:18:06 2005 Input: Mod(49*2401*6691*4261*6262*4992*3713*3277, 7387) Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '66.218.' ************** PARI ***************** Host 66.218.11.26 (66.218.11.26) Time: Mon Mar 21 20:29:48 2005 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.237.148 (168.122.237.148) Time: Mon Mar 21 21:25:08 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.237.148 (168.122.237.148) Time: Mon Mar 21 21:27:14 2005 Input: factor(452) Output: ? [2 2] [113 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.237.148 (168.122.237.148) Time: Mon Mar 21 21:28:29 2005 Input: factor(329) factor(1080) Output: ? [7 1] [47 1] ? [2 3] [3 3] [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.237.148 (168.122.237.148) Time: Mon Mar 21 21:35:12 2005 Input: Mod(329,1080) Output: ? Mod(329, 1080) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.237.148 (168.122.237.148) Time: Mon Mar 21 21:35:31 2005 Input: Mod(329,1080)^(-1) Output: ? Mod(929, 1080) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.004s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.237.148 (168.122.237.148) Time: Mon Mar 21 21:37:00 2005 Input: Mod(452,1147(^929 Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Mod(452,1147(^929 ^----- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.237.148 (168.122.237.148) Time: Mon Mar 21 21:37:11 2005 Input: Mod(452,1147)^929 Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Mon Mar 21 21:40:25 2005 Input: Mod(5,23)^13 Output: ? Mod(21, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Mon Mar 21 21:40:49 2005 Input: Mod(28,1147)^749 Output: ? Mod(289, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Mon Mar 21 21:41:31 2005 Input: Mod(28,1147)^16 Output: ? Mod(90, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Mon Mar 21 21:41:39 2005 Input: Mod(28,1147)^32 Output: ? Mod(71, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Mon Mar 21 21:41:49 2005 Input: Mod(28,1147)^64 Output: ? Mod(453, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Mon Mar 21 21:41:59 2005 Input: Mod(28,1147)^512 Output: ? Mod(1032, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Mon Mar 21 21:42:06 2005 Input: Mod(28,1147)^237 Output: ? Mod(566, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Mon Mar 21 21:43:03 2005 Input: 1043*453*71 Output: ? 33546009 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Mon Mar 21 21:43:21 2005 Input: Mod(33546009,1147) Output: ? Mod(847, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Mon Mar 21 21:43:40 2005 Input: 144*784*28 Output: ? 3161088 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Mon Mar 21 21:43:58 2005 Input: Mod(3161088,1147) Output: ? Mod(1103, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Mon Mar 21 21:44:12 2005 Input: Mod(847*1103,1147) Output: ? Mod(583, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '216.148' ************** PARI ***************** Host 216.148.246.90 (216.148.246.90) Time: Mon Mar 21 21:44:50 2005 Input: Mod(1032*583,1147) Output: ? Mod(628, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '216.148' ************** PARI ***************** Host 216.148.246.90 (216.148.246.90) Time: Mon Mar 21 21:45:12 2005 Input: Mod(28^749,1147) Output: ? Mod(289, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '70.27.1' ************** PARI ***************** Host 70.27.136.17 (70.27.136.17) Time: Mon Mar 21 22:06:12 2005 Input: exp(cos(x)) Output: ? 2.7182818284590452353602874713526624977 - 1.3591409142295226176801437356763312488*x^2 + 0.45304697140984087256004791189211041628*x^4 - 0.11703713428087555874467904390546185754*x^6 + 0.025551309845882394449443178364153251156*x^8 - 0.0049110051993434470246423183041743979649*x^10 + 0.00085321417428874766199357968956763704729*x^12 - 0.00013636765988565653870127748276797477168*x^14 + 0.000020306178938881385743747795658556176692*x^16 + O(x^17) ? Errors (if any) and Timing Info: Timing: real 0m0.066s user 0m0.005s sys 0m0.009s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Mon Mar 21 23:08:18 2005 Input: phi(1147) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: phi(1147) ^--------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: phi(x) ===> eulerphi(x) eulerphi(x): Euler's totient function of x. Timing: real 0m0.021s user 0m0.008s sys 0m0.004s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Mon Mar 21 23:08:30 2005 Input: eulerphi(1147) Output: ? 1080 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.008s sys 0m0.002s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Mon Mar 21 23:09:35 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Mon Mar 21 23:10:01 2005 Input: 30*36 Output: ? 1080 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Mon Mar 21 23:25:25 2005 Input: Mod(452,1147)^151 Output: ? Mod(917, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Mon Mar 21 23:26:35 2005 Input: Mod(917,1147)^329 Output: ? Mod(236, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Mon Mar 21 23:32:53 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '216.148' ************** PARI ***************** Host 216.148.246.90 (216.148.246.90) Time: Mon Mar 21 23:35:01 2005 Input: Mod(1/1789,6912) Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Mon Mar 21 23:35:56 2005 Input: Mod(5192^85,6912) Output: ? Mod(2816, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Mon Mar 21 23:36:05 2005 Input: Mod(5192,6912)^85 Output: ? Mod(2816, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Mon Mar 21 23:36:41 2005 Input: Mod(5192,7081)^85 Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Mon Mar 21 23:36:58 2005 Input: Mod(2604,7081)^85 Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Mon Mar 21 23:37:16 2005 Input: Mod(4222,7081)^85 Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 22 07:32:25 2005 Input: isprime(129) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.366s user 0m0.005s sys 0m0.007s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 22 07:32:42 2005 Input: isprime(127) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '220.244' ************** PARI ***************** Host 220.244.224.105 (220.244.224.105) Time: Tue Mar 22 07:32:56 2005 Input: factor(127) Output: ? [127 1] ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.006s sys 0m0.007s '139.78.' ************** PARI ***************** Host 139.78.115.191 (139.78.115.191) Time: Tue Mar 22 17:45:11 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.268s user 0m0.023s sys 0m0.010s '139.78.' ************** PARI ***************** Host 139.78.115.191 (139.78.115.191) Time: Tue Mar 22 17:45:26 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.027s sys 0m0.004s '139.78.' ************** PARI ***************** Host 139.78.115.191 (139.78.115.191) Time: Tue Mar 22 17:48:52 2005 Input: {f(n)=sumdiv(n,x,x)-n} Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.006s '139.78.' ************** PARI ***************** Host 139.78.115.191 (139.78.115.191) Time: Tue Mar 22 17:51:13 2005 Input: {f(n)=sumdiv(n,x,x)-n}; y=210; for(x=1,10,y=f(y);print1(y,",")) Output: ? ? Errors (if any) and Timing Info: *** Warning: unused characters: };y=210;for(x=1,10,y=f(y);print1(y,",")). Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '139.78.' ************** PARI ***************** Host 139.78.115.191 (139.78.115.191) Time: Tue Mar 22 17:53:57 2005 Input: y=210; for(x=1,10,y=sumdiv(y,x,x)-y;print1(y,",")) Output: ? 366,378,582,594,846,1026,1374,1386,2358,2790, ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.008s sys 0m0.004s '139.78.' ************** PARI ***************** Host 139.78.115.191 (139.78.115.191) Time: Tue Mar 22 18:00:41 2005 Input: y=210; for(x=1,10,y=sumdiv(y,x,x)-y;print1(y,",")) Output: ? 366,378,582,594,846,1026,1374,1386,2358,2790, ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '139.78.' ************** PARI ***************** Host 139.78.115.191 (139.78.115.191) Time: Tue Mar 22 18:00:53 2005 Input: y=210; for(x=1,10,y=sumdiv(y,x,x)-y;print1(y,",")) Output: ? 366,378,582,594,846,1026,1374,1386,2358,2790, ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '139.78.' ************** PARI ***************** Host 139.78.115.191 (139.78.115.191) Time: Tue Mar 22 18:06:46 2005 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: ? 366,378,582,594,846,1026,1374,1386, ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '139.78.' ************** PARI ***************** Host 139.78.115.191 (139.78.115.191) Time: Tue Mar 22 18:07:14 2005 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '139.78.' ************** PARI ***************** Host 139.78.115.191 (139.78.115.191) Time: Tue Mar 22 18:07:35 2005 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: ? 366,378,582,594,846,1026,1374,1386, ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 22 18:54:45 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.004s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 22 18:55:17 2005 Input: 30*36 Output: ? 1080 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 22 18:56:21 2005 Input: Mod(329,1080)^(-1) Output: ? Mod(929, 1080) ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 22 18:57:36 2005 Input: Mod(452,1147)^929 Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 22 19:06:25 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 22 19:07:02 2005 Input: 72*96 Output: ? 6912 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.006s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 22 19:08:18 2005 Input: Mod(1789,6912)^(-1) Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 22 19:09:09 2005 Input: Mod(5129,7081)^85 Output: ? Mod(4532, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Tue Mar 22 19:09:10 2005 Input: factor(7393) Output: ? [7393 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 22 19:09:14 2005 Input: Mod(5129,7081)^85 Output: ? Mod(4532, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.007s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 22 19:09:33 2005 Input: Mod(2604,7081)^85 Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 22 19:09:51 2005 Input: Mod(4222,7081)^85 Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Tue Mar 22 19:11:24 2005 Input: factor(7387) Output: ? [83 1] [89 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:14:12 2005 Input: 53^2 * 62^2 Output: ? 10797796 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:14:31 2005 Input: 53^2 + 62^2 Output: ? 6653 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:14:40 2005 Input: factor(6653) Output: ? [6653 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:15:33 2005 Input: 6653 / 3 Output: ? 6653/3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:15:47 2005 Input: 6653 % 3 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:16:15 2005 Input: 6653 * (1/3) Output: ? 6653/3 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:16:36 2005 Input: 6653*0.333333 Output: ? 2217.6644489999999999999999999999999999 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.003s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Tue Mar 22 19:16:48 2005 Input: factor(7393) Output: ? [7393 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:16:57 2005 Input: 6653*0.25 Output: ? 1663.2500000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:18:46 2005 Input: sqrt(6652) Output: ? 81.559794016414730030648168618602305281 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:19:03 2005 Input: sqrt(6649) Output: ? 81.541400527584758917889085529270119460 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:19:12 2005 Input: sqrt(6644) Output: ? 81.510735489259327379548905871793367800 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:19:26 2005 Input: sqrt(6637) Output: ? 81.467785044151040795147956929878361508 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.003s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:19:34 2005 Input: sqrt(6628) Output: ? 81.412529748190480854679040608382009555 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:19:55 2005 Input: sqrt(6653-144) Output: ? 80.678373806119815716727720257998633455 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:20:04 2005 Input: sqrt(6653-121) Output: ? 80.820789404707004507294778468028095254 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:20:17 2005 Input: sqrt(6653-144) Output: ? 80.678373806119815716727720257998633455 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:20:28 2005 Input: sqrt(6653-81) Output: ? 81.067872798044972508494005207864882927 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:20:36 2005 Input: sqrt(6653-100) Output: ? 80.950602221354721679537893925571527562 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:20:47 2005 Input: sqrt(6653-169) Output: ? 80.523288556789581729358602927676628296 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:20:58 2005 Input: sqrt(6653-204) Output: ? 80.305666051655408706352791790430155932 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:21:10 2005 Input: sqrt(6653-184) Output: ? 80.430093870391572482817535414811645742 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:21:38 2005 Input: sqrt(6653-225) Output: ? 80.174809011309780606225634180425939814 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.225.176 (168.122.225.176) Time: Tue Mar 22 19:21:49 2005 Input: sqrt(6653-256) Output: ? 79.981247802219239945360510955074873665 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Tue Mar 22 19:47:16 2005 Input: Mod(329,1080)^(-1) Output: ? Mod(929, 1080) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Tue Mar 22 19:50:03 2005 Input: Mod(452,1147)^929 Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Tue Mar 22 19:50:31 2005 Input: Mod(763,1147)^329 Output: ? Mod(452, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 22 19:50:51 2005 Input: factor(6653) Output: ? [6653 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Tue Mar 22 19:54:48 2005 Input: sin(pi/6) Output: ? 1/6*pi - 1/1296*pi^3 + 1/933120*pi^5 - 1/1410877440*pi^7 + 1/3656994324480*pi^9 - 1/14481697524940800*pi^11 + 1/81329213300067532800*pi^13 - 1/614848852548510547968000*pi^15 + O(pi^16) ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.006s sys 0m0.008s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Tue Mar 22 19:54:58 2005 Input: sin(pi/6) Output: ? 1/6*pi - 1/1296*pi^3 + 1/933120*pi^5 - 1/1410877440*pi^7 + 1/3656994324480*pi^9 - 1/14481697524940800*pi^11 + 1/81329213300067532800*pi^13 - 1/614848852548510547968000*pi^15 + O(pi^16) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Tue Mar 22 19:55:38 2005 Input: Mod(198755616854654680546805408656646567546785476547547645674574576457467456767678911789001407476675675467546754674567457490,8745743198743987478309879341434836367367346767676743674367434131430101084874874567479834) Output: ? Mod(3463296996048199129930044390610516166047078128574110512060881870826340518587713446389752, 8745743198743987478309879341434836367367346767676743674367434131430101084874874567479834) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Tue Mar 22 19:56:04 2005 Input: Mod(198755616854654680546805408656646567546785476547547645674574576457467456767678911789001407476675675467546754674567457490,87) Output: ? Mod(33, 87) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Tue Mar 22 19:56:10 2005 Input: Mod(19875561685465468054680540865664656754678547654754745674574576457467456767678911789001407476675675467546754674567457490,87) Output: ? Mod(69, 87) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Tue Mar 22 19:56:14 2005 Input: Mod(1987556168546546805468054086566465675467857654754745674574576457467456767678911789001407476675675467546754674567457490,87) Output: ? Mod(5, 87) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Tue Mar 22 19:56:17 2005 Input: Mod(198755616854654680546805408656646567546785765475475674574576457467456767678911789001407476675675467546754674567457490,87) Output: ? Mod(76, 87) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Tue Mar 22 19:56:20 2005 Input: Mod(19875561685465468054680408656646567546785765475475674574576457467456767678911789001407476675675467546754674567457490,87) Output: ? Mod(83, 87) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Tue Mar 22 19:56:23 2005 Input: Mod(1987556168546546805468040865664667546785765475475674574576457467456767678911789001407476675675467546754674567457490,87) Output: ? Mod(39, 87) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Tue Mar 22 19:56:28 2005 Input: Mod(19875561686546805468040865664667546785765475475674574576457467456767678911789001407476675675467546754674567457490,87) Output: ? Mod(15, 87) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Tue Mar 22 19:56:36 2005 Input: Mod(19875561686546805468040865664667546785765475475674574576457467456767678911789001407476675675467546754674567457490,87) Output: ? Mod(15, 87) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Tue Mar 22 19:56:44 2005 Input: Mod(19875561686546805468040865664667546785765475475674574576457467456767678911789001407476675675467546754674567457490,88) Output: ? Mod(10, 88) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Tue Mar 22 19:56:53 2005 Input: Mod(19875561686546805468040865664667546785765475475674574576457467456767678911789001407476675675467546754674567457490,89) Output: ? Mod(67, 89) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 22 19:59:52 2005 Input: factor(1508) Output: ? [2 2] [13 1] [29 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 22 20:00:10 2005 Input: factor(3562) Output: ? [2 1] [13 1] [137 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Tue Mar 22 20:03:02 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Tue Mar 22 20:03:50 2005 Input: Mod(763,1147)^329 Output: ? Mod(452, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Tue Mar 22 20:04:12 2005 Input: Mod(1789,6912)^(-1) Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Tue Mar 22 20:04:52 2005 Input: Mod(5192,7081)^(85) Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Tue Mar 22 20:06:04 2005 Input: Mod(2605,7081)^(85) Output: ? Mod(2543, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Tue Mar 22 20:06:44 2005 Input: Mod(4222,7081)^(85) Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Tue Mar 22 20:27:50 2005 Input: factor(6653) Output: ? [6653 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.001s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Tue Mar 22 20:38:14 2005 Input: factor(1508) Output: ? [2 2] [13 1] [29 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Tue Mar 22 20:38:43 2005 Input: factor(3562) Output: ? [2 1] [13 1] [137 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 22 21:36:00 2005 Input: factor(7387) Output: ? [83 1] [89 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 22 21:36:08 2005 Input: factor(7393) Output: ? [7393 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Tue Mar 22 21:37:22 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Tue Mar 22 21:38:33 2005 Input: Mod(329,1080)^(-1) Output: ? Mod(929, 1080) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Tue Mar 22 21:39:48 2005 Input: Mod(2,1278)^(-1) Output: ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(2, 1278). Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Tue Mar 22 21:41:55 2005 Input: Mod(452,1147)^(929) Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Tue Mar 22 22:47:25 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Tue Mar 22 22:52:23 2005 Input: mod(1789, 6480)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(1789,6480)^(-1) ^------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Tue Mar 22 22:52:36 2005 Input: Mod(1789, 6480)^(-1) Output: ? Mod(949, 6480) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Tue Mar 22 22:55:13 2005 Input: Mod(5192, 7801)^(949) Output: ? Mod(2118, 7801) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Tue Mar 22 22:57:22 2005 Input: Mod(2604, 7801)^(949) Output: ? Mod(2659, 7801) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Tue Mar 22 22:57:54 2005 Input: Mod(2604, 7081)^(949) Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Tue Mar 22 22:58:25 2005 Input: Mod(5192, 7081)^(949) Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Tue Mar 22 22:59:26 2005 Input: Mod(4222, 7081)^(949) Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Tue Mar 22 23:12:24 2005 Input: factor(975) Output: ? [3 1] [5 2] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Tue Mar 22 23:12:52 2005 Input: factor(975) Output: ? [3 1] [5 2] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Tue Mar 22 23:13:37 2005 Input: Mod(4222, 7081)^(949) Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '133.30.' ************** PARI ***************** Host 133.30.64.210 (133.30.64.210) Time: Wed Mar 23 00:36:10 2005 Input: 1+2; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '133.30.' ************** PARI ***************** Host 133.30.64.210 (133.30.64.210) Time: Wed Mar 23 00:37:11 2005 Input: 1+2 Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Wed Mar 23 01:09:38 2005 Input: nextprime(100) Output: ? 101 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.005s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Wed Mar 23 01:10:17 2005 Input: gcd(250283,22) Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Wed Mar 23 01:10:27 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Wed Mar 23 01:10:38 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Wed Mar 23 01:10:48 2005 Input: evalpi Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Wed Mar 23 01:11:01 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.131' ************** PARI ***************** Host 168.131.81.140 (168.131.81.140) Time: Wed Mar 23 02:41:02 2005 Input: r pollard.gp Output: ? ? Errors (if any) and Timing Info: *** unknown member function: rpollard.gp ^-- Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '168.131' ************** PARI ***************** Host 168.131.81.140 (168.131.81.140) Time: Wed Mar 23 02:41:42 2005 Input: "fac" "tor" "(1234)" Output: ? "factor(1234)" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.131' ************** PARI ***************** Host 168.131.81.140 (168.131.81.140) Time: Wed Mar 23 03:21:21 2005 Input: c Output: ? c ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '133.30.' ************** PARI ***************** Host 133.30.64.221 (133.30.64.221) Time: Wed Mar 23 03:31:00 2005 Input: 1 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.007s '133.30.' ************** PARI ***************** Host 133.30.64.221 (133.30.64.221) Time: Wed Mar 23 03:31:07 2005 Input: 123 Output: ? 123 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.131' ************** PARI ***************** Host 168.131.81.140 (168.131.81.140) Time: Wed Mar 23 03:56:32 2005 Input: S tr("$SHELL",1) Output: ? "" ? Errors (if any) and Timing Info: *** Warning: undefined environment variable: SHELL. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.131' ************** PARI ***************** Host 168.131.81.140 (168.131.81.140) Time: Wed Mar 23 03:57:30 2005 Input: S tr("$HOME",1) Output: ? "" ? Errors (if any) and Timing Info: *** Warning: undefined environment variable: HOME. Timing: real 0m0.014s user 0m0.006s sys 0m0.005s '168.131' ************** PARI ***************** Host 168.131.81.140 (168.131.81.140) Time: Wed Mar 23 03:57:57 2005 Input: S tr("$PWD",1) Output: ? "/home/was/www/cgi-bin/calc" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.131' ************** PARI ***************** Host 168.131.81.140 (168.131.81.140) Time: Wed Mar 23 04:00:45 2005 Input: S tr("$$",1) Output: ? "" ? Errors (if any) and Timing Info: *** Warning: undefined environment variable: . *** Warning: undefined environment variable: . Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.131' ************** PARI ***************** Host 168.131.81.140 (168.131.81.140) Time: Wed Mar 23 04:03:15 2005 Input: S tr("$SERVER_SIGNATURE",1) Output: ? "

Apache/2.0.53 (Debian GNU/Linux) mod_python/3.1.3 Python/2.3.5 mod_ssl/2.0.53 OpenSSL/0.9.7e Server at modular.fas.harvard.edu Port 80
" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.131' ************** PARI ***************** Host 168.131.81.140 (168.131.81.140) Time: Wed Mar 23 04:03:51 2005 Input: S tr("$CONTENT_LENGTH",1) Output: ? "399" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '219.77.' ************** PARI ***************** Host 219.77.78.184 (219.77.78.184) Time: Wed Mar 23 06:51:28 2005 Input: pollardrho(10) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: pollardrho(10) ^-------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '60.42.9' ************** PARI ***************** Host 60.42.97.98 (60.42.97.98) Time: Wed Mar 23 07:27:08 2005 Input: 1 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '70.110.' ************** PARI ***************** Host 70.110.193.138 (70.110.193.138) Time: Wed Mar 23 07:35:10 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '155.207' ************** PARI ***************** Host 155.207.120.6 (155.207.120.6) Time: Wed Mar 23 12:30:27 2005 Input: > R := PolynomialRing(Integers()); > K := NumberField(x^7 - x^6 + 8*x^5 + 2); > UnitEquation(a^3, a^2 + a^8, a^7 + a^80 + 4*a^2); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: >R:=PolynomialRin ^-------------------- *** unexpected character: >K:=NumberField(x ^-------------------- *** unexpected character: >UnitEquation(a^3,a^ ^-------------------- Timing: real 0m0.169s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 12:37:00 2005 Input: Mod(7^1734250, 1734251) Output: ? Mod(1660565, 1734251) ? Errors (if any) and Timing Info: Timing: real 0m1.064s user 0m0.899s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 12:37:11 2005 Input: factor(1734251) Output: ? [1171 1] [1481 1] ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 12:37:31 2005 Input: factor(64027) Output: ? [43 1] [1489 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 12:38:06 2005 Input: factor(52633) Output: ? [7 1] [73 1] [103 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '213.169' ************** PARI ***************** Host 213.169.63.31 (213.169.63.31) Time: Wed Mar 23 13:32:58 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '213.169' ************** PARI ***************** Host 213.169.63.31 (213.169.63.31) Time: Wed Mar 23 13:33:16 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '213.169' ************** PARI ***************** Host 213.169.63.31 (213.169.63.31) Time: Wed Mar 23 13:33:38 2005 Input: 1233 Output: ? 1233 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 13:35:19 2005 Input: factor(97) Output: ? [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 13:35:46 2005 Input: factor(8800) Output: ? [2 5] [5 2] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 13:41:36 2005 Input: factor(160) Output: ? [2 5] [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 13:43:12 2005 Input: phi(160) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: phi(160) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: phi(x) ===> eulerphi(x) eulerphi(x): Euler's totient function of x. Timing: real 0m0.016s user 0m0.004s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 13:48:23 2005 Input: factor(880) Output: ? [2 4] [5 1] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 13:49:57 2005 Input: factor(400) Output: ? [2 4] [5 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 13:51:14 2005 Input: factor(187) Output: ? [11 1] [17 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 13:52:22 2005 Input: factor(375) Output: ? [3 1] [5 3] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 13:53:55 2005 Input: factor(240) Output: ? [2 4] [3 1] [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 13:55:40 2005 Input: factor(891) Output: ? [3 4] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 13:56:17 2005 Input: factor(297) Output: ? [3 3] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 13:58:09 2005 Input: factor(375) Output: ? [3 1] [5 3] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:00:22 2005 Input: factor(161) Output: ? [7 1] [23 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:03:46 2005 Input: factor(374) Output: ? [2 1] [11 1] [17 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:05:09 2005 Input: factor(748) Output: ? [2 2] [11 1] [17 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:05:11 2005 Input: factor(748) Output: ? [2 2] [11 1] [17 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:06:05 2005 Input: factor(165) Output: ? [3 1] [5 1] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:06:25 2005 Input: factor(660) Output: ? [2 2] [3 1] [5 1] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:07:44 2005 Input: factor(80) Output: ? [2 4] [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:08:07 2005 Input: factor(220) Output: ? [2 2] [5 1] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:08:33 2005 Input: factor(880) Output: ? [2 4] [5 1] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:08:51 2005 Input: factor(440) Output: ? [2 3] [5 1] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:20:57 2005 Input: Mod(5^2,23) Output: ? Mod(2, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:21:02 2005 Input: Mod(2^2,23) Output: ? Mod(4, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:22:11 2005 Input: Mod(5^13,23) Output: ? Mod(21, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:24:04 2005 Input: Mod(16*17,23) Output: ? Mod(19, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.009s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:24:15 2005 Input: Mod(16*4*2*5,23) Output: ? Mod(19, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:24:17 2005 Input: Mod(16*4*2*5,23) Output: ? Mod(19, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:24:26 2005 Input: Mod(5^13,23) Output: ? Mod(21, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:24:37 2005 Input: Mod(5^2,23) Output: ? Mod(2, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:24:42 2005 Input: Mod(5^4,23) Output: ? Mod(4, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:24:47 2005 Input: Mod(5^8,23) Output: ? Mod(16, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:25:44 2005 Input: Mod(16*4*2*5,23) Output: ? Mod(19, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:26:09 2005 Input: Mod(640,23) Output: ? Mod(19, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:35:19 2005 Input: Mod(28^749,1147) Output: ? Mod(289, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:37:35 2005 Input: factor(7387) Output: ? [83 1] [89 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Wed Mar 23 14:37:52 2005 Input: factor(7393) Output: ? [7393 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '81.57.1' ************** PARI ***************** Host 81.57.122.24 (81.57.122.24) Time: Wed Mar 23 17:40:56 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 19:42:51 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 19:43:46 2005 Input: Mod(28,1147)^749 Output: ? Mod(289, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 19:45:38 2005 Input: Mod(7,7387)^7386 Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 19:46:12 2005 Input: Mod(7,7393)^7392 Output: ? Mod(1, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Wed Mar 23 19:57:22 2005 Input: 560/16 Output: ? 35 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Wed Mar 23 20:00:29 2005 Input: phi(8800) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: phi(8800) ^--------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: phi(x) ===> eulerphi(x) eulerphi(x): Euler's totient function of x. Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Wed Mar 23 20:00:37 2005 Input: eulerphi(8800) Output: ? 3200 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.008s sys 0m0.002s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Wed Mar 23 20:01:39 2005 Input: (10^2-10)*(2^3-2^2)*10 Output: ? 3600 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.004s sys 0m0.008s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Wed Mar 23 20:02:01 2005 Input: eulerphi(97) Output: ? 96 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Wed Mar 23 20:05:40 2005 Input: eulerphi(187) Output: ? 160 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Wed Mar 23 20:05:49 2005 Input: eulerphi(205) Output: ? 160 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Wed Mar 23 20:06:09 2005 Input: eulerphi(x)=160 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: eulerphi(x)=160 ^---- Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Wed Mar 23 20:06:15 2005 Input: eulerphi(x)=160,x Output: ? ? Errors (if any) and Timing Info: *** unexpected character: eulerphi(x)=160,x ^------ Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Wed Mar 23 20:06:24 2005 Input: eulerphi(x)=160, x Output: ? ? Errors (if any) and Timing Info: *** unexpected character: eulerphi(x)=160,x ^------ Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Wed Mar 23 20:06:31 2005 Input: eulerphi(x)=160: x Output: ? ? Errors (if any) and Timing Info: *** unexpected character: eulerphi(x)=160:x ^------ Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 23 20:06:43 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Wed Mar 23 20:07:03 2005 Input: factor(160) Output: ? [2 5] [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:08:24 2005 Input: Mod(7,7386)^7387 Output: ? Mod(3697, 7386) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:08:43 2005 Input: Mod(7,7387)^7386 Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Wed Mar 23 20:10:20 2005 Input: factor(7387) Output: ? [83 1] [89 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Wed Mar 23 20:11:52 2005 Input: Mod(5764801,7387) Output: ? Mod(2941, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Wed Mar 23 20:12:36 2005 Input: Mod(8649481,7387) Output: ? Mod(6691, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Wed Mar 23 20:14:10 2005 Input: Mod(44849809,7387) Output: ? Mod(3332, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Wed Mar 23 20:14:37 2005 Input: Mod(11102224,7387) Output: ? Mod(6950, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 23 20:15:18 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Wed Mar 23 20:15:22 2005 Input: Mod(190969,7387) Output: ? Mod(6294, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Wed Mar 23 20:16:16 2005 Input: Mod(1194649,7387) Output: ? Mod(5342, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Wed Mar 23 20:16:49 2005 Input: Mod((-2045)^2,7387) Output: ? Mod(983, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Wed Mar 23 20:17:11 2005 Input: Mod((983)^2,7387) Output: ? Mod(5979, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '216.148' ************** PARI ***************** Host 216.148.246.90 (216.148.246.90) Time: Wed Mar 23 20:17:29 2005 Input: Mod((5979)^2,7387) Output: ? Mod(2748, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.011s sys 0m0.001s '216.148' ************** PARI ***************** Host 216.148.246.90 (216.148.246.90) Time: Wed Mar 23 20:17:52 2005 Input: Mod((2748)^2,7387) Output: ? Mod(1990, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:20:22 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 23 20:21:06 2005 Input: Mod(1789,6912)^(-1) Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:21:42 2005 Input: Mod(329,1080)^(-1) Output: ? Mod(929, 1080) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Wed Mar 23 20:21:55 2005 Input: 1990*2748*(-1408)*(-1093)*(-437)*(-690)*2941*49 Output: ? 365690984610153068697600 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:22:23 2005 Input: Mod(452,1147)^(929) Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 23 20:22:33 2005 Input: Mod(1789,6912)^(85) Output: ? Mod(5965, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Wed Mar 23 20:22:51 2005 Input: Mod(365690984610153068697600,7387) Output: ? Mod(1619, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 23 20:23:07 2005 Input: Mod(5192,6912)^(85) Output: ? Mod(2816, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Wed Mar 23 20:23:12 2005 Input: Mod(7^7386,7387) Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:23:30 2005 Input: Mod(7,7387)^(8) Output: ? Mod(2941, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Wed Mar 23 20:23:30 2005 Input: Mod(7,7387)^7386 Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:23:43 2005 Input: Mod(7,7387)^(16) Output: ? Mod(6691, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:23:52 2005 Input: Mod(7,7387)^(32) Output: ? Mod(4261, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:24:00 2005 Input: Mod(7,7387)^(64) Output: ? Mod(6262, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:24:07 2005 Input: Mod(7,7387)^(128) Output: ? Mod(2448, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 23 20:24:13 2005 Input: Mod(5192,7081)^(85) Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:24:19 2005 Input: Mod(7,7387)^(256) Output: ? Mod(1847, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:24:27 2005 Input: Mod(7,7387)^(512) Output: ? Mod(6002, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:24:38 2005 Input: Mod(7,7387)^(1024) Output: ? Mod(4992, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:24:50 2005 Input: Mod(7,7387)^(2048) Output: ? Mod(3713, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Wed Mar 23 20:24:54 2005 Input: factor(7393) Output: ? [7393 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:25:09 2005 Input: Mod(7,7393)^(2048) Output: ? Mod(6527, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:25:40 2005 Input: Mod(7,7393)^(4096) Output: ? Mod(3263, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:25:50 2005 Input: Mod(7,7387)^(4096) Output: ? Mod(2227, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 23 20:25:59 2005 Input: Mod(2604,7081)^(85) Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 23 20:27:24 2005 Input: Mod(4222,7081)^(85) Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '170.224' ************** PARI ***************** Host 170.224.224.154 (170.224.224.154) Time: Wed Mar 23 20:28:36 2005 Input: Mod(5764801,7393) Output: ? Mod(5654, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '216.148' ************** PARI ***************** Host 216.148.246.90 (216.148.246.90) Time: Wed Mar 23 20:29:20 2005 Input: Mod(31967716,7393) Output: ? Mod(384, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '216.148' ************** PARI ***************** Host 216.148.246.90 (216.148.246.90) Time: Wed Mar 23 20:29:46 2005 Input: Mod(147456,7393) Output: ? Mod(6989, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Wed Mar 23 20:30:14 2005 Input: Mod(48846121,7393) Output: ? Mod(570, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Wed Mar 23 20:30:35 2005 Input: Mod(324900,7393) Output: ? Mod(7001, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Wed Mar 23 20:31:08 2005 Input: Mod(49014001,7393) Output: ? Mod(5804, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Wed Mar 23 20:31:41 2005 Input: Mod(33686416,7393) Output: ? Mod(3908, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Wed Mar 23 20:32:21 2005 Input: Mod(15272464,7393) Output: ? Mod(5919, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Wed Mar 23 20:33:04 2005 Input: Mod(35034561,7393) Output: ? Mod(6527, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Wed Mar 23 20:33:31 2005 Input: Mod(42601729,7393) Output: ? Mod(3263, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:35:23 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Wed Mar 23 20:36:03 2005 Input: Mod(21297601,7393) Output: ? Mod(5761, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Wed Mar 23 20:36:18 2005 Input: Mod(41438919,7393) Output: ? Mod(1154, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Wed Mar 23 20:36:30 2005 Input: Mod(3983730,7393) Output: ? Mod(6296, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:36:59 2005 Input: Mod(1789,6982)^(-1) Output: ? Mod(2849, 6982) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Wed Mar 23 20:37:18 2005 Input: Mod(6648194,7393) Output: ? Mod(1887, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Wed Mar 23 20:37:55 2005 Input: Mod(11880552,7393) Output: ? Mod(1, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:38:30 2005 Input: Mod(5192,7081)^(2849) Output: ? Mod(3058, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:38:48 2005 Input: Mod(2604,7081)^(2849) Output: ? Mod(3355, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 20:39:00 2005 Input: Mod(4222,7081)^(2849) Output: ? Mod(536, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Wed Mar 23 20:39:54 2005 Input: Mod(917^329,1147) Output: ? Mod(236, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Wed Mar 23 20:40:30 2005 Input: Mod(452^151,1147) Output: ? Mod(917, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Wed Mar 23 21:25:51 2005 Input: Mod(81,16) Output: ? Mod(1, 16) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 21:55:32 2005 Input: factor(975) Output: ? [3 1] [5 2] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 21:57:02 2005 Input: factor(6653) Output: ? [6653 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.246.99 (168.122.246.99) Time: Wed Mar 23 22:12:33 2005 Input: factor(96817818241074148177594033335528733) Output: ? [294729472947294397 1] [328497239427384289 1] ? Errors (if any) and Timing Info: Timing: real 0m0.157s user 0m0.104s sys 0m0.018s '66.218.' ************** PARI ***************** Host 66.218.13.246 (66.218.13.246) Time: Wed Mar 23 22:12:38 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.005s '66.218.' ************** PARI ***************** Host 66.218.13.246 (66.218.13.246) Time: Wed Mar 23 22:12:52 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.246.99 (168.122.246.99) Time: Wed Mar 23 22:12:52 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '66.218.' ************** PARI ***************** Host 66.218.13.246 (66.218.13.246) Time: Wed Mar 23 22:13:18 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.246.99 (168.122.246.99) Time: Wed Mar 23 22:13:18 2005 Input: 4! Output: ? 24 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.246.99 (168.122.246.99) Time: Wed Mar 23 22:13:25 2005 Input: 200! Output: ? 788657867364790503552363213932185062295135977687173263294742533244359449963403342920304284011984623904177212138919638830257642790242637105061926624952829931113462857270763317237396988943922445621451664240254033291864131227428294853277524242407573903240321257405579568660226031904170324062351700858796178922222789623703897374720000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.246.99 (168.122.246.99) Time: Wed Mar 23 22:13:52 2005 Input: 300! Output: ? 306057512216440636035370461297268629388588804173576999416776741259476533176716867465515291422477573349939147888701726368864263907759003154226842927906974559841225476930271954604008012215776252176854255965356903506788725264321896264299365204576448830388909753943489625436053225980776521270822437639449120128678675368305712293681943649956460498166450227716500185176546469340112226034729724066333258583506870150169794168850353752137554910289126407157154830282284937952636580145235233156936482233436799254594095276820608062232812387383880817049600000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.246.99 (168.122.246.99) Time: Wed Mar 23 22:15:04 2005 Input: factor(2920292874) Output: ? [2 1] [3 2] [103 1] [1575131 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.246.99 (168.122.246.99) Time: Wed Mar 23 22:15:36 2005 Input: factor(1022117) Output: ? [1009 1] [1013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.246.99 (168.122.246.99) Time: Wed Mar 23 22:15:49 2005 Input: 1008*1012 Output: ? 1020096 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.246.99 (168.122.246.99) Time: Wed Mar 23 22:16:25 2005 Input: 10000000000! Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.246.99 (168.122.246.99) Time: Wed Mar 23 22:16:33 2005 Input: 1000000000! Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.246.99 (168.122.246.99) Time: Wed Mar 23 22:16:35 2005 Input: 100000000! Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.246.99 (168.122.246.99) Time: Wed Mar 23 22:16:36 2005 Input: 100000000! Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.246.99 (168.122.246.99) Time: Wed Mar 23 22:16:38 2005 Input: 10000000! Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.246.99 (168.122.246.99) Time: Wed Mar 23 22:16:41 2005 Input: 1000000! Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.021s user 0m0.013s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.246.99 (168.122.246.99) Time: Wed Mar 23 22:17:04 2005 Input: 100000! Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 17378 Killed /usr/bin/gp -q -emacs Timing: real 0m21.035s user 0m20.994s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 22:24:13 2005 Input: factor(1508) Output: ? [2 2] [13 1] [29 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 23 22:24:38 2005 Input: factor(3562) Output: ? [2 1] [13 1] [137 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Wed Mar 23 22:37:42 2005 Input: Mod(28,1147)^8 Output: ? Mod(144, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Wed Mar 23 22:37:57 2005 Input: Mod(28,1147)^32 Output: ? Mod(71, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Wed Mar 23 22:38:08 2005 Input: Mod(28,1147)^64 Output: ? Mod(453, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Wed Mar 23 22:38:22 2005 Input: Mod(28,1147)^128 Output: ? Mod(1043, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Wed Mar 23 22:39:01 2005 Input: Mod(28,1147)^512 Output: ? Mod(1032, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Wed Mar 23 22:39:31 2005 Input: Mod(28,1147)^749 Output: ? Mod(289, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Wed Mar 23 22:44:19 2005 Input: Mod(7,7387)^7386 Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Wed Mar 23 22:52:23 2005 Input: Mod(7,7393)^7392 Output: ? Mod(1, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Wed Mar 23 23:32:26 2005 Input: Mod(329,1080)^(-1) Output: ? Mod(929, 1080) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Wed Mar 23 23:33:45 2005 Input: Mod(452^929,1147) Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Wed Mar 23 23:35:37 2005 Input: Mod(452,1147)^929 Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Wed Mar 23 23:36:53 2005 Input: Mod(763,1147)^329 Output: ? Mod(452, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Wed Mar 23 23:39:05 2005 Input: Factor(7081) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(7081) ^------------ Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Wed Mar 23 23:39:18 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Wed Mar 23 23:40:08 2005 Input: 72*96 Output: ? 6912 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Wed Mar 23 23:41:31 2005 Input: Mod(1789,6912)^(-1) Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Wed Mar 23 23:42:11 2005 Input: Mod(5192,7081)^(85) Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Wed Mar 23 23:44:47 2005 Input: Mod(2604,7081)^(85) Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Wed Mar 23 23:45:55 2005 Input: Mod(4222,7081)^(85) Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Wed Mar 23 23:46:40 2005 Input: Mod(5192,7081)^(1789) Output: ? Mod(5557, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Wed Mar 23 23:46:51 2005 Input: Mod(1615,7081)^(1789) Output: ? Mod(5192, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.192.86 (168.122.192.86) Time: Thu Mar 24 00:00:09 2005 Input: 1 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.192.86 (168.122.192.86) Time: Thu Mar 24 00:00:11 2005 Input: 12 Output: ? 12 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 00:46:11 2005 Input: 7^16 Output: ? 33232930569601 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 00:47:21 2005 Input: Mod(7,7387)^16 Output: ? Mod(6691, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 00:47:41 2005 Input: Mod(7,7387)^32 Output: ? Mod(4261, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 00:48:00 2005 Input: Mod(7,7387)^64 Output: ? Mod(6262, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 00:48:33 2005 Input: Mod(7,7387)^128 Output: ? Mod(2448, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 00:50:20 2005 Input: Mod(7,7387)^256 Output: ? Mod(1847, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 00:50:37 2005 Input: Mod(7,7387)^512 Output: ? Mod(6002, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 00:50:52 2005 Input: Mod(7,7387)^1024 Output: ? Mod(4992, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 00:51:16 2005 Input: Mod(7,7387)^2048 Output: ? Mod(3713, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 00:51:34 2005 Input: Mod(7,7387)^4096 Output: ? Mod(2227, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 00:56:58 2005 Input: 2227 x 3713 x 4992 x 2448 x 6262 x 6691 x 2941 x 49 Output: ? 2227 ? Errors (if any) and Timing Info: *** Warning: unused characters: x3713x4992x2448x6262x6691x2941x49. Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 00:57:18 2005 Input: 2227 x 3713 Output: ? 2227 ? Errors (if any) and Timing Info: *** Warning: unused characters: x3713. Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 00:57:24 2005 Input: 2227 x 3713 Output: ? 2227 ? Errors (if any) and Timing Info: *** Warning: unused characters: x3713. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 00:57:32 2005 Input: 2227 x 3713 = Output: ? 2227 ? Errors (if any) and Timing Info: *** Warning: unused characters: x3713=. Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 01:06:33 2005 Input: factor(7387) Output: ? [83 1] [89 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 01:07:41 2005 Input: factor(7393) Output: ? [7393 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 01:09:42 2005 Input: Mod(7,7393)^8 Output: ? Mod(5654, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 01:10:26 2005 Input: Mod(7,7393)^16 Output: ? Mod(384, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 01:10:38 2005 Input: Mod(7,7393)^32 Output: ? Mod(6989, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 01:10:53 2005 Input: Mod(7,7393)^64 Output: ? Mod(570, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 01:11:07 2005 Input: Mod(7,7393)^128 Output: ? Mod(7001, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 01:11:27 2005 Input: Mod(7,7393)^256 Output: ? Mod(5804, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 01:11:41 2005 Input: Mod(7,7393)^512 Output: ? Mod(3908, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 01:11:58 2005 Input: Mod(7,7393)^1024 Output: ? Mod(5919, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 01:12:15 2005 Input: Mod(7,7393)^2048 Output: ? Mod(6527, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 01:12:35 2005 Input: Mod(7,7393)^4096 Output: ? Mod(3263, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 01:27:14 2005 Input: for(i=1, i<3, print(i)) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 01:31:10 2005 Input: for i:= 0 to 2 i; end for Output: ? ? ? ? ? endfor ? Errors (if any) and Timing Info: *** unexpected character: fori:=0to2 ^----- Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 01:35:08 2005 Input: for(i=0,i<2,print(i)) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 01:35:21 2005 Input: for(i=0,i!=2,print(i)) Output: ? 0 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 01:35:33 2005 Input: for(i=0,i!=3,print(i)) Output: ? 0 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 01:35:52 2005 Input: for(i=0,i!=3,gcd(i,2)) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 02:24:13 2005 Input: (2^1485-1) Output: ? 1070393741163148155140002073983180480759399898691736719484735047143278926103617010609652126665801063893223584191755295330789018217207945549138520474792623927242735488443881142104699789782210172928975896738895832197612166084745676956951404400308684101704866105705305247055335973308139964471316824642504293039366278387990046613544517844635154824075842045095053209331444802766174109712300516774551695312505342204453401455091375199535727402456168005631 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 02:38:45 2005 Input: (2^6048)-1 Output: ? 426004096906348104822022259383788929555454135640052985497481613096970325437281976891890246071728963832595187686654825431170298083258827734019898049713842074954703476153029867300842186610676331887351434660344386771731872577494842244525209835422239177072585404525929807628644658931667483676700082351700216206656351705966905561674359515697283859128582456189164925128111801226177126926187673340876309242231272227058236302103999523819946424720633953292452920059333376476809914639195916379551094715126638900861425678918872101216657432842962038401929822419112727628958774863754354224078286774318554133907121506935575181004364380701956399444205955329219184008273501007866204686778968607675603107861761417933529452308268161472298771517583647896231909954016405054183206019349063837307819834234253916785721651512730067977510570863576404113380806124766999985797965329305419797494154575803530476863202598500278940088241228999774762675298813778178955159960171525065221825617222254612009511014594193750362529823544771901048406155528058339608551974681958976999082847566113552253928300645079968103496092180920774308657176815202116421088909611425209285075601126883422597277900775473716765900290027781971821629678337816923463658655193856039496683849161182223577992133116175107752093867805434898055286044667218484612579506381394741222435857547975147173533648677430872299227131645828409715254671554576849153974719663561194696229694741790682545818183156195515852447043237047463718981831935566916205075833830212611726112894754773599526902447342273414794263185301884647522617757809780194123873686505031730762171628394838596922947018482986035517732038033649061089332790033477085558792269736423274073866175133744100434798334898591870521953729578480071092407593503468496686083653768869848380023323033529663705921798259062429249932275928264035270655 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 02:38:59 2005 Input: (2^3024)-1 Output: ? 20639866688192249678690979427047744716670419422978338405490767656712605070613300830961151335902735607601692030339466006139980896685912793208440823179426475068368459772139688719662053454545441962864930352619700970232691192549708975533834320861293755528582525396944795278184961346348121152405537193811559544560528122472766855879578363826574119600278907314987542926997237378746730499786212713008347110671443879490481628971586456347856297569099192539115056245819004213727631262285862613802315336376080691028745451394187818329012215737168247703065165176763236436188268622714806030476205940112438517662309257595469092710023367459009590744249233592976505063469657896200879783774178059516715294055766886940027007433396687814278648206918025537489162479394046257364519031954709690026927019765539112214281096766958661032472041467681013226556685362979770990378092763807981815343641872998542497684604695404128952469438857215 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 02:40:42 2005 Input: 523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561/2743062034396844341627968125593604635037196317966166035056000994228098690879836473582587849768181396806642362668936055872479091931372323951612051859122835149807249350355003132267795098895967012320756270631179897595796976964454084495146379250195728106130226298287754794921070036903071843030324651025760255 Output: ? 523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561/2743062034396844341627968125593604635037196317966166035056000994228098690879836473582587849768181396806642362668936055872479091931372323951612051859122835149807249350355003132267795098895967012320756270631179897595796976964454084495146379250195728106130226298287754794921070036903071843030324651025760255 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.011s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 02:43:56 2005 Input: ((2^3326400)-1)/14510642956629460126286667764218111732339625499480335264478327629658324054225616417 Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 20039 Killed /usr/bin/gp -q -emacs Timing: real 0m21.016s user 0m20.985s sys 0m0.016s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 02:44:58 2005 Input: ((2^6048)-1)/14510642956629460126286667764218111732339625499480335264478327629658324054225616417 Output: ? 29358044173481652760821532785927739720464558978695178402353227483133121206333325535902638921264356998672055054078651306721212845891250137884898812777179114961522494546526060891873888096515914923383204441719450865898388397163580530486854715858209673737451311881929716350621807464327280230955402016528342552071351991021305525517311616736946896784906918734743975266857441596255952596237320060215286852026864911570642985124373822371247545652885563280523831823924307470733248955855424008664576828904922515574623460784749333750109165686771108992248221342119282831677732815158501239067711882266395343841267349600050496157325485492890847476017038193821402200887361884741572515702100498423059555995488334194348693738272195011669307890602305984001281634578133407215052103600047539860089015569785857510367812086694669419881093102182090913733602714443512866392167282137231597092111816459903170636783179079530617014507234642168717413134281026836638154006521158855858732385768400934375633231431321147449637468962915384968044430052924500998216674390145757375344827105740369249272470929295840809472849982267389095737483197364145369514699457710374607200000941480203678371923124319563275124605760518278528095407320822948249685397112607434767177807984461154633293179968755987731591145975298103729938302992574200288447655983515470776844527213698501633337228434170436624525507937061872066163679638148498906640638867080865943823485354876569437322376940189392314672441766603068535060433018743154615265549697613609191018825535161872539361850519743859176217780038717438286665559377233538054810898675000816056845743014416664823808553668160295597922624519307699792040320628553962717428634152439851338417167726112777807562265885280787061925767623556674448363762973215 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 02:47:38 2005 Input: ((2^6048)-1)/14510642956629460126286667764218111732339625499480335264478327629658324054225616417 Output: ? 29358044173481652760821532785927739720464558978695178402353227483133121206333325535902638921264356998672055054078651306721212845891250137884898812777179114961522494546526060891873888096515914923383204441719450865898388397163580530486854715858209673737451311881929716350621807464327280230955402016528342552071351991021305525517311616736946896784906918734743975266857441596255952596237320060215286852026864911570642985124373822371247545652885563280523831823924307470733248955855424008664576828904922515574623460784749333750109165686771108992248221342119282831677732815158501239067711882266395343841267349600050496157325485492890847476017038193821402200887361884741572515702100498423059555995488334194348693738272195011669307890602305984001281634578133407215052103600047539860089015569785857510367812086694669419881093102182090913733602714443512866392167282137231597092111816459903170636783179079530617014507234642168717413134281026836638154006521158855858732385768400934375633231431321147449637468962915384968044430052924500998216674390145757375344827105740369249272470929295840809472849982267389095737483197364145369514699457710374607200000941480203678371923124319563275124605760518278528095407320822948249685397112607434767177807984461154633293179968755987731591145975298103729938302992574200288447655983515470776844527213698501633337228434170436624525507937061872066163679638148498906640638867080865943823485354876569437322376940189392314672441766603068535060433018743154615265549697613609191018825535161872539361850519743859176217780038717438286665559377233538054810898675000816056845743014416664823808553668160295597922624519307699792040320628553962717428634152439851338417167726112777807562265885280787061925767623556674448363762973215 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 02:51:41 2005 Input: a=((2^6048)-1) b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; b/14510642956629460126286667764218111732339625499480335264478327629658324054225616417 Output: ? 426004096906348104822022259383788929555454135640052985497481613096970325437281976891890246071728963832595187686654825431170298083258827734019898049713842074954703476153029867300842186610676331887351434660344386771731872577494842244525209835422239177072585404525929807628644658931667483676700082351700216206656351705966905561674359515697283859128582456189164925128111801226177126926187673340876309242231272227058236302103999523819946424720633953292452920059333376476809914639195916379551094715126638900861425678918872101216657432842962038401929822419112727628958774863754354224078286774318554133907121506935575181004364380701956399444205955329219184008273501007866204686778968607675603107861761417933529452308268161472298771517583647896231909954016405054183206019349063837307819834234253916785721651512730067977510570863576404113380806124766999985797965329305419797494154575803530476863202598500278940088241228999774762675298813778178955159960171525065221825617222254612009511014594193750362529823544771901048406155528058339608551974681958976999082847566113552253928300645079968103496092180920774308657176815202116421088909611425209285075601126883422597277900775473716765900290027781971821629678337816923463658655193856039496683849161182223577992133116175107752093867805434898055286044667218484612579506381394741222435857547975147173533648677430872299227131645828409715254671554576849153974719663561194696229694741790682545818183156195515852447043237047463718981831935566916205075833830212611726112894754773599526902447342273414794263185301884647522617757809780194123873686505031730762171628394838596922947018482986035517732038033649061089332790033477085558792269736423274073866175133744100434798334898591870521953729578480071092407593503468496686083653768869848380023323033529663705921798259062429249932275928264035270655 ? ? 523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561/14510642956629460126286667764218111732339625499480335264478327629658324054225616417 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:43:11 2005 Input: a=((2^6048)-1) b=13059210352149606733529404775036023154586871752956798087178673391940951190449085377740873416793004358770660137663397439822846995955261067200932037746050368615013431685012063613275339665251994269446225659149953157661404237247635652082187523399757426800639759453651962539313938621507578848147115200787892070799865808242173847812591263151464644216108030215361173037402349591934134749790155512466980861293721756280591562570827044696201718699732105806480263738856894804467483443405232036889958476816355520795665426805419836958428264485027255707151822543803035920282148444249541621478718022473082130592038140453880494261208043917397924813728915539445285189935489469776807371684116494748404152861642920947038648701064943870446023214470280851684199921509880908902421815542355945556411963056017173845668144744135609553434304497088183923456318487020133687979759159904738270989406402719300901745484166455833881349902883638010290418458483647798034319291367628988610766092845244018739095149136523339769793450331979615400557150410524886438001857957690295279840270629477740764098477058879452745098903220902429984405982518128430508907636708995013252358133015535786391162533874714069722310439236303908005309255919314626635110433363600496400019071473055777502124920999336729039307892734405028195433420634458860397436288956209583387210126707056077118756396941835793192202165989811138814427937809184666378531196348045652931359929921673730592918039954256535379191942207975560969995211786266633933991950982061759525702534957388370716995520374861725234250863902950190113139647308293162473119594699319383692180306174813834082198301742279810818222745205578398636895842818954446529390379255583152347862236796580695939926598448803028789642506604584884682107966878755570425860802323161778883462051241614643885966585158472356381332238842080732895187090035653782606499019609344224441450215076228803849757560736056082329624326510992239210357932192162431761669251011635753878837913245021144470830826099116779981824165201433072325783633108746432581651036779681157987939416547469946082469829334401; c=20599554602046101491103622943218704819395019390901566892952855872696818420862893821060116778396212643763560336178860111043386700236638833963136823881387266654652239143989153443039254895360910896411384931457874182561750135868788634991091026428916092893864889659441816507017080746265168894410307930808311335864746001930511677217710169012473472177408695249255118949069583278431950967547352003343435608958682436186258875725218083167513696919282325910220354249913677914719791398082370208531132508182050235458774948039679947983394594733366146781461540938554618017315074224387272086390615414845260727868653043678689831461718837542293534745351703498680956427970811814321029331940317712635701770603633866275650111954719205101867559757200185984349875595922626780772288931675628968832592644137150364513275880670646881512395068248129970304265017406432905343705358544567897169663306975577873323688566031334276546190221770241; gcd(b,c) Output: ? 426004096906348104822022259383788929555454135640052985497481613096970325437281976891890246071728963832595187686654825431170298083258827734019898049713842074954703476153029867300842186610676331887351434660344386771731872577494842244525209835422239177072585404525929807628644658931667483676700082351700216206656351705966905561674359515697283859128582456189164925128111801226177126926187673340876309242231272227058236302103999523819946424720633953292452920059333376476809914639195916379551094715126638900861425678918872101216657432842962038401929822419112727628958774863754354224078286774318554133907121506935575181004364380701956399444205955329219184008273501007866204686778968607675603107861761417933529452308268161472298771517583647896231909954016405054183206019349063837307819834234253916785721651512730067977510570863576404113380806124766999985797965329305419797494154575803530476863202598500278940088241228999774762675298813778178955159960171525065221825617222254612009511014594193750362529823544771901048406155528058339608551974681958976999082847566113552253928300645079968103496092180920774308657176815202116421088909611425209285075601126883422597277900775473716765900290027781971821629678337816923463658655193856039496683849161182223577992133116175107752093867805434898055286044667218484612579506381394741222435857547975147173533648677430872299227131645828409715254671554576849153974719663561194696229694741790682545818183156195515852447043237047463718981831935566916205075833830212611726112894754773599526902447342273414794263185301884647522617757809780194123873686505031730762171628394838596922947018482986035517732038033649061089332790033477085558792269736423274073866175133744100434798334898591870521953729578480071092407593503468496686083653768869848380023323033529663705921798259062429249932275928264035270655 ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:43:26 2005 Input: b=13059210352149606733529404775036023154586871752956798087178673391940951190449085377740873416793004358770660137663397439822846995955261067200932037746050368615013431685012063613275339665251994269446225659149953157661404237247635652082187523399757426800639759453651962539313938621507578848147115200787892070799865808242173847812591263151464644216108030215361173037402349591934134749790155512466980861293721756280591562570827044696201718699732105806480263738856894804467483443405232036889958476816355520795665426805419836958428264485027255707151822543803035920282148444249541621478718022473082130592038140453880494261208043917397924813728915539445285189935489469776807371684116494748404152861642920947038648701064943870446023214470280851684199921509880908902421815542355945556411963056017173845668144744135609553434304497088183923456318487020133687979759159904738270989406402719300901745484166455833881349902883638010290418458483647798034319291367628988610766092845244018739095149136523339769793450331979615400557150410524886438001857957690295279840270629477740764098477058879452745098903220902429984405982518128430508907636708995013252358133015535786391162533874714069722310439236303908005309255919314626635110433363600496400019071473055777502124920999336729039307892734405028195433420634458860397436288956209583387210126707056077118756396941835793192202165989811138814427937809184666378531196348045652931359929921673730592918039954256535379191942207975560969995211786266633933991950982061759525702534957388370716995520374861725234250863902950190113139647308293162473119594699319383692180306174813834082198301742279810818222745205578398636895842818954446529390379255583152347862236796580695939926598448803028789642506604584884682107966878755570425860802323161778883462051241614643885966585158472356381332238842080732895187090035653782606499019609344224441450215076228803849757560736056082329624326510992239210357932192162431761669251011635753878837913245021144470830826099116779981824165201433072325783633108746432581651036779681157987939416547469946082469829334401; c=20599554602046101491103622943218704819395019390901566892952855872696818420862893821060116778396212643763560336178860111043386700236638833963136823881387266654652239143989153443039254895360910896411384931457874182561750135868788634991091026428916092893864889659441816507017080746265168894410307930808311335864746001930511677217710169012473472177408695249255118949069583278431950967547352003343435608958682436186258875725218083167513696919282325910220354249913677914719791398082370208531132508182050235458774948039679947983394594733366146781461540938554618017315074224387272086390615414845260727868653043678689831461718837542293534745351703498680956427970811814321029331940317712635701770603633866275650111954719205101867559757200185984349875595922626780772288931675628968832592644137150364513275880670646881512395068248129970304265017406432905343705358544567897169663306975577873323688566031334276546190221770241; gcd(b,c) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:43:48 2005 Input: b=13059210352149606733529404775036023154586871752956798087178673391940951190449085377740873416793004358770660137663397439822846995955261067200932037746050368615013431685012063613275339665251994269446225659149953157661404237247635652082187523399757426800639759453651962539313938621507578848147115200787892070799865808242173847812591263151464644216108030215361173037402349591934134749790155512466980861293721756280591562570827044696201718699732105806480263738856894804467483443405232036889958476816355520795665426805419836958428264485027255707151822543803035920282148444249541621478718022473082130592038140453880494261208043917397924813728915539445285189935489469776807371684116494748404152861642920947038648701064943870446023214470280851684199921509880908902421815542355945556411963056017173845668144744135609553434304497088183923456318487020133687979759159904738270989406402719300901745484166455833881349902883638010290418458483647798034319291367628988610766092845244018739095149136523339769793450331979615400557150410524886438001857957690295279840270629477740764098477058879452745098903220902429984405982518128430508907636708995013252358133015535786391162533874714069722310439236303908005309255919314626635110433363600496400019071473055777502124920999336729039307892734405028195433420634458860397436288956209583387210126707056077118756396941835793192202165989811138814427937809184666378531196348045652931359929921673730592918039954256535379191942207975560969995211786266633933991950982061759525702534957388370716995520374861725234250863902950190113139647308293162473119594699319383692180306174813834082198301742279810818222745205578398636895842818954446529390379255583152347862236796580695939926598448803028789642506604584884682107966878755570425860802323161778883462051241614643885966585158472356381332238842080732895187090035653782606499019609344224441450215076228803849757560736056082329624326510992239210357932192162431761669251011635753878837913245021144470830826099116779981824165201433072325783633108746432581651036779681157987939416547469946082469829334401; c=247330401473104534060554895269373528305051560136361081500498522363285371560389766604315961281959772968457965711024595445761201095651758114601212404870944498141050407516897281; gcd(b,c) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:44:04 2005 Input: b=13059210352149606733529404775036023154586871752956798087178673391940951190449085377740873416793004358770660137663397439822846995955261067200932037746050368615013431685012063613275339665251994269446225659149953157661404237247635652082187523399757426800639759453651962539313938621507578848147115200787892070799865808242173847812591263151464644216108030215361173037402349591934134749790155512466980861293721756280591562570827044696201718699732105806480263738856894804467483443405232036889958476816355520795665426805419836958428264485027255707151822543803035920282148444249541621478718022473082130592038140453880494261208043917397924813728915539445285189935489469776807371684116494748404152861642920947038648701064943870446023214470280851684199921509880908902421815542355945556411963056017173845668144744135609553434304497088183923456318487020133687979759159904738270989406402719300901745484166455833881349902883638010290418458483647798034319291367628988610766092845244018739095149136523339769793450331979615400557150410524886438001857957690295279840270629477740764098477058879452745098903220902429984405982518128430508907636708995013252358133015535786391162533874714069722310439236303908005309255919314626635110433363600496400019071473055777502124920999336729039307892734405028195433420634458860397436288956209583387210126707056077118756396941835793192202165989811138814427937809184666378531196348045652931359929921673730592918039954256535379191942207975560969995211786266633933991950982061759525702534957388370716995520374861725234250863902950190113139647308293162473119594699319383692180306174813834082198301742279810818222745205578398636895842818954446529390379255583152347862236796580695939926598448803028789642506604584884682107966878755570425860802323161778883462051241614643885966585158472356381332238842080732895187090035653782606499019609344224441450215076228803849757560736056082329624326510992239210357932192162431761669251011635753878837913245021144470830826099116779981824165201433072325783633108746432581651036779681157987939416547469946082469829334401; c=11112382566050265046201267311127854032287645974415860346290590498168586174867795883723807322077777737613405896828278368924739043841; gcd(b,c) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:44:22 2005 Input: b=13059210352149606733529404775036023154586871752956798087178673391940951190449085377740873416793004358770660137663397439822846995955261067200932037746050368615013431685012063613275339665251994269446225659149953157661404237247635652082187523399757426800639759453651962539313938621507578848147115200787892070799865808242173847812591263151464644216108030215361173037402349591934134749790155512466980861293721756280591562570827044696201718699732105806480263738856894804467483443405232036889958476816355520795665426805419836958428264485027255707151822543803035920282148444249541621478718022473082130592038140453880494261208043917397924813728915539445285189935489469776807371684116494748404152861642920947038648701064943870446023214470280851684199921509880908902421815542355945556411963056017173845668144744135609553434304497088183923456318487020133687979759159904738270989406402719300901745484166455833881349902883638010290418458483647798034319291367628988610766092845244018739095149136523339769793450331979615400557150410524886438001857957690295279840270629477740764098477058879452745098903220902429984405982518128430508907636708995013252358133015535786391162533874714069722310439236303908005309255919314626635110433363600496400019071473055777502124920999336729039307892734405028195433420634458860397436288956209583387210126707056077118756396941835793192202165989811138814427937809184666378531196348045652931359929921673730592918039954256535379191942207975560969995211786266633933991950982061759525702534957388370716995520374861725234250863902950190113139647308293162473119594699319383692180306174813834082198301742279810818222745205578398636895842818954446529390379255583152347862236796580695939926598448803028789642506604584884682107966878755570425860802323161778883462051241614643885966585158472356381332238842080732895187090035653782606499019609344224441450215076228803849757560736056082329624326510992239210357932192162431761669251011635753878837913245021144470830826099116779981824165201433072325783633108746432581651036779681157987939416547469946082469829334401; c=52476742974740753098399961248025269361700031009168356013815428578331071591213061550435271930194048701627179460828359257559355627931781551545676699271681; gcd(b,c) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:44:35 2005 Input: b=13059210352149606733529404775036023154586871752956798087178673391940951190449085377740873416793004358770660137663397439822846995955261067200932037746050368615013431685012063613275339665251994269446225659149953157661404237247635652082187523399757426800639759453651962539313938621507578848147115200787892070799865808242173847812591263151464644216108030215361173037402349591934134749790155512466980861293721756280591562570827044696201718699732105806480263738856894804467483443405232036889958476816355520795665426805419836958428264485027255707151822543803035920282148444249541621478718022473082130592038140453880494261208043917397924813728915539445285189935489469776807371684116494748404152861642920947038648701064943870446023214470280851684199921509880908902421815542355945556411963056017173845668144744135609553434304497088183923456318487020133687979759159904738270989406402719300901745484166455833881349902883638010290418458483647798034319291367628988610766092845244018739095149136523339769793450331979615400557150410524886438001857957690295279840270629477740764098477058879452745098903220902429984405982518128430508907636708995013252358133015535786391162533874714069722310439236303908005309255919314626635110433363600496400019071473055777502124920999336729039307892734405028195433420634458860397436288956209583387210126707056077118756396941835793192202165989811138814427937809184666378531196348045652931359929921673730592918039954256535379191942207975560969995211786266633933991950982061759525702534957388370716995520374861725234250863902950190113139647308293162473119594699319383692180306174813834082198301742279810818222745205578398636895842818954446529390379255583152347862236796580695939926598448803028789642506604584884682107966878755570425860802323161778883462051241614643885966585158472356381332238842080732895187090035653782606499019609344224441450215076228803849757560736056082329624326510992239210357932192162431761669251011635753878837913245021144470830826099116779981824165201433072325783633108746432581651036779681157987939416547469946082469829334401; c=923464919899743469986398557995829247144044653039454920479216029856852076464008015654992338651260559659287251795564734525918380907892557250964168359222397194013392736887094542636295787007442236974085650569694529582173235855750426030179303554061221362231806667553118231511946807216778701527050633313116417698983819945005491706598981212869552874164780877354468919912853616655557132746458301627301432329021008965716814415987810354660963324913105617893858317364982159368004766685201534065089722978264883013854065450954131592677746046005997173273696828810033667168799481584233788379017226309937547773176648996343003038981894375624021886333254918143232783374957784135976349755415834060450927203563264806426607907321; gcd(b,c) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:45:01 2005 Input: a=(2^15120-1); b=13059210352149606733529404775036023154586871752956798087178673391940951190449085377740873416793004358770660137663397439822846995955261067200932037746050368615013431685012063613275339665251994269446225659149953157661404237247635652082187523399757426800639759453651962539313938621507578848147115200787892070799865808242173847812591263151464644216108030215361173037402349591934134749790155512466980861293721756280591562570827044696201718699732105806480263738856894804467483443405232036889958476816355520795665426805419836958428264485027255707151822543803035920282148444249541621478718022473082130592038140453880494261208043917397924813728915539445285189935489469776807371684116494748404152861642920947038648701064943870446023214470280851684199921509880908902421815542355945556411963056017173845668144744135609553434304497088183923456318487020133687979759159904738270989406402719300901745484166455833881349902883638010290418458483647798034319291367628988610766092845244018739095149136523339769793450331979615400557150410524886438001857957690295279840270629477740764098477058879452745098903220902429984405982518128430508907636708995013252358133015535786391162533874714069722310439236303908005309255919314626635110433363600496400019071473055777502124920999336729039307892734405028195433420634458860397436288956209583387210126707056077118756396941835793192202165989811138814427937809184666378531196348045652931359929921673730592918039954256535379191942207975560969995211786266633933991950982061759525702534957388370716995520374861725234250863902950190113139647308293162473119594699319383692180306174813834082198301742279810818222745205578398636895842818954446529390379255583152347862236796580695939926598448803028789642506604584884682107966878755570425860802323161778883462051241614643885966585158472356381332238842080732895187090035653782606499019609344224441450215076228803849757560736056082329624326510992239210357932192162431761669251011635753878837913245021144470830826099116779981824165201433072325783633108746432581651036779681157987939416547469946082469829334401; c=923464919899743469986398557995829247144044653039454920479216029856852076464008015654992338651260559659287251795564734525918380907892557250964168359222397194013392736887094542636295787007442236974085650569694529582173235855750426030179303554061221362231806667553118231511946807216778701527050633313116417698983819945005491706598981212869552874164780877354468919912853616655557132746458301627301432329021008965716814415987810354660963324913105617893858317364982159368004766685201534065089722978264883013854065450954131592677746046005997173273696828810033667168799481584233788379017226309937547773176648996343003038981894375624021886333254918143232783374957784135976349755415834060450927203563264806426607907321; gcd(a,c) Output: ? ? ? ? 923464919899743469986398557995829247144044653039454920479216029856852076464008015654992338651260559659287251795564734525918380907892557250964168359222397194013392736887094542636295787007442236974085650569694529582173235855750426030179303554061221362231806667553118231511946807216778701527050633313116417698983819945005491706598981212869552874164780877354468919912853616655557132746458301627301432329021008965716814415987810354660963324913105617893858317364982159368004766685201534065089722978264883013854065450954131592677746046005997173273696828810033667168799481584233788379017226309937547773176648996343003038981894375624021886333254918143232783374957784135976349755415834060450927203563264806426607907321 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:45:22 2005 Input: a=(2^(15120/2)-1); b=13059210352149606733529404775036023154586871752956798087178673391940951190449085377740873416793004358770660137663397439822846995955261067200932037746050368615013431685012063613275339665251994269446225659149953157661404237247635652082187523399757426800639759453651962539313938621507578848147115200787892070799865808242173847812591263151464644216108030215361173037402349591934134749790155512466980861293721756280591562570827044696201718699732105806480263738856894804467483443405232036889958476816355520795665426805419836958428264485027255707151822543803035920282148444249541621478718022473082130592038140453880494261208043917397924813728915539445285189935489469776807371684116494748404152861642920947038648701064943870446023214470280851684199921509880908902421815542355945556411963056017173845668144744135609553434304497088183923456318487020133687979759159904738270989406402719300901745484166455833881349902883638010290418458483647798034319291367628988610766092845244018739095149136523339769793450331979615400557150410524886438001857957690295279840270629477740764098477058879452745098903220902429984405982518128430508907636708995013252358133015535786391162533874714069722310439236303908005309255919314626635110433363600496400019071473055777502124920999336729039307892734405028195433420634458860397436288956209583387210126707056077118756396941835793192202165989811138814427937809184666378531196348045652931359929921673730592918039954256535379191942207975560969995211786266633933991950982061759525702534957388370716995520374861725234250863902950190113139647308293162473119594699319383692180306174813834082198301742279810818222745205578398636895842818954446529390379255583152347862236796580695939926598448803028789642506604584884682107966878755570425860802323161778883462051241614643885966585158472356381332238842080732895187090035653782606499019609344224441450215076228803849757560736056082329624326510992239210357932192162431761669251011635753878837913245021144470830826099116779981824165201433072325783633108746432581651036779681157987939416547469946082469829334401; c=923464919899743469986398557995829247144044653039454920479216029856852076464008015654992338651260559659287251795564734525918380907892557250964168359222397194013392736887094542636295787007442236974085650569694529582173235855750426030179303554061221362231806667553118231511946807216778701527050633313116417698983819945005491706598981212869552874164780877354468919912853616655557132746458301627301432329021008965716814415987810354660963324913105617893858317364982159368004766685201534065089722978264883013854065450954131592677746046005997173273696828810033667168799481584233788379017226309937547773176648996343003038981894375624021886333254918143232783374957784135976349755415834060450927203563264806426607907321; gcd(a,c) Output: ? ? ? ? 2404950987485123494400140808949208387509866835543550506192637491519142224196381176161060135585566999825274906891256376989360309278674861961205755973916934624553192383096242585955431988018486197225517993511827430041591770913414911808896116576940332115811672118101904093043183559670267011564428303190225401 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:46:48 2005 Input: a=(2^(15120/2)-1); b=13059210352149606733529404775036023154586871752956798087178673391940951190449085377740873416793004358770660137663397439822846995955261067200932037746050368615013431685012063613275339665251994269446225659149953157661404237247635652082187523399757426800639759453651962539313938621507578848147115200787892070799865808242173847812591263151464644216108030215361173037402349591934134749790155512466980861293721756280591562570827044696201718699732105806480263738856894804467483443405232036889958476816355520795665426805419836958428264485027255707151822543803035920282148444249541621478718022473082130592038140453880494261208043917397924813728915539445285189935489469776807371684116494748404152861642920947038648701064943870446023214470280851684199921509880908902421815542355945556411963056017173845668144744135609553434304497088183923456318487020133687979759159904738270989406402719300901745484166455833881349902883638010290418458483647798034319291367628988610766092845244018739095149136523339769793450331979615400557150410524886438001857957690295279840270629477740764098477058879452745098903220902429984405982518128430508907636708995013252358133015535786391162533874714069722310439236303908005309255919314626635110433363600496400019071473055777502124920999336729039307892734405028195433420634458860397436288956209583387210126707056077118756396941835793192202165989811138814427937809184666378531196348045652931359929921673730592918039954256535379191942207975560969995211786266633933991950982061759525702534957388370716995520374861725234250863902950190113139647308293162473119594699319383692180306174813834082198301742279810818222745205578398636895842818954446529390379255583152347862236796580695939926598448803028789642506604584884682107966878755570425860802323161778883462051241614643885966585158472356381332238842080732895187090035653782606499019609344224441450215076228803849757560736056082329624326510992239210357932192162431761669251011635753878837913245021144470830826099116779981824165201433072325783633108746432581651036779681157987939416547469946082469829334401; c=923464919899743469986398557995829247144044653039454920479216029856852076464008015654992338651260559659287251795564734525918380907892557250964168359222397194013392736887094542636295787007442236974085650569694529582173235855750426030179303554061221362231806667553118231511946807216778701527050633313116417698983819945005491706598981212869552874164780877354468919912853616655557132746458301627301432329021008965716814415987810354660963324913105617893858317364982159368004766685201534065089722978264883013854065450954131592677746046005997173273696828810033667168799481584233788379017226309937547773176648996343003038981894375624021886333254918143232783374957784135976349755415834060450927203563264806426607907321; gcd(b,c) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.012s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:47:11 2005 Input: a=(2^(15120/2)-1); b=13059210352149606733529404775036023154586871752956798087178673391940951190449085377740873416793004358770660137663397439822846995955261067200932037746050368615013431685012063613275339665251994269446225659149953157661404237247635652082187523399757426800639759453651962539313938621507578848147115200787892070799865808242173847812591263151464644216108030215361173037402349591934134749790155512466980861293721756280591562570827044696201718699732105806480263738856894804467483443405232036889958476816355520795665426805419836958428264485027255707151822543803035920282148444249541621478718022473082130592038140453880494261208043917397924813728915539445285189935489469776807371684116494748404152861642920947038648701064943870446023214470280851684199921509880908902421815542355945556411963056017173845668144744135609553434304497088183923456318487020133687979759159904738270989406402719300901745484166455833881349902883638010290418458483647798034319291367628988610766092845244018739095149136523339769793450331979615400557150410524886438001857957690295279840270629477740764098477058879452745098903220902429984405982518128430508907636708995013252358133015535786391162533874714069722310439236303908005309255919314626635110433363600496400019071473055777502124920999336729039307892734405028195433420634458860397436288956209583387210126707056077118756396941835793192202165989811138814427937809184666378531196348045652931359929921673730592918039954256535379191942207975560969995211786266633933991950982061759525702534957388370716995520374861725234250863902950190113139647308293162473119594699319383692180306174813834082198301742279810818222745205578398636895842818954446529390379255583152347862236796580695939926598448803028789642506604584884682107966878755570425860802323161778883462051241614643885966585158472356381332238842080732895187090035653782606499019609344224441450215076228803849757560736056082329624326510992239210357932192162431761669251011635753878837913245021144470830826099116779981824165201433072325783633108746432581651036779681157987939416547469946082469829334401; c=25435999094089869005186806358949569337458761; gcd(b,c) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:47:33 2005 Input: c=1385135374054442487556510269150825341160654863048488873202997699188758558763387496579934678431288691377835374838957531624672788047807309262352062199702547368805143543995261710160331872907285608780481328493865905088110523899649386447462254439114887482917265249150701893871050540311194123422560080613414648226680964726584058498011545027829379976212667752670265807301670575960064669183076376931812309191721434924415555538901439333165617269112851100262995808989609639923333716645151675282169642520063149560007298529921261014814853629480423083295927256194382852758904680648919101711962979977123412431246199258438630033802092124832662816703326225348120092204873946618853290005736272945677118529453674196347608711648342586146974335049; a=(2^(15120/2)-1); b=13059210352149606733529404775036023154586871752956798087178673391940951190449085377740873416793004358770660137663397439822846995955261067200932037746050368615013431685012063613275339665251994269446225659149953157661404237247635652082187523399757426800639759453651962539313938621507578848147115200787892070799865808242173847812591263151464644216108030215361173037402349591934134749790155512466980861293721756280591562570827044696201718699732105806480263738856894804467483443405232036889958476816355520795665426805419836958428264485027255707151822543803035920282148444249541621478718022473082130592038140453880494261208043917397924813728915539445285189935489469776807371684116494748404152861642920947038648701064943870446023214470280851684199921509880908902421815542355945556411963056017173845668144744135609553434304497088183923456318487020133687979759159904738270989406402719300901745484166455833881349902883638010290418458483647798034319291367628988610766092845244018739095149136523339769793450331979615400557150410524886438001857957690295279840270629477740764098477058879452745098903220902429984405982518128430508907636708995013252358133015535786391162533874714069722310439236303908005309255919314626635110433363600496400019071473055777502124920999336729039307892734405028195433420634458860397436288956209583387210126707056077118756396941835793192202165989811138814427937809184666378531196348045652931359929921673730592918039954256535379191942207975560969995211786266633933991950982061759525702534957388370716995520374861725234250863902950190113139647308293162473119594699319383692180306174813834082198301742279810818222745205578398636895842818954446529390379255583152347862236796580695939926598448803028789642506604584884682107966878755570425860802323161778883462051241614643885966585158472356381332238842080732895187090035653782606499019609344224441450215076228803849757560736056082329624326510992239210357932192162431761669251011635753878837913245021144470830826099116779981824165201433072325783633108746432581651036779681157987939416547469946082469829334401; gcd(b,c) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:47:52 2005 Input: c=28301479621116288723240373870524716203; a=(2^(15120/2)-1); b=13059210352149606733529404775036023154586871752956798087178673391940951190449085377740873416793004358770660137663397439822846995955261067200932037746050368615013431685012063613275339665251994269446225659149953157661404237247635652082187523399757426800639759453651962539313938621507578848147115200787892070799865808242173847812591263151464644216108030215361173037402349591934134749790155512466980861293721756280591562570827044696201718699732105806480263738856894804467483443405232036889958476816355520795665426805419836958428264485027255707151822543803035920282148444249541621478718022473082130592038140453880494261208043917397924813728915539445285189935489469776807371684116494748404152861642920947038648701064943870446023214470280851684199921509880908902421815542355945556411963056017173845668144744135609553434304497088183923456318487020133687979759159904738270989406402719300901745484166455833881349902883638010290418458483647798034319291367628988610766092845244018739095149136523339769793450331979615400557150410524886438001857957690295279840270629477740764098477058879452745098903220902429984405982518128430508907636708995013252358133015535786391162533874714069722310439236303908005309255919314626635110433363600496400019071473055777502124920999336729039307892734405028195433420634458860397436288956209583387210126707056077118756396941835793192202165989811138814427937809184666378531196348045652931359929921673730592918039954256535379191942207975560969995211786266633933991950982061759525702534957388370716995520374861725234250863902950190113139647308293162473119594699319383692180306174813834082198301742279810818222745205578398636895842818954446529390379255583152347862236796580695939926598448803028789642506604584884682107966878755570425860802323161778883462051241614643885966585158472356381332238842080732895187090035653782606499019609344224441450215076228803849757560736056082329624326510992239210357932192162431761669251011635753878837913245021144470830826099116779981824165201433072325783633108746432581651036779681157987939416547469946082469829334401; gcd(b,c) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:48:05 2005 Input: c=19672078294358390450363783460310174084366087559093203007571119194731463934569456558455821744372926703545253211836467631983310898120319053778093737077233178358957380166197676273810192724934465096152776961; a=(2^(15120/2)-1); b=13059210352149606733529404775036023154586871752956798087178673391940951190449085377740873416793004358770660137663397439822846995955261067200932037746050368615013431685012063613275339665251994269446225659149953157661404237247635652082187523399757426800639759453651962539313938621507578848147115200787892070799865808242173847812591263151464644216108030215361173037402349591934134749790155512466980861293721756280591562570827044696201718699732105806480263738856894804467483443405232036889958476816355520795665426805419836958428264485027255707151822543803035920282148444249541621478718022473082130592038140453880494261208043917397924813728915539445285189935489469776807371684116494748404152861642920947038648701064943870446023214470280851684199921509880908902421815542355945556411963056017173845668144744135609553434304497088183923456318487020133687979759159904738270989406402719300901745484166455833881349902883638010290418458483647798034319291367628988610766092845244018739095149136523339769793450331979615400557150410524886438001857957690295279840270629477740764098477058879452745098903220902429984405982518128430508907636708995013252358133015535786391162533874714069722310439236303908005309255919314626635110433363600496400019071473055777502124920999336729039307892734405028195433420634458860397436288956209583387210126707056077118756396941835793192202165989811138814427937809184666378531196348045652931359929921673730592918039954256535379191942207975560969995211786266633933991950982061759525702534957388370716995520374861725234250863902950190113139647308293162473119594699319383692180306174813834082198301742279810818222745205578398636895842818954446529390379255583152347862236796580695939926598448803028789642506604584884682107966878755570425860802323161778883462051241614643885966585158472356381332238842080732895187090035653782606499019609344224441450215076228803849757560736056082329624326510992239210357932192162431761669251011635753878837913245021144470830826099116779981824165201433072325783633108746432581651036779681157987939416547469946082469829334401; gcd(b,c) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:48:21 2005 Input: c=18518800563924107521; a=(2^(15120/2)-1); b=13059210352149606733529404775036023154586871752956798087178673391940951190449085377740873416793004358770660137663397439822846995955261067200932037746050368615013431685012063613275339665251994269446225659149953157661404237247635652082187523399757426800639759453651962539313938621507578848147115200787892070799865808242173847812591263151464644216108030215361173037402349591934134749790155512466980861293721756280591562570827044696201718699732105806480263738856894804467483443405232036889958476816355520795665426805419836958428264485027255707151822543803035920282148444249541621478718022473082130592038140453880494261208043917397924813728915539445285189935489469776807371684116494748404152861642920947038648701064943870446023214470280851684199921509880908902421815542355945556411963056017173845668144744135609553434304497088183923456318487020133687979759159904738270989406402719300901745484166455833881349902883638010290418458483647798034319291367628988610766092845244018739095149136523339769793450331979615400557150410524886438001857957690295279840270629477740764098477058879452745098903220902429984405982518128430508907636708995013252358133015535786391162533874714069722310439236303908005309255919314626635110433363600496400019071473055777502124920999336729039307892734405028195433420634458860397436288956209583387210126707056077118756396941835793192202165989811138814427937809184666378531196348045652931359929921673730592918039954256535379191942207975560969995211786266633933991950982061759525702534957388370716995520374861725234250863902950190113139647308293162473119594699319383692180306174813834082198301742279810818222745205578398636895842818954446529390379255583152347862236796580695939926598448803028789642506604584884682107966878755570425860802323161778883462051241614643885966585158472356381332238842080732895187090035653782606499019609344224441450215076228803849757560736056082329624326510992239210357932192162431761669251011635753878837913245021144470830826099116779981824165201433072325783633108746432581651036779681157987939416547469946082469829334401; gcd(b,c) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:48:34 2005 Input: c=28339556086242018044265074616924417415900891375897512924038750812976793015271075764743857097324446654009284375664531272671336874072891707096004934670035599037382520991; a=(2^(15120/2)-1); b=13059210352149606733529404775036023154586871752956798087178673391940951190449085377740873416793004358770660137663397439822846995955261067200932037746050368615013431685012063613275339665251994269446225659149953157661404237247635652082187523399757426800639759453651962539313938621507578848147115200787892070799865808242173847812591263151464644216108030215361173037402349591934134749790155512466980861293721756280591562570827044696201718699732105806480263738856894804467483443405232036889958476816355520795665426805419836958428264485027255707151822543803035920282148444249541621478718022473082130592038140453880494261208043917397924813728915539445285189935489469776807371684116494748404152861642920947038648701064943870446023214470280851684199921509880908902421815542355945556411963056017173845668144744135609553434304497088183923456318487020133687979759159904738270989406402719300901745484166455833881349902883638010290418458483647798034319291367628988610766092845244018739095149136523339769793450331979615400557150410524886438001857957690295279840270629477740764098477058879452745098903220902429984405982518128430508907636708995013252358133015535786391162533874714069722310439236303908005309255919314626635110433363600496400019071473055777502124920999336729039307892734405028195433420634458860397436288956209583387210126707056077118756396941835793192202165989811138814427937809184666378531196348045652931359929921673730592918039954256535379191942207975560969995211786266633933991950982061759525702534957388370716995520374861725234250863902950190113139647308293162473119594699319383692180306174813834082198301742279810818222745205578398636895842818954446529390379255583152347862236796580695939926598448803028789642506604584884682107966878755570425860802323161778883462051241614643885966585158472356381332238842080732895187090035653782606499019609344224441450215076228803849757560736056082329624326510992239210357932192162431761669251011635753878837913245021144470830826099116779981824165201433072325783633108746432581651036779681157987939416547469946082469829334401; gcd(b,c) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:48:59 2005 Input: c=6277101361242261607125971590980905998814908364881668341761; a=(2^(15120/2)-1); b=13059210352149606733529404775036023154586871752956798087178673391940951190449085377740873416793004358770660137663397439822846995955261067200932037746050368615013431685012063613275339665251994269446225659149953157661404237247635652082187523399757426800639759453651962539313938621507578848147115200787892070799865808242173847812591263151464644216108030215361173037402349591934134749790155512466980861293721756280591562570827044696201718699732105806480263738856894804467483443405232036889958476816355520795665426805419836958428264485027255707151822543803035920282148444249541621478718022473082130592038140453880494261208043917397924813728915539445285189935489469776807371684116494748404152861642920947038648701064943870446023214470280851684199921509880908902421815542355945556411963056017173845668144744135609553434304497088183923456318487020133687979759159904738270989406402719300901745484166455833881349902883638010290418458483647798034319291367628988610766092845244018739095149136523339769793450331979615400557150410524886438001857957690295279840270629477740764098477058879452745098903220902429984405982518128430508907636708995013252358133015535786391162533874714069722310439236303908005309255919314626635110433363600496400019071473055777502124920999336729039307892734405028195433420634458860397436288956209583387210126707056077118756396941835793192202165989811138814427937809184666378531196348045652931359929921673730592918039954256535379191942207975560969995211786266633933991950982061759525702534957388370716995520374861725234250863902950190113139647308293162473119594699319383692180306174813834082198301742279810818222745205578398636895842818954446529390379255583152347862236796580695939926598448803028789642506604584884682107966878755570425860802323161778883462051241614643885966585158472356381332238842080732895187090035653782606499019609344224441450215076228803849757560736056082329624326510992239210357932192162431761669251011635753878837913245021144470830826099116779981824165201433072325783633108746432581651036779681157987939416547469946082469829334401; gcd(b,c) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:49:57 2005 Input: c=6277101361242261607125971590980905998814908364881668341761; a=(2^(15120/2)-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(b,c) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:50:18 2005 Input: c=20599554602046101491103622943218704819395019390901566892952855872696818420862893821060116778396212643763560336178860111043386700236638833963136823881387266654652239143989153443039254895360910896411384931457874182561750135868788634991091026428916092893864889659441816507017080746265168894410307930808311335864746001930511677217710169012473472177408695249255118949069583278431950967547352003343435608958682436186258875725218083167513696919282325910220354249913677914719791398082370208531132508182050235458774948039679947983394594733366146781461540938554618017315074224387272086390615414845260727868653043678689831461718837542293534745351703498680956427970811814321029331940317712635701770603633866275650111954719205101867559757200185984349875595922626780772288931675628968832592644137150364513275880670646881512395068248129970304265017406432905343705358544567897169663306975577873323688566031334276546190221770241; a=(2^(15120/2)-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(b,c) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:50:33 2005 Input: c=247330401473104534060554895269373528305051560136361081500498522363285371560389766604315961281959772968457965711024595445761201095651758114601212404870944498141050407516897281; a=(2^(15120/2)-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(b,c) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:50:49 2005 Input: c=11112382566050265046201267311127854032287645974415860346290590498168586174867795883723807322077777737613405896828278368924739043841; a=(2^(15120/2)-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(b,c) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:52:57 2005 Input: c=11112382566050265046201267311127854032287645974415860346290590498168586174867795883723807322077777737613405896828278368924739043841; a=(2^(6048/2)-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(b,a) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:53:05 2005 Input: c=11112382566050265046201267311127854032287645974415860346290590498168586174867795883723807322077777737613405896828278368924739043841; a=(2^(15120/2)-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(b,a) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:53:17 2005 Input: c=11112382566050265046201267311127854032287645974415860346290590498168586174867795883723807322077777737613405896828278368924739043841; a=(2^(15120)-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(b,a) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:53:27 2005 Input: c=11112382566050265046201267311127854032287645974415860346290590498168586174867795883723807322077777737613405896828278368924739043841; a=((2^(15120))-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(b,a) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:53:39 2005 Input: c=11112382566050265046201267311127854032287645974415860346290590498168586174867795883723807322077777737613405896828278368924739043841; a=((2^(15120))-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(a,b) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:53:57 2005 Input: c=11112382566050265046201267311127854032287645974415860346290590498168586174867795883723807322077777737613405896828278368924739043841; a=((2^(6048))-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(a,b) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:54:04 2005 Input: c=11112382566050265046201267311127854032287645974415860346290590498168586174867795883723807322077777737613405896828278368924739043841; a=((2^(6048*2))-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(a,b) Output: ? ? ? ? ? 523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:54:22 2005 Input: c=11112382566050265046201267311127854032287645974415860346290590498168586174867795883723807322077777737613405896828278368924739043841; a=((2^(6048*2))-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(c,b) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:54:48 2005 Input: c=20599554602046101491103622943218704819395019390901566892952855872696818420862893821060116778396212643763560336178860111043386700236638833963136823881387266654652239143989153443039254895360910896411384931457874182561750135868788634991091026428916092893864889659441816507017080746265168894410307930808311335864746001930511677217710169012473472177408695249255118949069583278431950967547352003343435608958682436186258875725218083167513696919282325910220354249913677914719791398082370208531132508182050235458774948039679947983394594733366146781461540938554618017315074224387272086390615414845260727868653043678689831461718837542293534745351703498680956427970811814321029331940317712635701770603633866275650111954719205101867559757200185984349875595922626780772288931675628968832592644137150364513275880670646881512395068248129970304265017406432905343705358544567897169663306975577873323688566031334276546190221770241; a=((2^(6048*2))-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(c,b) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:55:59 2005 Input: c=123003155723136208567873494614602101346489993601772570858200800329283517240093758209115184702539626785395362644480217819082595357919726576327339314062556689726154779862551765284229496668248105141692341442962332192569281010485085830736385553031857206998461317121; a=((2^(6048*2))-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(c,b) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 03:56:13 2005 Input: c=2948552384027464239812997061006820673810059917568334057927252522387515010087614404423021619414676515371670290048495143734282985240844684744062974739918067866909779967448526959951721922077920280409275764659957281461813027507101282219119188694470536504083217913849256468312137335192588736057933884830222792080075446067538122268511194832367731371468415330712506132428176768392390071398030387572621015810206268498640232710226636621122328224157027505587865177974143459103947323183694659114616476625154384432677921627741116904144602248166892529009309310966176633741181231816400861496600848587491216808901322513638441815717623922715655820607033370425215009067093985171554254824882579930959327722252412420003858204770955402039806886702575076784166068484863751052074147422101384289561002823648444602040156680994094433210291638240144746650955051854252998625441823401140259334805981856934642526372099343446993209919836745; a=((2^(6048*2))-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(c,b) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 04:05:05 2005 Input: c=228910131428177603701755406038597370992866256605996714416239305740707356279544553417171943717222418048031704055437474355264974244183248183969237882956710039801299923181802452646148061153788227677277965884902793446491028711133062657998139349054343049367747004344785156691707908131586596365554457124805603923870620806305650392140221379383445551992981112966147421200587747313925618355818327823454494954794133756798649738169838306609522777468707654607425214697979874770835286273796623263288865390280683815440951134409136329290525783147797514821993152689695202170826035278077217140197496526428251377159771224215120264958119359992857592027894828706037855688522527193797862526527618880752124310864388467033125757827116213051750659315848638177185612187202001358925492266066025428880205164358407876276362251416063362563890217299426217876326088262897796185812553044424835906418234957731328636799364051906201306593466794922102200262531006604112086988398295308663632070235737952627533709896371736685027972692272576651087594565631790027005487310207713281; a=((2^(6048*2))-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(c,b) Output: ? ? ? ? ? 523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 04:05:25 2005 Input: c=15129776317850095820092511389349266990292719408258266219420927185678994592533679211200550904631551230515462488284936050530907075655190244387674151998517361457093540115541854088138667757807106324129106755260554141040568814962192748352553244562338621893443362946594517098025227234523648360971727556117573995584499218307940389775331590089316176143477945461613461463440590060967559269791701126098857160294194178403078548229166387092805257403433922214744176993216503332253393264584629375283096197468422856367223718248752087041; a=((2^(6048*2))-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(c,b) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '145.89.' ************** PARI ***************** Host 145.89.51.113 (145.89.51.113) Time: Thu Mar 24 04:09:22 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 04:16:28 2005 Input: c=286299006811440393557125872450071266048666315143181899661536055577260490723580791785798506975062493506960093413531427283187725532663912868006165902037012797427327402293544558733540546658098181913588579594098460910149593734094128955146435108306587078189280137872382997706854417629289246021007501723949448162702766957085404330415452988813848301301046189415634873831123940798286374755758652521472427954020338678918350873989286281345579448040529624227283546646639163551643664764678174837730119847853550345507536037462011711500904462835961751699634019954919265940800077585018988087581070188045555253632645432181615735082473633323115253494113352663396857562962914719522038175494165254286458802956202538455678615620002864174729523417011644802391085337956449574926253085083544198280253791939276299962780124549077476753676303324833069576363078238792221753848612006407971866633887170106449244243626106533486441835632850138359847910685489000612196030084352426778860682947620166648024065913827085471485106963629092299676436346535987532815718007585907397267218940273200900533483976971398087890064221924260307079345004124872134050527363094598363394036440636101842532416111069837285811481305226199904875030247732390667043862667291115946956370603441176047034841541309826955150093935961357278568183690612811955645990745188488255426571686564677716074315952118880133263813284800387685500016470549969666173092638538623792503325009001696714256801199391149523326900267797803410318475980228947681297316877608554501599596224368806922651849268937906454529364780613317368671560294593; a=((2^(6048*2))-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(c,b) Output: ? ? ? ? ? 523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 04:20:46 2005 Input: c=228910131428177603701755406038597370992866256605996714416239305740707356279544553417171943717222418048031704055437474355264974244183248183969237882956710039801299923181802452646148061153788227677277965884902793446491028711133062657998139349054343049367747004344785156691707908131586596365554457124805603923870620806305650392140221379383445551992981112966147421200587747313925618355818327823454494954794133756798649738169838306609522777468707654607425214697979874770835286273796623263288865390280683815440951134409136329290525783147797514821993152689695202170826035278077217140197496526428251377159771224215120264958119359992857592027894828706037855688522527193797862526527618880752124310864388467033125757827116213051750659315848638177185612187202001358925492266066025428880205164358407876276362251416063362563890217299426217876326088262897796185812553044424835906418234957731328636799364051906201306593466794922102200262531006604112086988398295308663632070235737952627533709896371736685027972692272576651087594565631790027005487310207713281; a=((2^(6048*2))-1); b=523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561; gcd(c,b) Output: ? ? ? ? ? 523851779434872868940058848296639064165204634330643765802567474703703671661923349795444652731446715683173014468595774852962769007525619921955735036808432712292610538097242644908256808437324088792859558145159377138902088090823477408795688952504093742707457997519523438233326350156875602899364918122243825584976482708107428420559198563157374037585827140168967779144502817189335950876238040706995716210278977071820567887563073636542403930213925438794221613573649191475658097700235428664355416863975126627540249501028717458091290203971678971849840694423148140386539416290151208484096746922027923010235028604307797275487295448671513360843147996492350073404908181943925420226607995374363012572697371546335414431807147996842930212737071633288173320934440905133177552210822329201996310534495815121404261147953611308715540245466030690226801510845517086642464131504790749420127376291156505189166452387221517736170135014604900244842280720541796620774043980448129717377025395527693736443319498521678639570561 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 04:35:53 2005 Input: c=1250704829118797703570514291919423575290792709618770457090264295749276233159765165842816475541998117757746754425472104697933956820301747903420199388155522977357488643096788797895235823576680691421766285464210477063781831442687670360631003105095364296391118702702696296439218585973683422416444371010793915481896273316354500270755690674490880064766301187204551662680052084067748968322038615036691507009522540993889274053828749863007791799903606035772850871556295224622087564237796922814176754357974940594132736897474753; a=((2^(6048*2))-1); b=4992679136035358713351811618087572638282077725057974536974435415747267082108779566637963573792109263527472593560542218809703059254171528599079386231114709983130799215279414032993750509003444564997721564444772755382147484900856453623495527973681621555062694932406510900408023434790438448371983901256717295420157790349918864636101157965764597331016239088656195277238290412412670590677702415342797257584972352196979735070980626903991450748490607417716928638934371532413976448460067743454183873; gcd(c,b) Output: ? ? ? ? ? 4992679136035358713351811618087572638282077725057974536974435415747267082108779566637963573792109263527472593560542218809703059254171528599079386231114709983130799215279414032993750509003444564997721564444772755382147484900856453623495527973681621555062694932406510900408023434790438448371983901256717295420157790349918864636101157965764597331016239088656195277238290412412670590677702415342797257584972352196979735070980626903991450748490607417716928638934371532413976448460067743454183873 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 04:46:45 2005 Input: c=14510642956629460126286667764218111732339625499480335264478327629658324054225616417 ; a=((2^(6048*2))-1); b=4992679136035358713351811618087572638282077725057974536974435415747267082108779566637963573792109263527472593560542218809703059254171528599079386231114709983130799215279414032993750509003444564997721564444772755382147484900856453623495527973681621555062694932406510900408023434790438448371983901256717295420157790349918864636101157965764597331016239088656195277238290412412670590677702415342797257584972352196979735070980626903991450748490607417716928638934371532413976448460067743454183873; gcd(c,b) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.003s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 05:07:17 2005 Input: c=955929737454207687430785183124590963593849532159132710651280130083227697216217556202031973312533680470386610623139316976258203349041677908455632326266963635594414222889007226990237514901898125822355942726706222269141469145536177852068566962340709682490313928026274973430103943479937085943658987423899192234937504825045690946054047914958586882220060546526650584357010367086604755038949664048013044751367411557865523276112011712086033058866081758823997945420634284845691327542062212310758719013731112287688042913133927466082797820414760318627824446102504177540225305858759668356346842302534036184998551822057094551424313868408997561320485270076932509214432145201881448784988756867330804742460218616660477353789917516363490464949560878905263817749339156922501030088649797687650700780960630236124734202898594021194599709997679054804046226909283018387617702731784909429015754162303394056189900253796793740721835829148423820878779698626790836597761748678898664288448545219809664185406088473083434534612979766912396693525907473419003373071164091088775286880439062398857548302867692784377610420466972426200744380826089772593853639633197510757771467697290382351227357537572087512390960260948375656106348552209331291160322974264109997715798107304907267828154184653239516655306650809432356056555408592212200451718848001955817241050846597833485810342636483831656465338287387704225035560770796797213203100982176637130647964166581864566374300090369206533636239883968610144562085463123002335993883835201056933780257885275909636390790098008914729379707079812672602164065976228370870313342264733335379869698621210774716951198032171908352982740069327488973888060643483296081262493440908257614173560550754479099424195380580340278662001302180319078438560079214272961835641229920600827136426137358709574632154873909304311770596560004257469134049565447289465136358157106289530751131269903568919733471660403352834048327139258932353182340872848717499122876190279587513959057326572912806425192673418683702258950890001979345324452564463550746107703041676931124137709902956871754473012533058228131517055625762267304902502301308698773004960864994973670003073570888303609752553562492918022277934420929784468356641593177931147499396531951306020958076529542088495496382241553838514751951868753613788476204474788569089515232409151712823475072468101701092686678423570846150159894659992457468584011550326159774982062463609229244947526658405769598188795126310607414552895603184535853819162462601599055926104668946289092608695095442083620274569113213834397325006007499231569751184719621571110207748515166849556103403206226348791573001654398947891555336250485188979501883134009759746675071247211331076082970034147722562034370612020797625554168788859302928276791231216431898585469207752898144636881190645230374153046577564798412705918866017440475199911280706166960224828901404213406606477178350500519205520315021651241150323257942684207229792671661663130005362816222941751894611481675003472443238208887882793554119447165624523026380928009913432103141253789975008810258148748710570806850728065263577986935128517675053968837511782061197007157661445508911682526301306708244340913397552387086108214778390515470687695352249764184913952427452448178692252523283350165369553136021427577600016032018559826975122906770165088364898944809549969045724948421183751212685514428207304266668789035797150837407820376996770708142790916194062546174226651755360276170299143463186365827279914948017764128286982775914734711428508766105152074419943962618749911645456065397681712631276879011353746429124004605044529071787212507156093095276904783444982079694711877318263326440482886515962074873178326962176181790687556463801864181483128438231354068480030272898577179831901765128677944086486313114349427494525365588369377298886586679425616139265893062821272245805406269617485050588566122125385370951579880436932417090592527712488659721390440593107230931628375639693751240258466920145142197435173073636218135985811615772963113112399932175301280516643346525021486196212614177226258815580355659347440678520517972519945109408122206892332967038505959075288880023246377928059661556620060370208771410529511433361357994406974928005181926412975368113498163965225581713284249322050144388096385592829711595377590944987291021832017042818209133527584628143492393589959931051961910606553432265099460345920195433336594350650035944565059117795082479332367289985674857352526737828692571531163021957788552819955620301607884782346006108719409194130371181316175002595822306212554625172029805283043870595448584462025358519863495745843646174048745836718307993798152149083833205619963148149785549872691447258984568308957795567585332592496654361610634809309223057448404223855106091783053549751641974257224466243737840882886473119822059763389661141190494799306167417443403660431974256139912653698772792336179284884763262678586404826587392675506019005693839054592818591274585112201706758959159669759348447409015124049200887424175334969287855781287559701444836541165799506759500238745192794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a=((2^(6048*2))-1); b=597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049; gcd(c,b) Output: ? ? ? ? ? 597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.010s sys 0m0.021s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 05:07:57 2005 Input: c=1363521346528864752252436587154937989870441984681666813861259381034805113452886972370069172038048625830207606666455167730807432623067433787290458916335245600921889260912563360258223667921243525507871481231257676321245683541816558629343764097537064579459876479958172125451259116206106597091869513779729465297681828979780186521458162409400912673283163261571509574981746692831287632342199874922045970480731999170891907121342075039348034835282167662610323896969435799985947593323638096893521885307849638541453100137541218436543921064748352634041015142697647756508003604159437051254634656598334240527681615734427310085027571002553050863335684367954961248614520529046385536743097841550081625269082736350925815240748867976451206562065117311404315953396833738225618857028529209394950590473071931592572138953523836588280611384529606775252093890063623697832933726003279914366628027515073599661737589809289460978066963295362313751493399588509594123999010612350447942584945705670084765926641474796947453194590573738323762191787542340663962803232868495218312243357317925367535321474832160623306437766664311229785932409166537590933796479906916915451824204563394210327343916254947044657345856004703500040157463780234299074549213872925378928762848911282322175420434592207569794791050849886815844659724940521252360073980994491753609041670706140842127259430005611919508048321191220384078306917535038184740324780206526933018839359774160548677138897153519316911617957521405488286741059290042756301842725714440018251475548111710464423813133923577518683407923978602988969415107884084934385775871603590441729211896836715894293452374007781619798681133012300340057358256129060176784260516808471382621589360109728089903042566601522028186125668945382841117622294315439388414985414621253450927751134808374963933426567523175060229897902112959218042147920314578407666099602159138498146302461068991519891403757442275609092540100928911311154188874330034464155565830193629515134022700595549961332430158259240227333328380410902972750326291676880287601495158831848172020278849688984110447853529272466449922347016561194607358667714984548094301986852353982249693672958868167815239274585516340238178130283714238155284754886876360729484116337644949076005247347174731068293457742968262715456175512818594079629483755720420986026167736482427332749306508357298098615469949318495455121149316881987119137435652071262789499600940482021651073654060520551533071733268742540243096237824105153192249754672009322830245739923903311337254037967483035833739962946488905499382516249312582381446996265560455818607860508025407104787006032531906823117796628797780766813332973867001977178653006248294128951621756730854046390275414867523818947437832727652940399054930593434590191474267482436188229824055572091824624241979003938467743416441968878999875556709548687968537092724217963274088509908293183179575149082461782719399271506859634452809387235801708382346455997332780548663630443276671997811199140989189097097135564404015639689093663219392495993147872438309451790943655708063150036366235831514937631563871664237054098334785042386041615029872664182578016617980825534363605827388965139723412580540404791301167256882237961714975948214696256634875468791670788663646575356715168101200993218189742414295391780331248264333891972960859660081420682506442244869546609712408231849824578124113939808257918334176416634198966217197772809735852827948218383610253577619621093083223706047458019988162764406430478109035754955093605697830962939161131710002102363598905264907186525171102984691273755861243680534429762769063890354890264893105005919191350453353198826146565521390667353910007131643997318631516166372786279930391223990217282008054565836159161893565662795208388530556605610689674564074245511360311581489725833002459416165090325481561314030185224590471888023969189034935372706973834124591061236585688959240775678330811560864338859636999453367584027358182835010286564647943937158338160693884791364777721497862959371598580042684943985077358649473862035001908550745159800656320470611799109965199184088300381904214749075408752267286431497131102787326616546312144501228168912817992209662835302844618260257238295872998787921598291039066549012523108504810919577000053883577545859603711338035353372898836825945989867375537618609223452353341624901263507134902693979445163175260786594797707815454993004954310912438959462710445321550856483463528979620255715269540383630361219230847032486901789121803859807059130125573361874855802873473377775996803226399788569843374433091647038739400785008215098731678028600083223457833007585559438548047438767537485645383520750469343989089865719331432085248398429408614097336050934091546169048567755406685175237976709285143998732590717634171256414787092436783345384785630616793506642752277974550288093450817098471825638027288283870442253717732468061658986646043014189195448652725819182096551899870183412258642659074601404135400255786076287602202708517520279546750722709547655853434000365915946457924701779778639930147117302629878110042227142815863713320938783120250658798369347830219325706024480989227455238483653615943619946050416507089568293299439469709767689643555182899113574429867272689934968676045949936296513784390991251342651797462021173719189063856107684036844239825353403778063589517181702167104277638727601151646942517475070576402232931309987471783639228434294171367787730167542657479819709649605557042633682017868585951488941320774487726314490700925630724638775689478639650384042715763359198820635542245339120329070662464098937608385941193017172811833210002687201241487970168851680289616752074497406066702226924009294123677105650865969164624154726234776926511218164705581837888907704490363371697450013525199445540841820877052064283339030789678856530944383130367663277468677856680078829203542405834488714636191242627178234242191476518843455528750807211805748026411295170554620337734246830216029664409484337732781771961974903942425141477718907746442692682876974510122323497791462130578727126337543657149099593907246446257779181341059412871219695173512585823936535890375449704384635229035048672403328897179274474456199526580677773565900633073600592857668991295090775516301972903481597645591643142658883690954241; a=((2^(6048*2))-1); b=597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049; gcd(c,b) Output: ? ? ? ? ? 597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.015s sys 0m0.012s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 05:10:47 2005 Input: c=1473243233277471965951978118726481524756276762126008968915174419909334384631437049432525573919176236065138550581664856663798789814958508802766709766302648106036703487827890425694774181621187087713976502484086063286911596759498899781087991960917569987114025093762120606806791232075324972364065665791692891416191995465255624736893890079546115762162636791605963837241964775112094479946681182325159626129461300568957372827019626363393061088248344461271131956235241997988373954159164419771386076910161877097836055146845000073933601204932396625002116008406677743515403644932057562636368043006309607103936724537995850328653612167450512868009188117693968552217869598789844447378312847867175342065157935651540992641092074495769642925848483197321090094494566707201292615348812559100848009440924836636550981202470760295147498816505218897439023810902143965838767793415966290963907395186024363554400119243119613370384678373584767377904352156105552331811017773759168691541276915908671244996402441688057190999352021881555785184449209834537315887983711544332911976180522724960042575661588032437390180761355774475058000533182926358916443749961362596134862837324618312955164088986514157711947212123739568312427112744471951676070964961014656285519283443924308487119634387696359343824981766185840393757615130521846333650303244390341637889255791651882661149625484984203276647473193007418269559271490558496500461403414062891027931236481595001369196092301392091529540772595706746152933801668293441769147734777782978422918308598257870900443474473733711176814575433221155079259003875851210000924595960030912682605723326607934704361176566678625164355395269843841657119511403108244103402186365015020532885497902820002873395537004257852980327824936821457032972208462890469270622038316735314569755555423812749823169323477607382174289957534499265418475048731479297014986762172778380524985637466640076068519738921039462253895323274095558762090596983774974137596994351180015334732753467461965196757663829256846105152541761972941104766775997515854570749283508426382744059454136193211249818758526518481452228380609403684243475967541247809426821537369072968638244622608796275263124794577628867748838849562829706972302781684729213063698579626223588556670521562913868079324525817495446008622761913278853938238973249519909105140424404907693465850409453664033514306628902748769883290599799529425274374158311459647545032805508114000631551300920250072927914072486600159687550971140373108775580827246905490119277157586785870522494822248966843490261488523099850599137870800937274248469870558264536135998025487062046802970712077586334422900356618626292622773590044727112821079496774839010857953279570912266748410298451123202311896710717308510394613622049809750433075891299387254332318637293247989951609574761853408564121154923716728026573998873336449244688530934312722812248445397296956136167828222197224857381929906360424593857555002863375931065252833103168434598908700568097440507826859921192973305595922279507074219295755290789749393821138742302954523964437198585300707214221108526002204304296707530150285803664278784099815710857622611439310232379935043268356912624275025685765700255940830130087730645296398149904253393788123918991305168767825340482413374691231806583078272771577943470034462189709390379167838633279910545092236142965836089309120175948519537359608539757425180003976725385616708528123752492082321569295577288706915870815252157818033225344900372814791029133342017328643230621946339490062140014612597896557835145928806949639210641731556214187155176596610945930151471275664305401974933799150660771098093376164605010050609326229744175229238990356134662936328736631450711490694228376191883615694627419301560505969029488536676944240847248260864522727943511695503881168150632200556229006968625595940010128714637588569678272224045662734223056863742774391018106834749776561036988931131952516862963727628151011456316253372513711180073374933671607387783179292940643247557601251211041206244650260474889496127835501662400153445265408505788215321538147245226343785665325766214979642202561669932408845640989758543091915714864589866422994929129970046318851070258645452143401093342063421794225789505604359587441163786584317392061120965003719959172704407744237345680979515941137406524552150364088215024596768117349717498576295672402253547780582241808830138239885084569445029046294713149225261232017341496677088605817794820529333250125260465099405871403469549359129420696978105732180033638640100077823914856225888881783103216763095934006073690463712361849601280218679488958798708414589281627220743896869205457926365279341444929849746223958037572630280660051618455310381630894402839679567311881011559954903207706007879121721282771787931337618613841046567890504847903738723674614899979055019313526037250220871083660583290749365584297715662120712349703559357757973397450956152358085576170355581234826760846974134373512788119807581241279139829452017779772498955300407785014947801746809390652397434437782066391689756329389963558141825070042965606743479895082052597188819636379183076399650277702467632342235871467231901237649189939862373176943032212151261494082318659349727479813061382272489630443637649288987247292292215165346642786169663271552669307775331788529478335278480079546036130173809794203560402116001696230549679318201387441284912866915575872306019841; a=((2^(6048*2))-1); b=597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049; gcd(c,b) Output: ? ? ? ? ? 597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049 ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.011s sys 0m0.013s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 05:17:19 2005 Input: c=48426234294551844714668891336177007564088711630281369511411625659863346280915109409608756489289747314284254105027488159011717298296548913334328669347032578268584855173591523463715312385108541227577383999581493660369940173663213114403815501177829920710216840976730706777742281000401401867632854052151923524252291480291286712642524922561793967105945842361823783145871889840686223882978546766569302513944499237012805448823371242130995158669068635292014032562929186987830108279336064788702233998749801352589719539214709200685928250899281903784301561909212479727589265377661955945990473517923491633685497678037613573744936428571558896642638219177522518539288755539640377609190088766905424825828780517565321009097556845203187206123591598483930982266616400289580137616501945295727449011389014486921940221346885408874991868582976547116388939924194337711069127842669827987662419710383936250380787106485233482250832882866803727794342195463856967181057183470280134489156631222342121402510270249336622998101751345905138778916250162417893200759194856271973253096198090087807111459723659886976366280080089645883932132726951328953577691821150966395745028022340450438939414142959724567997735534313127194802268276972577740642415829869488517750783472236188950295580549543723934811353933453355763857783410025242553034287117242695415301946890089945274020744022179686540297826820093425801936567260521884104406261585619361877741574582754406923941956833703789216967821260284158879309676371593360957420283551546685540521088770973572206509545311925247874675347401064332377558964375404421653406696908507737223200231360340183332524402582570031033275798802209504449504127443219558113995899887192150348668128879629033605001579631158755172581553683299063041178472728921296792659312406595934479649239991846751926337342304449136631500460431193996484365349831810608078938071488445388682962751642768043005831225649847288045161758202470422842327122144988552655164978771030175394396142760387653415169633816501937119512909656989239964901929131388790065861425385777207694806539819277706470939181045644796323958338965045665256102528062788180795500896742225259462274452582606556508494280214170112607825872053300160645053574394321438699942657010001814610704437004863801055485985679639061294203123831430346794427961683115140440142264361775456102960330462373428205419497177330128263342303373633202671062437880441888639003607353011204841025121673659453543367483372408239663830088743280491636731245287744385009886732230146938310070043007250015839840376165427390626649355256682726529567795389164698621704704564689090891677043757320539683456312119694517696478815712639019069922761374079131510836129061447698770373286757594498459005413265706199977797031149884475250489442145643583566626065133673161211360255122186982258433756927750430636396136882836942299613571346892825054824205793866668731536847392636499288409017270410450347852698924519914387489652217144181641178517897603668711660234975812436720617839326864381006700178935861822547834222771516407378986737984242222903630191250387301256175055408574006472280587680403138612625795414748692011610105382544218387394754931217526733730004773440747592078397509646886710324141510731722616728558563932970679033328421084605702953653823010364276791204133360644813874926711133581163046126386484888438920274418766502744523394711061965944030231125370177080335402255194559817152742013715233015481105264100762330650335962734738870742748380758330034506889113248173526081870304098308412773114070615141354918983810487711259515747606106682960141494110888017486481662430823661334849355096010163883824283637293155575235601201248091459411549400262010266220328060213173289476619664724743617006930005981922594329364175418968900546805071904712586415017019938524698186245298539389666121072961105469079800444168777272792824664518279995773243997236899378509818853848861936280019782958403235088676524807611338171087124278479331268250218492668765126647181951713705888986311087887296061102421286778134867314140114778554218045590259240445499546832442811932344940145179836769147533755655504629948381993805506109290001695583083102358553780641602497469397854234702574576306292601771030545012989647762652005770488688019996979920878183798722488739836593848194661124216710173176383080566146861609767792451105725180429698647577708992960671576390597500887335369319453069265567913076736488663428267178716490617576006256421616873303322041670462472927444786275283593359185800412626645071797411633787729693474089283917255876961631881686544127399171018229643334489398935911550053090739953090084697459245056132465985179143259900501351730900270942812565604359300695947075078566671871977948724882650549622762622826529070495888221769321912008269621932718277759418395238259439210473108683778547066552706634640603939278720026146916822648547266869673113777351646282713575522852020917737737582379198645833571288846607058992641; a=((2^(6048*2))-1); b=597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049; gcd(c,b) Output: ? ? ? ? ? 597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049 ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.010s sys 0m0.013s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 05:20:39 2005 Input: c=13236240411088089536147819004298856901746897696792111239083064502315708643673006980513584973822404286083985925814779678932895660375924126320330508524244801507244198500469433533103724813316110496196007852514936499386959239249639160192108496285271849056786426620210732184534759937217904272413409566911591476217919303255425117329989152815017149768247631617001635051066717285438408400278967213477811293774566121561905042305393985467639888318822761400924402560853800968877621985524944206165097418153517227990357728819297090073289237539749791071509301954763795262166276920649217911891788294018996166188143810108856090883517054352949874835252497330139646902929284764212017933728816103068192446957819709798305376562682835725693474177993188853193631679950342692653943540576789357802164617961092935424287052563522735916884430995188091378767082232980670095652770239438204756050479451230293643557477182790179380299479133462671330532848973093434729886244382554325604595970083093007038788506913136296102724352949317385512229318392870646021279722087815528834604769679893530954311890500690042634953101037029381108441335082888108782468820774559056404469962950757538473434006428381804541978691752878346098483992742364244651538945283388192756649851755176117008674436339141802477562657113370785965366050153646419081164727804276666081729626982849227236435365475763045531756494826283927475632372909413693958488695957485223035353199485027702213991369117378753333602583630505684126844345115047431388004569712309183991353672019992771723444608844631513570422921534960838178105796492469162589443328904422929589650955382672338245643675200802130743931837710117809444307372406913099975278935362948718765200605628245198421641803784514969765488094642119872911284143486941308540389037499000817005518706230427787342817238583239176990734544310140847155677747738046657937728647693506724603585141528621616982969824102538039885131995585365566137961905887898650567769737325738834088152881467658599655505955667071063564475504637794458663834843614153893437300317357178644383229954304189115358790024843748884653302039031070532032984908181529002747562379473008355042997077286153943012597436738615899158295222162430748288012481139216263051683109196363790426687568638519998086770269727664385729875169631062123655701066562346496278875824903558977553445644689840796060012257249890695558309797630907321128310143302843509164119438612324399019148345491759609722606000110778334851215314608211724079413619286279052432373917820284134591886316180973491679898082271166203668857870954714483911851863040989307051773332731722310492899693417754650015496140462293513896343723142578197822734290533062141434865564639462378575054003124310300618042917237976565395270507633114737869874368252203792245779424126283626330038367116195581275962257439998059461724056558879270508343672131161648376047367190511726242203813218032267506252751577520798582519696175306706787249390844877446612869420395758765617886417725521032639236424113344632397599386232031941583083937335539913628423970962055884085557440752292779261567546553965760093539233009981688790447696205869787003456072812380445295423666995156432512598727736987746729246467188174268350064653890914365069775957723998596371196902727166696531249340221408709636950312185244662409118908562911310794819732452187191952538220958591604715043765797582859450665915797098701207600232221469903709340131376719716648843784927165985134611948432293289008849960808049435026749824555701986087348518463771389829368650298853068893922248535171336774043475831903552609780379905898171314789947365712027413506131401788699353132820028389485909186592162555254883281649416751618049978170687362334379353376510535522713844098544297442509546916409586795217778715109980273002339928053037021403170698560373265082451661460532194379439058053400984689646084884271589904878217011558331547918871517203384086556517729564941364276054210153968242194002089785772153823892231542079542777815260060751197348232453877978524277229526272178500095355739272083855007299966960313060342937294279381187124900297156994620094192724923597618231635608140741751846087320548867596086031005342812623494467746779471054701937495753572654884214617556873908725907576219439836270989255973811604269277275273473485374948131057294339749824905138345452315619394656657146168303134959701403474260267644015057694494578065490066949336983101872856377003817218284885027734090736635626266725559394018018016397146305733399393123851771628431891856663842496827902081039560490822473410077483518167769020666765533439686210778280107711836897861450318796424621888051367950184833703902750578029349443672254027195913570578542610676186872144464788388548831052167470689128353044038798669336122143518559935393089796349201536006780768671990070320187827083300900340509190569436778941739039899147560799337955845894129464181798229106596736239960139263666281561601414770012064726418244586405734649970199803445886118154436528970694725994653469067783958825423539909304914473378024165790790754366977562547587765785291158174114898998812214170208438085644281150046555583584686732148544341304430575481103593399568230070280388531264757785981350757108857157267740844691027867823516922904367396563351049778322260406883486310899883106820712881011599811749108022920400538046662541930505097583252809227839376959710264045907620067223292447304688496453546119483080587152388842256158059263097721442266655085612070874856619247451272248088727261150664239771972367788761478006414149054531969471524645626521785281156335123489791364167152339033504604364601534621122554547239329098475494913294950669469442306781729855905557021758352423359154395429037722972125171252751466775082925858764355868350058507567442088141331007609294219765727108384992686623064072707986989808092956328836027749606845985811939324856601204363158890714193959124067281119586827624849947122568062851850725253212652709522213330556778184600756821905230218625623107027061429777940993630313309278321242306031148813699227962662623304850595479804971147915946570272219218193010823687679243630808791151593731929733710285669904780653732662113132178617108355888366759427305383724649165884070898091707334701431583804823638098578126592038236939452662389797904364502150701886817104222866137435706992572705751617599337992422013446813616366948640949562188149951241623410256591602886231084048380050470116181416429209719566331900955431956788335399947018245782813822993211963123815481653717864246277156299536227641784019718572242237931415352311041; a=((2^(6048*2))-1); b=597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049; gcd(c,b) Output: ? ? ? ? ? 597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049 ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.011s sys 0m0.017s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 05:23:16 2005 Input: c=44819621567671868386738640774578000100404708471382496148313375748045395480670044277056572057900663744970155149830663287465584297850081495589855993786750848570908065412304592199961984489239352710412671745258768106795475627995187998730835234096870981694057849002581668779526377992726993866670172410505308020232907411785829220529969275979815946589429831009686566189584566682735193949889620215360409489213530086882353177650027751228442587987397795405367949512485605024946590511487826483102994242339669351604424541964685064354126730108202738645876940613798812191128252573613361485748755422816156548193660782402046368036063317932737708353651778575751291572907872111644513220581451443236237476273241483207412152767053931366885048500633134679239411989176935695644467210380442170967415093347017655238114173894637965182745515945634466716222006176563265700218077827755094735511424182918292104123565954348004791367935430956816806651497925535908440687064039958235233334501803482296380935632114486715969588620648386941937928886898481643731276288013605975616463264115744066891835945049808508954439719013993163705191817802633167059077702184923901173954985947213217717811404554201431216833949740369614146371675901582741189543917848859513489243870693524207505694876737297663815836467857216917936251851255145823793933982061049982164924697848884122266125849548181058332275930408857177060044015672117460973276897894436510394800756049298182806640029505229188271900492601405137159571024755479015854243300176223855925049245011097365658897624492274984464298828489638195470833709140390928921970328211146022993174582126795125201946454837600249161978403614538564247387758487335554845347618632460608505900651942657340593338828830656385886905860721931125464389468224234319964441513613199597824302346296709153824943555274331513530631080970438168066011886888439065561346684324579365651650262364354076217860768105821824438120773135022436062793533416137981264670089983898270242189505491045171282519323213762666368931872903682871203383569280841293364278140280408262467155919864532367139281347778575370480632392372907126225443814734817258542244213109193661704157731709439953586435978340280539544493481992427687180116151608450584999165166602633752893438796424144291286346551994162748412387192923863693095888537264786666032494468271930828749708531322212486121373157204347109542690724495694364884347123495326305562359146573873555658119388306489869828014865089226491386741587768903322708987950180797008108719411373970434185686532104760980837149060509500095686818809094108011244526596270260163168723962526575503631226623665623197172295188000756177634258765850683437501683241493276790957020110085296149832887589678453130804175432769576731451540152460500894295644433506787129145043660652869902104160566500456387951917977333257467808128261410501625380353771988978673898628173963761106888482074494331132839559411389068101571252973869881978082371590031726193459108805483600564310180042240971965756023424216747266888864531094485880992458196024007054138731990327852978628065677875122301086064387083382123598692497183106831513218601312524792757387096792317521983900737996598020658997369533925818614828113365385047903743648821649850398922260392967806224043499932950308974858722764734867878330695027069963122628524124219735137339644437841409050710136555829067254576639854840202159268978938154405100673468358065633188957746008115374497492499821946301466372236670627892052062447292307350706596794058751643047997676533080013396880444933642925502056400752071497442224710174884629156240777587215460070912284972452356505397131270996566733768382819116556109339640891686944462755266391560578245422285988911718009955592983485098176115172883127922652237990044659910357936253617745823389601549912606071147130056225222596082333710820321563431354554890318139340556395928942661772238095939792859042430158001478978473272085482554540239851094826710293549613857223023870771083288522490543018030781492855961875088424559083954826752647183929743909937535222302111337228969424351812186886016318011060180755301169199533449238612930272480983776342374993547101043546608510692779768796424221636676100568962007358615394956913474349870537011241893230756976986502705670295175512407412990021418524169023644804777131353990713517952926844553960973537648965588844046616402020659567714827014921954109001019706635294110435979262730849603266180458196987311382391962717234690309018469713899163853705349614235699324042354890690040148684445785740639822367366096672436161047541932363585269373495770678479265859564888921006713887733941279506364392868064030447899555141601356880723785402974941949501832694110693732029261214750397083434297133712578286981546247927285385812700874849007856602967004459148507107326838904617241958113963170013474440573179017035018693353503512588836715723722327064167885214745619974981139265322109382043890274030128151574718537153185742256918405136806611439881770784332267327022381196247903286716467296360413743661296150463962932495625406638951626854937171823485486352151265605192691790475410269203908085568716395352897301617519769579828381756647483526271421608592942607192083273179323855619707947539844923175477753494995073132983196927627064079463348992927762827346696671477422281815011192612150823010739409006290452534031220720951506243322246698805569757921191696781138931858301993354499388343360313006754664038453951693550435244736762023001697456195586246503884074688164056378390166817984037652312645336224456536828330018366274664733008739752812527940599660468827287166909978118750507549044171966227142586869202239477059461183656504758010365956256383112407308799093937512043460643905609522416710987801572346122544126003458943664374577733921220714647718698330491483142837609667682000811610356902935031447041; a=((2^(6048*2))-1); b=597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049; gcd(c,b) Output: ? ? ? ? ? 597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049 ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.015s sys 0m0.011s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 05:35:25 2005 Input: c=2050519858899535173335110023960332278140890000455869153520387872917006502297337568121243588236050540382328854712931923025913890281900243420518133450287443741561691039033003989096784805852650478613054931536915693803691330332743734309066696805819553176989195388219872805508510121100805135039617252649193718507398042418692580698222046891493758870403502426744639277139893140954210096297094419114395430430104118543257507280552304201047869214613551233853417257712190368276966693762164332635126858591071972616823340967437728145780859902674852932127892098453744291419859142155027792309617776979830379635156927884081377244597767237213889025746871362491110563229572793576891084742836491229263017193083367079779883561075222914663535268327929886165920205868030475423669884474884186043900336958459717495956950702864764887380117209472028660239807684125263125269241484455328063342017948321417003450173838105428757919660366895526602244136226345294398160557078869729119366221386239852373406051561853698588465496051901341566702575864395658752385533253382899436008695420737269444161683337213029199362480808782889591999281973091288885132340643596116904833861798329556035536641006524600666060481944456075861011971867898720098902272700629478843641964839473948541008422981345537925379069859431560658030356930198283986247632691769963861639327868655836880752435218186746283365513088684126710702708820844347461013913039266278293106663456771915813222329777305794925988650035991316737393885321310650251570247527139836935467893049387461670872463768890954167963622906493685667300161753710042778321941584659271649617712216334964784788549232942251398434735828014450314355286895015888351568614632569578187526144615740293424553512307827802471393710937863399433548326213964678684001731443821408377059859145223615602329064071417893213815479186596407019646413120810860322980670892239572224554173523646268560996602477176906005905936020761010295150691621107983908504241461490037358872224065387733069585300499605816867218361184905196179751301494003470438635006508254481858150223486837277103603296032992027655824676997201198667917011428874952231811006950119498481694734750378788745919221219411026017830395255916003839480729014658201720108679537620411979099921486679356914176159119146138866602414665663098077102771348623902446436114754741484784859008078571574166068706990466471999333511588242947307014251001572427061921425057177651658228062519219621541421271938035638981482631967795562227800264870105032944102867481784126105556002598657098112037606496362878670032048821676229136677543183260028918077888449650908172169675764934936870597238836287613164160318984854866802703082451248874483172717770829802442010806668108571011959201764316986175129258317896458376259179086029895051388986335338919927923120526246131134968963824372278729123446321311365961196987455184591314145728716172491920306939250391029614351700333115045649341046864606745824898866902308665657354550097747606727181415062785168801054067951699903475186078372728681052548695018370513392161668647898219789879459372993861604599750962386171643250121075611046963651067326949800944302117252208266530244445284897748189843679646644858826019142684017197436734880993622733791417693605343016976867247269843096354721039984439960185606457289791388646346860025535499817733568607222356024614169769011288597604081151921684702754370657917760724215987984043744148542545758352180427654650424943349609680176246207615397690137107773067489994291383044763071945447028319817724883984205389602086430471460984870074020318021331388530081475254117419745836146685747459253946346461160308188331590982815962138293388520620148000269438575982039453368782708778828750624205456049511825955657196745479742519353917365675167986891137741192359101856935162735307919092430745655587259174866046145676456369043619761855897963367957188731494087679071784226646539434931752968294117710387083996296950173214603231907477391868506545740447275606410212548394486262680823683617781615222568665442701353542345107112396928724166184761349409724538575789850403090203013462330474994310519598115898863975288600984603399776878732921213913014894371496626131239491073419234053206543778772142424430498746413760290586445619153962827950470268869346259058714127091181837404782583054604013453055367325723591313716696315148151634433075554149406967561103214492503697013440855914203252517000899397634190641912362233694266560939727941244352965315461435321298277283982628582185672329896341024234405427128393638076580961938936116174268811822787618563782677376183545462001251137109666570398142672031755850021468576075398177476524652354393702967732160628325376599461518949937936303410466495738101481261454501933548862171914545937706817161998575677386016197321864327871843900245598474457961546910404695308569209062722829081420848549905194563672500158838919771933271384776354224022798275476258710816967965055869810778874546998810959605137715963264551618067535919394123440852020955235423400798728525873268844810510632349715773363197343331182147934256274918714038400491679796913633489878601303509689552577300303666521563625867572565901962172057534357046794220486545228167422432637841927678876368240946417582700518034328506034336979676305283766166357641497218464274427396735317337168048173559717621025395219410526259589803172718703853775119668801415659112797724149595457565419874379440963797144963002193225143227376082932119144854498947468850753832521844049346928307583801698370570295327004038351393421095398766870965574797416527829466141171742072182751186326139458995584043892448688360422616205545070916048820782695083846279727409122874419724510119718776521385075171368298508243054280701526274462827486112013610647466466502463310714877934867698623863262457171091952064486564100523844589329; a=((2^(6048*2))-1); b=597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049; gcd(c,b) Output: ? ? ? ? ? 597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.013s sys 0m0.014s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 05:43:42 2005 Input: c=2819631289451792761341016284349185657565742813689457053833617549775228550914019368510541486080406110546231614799959390787413550216547656455214741463343037691262753342166784857070568797626199413994025324334704977258122418178622603145395949690348505713550625443997512446625020092519016726066049918841404649323298768832450426327217165087785283904151918476082895725951410368099365052460525465054433082247665721037475148818729563130784120225663918477389313444404844271217198835689374699843921318232269273307438014578865106369126844519539204200205922083372455511925049018999557713238137912572877124115299551642405157192209824640089162791318255726795275423514354947562502609541090581129156811693927234197126778671430446869266733110495103650089655012685052973212200942139968103962544012398935063024269306963120291638848599283968430480630118667260644108662582567434799659701629541093978113970815162651760373956075136333485202377361911087358580838057485889294782208465132317409738466086007013887733270244475640272731525309533956210367252003919265222786567617180833148523706351313655351786685194646584918168848937325949265577335327874279629987038368969656433796119297457823420217825739982594035449140188626336910727113685890934000107856857355487702409388756969335065885971555335766305373535638699494580575901748849281601248261204696879013924841302598863287938579701784537018295401121749450481393556731803696002287891528044671293591491255159742943435728688689489212594085227300289375565275104786381376942117274715045261431401549232502085935053743739271802831862081456789224563168973956986321450994528529928105754000924339094796586551887332481120936984455690823049303419626155222186578585210001037551293920043261052740150948491005580812138865300770695677770300846505591942338080434853126345869276437929958168562758589226143305665186237835832997758167276753396284821087802742688692236787035744084375418700089588718961898194660677280041826818268526527038757524354396822224104293725215271510059140032972928236110306040788300188802640314329887120229929958191260675668772287042523499470839781456256253705733997433268594284605077865710885736813514289495303554440683257183443914748955170330471900109025653409210316513503398522877142404216323577929631660744529311487969463611726940629382927549832128531883416890137877691533016730695833238182515843405560540057331403435797614189007008241000316172432833712297944941329213895315446209646075877736377717596769442369143278873300137894016612048988429893578521850033015261324320831445165107925284720600164791418000361118720555054073177368219994209307236829716345583141047438944178050453035345643341035581353756051684161234397111112123413053508050101745392132332189011682314878321267303711957196688758439081399337435432722835700952856673771644951463701805482679332055506849569617151187649636969480337522110025209426804568619961924998318767937796941171586823112438090279756311034356778873773770216470361986730261436568333397995679248701590597808352992032277322065260538091455519313751427981062034385624865251144630267967730341510771814595797182593900985362803513601767318256663948391917284051642849447027837431317354301736928091967259918820073950084153433764416127730177253059664180937767048849448382606374885501881143018160443664368160103765973579640725995383624389074938147016418604549034486642839724870067294542350691283784076497966314235360329830415186986427717826352308590627566530396406808551144491381435422530908277082378645046516285401892557574060371004577409404907175442086242693049097478851382056251027606921263831567844551531076565201476037867685919185371999251087060545425305787258574137418462398576343987082849627645959317793761986732952733245866464312225305369525273585016945553153211166579591366633886516611351296392414985423685391586855704371602724359997804197023323894743466242267489561724874699735324312782418712423349287408586494600888280635288146993936097; a=((2^(6048*2))-1); b=597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049; gcd(c,b) Output: ? ? ? ? ? 597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.011s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 05:48:59 2005 Input: c=878309308169639279626301960148939565207947943201546301533429009989963214366505792262015990534598181138416394921456084015675173944996567636247399575547340279703410065431908045434875272316583354198824695031597675937069139183752051363675505275238267197253274641957982494109888119459275861108895327937984159397712406591020481559153549769438452938359301070850237816934635268579908447792401521497001506280297107705381608123934176121246953748618014008767630807164838794674578004707286081459855188331418887962043411840145733188758150867176972952708458270661285226470846428876782083191431940940240022689479727722348666831568901697077950022859539883604407408165300301823319431696765387630499722737274569862652573989762043505799923172980557834413074531917371966631315947912285202956054208469238516830935356580305939463114094628411896193433017793765552065535453921972743494077842415082825373424528403435470924623331797571452670448257373199117210847839369047895554628732041205610535713060346308513467178504349399404728435486284514059741697160203164701428167130223991252993586488389857369842829585521024593403550468525451873567356508261787903675456978199252167783331857127982020969747348762821050442380728590603877816525777744693921007301958094085666654868487892942844970972367410772550083003087448458476879759546775465483123527841193645520826500566765985355052700385638835612513545327653578598616123030906671400973489105141119248124022215888809460714883810345021044853025430102893267862127460058243320042969804693645030940137871964696257933828518673162777640838455933618227580848023991839361240741874794382599129181630785154857764995532861791156153394048186726129854153093100213657026875759260750189500906619994483905666114809446857049571372843502819389356090741019394583965935203510388954060380894577749300149168985752893851488109635331602996903792001692085349501007332999477290205153378484397550035414628767958434817040376061267839492867193246561798837956537536490004218678895069935354371625023649974439717798123368614520237039409461124608764948625792121837349584663556106804313209446252774881757289325277485336736939897997183159339830680168820816593198971868333836561844142428410175341467503444087502653029003930690614850666475507169622310496117314343481286268091054349120047434909359270914042789004574805116481047796166460696396605286696411221742344385170583755542680904557219957310880902053254535327256453757133461019383420079412530401094117767819958486128945283527541361958635689266705738761804787726319558095803777378160079074652341393565602111487761738312744829681198395732429179397567381802319510241735709154944321563721968791918361845324745453906026473813157772304514920465053671511451954610370482803186205441074803182054814429773551827490643526764296250027207637711639183807873513124814335837098034556745335978389725219994965121008204594024315406123785153713576291904185089718866708146849534113010334695552404472977517736933086718611622693540671211922662167685224102877241374464837166317220855353376700059320452057214384716447388271086497873222555365162126928414570314912385174381344124713502760008029191784087143642451542053644309856486539660774311374897332453148437246283061950299474259616543109625850392504674674668989253771985177303965534225839351446782858009759505683077965838921564229942098118474292593645211701463008604280638020104613388917247609567154158442650890811498826754520702508507219627495361383135868332811728391949862506286152684922761314166531102864483166247330503384278689746138520818706433937772096931382396358883361771676613125411417362978717795839005038151746688408973675490321765004824234453866013549471022758576405065169906638493846662931755170369965191844551744323800162182596719487928985564205496257002076925622048545517499083233455044110788136870631531060480603257604454199506118461240711792444745190258475297912095257778899390586212134475721076510122446685147832656624831403784611233137538414338747584910364313178030953652997187974743544008067027640918646699052426990900247995043972298963667771389734786640823070721824081822130186311060938606025251612826571305958138068225917584523893894585990443243816186556677843124855405922823090070933371641116082353837101636803442381962266025269536033756984403877589700909649942238353910685465075660095105602212640172826522530710451326460602724153610520942263491355263571404180079353384200581775007213292308308510883038429430103741822626604684358398677919438175609383139990778404366675107892204156857184950382015895147626501725925252580890634145199737196114806443741643676898538639669544351032168057922469700423813766477569551967807031889727150155587090218195219573807914927025145465377409168907110677667954129182292318394551498452484320114576758223401407228670276338512860181085779916130921794000232284777927393646144204096756914687231625629986918699890579202660022008850146817828207925663966076677251784682010465794364368772651641266486799116167930106161803990917629513002374269091092287599868587150450590048749758491171015507524124011597072313566586668137009089440416510058562935724648552218895789427149496417748441700219819763393212247640353842534106666252326760359729089528216209509126637262860995627655632798206574629517461374175160644505360988389142098262986556315972234356733533357621902827074464256238247220574058620530430169621503038911002105382357459970703817203646943451910027061042575934710188116519219792793859927001822387937136876064861707844965770844420985614655652319136019101094718061804285919718804190743365848382072127697970384138242354329292101482962273668815318245156384534212686466468730434421847264767020853598086622458933221490588022306652617334905000691229529352549259790210350487835360722734193151978442156506721257395809822369908627543008255759278323218324579540223378007942107621665982346044685496190967079442215385380590313341831442440672156792781972810512295560056461332363357454915096235193671773643315193656230629670747974924689746895450604768321033968206286455637641211362973643518147065443532395795486905541251887020716874123909199604419273228432275122445683200423413188054145017153604417664415606917579272034329741918146101887443275134296961556179730824964364549352774645471381952637404790741936395256808105112708357695370437632433603657241777312729614121746335190167546576697502059218019862348302307198262336408827868071418669091578905185491815641353939796088619553837566709814242151108279794183184736448265163569657703651198207440483024571649333449573195351485334934739490680944925757650365092458622166222151419328373453102837529751346567714966334943498516442888882078432608839198563680880632111468483319246168885767382622162504652056879251835174253560015795451555521620636167872402031474455666772066957441687583232506036321253210716311839781995549724244062977251687178601857196439421378123908554608034056385386480054445843145431685026097553402322415591181419435160696367935252484446571107842724824560744141722078414792118211682046390787183675792032900257529239283789149048211319764680936260453240574411805595318919036905999567353860862456672623957313310261451929807540470354868714279052581164650697127979580552346378869231824792402732097200240341610038067884774950627767456705695177836637186028228335855283831551617014387899914803316778016636104140218401981184493469359782890800690732880443947299753406310279650049578493254983815377531478500477324370687684070780572192559982215338280990110469241834875675694707902296209299378024604166329350402630600836685411171159011176260271636739667878004759487229332911705898735214384231905101833594814139468235830274729301800695922462055501898106746569481400126669175057531005339908305495816372936759809617481449672543915461722051021499751378412254520556327753; a=((2^(6048*2))-1); b=597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049; gcd(c,b) Output: ? ? ? ? ? 597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049 ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.013s sys 0m0.015s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 05:49:27 2005 Input: c=792797983421427888538909278001499070395744676143993330297550854944455690354015592014301661779165739675368084739244200001911497274887039216830686154824314767319557344285039719713291895196726267530875824845041612641751614967115314986350455401145048654986859947976021538770768829869177662064503223621035934515906161009745937576062999188325142884622165547253676748472676585281207318540427323854378192831776459201842702511868773000354834762126956741919010788037742961905664463216862872523590772805075392501395041960082460061253179871760261229547034667741640183056440132426071164300445002469903425745174161163388573188761680456894602997869321649443441911141569488502724449739167116926349900327345571032539584715078878457849227693643131755114235089024675473395546397091348683464513765163421994726819020303180363302871091185956133054539474271985146494047975486990292791638036565572418981341737828939397758433033592618144231488519988915736560605454588202287756191729011078361686467459258957051657572249004757745677371877403901389512975433812341425762525086676988055456735160133809132369733250731921999731808242674064845572705112321305836934896290770384984212768053771762897359320101811661866759831222587612837536836542941967324053661438464173688135554292498857090318734822307763942272813568381409656455147388307450078872031269989133511648981194502069905438246196804305507226389361142249286850761055890432195409757027759670571960721832828563122926021952766701089753624922388260548672994042028956238889850595833312185623700166397171463981003444882793620812663172971046104898356598865896936059046047289743166631855773248528751827223346281366687024807816550343042254826325222497498503388157404448358632713678846837743901524730915842756552910349135485766571215395914331515336574855693134175592767063219056353073865601910023545066270284040952215454125358598180658348205101888237366446195833868929187553635580022270107580973869676497882722375896702487120711754078550002651690952597132312946375177693270306865489868995518074428538651014870303336368787916795595848857143715071920822982163120715856043007547483107687714178751019282784371674797353823903039146221793708275256423568244082976302849523621370612853490362854826675637045830094784890835241357137149827840210825100129453947385744675593478363892405186416104562476723296839486438652389584944745934219340732712222756011559126425380661713132346637284666518625488821126285580546027598628730742597225654151019918013240962918753464131531229571336729528556668784935995364846948795095827273170560542572436432463416363078451885646819619597154892507652834391333243401011201; a=((2^(6048*2))-1); b=597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049; gcd(c,b) Output: ? ? ? ? ? 597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.011s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:17:19 2005 Input: c=792797983421427888538909278001499070395744676143993330297550854944455690354015592014301661779165739675368084739244200001911497274887039216830686154824314767319557344285039719713291895196726267530875824845041612641751614967115314986350455401145048654986859947976021538770768829869177662064503223621035934515906161009745937576062999188325142884622165547253676748472676585281207318540427323854378192831776459201842702511868773000354834762126956741919010788037742961905664463216862872523590772805075392501395041960082460061253179871760261229547034667741640183056440132426071164300445002469903425745174161163388573188761680456894602997869321649443441911141569488502724449739167116926349900327345571032539584715078878457849227693643131755114235089024675473395546397091348683464513765163421994726819020303180363302871091185956133054539474271985146494047975486990292791638036565572418981341737828939397758433033592618144231488519988915736560605454588202287756191729011078361686467459258957051657572249004757745677371877403901389512975433812341425762525086676988055456735160133809132369733250731921999731808242674064845572705112321305836934896290770384984212768053771762897359320101811661866759831222587612837536836542941967324053661438464173688135554292498857090318734822307763942272813568381409656455147388307450078872031269989133511648981194502069905438246196804305507226389361142249286850761055890432195409757027759670571960721832828563122926021952766701089753624922388260548672994042028956238889850595833312185623700166397171463981003444882793620812663172971046104898356598865896936059046047289743166631855773248528751827223346281366687024807816550343042254826325222497498503388157404448358632713678846837743901524730915842756552910349135485766571215395914331515336574855693134175592767063219056353073865601910023545066270284040952215454125358598180658348205101888237366446195833868929187553635580022270107580973869676497882722375896702487120711754078550002651690952597132312946375177693270306865489868995518074428538651014870303336368787916795595848857143715071920822982163120715856043007547483107687714178751019282784371674797353823903039146221793708275256423568244082976302849523621370612853490362854826675637045830094784890835241357137149827840210825100129453947385744675593478363892405186416104562476723296839486438652389584944745934219340732712222756011559126425380661713132346637284666518625488821126285580546027598628730742597225654151019918013240962918753464131531229571336729528556668784935995364846948795095827273170560542572436432463416363078451885646819619597154892507652834391333243401011201; a=((2^(6048*2))-1); b=597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049; d=6007168150991414346762849841018487400293912358559072057576776701050149134417831827710448536647443330075468767848894478405465223751836468899641873575786586910954816404818813101190012842462274620892808337622852554482353571409739606580869128384108992494320279836337473324497258609044942668146003558832512817263264873740812838603044249282977185816650957058493232683464630996287710302607818481; gcd(c,d) Output: ? ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.010s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:18:34 2005 Input: c=792797983421427888538909278001499070395744676143993330297550854944455690354015592014301661779165739675368084739244200001911497274887039216830686154824314767319557344285039719713291895196726267530875824845041612641751614967115314986350455401145048654986859947976021538770768829869177662064503223621035934515906161009745937576062999188325142884622165547253676748472676585281207318540427323854378192831776459201842702511868773000354834762126956741919010788037742961905664463216862872523590772805075392501395041960082460061253179871760261229547034667741640183056440132426071164300445002469903425745174161163388573188761680456894602997869321649443441911141569488502724449739167116926349900327345571032539584715078878457849227693643131755114235089024675473395546397091348683464513765163421994726819020303180363302871091185956133054539474271985146494047975486990292791638036565572418981341737828939397758433033592618144231488519988915736560605454588202287756191729011078361686467459258957051657572249004757745677371877403901389512975433812341425762525086676988055456735160133809132369733250731921999731808242674064845572705112321305836934896290770384984212768053771762897359320101811661866759831222587612837536836542941967324053661438464173688135554292498857090318734822307763942272813568381409656455147388307450078872031269989133511648981194502069905438246196804305507226389361142249286850761055890432195409757027759670571960721832828563122926021952766701089753624922388260548672994042028956238889850595833312185623700166397171463981003444882793620812663172971046104898356598865896936059046047289743166631855773248528751827223346281366687024807816550343042254826325222497498503388157404448358632713678846837743901524730915842756552910349135485766571215395914331515336574855693134175592767063219056353073865601910023545066270284040952215454125358598180658348205101888237366446195833868929187553635580022270107580973869676497882722375896702487120711754078550002651690952597132312946375177693270306865489868995518074428538651014870303336368787916795595848857143715071920822982163120715856043007547483107687714178751019282784371674797353823903039146221793708275256423568244082976302849523621370612853490362854826675637045830094784890835241357137149827840210825100129453947385744675593478363892405186416104562476723296839486438652389584944745934219340732712222756011559126425380661713132346637284666518625488821126285580546027598628730742597225654151019918013240962918753464131531229571336729528556668784935995364846948795095827273170560542572436432463416363078451885646819619597154892507652834391333243401011201; a=((2^(6048*2))-1); b=597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049; d=1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441; gcd(c,d) Output: ? ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.009s sys 0m0.012s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:19:10 2005 Input: c=792797983421427888538909278001499070395744676143993330297550854944455690354015592014301661779165739675368084739244200001911497274887039216830686154824314767319557344285039719713291895196726267530875824845041612641751614967115314986350455401145048654986859947976021538770768829869177662064503223621035934515906161009745937576062999188325142884622165547253676748472676585281207318540427323854378192831776459201842702511868773000354834762126956741919010788037742961905664463216862872523590772805075392501395041960082460061253179871760261229547034667741640183056440132426071164300445002469903425745174161163388573188761680456894602997869321649443441911141569488502724449739167116926349900327345571032539584715078878457849227693643131755114235089024675473395546397091348683464513765163421994726819020303180363302871091185956133054539474271985146494047975486990292791638036565572418981341737828939397758433033592618144231488519988915736560605454588202287756191729011078361686467459258957051657572249004757745677371877403901389512975433812341425762525086676988055456735160133809132369733250731921999731808242674064845572705112321305836934896290770384984212768053771762897359320101811661866759831222587612837536836542941967324053661438464173688135554292498857090318734822307763942272813568381409656455147388307450078872031269989133511648981194502069905438246196804305507226389361142249286850761055890432195409757027759670571960721832828563122926021952766701089753624922388260548672994042028956238889850595833312185623700166397171463981003444882793620812663172971046104898356598865896936059046047289743166631855773248528751827223346281366687024807816550343042254826325222497498503388157404448358632713678846837743901524730915842756552910349135485766571215395914331515336574855693134175592767063219056353073865601910023545066270284040952215454125358598180658348205101888237366446195833868929187553635580022270107580973869676497882722375896702487120711754078550002651690952597132312946375177693270306865489868995518074428538651014870303336368787916795595848857143715071920822982163120715856043007547483107687714178751019282784371674797353823903039146221793708275256423568244082976302849523621370612853490362854826675637045830094784890835241357137149827840210825100129453947385744675593478363892405186416104562476723296839486438652389584944745934219340732712222756011559126425380661713132346637284666518625488821126285580546027598628730742597225654151019918013240962918753464131531229571336729528556668784935995364846948795095827273170560542572436432463416363078451885646819619597154892507652834391333243401011201; a=((2^(6048*2))-1); b=597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049; d=12752440873419489391897458677832898035627230401180699332150046969714889979343844664892436417260660294360761928562077702011550204581356516164006418243061278233898108937461759698236434350412400326341621878255795749707059838108915261119331262061956559082433330970066419549047734972679954925896317663334810476085019511870297813056105646947316076538612187258932230711995821698189257958946536065526575655107444070765093586653951197935458275093103359443409091722547597769677534713485104718008379224534230013996596220534196195581370924267531408445232701996917561815585949799717926388313752210764111102911875910472015755272432573394977855275252392472517248065708152094409802725684411156375478285865018507676168303699275565972544096864866309613556656924031041314690172701904353953427335804957105040426834268921033807988010028831462252499921054282384118863897376316395189851298636265540138256715924757559362826186652408017410642044823909212189158229993749875846037736216883236528328244687820102369644567308758692365726416094852082212368172445934117203405544670110928719962447306221253249593836880723360623070096974211138215411502860552870997468663477368616174640601174863997854170707336998140971856685746013663451419869224592765771894342581740535712793112917814673943773678447722668944867307859760146395753102698665798595456982475925031684654670338470074700746947122353073790679187428831350881485756773936206502398962751541091754971052672586941784829843899074389326685913665285427803116013416882223058492674461120384533722520652927841739428451748257553923511493403275870781990765456545584293065657224838235365145714281478172968630645666137763801790182333988604527405274717884798971666236100482433992217959954463980671759988805456144924935360917226246044586667253854694556816677813295819256774908734939749173519271119707663280437517984782685125270225055764465590556031020558866766272122062460591336651255834506656032080339454653042641453119848939061967479398396761442418105624535620993304301526818643915033631384439743562887857495624930862521580060390239982656460767608438271376238117661276962373117221404581191057941763530765061238781858340350256942734617371977074150875829315448016355103033666378376887854080699725159110098602624649960087456712169260968376936948355609325245489527237669283651461890797032611511353304213826044586265547425548971216928586050468991001998764858407297208331703072949938987051716978220622751478077918698016026809524985123841042317950444158537749623542685183297670605916727118235414226192746436769667859823107641570121722074714811088045675466788198681555707920443477946547417635850270370859952723785862021118928558913214503554577353301425281202773255282735667502526794445082046783129482301812282944796663133910443451932327736425892945494536394147437626823105495581043384188654360293237365267524631242490935529305655854208362914253741334357027486604138026075929364242708420538352216638823861877088924576154516505056043986713808257739663600740663075559905032233490321420295611112709510847674381766415292708645592469024538537315105086027721242587625364699173617727450719721993121242190637865973695080388629751203011847077451193935374624525470724639074668209409340085676347821218349413484607917433062383403919689103237686902742418688844555281740061844968586153839729124239581800871968742148598517880323011114773863632314359359292124398385426699216136241321625518795753757108678482060395754727104705435649632774150755945782646314486764773382237626409231516468427024136297066523954736677621717896572035429706613180469137842383529778204491374095748343498610617303883572207542263309316242523923199109969604342738338079674042988502459520507782241799366813450822434284345433813986594229157980592431015251344432243025865489841511513032633070215184274342411036874589090916187569139452664555456206830775503371898747651274248091014115332420723927716955616340477354021405100140231671213862027325217730160114737850064047071426493331479958517587479748750366265718330322562429737634804117768571232168609339320583030015377642994559355139308015408365810832640204554855693095275265851856324138914301027430223223413731659147058773409743860546783423276193063370056991009445725339982343738580587657336863401264151429345626320741659738969222532795182020623771672765052470087211995859103379698893002261569674262205343492226530223318165420138638936316627721666062162262792627070036620753167447381493641836054628009402657405840119521481441599719061031034687542250535612159069726213983013510925949545119417069438392416910236147860926344834358508207050814338543476884290032207774716639984566681413338317869290912885250883416077203853564210553598402202973433565911760733062446328539064444577699838811890346645408959044048698449959889895426349776406811462984673683376053639333241766149055946252272683186081058751299311097510927201694988822693364634058932317664084493462204766849920703099485187350009426724639438230023966110076190564608167407167778748535625378879802192617629669762115208415071541933040173635135579285839140659394603031719747679095489587782665698180226674879428781910879252068217552999125141509587667282883942577691255594373818667531922961369140229726243629121; gcd(c,d) Output: ? ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.015s sys 0m0.015s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:19:19 2005 Input: c=792797983421427888538909278001499070395744676143993330297550854944455690354015592014301661779165739675368084739244200001911497274887039216830686154824314767319557344285039719713291895196726267530875824845041612641751614967115314986350455401145048654986859947976021538770768829869177662064503223621035934515906161009745937576062999188325142884622165547253676748472676585281207318540427323854378192831776459201842702511868773000354834762126956741919010788037742961905664463216862872523590772805075392501395041960082460061253179871760261229547034667741640183056440132426071164300445002469903425745174161163388573188761680456894602997869321649443441911141569488502724449739167116926349900327345571032539584715078878457849227693643131755114235089024675473395546397091348683464513765163421994726819020303180363302871091185956133054539474271985146494047975486990292791638036565572418981341737828939397758433033592618144231488519988915736560605454588202287756191729011078361686467459258957051657572249004757745677371877403901389512975433812341425762525086676988055456735160133809132369733250731921999731808242674064845572705112321305836934896290770384984212768053771762897359320101811661866759831222587612837536836542941967324053661438464173688135554292498857090318734822307763942272813568381409656455147388307450078872031269989133511648981194502069905438246196804305507226389361142249286850761055890432195409757027759670571960721832828563122926021952766701089753624922388260548672994042028956238889850595833312185623700166397171463981003444882793620812663172971046104898356598865896936059046047289743166631855773248528751827223346281366687024807816550343042254826325222497498503388157404448358632713678846837743901524730915842756552910349135485766571215395914331515336574855693134175592767063219056353073865601910023545066270284040952215454125358598180658348205101888237366446195833868929187553635580022270107580973869676497882722375896702487120711754078550002651690952597132312946375177693270306865489868995518074428538651014870303336368787916795595848857143715071920822982163120715856043007547483107687714178751019282784371674797353823903039146221793708275256423568244082976302849523621370612853490362854826675637045830094784890835241357137149827840210825100129453947385744675593478363892405186416104562476723296839486438652389584944745934219340732712222756011559126425380661713132346637284666518625488821126285580546027598628730742597225654151019918013240962918753464131531229571336729528556668784935995364846948795095827273170560542572436432463416363078451885646819619597154892507652834391333243401011201; a=((2^(6048*2))-1); b=597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049; d=12752440873419489391897458677832898035627230401180699332150046969714889979343844664892436417260660294360761928562077702011550204581356516164006418243061278233898108937461759698236434350412400326341621878255795749707059838108915261119331262061956559082433330970066419549047734972679954925896317663334810476085019511870297813056105646947316076538612187258932230711995821698189257958946536065526575655107444070765093586653951197935458275093103359443409091722547597769677534713485104718008379224534230013996596220534196195581370924267531408445232701996917561815585949799717926388313752210764111102911875910472015755272432573394977855275252392472517248065708152094409802725684411156375478285865018507676168303699275565972544096864866309613556656924031041314690172701904353953427335804957105040426834268921033807988010028831462252499921054282384118863897376316395189851298636265540138256715924757559362826186652408017410642044823909212189158229993749875846037736216883236528328244687820102369644567308758692365726416094852082212368172445934117203405544670110928719962447306221253249593836880723360623070096974211138215411502860552870997468663477368616174640601174863997854170707336998140971856685746013663451419869224592765771894342581740535712793112917814673943773678447722668944867307859760146395753102698665798595456982475925031684654670338470074700746947122353073790679187428831350881485756773936206502398962751541091754971052672586941784829843899074389326685913665285427803116013416882223058492674461120384533722520652927841739428451748257553923511493403275870781990765456545584293065657224838235365145714281478172968630645666137763801790182333988604527405274717884798971666236100482433992217959954463980671759988805456144924935360917226246044586667253854694556816677813295819256774908734939749173519271119707663280437517984782685125270225055764465590556031020558866766272122062460591336651255834506656032080339454653042641453119848939061967479398396761442418105624535620993304301526818643915033631384439743562887857495624930862521580060390239982656460767608438271376238117661276962373117221404581191057941763530765061238781858340350256942734617371977074150875829315448016355103033666378376887854080699725159110098602624649960087456712169260968376936948355609325245489527237669283651461890797032611511353304213826044586265547425548971216928586050468991001998764858407297208331703072949938987051716978220622751478077918698016026809524985123841042317950444158537749623542685183297670605916727118235414226192746436769667859823107641570121722074714811088045675466788198681555707920443477946547417635850270370859952723785862021118928558913214503554577353301425281202773255282735667502526794445082046783129482301812282944796663133910443451932327736425892945494536394147437626823105495581043384188654360293237365267524631242490935529305655854208362914253741334357027486604138026075929364242708420538352216638823861877088924576154516505056043986713808257739663600740663075559905032233490321420295611112709510847674381766415292708645592469024538537315105086027721242587625364699173617727450719721993121242190637865973695080388629751203011847077451193935374624525470724639074668209409340085676347821218349413484607917433062383403919689103237686902742418688844555281740061844968586153839729124239581800871968742148598517880323011114773863632314359359292124398385426699216136241321625518795753757108678482060395754727104705435649632774150755945782646314486764773382237626409231516468427024136297066523954736677621717896572035429706613180469137842383529778204491374095748343498610617303883572207542263309316242523923199109969604342738338079674042988502459520507782241799366813450822434284345433813986594229157980592431015251344432243025865489841511513032633070215184274342411036874589090916187569139452664555456206830775503371898747651274248091014115332420723927716955616340477354021405100140231671213862027325217730160114737850064047071426493331479958517587479748750366265718330322562429737634804117768571232168609339320583030015377642994559355139308015408365810832640204554855693095275265851856324138914301027430223223413731659147058773409743860546783423276193063370056991009445725339982343738580587657336863401264151429345626320741659738969222532795182020623771672765052470087211995859103379698893002261569674262205343492226530223318165420138638936316627721666062162262792627070036620753167447381493641836054628009402657405840119521481441599719061031034687542250535612159069726213983013510925949545119417069438392416910236147860926344834358508207050814338543476884290032207774716639984566681413338317869290912885250883416077203853564210553598402202973433565911760733062446328539064444577699838811890346645408959044048698449959889895426349776406811462984673683376053639333241766149055946252272683186081058751299311097510927201694988822693364634058932317664084493462204766849920703099485187350009426724639438230023966110076190564608167407167778748535625378879802192617629669762115208415071541933040173635135579285839140659394603031719747679095489587782665698180226674879428781910879252068217552999125141509587667282883942577691255594373818667531922961369140229726243629121; gcd(c,d) Output: ? ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.038s user 0m0.016s sys 0m0.016s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:19:37 2005 Input: c=792797983421427888538909278001499070395744676143993330297550854944455690354015592014301661779165739675368084739244200001911497274887039216830686154824314767319557344285039719713291895196726267530875824845041612641751614967115314986350455401145048654986859947976021538770768829869177662064503223621035934515906161009745937576062999188325142884622165547253676748472676585281207318540427323854378192831776459201842702511868773000354834762126956741919010788037742961905664463216862872523590772805075392501395041960082460061253179871760261229547034667741640183056440132426071164300445002469903425745174161163388573188761680456894602997869321649443441911141569488502724449739167116926349900327345571032539584715078878457849227693643131755114235089024675473395546397091348683464513765163421994726819020303180363302871091185956133054539474271985146494047975486990292791638036565572418981341737828939397758433033592618144231488519988915736560605454588202287756191729011078361686467459258957051657572249004757745677371877403901389512975433812341425762525086676988055456735160133809132369733250731921999731808242674064845572705112321305836934896290770384984212768053771762897359320101811661866759831222587612837536836542941967324053661438464173688135554292498857090318734822307763942272813568381409656455147388307450078872031269989133511648981194502069905438246196804305507226389361142249286850761055890432195409757027759670571960721832828563122926021952766701089753624922388260548672994042028956238889850595833312185623700166397171463981003444882793620812663172971046104898356598865896936059046047289743166631855773248528751827223346281366687024807816550343042254826325222497498503388157404448358632713678846837743901524730915842756552910349135485766571215395914331515336574855693134175592767063219056353073865601910023545066270284040952215454125358598180658348205101888237366446195833868929187553635580022270107580973869676497882722375896702487120711754078550002651690952597132312946375177693270306865489868995518074428538651014870303336368787916795595848857143715071920822982163120715856043007547483107687714178751019282784371674797353823903039146221793708275256423568244082976302849523621370612853490362854826675637045830094784890835241357137149827840210825100129453947385744675593478363892405186416104562476723296839486438652389584944745934219340732712222756011559126425380661713132346637284666518625488821126285580546027598628730742597225654151019918013240962918753464131531229571336729528556668784935995364846948795095827273170560542572436432463416363078451885646819619597154892507652834391333243401011201; a=((2^(6048*2))-1); b=597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049; d=156426253202426171708365492774858828214315868209092743306592016276199046762296420758599244630288704173377309828822902202404612411204898473152329438445898533879573962085107402222401614862688394370855210228243767321342735679167923251619131988132542067680281578743215527712742384238155998074075873483832998125592209115986776600013435345919361474005237139465541009869593340065532892994706088065472028905878308702633102544543838228263021263791393172973435922560942117157088330877655309127675362986968411295820622936832787478104223456260805946353393904537181061757659971176149630641484870750057109580233289777931147767661218050305104090184582168743710144858205075356129274052342981591928388765882248998422915429199800111754411855646883499890766677007608986811878308507068054160556705301950039093176221111896143050152450141126736105320492487009621632738061068171956464487373395910431985286562845708165908937526675986515659361385128821259935780050413676290922143134082367569795540734238082875727763902034265014844563746363427457372983470379549633306638264551109637730803484395381398144203010615775318172752266664985430825057403024960285258333738316209964139968210019662205320294284180798355474538954198641456006924151213861554752948067282216367218989736730395426526889604963049318921315172457288598617296910250529755366824635244686820050176190747037436206100946602972153063736870756363700602672113644857206713767217942840816428426118487344877617970262718243094979721114820487002704503919023509148985689049968577500060131800826667023293040366214809542408927798245175819048260211878246654849854137145145152694066082003192481827010257023828621786217391352228585992339998230172785350250940107273787546416395439893756852371488860837188157364863920078232433847729551728606646344917630631331863451623061222502221318800371248148795763724332104599443437732145310247854301424706462168285339289382196068446196843696638872029136763078208798598392198547848027277670843884359586781004178281192696788010754198841926257686383497003990825593132135051106656823068358890721054007545520820921240615855446631267795261799383124571943254232432614017674057219499146470046513248367860420028492636100453259861919190917448007746864583795404332267664793842170976072211380538682476156304181836565324386167267191603124792186489104257067010824301044270670651404884396870542750492655378393736528480981697194943306936567785185975872466184927794822691456584762637905790301331631306603580747444262705394055303386917619250702089395242895512870778581864170066605504147081510254532251421027236728454078278976174717402849375501698219491924619364306422250138728631947106759244392632780774994274720162640925248236798456778979283277106960781861000517325618589644228162221661840447429845341005567979518489037192016988626572054917671820247296947826484301417826043066499431340963836045664038979800150079355305123584143043245333334754293540781703718273950115595448777654169586073259630050509454065249531342101445608459935612302697210933392344188922706667046499561241288325551943020288087668222291401929330044021017379990249493258191559014227573262710790362035166193711688605141108884531495510299803907472239090963516781903536178668713511557788965991231833790035532970678201099758782356665382799834003760101587193858289234025955471540285888335129770963011721855205698113588854519539625964392915406926593650475086013702478773088537352336230937109961723394685258844628057362614603913627089544228173134397029649430224166810115387479387585528130393543951489420415230105268450260860745455288310571130699583414032024918813391368757129789388703147365808771746618342958563867401713899005180406132640004878271767242131304250311480643626815377562144689126396726540097328794040569801498855202767149454283072341513998887847510498220569698617282615888671979062026309649819084918173704646929372097025996332663456460803613942654981684839170176142642339252239369206284004551893542163717192388152910678414835195394267791105535998481995368127160003719373391765209446633892827151903917609570237500935444374892677139307199580377211814575281249404791395685190945194969621330337157834544570773600003191452972435138382812513042979637704468386893513241140060135379571626202424485572243145347910487324152283298257261894892371874133956973556042542289593812955367189714302826981713974582708950228548105960779611540829079949296206798779172966170933929039013594513875901106114835005267822292749885634281506383897836958395160793803183943127598700156680609050436028847033988121656921534730242532583680079231286106655860960187966876426313880430944106697160585123016549707964156001314808490241; gcd(c,d) Output: ? ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.017s sys 0m0.012s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:19:56 2005 Input: c=792797983421427888538909278001499070395744676143993330297550854944455690354015592014301661779165739675368084739244200001911497274887039216830686154824314767319557344285039719713291895196726267530875824845041612641751614967115314986350455401145048654986859947976021538770768829869177662064503223621035934515906161009745937576062999188325142884622165547253676748472676585281207318540427323854378192831776459201842702511868773000354834762126956741919010788037742961905664463216862872523590772805075392501395041960082460061253179871760261229547034667741640183056440132426071164300445002469903425745174161163388573188761680456894602997869321649443441911141569488502724449739167116926349900327345571032539584715078878457849227693643131755114235089024675473395546397091348683464513765163421994726819020303180363302871091185956133054539474271985146494047975486990292791638036565572418981341737828939397758433033592618144231488519988915736560605454588202287756191729011078361686467459258957051657572249004757745677371877403901389512975433812341425762525086676988055456735160133809132369733250731921999731808242674064845572705112321305836934896290770384984212768053771762897359320101811661866759831222587612837536836542941967324053661438464173688135554292498857090318734822307763942272813568381409656455147388307450078872031269989133511648981194502069905438246196804305507226389361142249286850761055890432195409757027759670571960721832828563122926021952766701089753624922388260548672994042028956238889850595833312185623700166397171463981003444882793620812663172971046104898356598865896936059046047289743166631855773248528751827223346281366687024807816550343042254826325222497498503388157404448358632713678846837743901524730915842756552910349135485766571215395914331515336574855693134175592767063219056353073865601910023545066270284040952215454125358598180658348205101888237366446195833868929187553635580022270107580973869676497882722375896702487120711754078550002651690952597132312946375177693270306865489868995518074428538651014870303336368787916795595848857143715071920822982163120715856043007547483107687714178751019282784371674797353823903039146221793708275256423568244082976302849523621370612853490362854826675637045830094784890835241357137149827840210825100129453947385744675593478363892405186416104562476723296839486438652389584944745934219340732712222756011559126425380661713132346637284666518625488821126285580546027598628730742597225654151019918013240962918753464131531229571336729528556668784935995364846948795095827273170560542572436432463416363078451885646819619597154892507652834391333243401011201; a=((2^(6048*2))-1); b=597433735206384495554141005402498707350142922602347545358470613380999834505424853248666034082684181854558879163438729186759710467385584659471308549415570394581106579002613482847145987404276420898311463928260449402151805553239706779274516233279851449099910062508924177644810384076629287172527076575661133481890901013686428232413504212333512329099030917299953285974692303044933831674675241984646972692573197993136051078187793828965294959629384284934051139939820269229418266212413024102837092063866035057009070413844551779360993141266532094022969206745914856566574508516026145157589725172967955292215987627441237182685332283687749564087351669277629196195764173553780431835719011760190343701078030231695952576187344216886815855616581187322889365276510828775075692446716902677172422536125509516202232714376452091111000762975280323042876942838689731067726633349213238845176396022773277334425436674332925925020743334544267140496427889981238115503318101965930078040972024929421901233956394571019186552019112302038621058117988209669848703843324965387408796282913338557860542537014239972898257575726985873580415732561068951811390981978891606452005959022270586592930859400370009650936203970162638116590264694809011058714824242919551304186264574334215519761540961637131262101330406588934703813033628108376294804971981883389161253676338821617200793797771144902494305093578048080214252402268798339957103167011894177939671406238559832330884882367926397870400434120801245684727746660704204077298870183050921046583353174844173676295937560873106941222321211442665869266820112892347210306976320443811996694357827493719786212508437374913197739492117899153707032403077605729463978413967903384893428487842503388274397091213347821059833784972649229686693877916908555323733331734993685834933271051653537955726402888683740721035422278864669765007704636651590737490807650689104765680211791377349265073653514244660589658738848885468912426758380690261914988054447885157039628116348262888044003950096276575509742514979243079002660460234588883008884504114055066920946111131846230427265454206414530521050039559710274419474765803459757960640648440799179828589378717787135134535510758428910871662187574869080527439534037162526164906223169393680804278379210545562645154853759597452532551552562970303596614734999348999393263454391376679336240311336564382064982802830312433477963764354158091891348970339643492330055735488269899323635608174913824512198074771875089431016778346871027181168097961474574813373425919902384463855389542213263055953193604661890977444683451766531408127218111222049; d=36908148345776022749280107983609692993793777434044953106354403035231897449210478643871412823070148459476047072991757120730365781919121924464051221018403832233423061268210196474007309675590200851788680161808491602780491791172607323887077150656042927999964187910699094723814542389226524505407175324048834332504934667732429249839438566481862224909832956590257907065531261889599847606165131478606639427626775666846500672797362762724734071648666394661489838882760790271763111242555888955131860512334153692515598000812452871183394483969; gcd(c,d) Output: ? ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.009s sys 0m0.012s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:27:38 2005 Input: c=792797983421427888538909278001499070395744676143993330297550854944455690354015592014301661779165739675368084739244200001911497274887039216830686154824314767319557344285039719713291895196726267530875824845041612641751614967115314986350455401145048654986859947976021538770768829869177662064503223621035934515906161009745937576062999188325142884622165547253676748472676585281207318540427323854378192831776459201842702511868773000354834762126956741919010788037742961905664463216862872523590772805075392501395041960082460061253179871760261229547034667741640183056440132426071164300445002469903425745174161163388573188761680456894602997869321649443441911141569488502724449739167116926349900327345571032539584715078878457849227693643131755114235089024675473395546397091348683464513765163421994726819020303180363302871091185956133054539474271985146494047975486990292791638036565572418981341737828939397758433033592618144231488519988915736560605454588202287756191729011078361686467459258957051657572249004757745677371877403901389512975433812341425762525086676988055456735160133809132369733250731921999731808242674064845572705112321305836934896290770384984212768053771762897359320101811661866759831222587612837536836542941967324053661438464173688135554292498857090318734822307763942272813568381409656455147388307450078872031269989133511648981194502069905438246196804305507226389361142249286850761055890432195409757027759670571960721832828563122926021952766701089753624922388260548672994042028956238889850595833312185623700166397171463981003444882793620812663172971046104898356598865896936059046047289743166631855773248528751827223346281366687024807816550343042254826325222497498503388157404448358632713678846837743901524730915842756552910349135485766571215395914331515336574855693134175592767063219056353073865601910023545066270284040952215454125358598180658348205101888237366446195833868929187553635580022270107580973869676497882722375896702487120711754078550002651690952597132312946375177693270306865489868995518074428538651014870303336368787916795595848857143715071920822982163120715856043007547483107687714178751019282784371674797353823903039146221793708275256423568244082976302849523621370612853490362854826675637045830094784890835241357137149827840210825100129453947385744675593478363892405186416104562476723296839486438652389584944745934219340732712222756011559126425380661713132346637284666518625488821126285580546027598628730742597225654151019918013240962918753464131531229571336729528556668784935995364846948795095827273170560542572436432463416363078451885646819619597154892507652834391333243401011201; a=((2^(6048*2))-1); b=533382613945833573221243962086602384259629570437891726818853280842947366065471351560750189788300083919209666083839444033189126439947601806024975094234649030318675430710657994643517032160286925168684304743017004289246611555949220030929584532116367740679862292624908487117838663095526978972108422605736750948718806964186179869837928266153824012109285728325551445924526403455204553239288848757179991337051618880085145841970851163345009648264821965788316611977777662114756877491266178514095437103227821847257465520152122653126645584872193549823713867829136654312060757526625792908701419381341024932620312657518753277922477576364949238560040365021301206906648179670620301321831446295937119246652662584942557402334526373365970249791287930812036688231474327521068922076126802092283616083818481078468828053682366919146317393265044870945863507101354659232129677020326286721119158324323158615961988639141341973362542727236721131916929778293750568353199395431127479154569407893615510159662754884556689634673743191599363263858624919654553821039473673062425990917384650990654951779828491304736588873874522519563831065599516805372617159464922263358534830284071846575836727820131811009042609889795472820861007744117733660314167953829633790277702707889089168309969850514831527460308794247457217823666910958571564269834926888134971411300719161065133922865333124075803322710815931448794127282143541013507734381467234520531909776253206693033115334725516473752750597496319734515043472272017957991559594534295515221904048823284453333538445413026502878822856740651063031547495894667970940026049862864363103556163550110059432576394029582091048721103863431740328814644207912604705437940739070711034860087121567306967234771762517152374759398029629933603152765395449587185861316231547628714431726239762711185431416673529227324961146031701841171127178656762491186995307422837761125045648810754700433225046702749714727664527919896624578043163203963945371818067889582648631176786414557687948596305182435339337932219228711131752480449884033318368963454504379270818005033533170132664824203854857029445837511582336578921899746755223540267646839305721926784799630021934126963321459632959336351195107559290323959762412547454860260944834130621275130282719086801410039998824567613340332928337858258080365254716789122954844229859100805277308812115813080460138032615336029771233041578857660411802599211911337253977053601734106578309860785345062060010043575437511786837698094857074073375703881643558855048230999943229639601046700539339068606794863611445771725595638859679280559912719602684083637664166639850535559683056024511070077720739396784865047219151721059750990539238418437705188773603776442503032356596352431087533337770977036147586738967560559695061308705692124612548126697507912375865971723350945365753439589862827154322732651591973219885355206126828961619557575132291148785645783231199785410507243675730846401273827942253980345525772454063100625427102712125242759303428016835722769251362807671756853944998300453773031548836225698200462500344948077944362898557432271789139699612334155168062110173938202368256149572314509072894661551031402359011540621772435427844542884893562626839975030526904997565021677889975279877866837153787139736431328007170549751027359233316547289458197091769936822590407186607590257187361855040126565267512523313278296811032869517564490393332536226296492471372666924131812161063968833574776221743313155581358546622455092507201; d=36908148345776022749280107983609692993793777434044953106354403035231897449210478643871412823070148459476047072991757120730365781919121924464051221018403832233423061268210196474007309675590200851788680161808491602780491791172607323887077150656042927999964187910699094723814542389226524505407175324048834332504934667732429249839438566481862224909832956590257907065531261889599847606165131478606639427626775666846500672797362762724734071648666394661489838882760790271763111242555888955131860512334153692515598000812452871183394483969; gcd(c,b) Output: ? ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.008s sys 0m0.014s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:28:13 2005 Input: c=2281143677455199587340451421441909037765990224052563037066075916944356380452059178385046267057172766396569505123947454574898793702146995027276331510842180603174569552269170556492368073610534331890285660275624547253038969878071591188910642657694479980681198227910711536773047701974592412430963169424499830676333518217397062208593164104493475117871402623057626498345544974420246960610672388452993186524654237980009560838792600305808472995155153869458910689909905306407700115573656244082891502347843922573705994293799990930133927407718060228899051043926045340557469544113468518442571372432795701311666181755122963865364041379322727382207109775017185744952665868268353809829828008172471482236403799609905073207706517370049514844351338148611481241885048502630580207646417332546225228614179201314819302710831387670386707401624899509469624721796143404392025317183340528787233600485238388808089873194293123500711870542578756250459367586133450631550446369402423629522841114843631533383757857607765215041792135887528792386169948083070953413916917692172442785916393406335388926793178059324450610277850504151563003406194219318926609808539693254477071404791745441270858200060436950099654062209322867618097052846092359322751028681571951338999018137277267496819564013926572766384445215791612577807220790618946090055320087319416096890647131035843586532684068356450475227936112233762839730416897351840379465540244792186265037812383757825988882020672194490641922786044756700068734785101707950507597901031413378341574074911527678619264046897515142208735812903341394850533237046100717977093848270058842312160329221701524862350766920069610178364451075906020222056119340309167819054559636225484975506635515363720305103744017305217066569687552986672309742508724027411455377335999612122249985157662687452838624838030367593340260212093426809562856500108851069366768107982007975137204649325868638591577253254266067503523747726694485957922282550928185296668885526738798464536715067996255813325277660584781026389755064732840666961194176311194520470097471131757789603600855024456115266341263544033342156230596766527325452921611246784322717476915802174645580506465510903523199002338472750965848740590148762109594813210155545209071099593270881095137341855799251458488179935407700166047484359213627042773494861335499066224873040695962492699667016781778983372325301612429099386910448548156743848485084277732348917928747672612682231622698741908490619864057750593218996933758141021560659851138414166640487277209163743059065408456905225823571357113805541596284367750244238579315002348497385003806069661438838028267768547173409103143136465896828647425249684340843289797902817638704622284331400370829649626542072726340605726451405764607624883814265135926851879620251120868186207236377089838374504010047380318123607746397683894668285017907846386890038400052380187337121259060032177460728064528281608780210173474797587772146835129554317376926727928260625068413946491744531275502657777581626113327377239376807592655907848261914852096591452889756698902424899592163508106996069328264038806607080989873750872284981649264655091118636743674935290079799726514234630689300665633740229647537182148994594211429906815760743484369694137179029667218762204996259411150919174452650769395403021831095887373387824933752260792830168747910695447827764493440667262570152196266954339845576957176957236942989185806791144048413646581753961908333361036709140488144750879697206538655334106212609724456068977851331853272840689933383644975226543288476765112980084374956317067623314195866565701673789650056620170281929007155557005284912974974526435404645722040741172290939749035231305904696783191642541070837607523604258575725747271092184598666999644965438914557948047997453550866662485991141625861942776478831463996667291273374905793584405432789398730150892481912225443725137502858219344520496744574548559716383204638618201317509584134337716397298236474377985880139783970250496199941602070031213750496402990969289742329006677940437521343996723672361448452220799211842634675345586478497583152419967521129793938372564222875483134271319405254157669058019504720496858204885620945664802925848507928936933514310171255433394431086906256589346020951640224809784827146118916607763644021775778362308006925437063503672218585998593779265810269300342200891125284771666593436372769539142356342205933130941678758171975541439036987535647917738620408881823520740695135169565795658409524207113759247352820990322014365888267452425464021554207108139169170585416719494423033823055963114041838135545129992419058709821542627908928873450979611160747974996592319891274181202106925993385064130808013704032207614578705883177986094486463268875647464831540002570233508872936090554026966344997720094508795967710187294210517429605086054498093974460619666807349356748961439186988577777494769300845177452052954119480967018641528067064166826918806802330757544632346651063358108512927292867292180271869841408580718744663316432622462959439895097001065053076416427384071922774954590725165804886677904741860197569103607821070045888176393917890890446766992450282872175391334989554656302756998488938428379309970368760349293968063523039299834905592454626576157313066258731433813501300247900588778464972528447833512168102423696311843538460101814738763332846686560326156624658656059628734982117575653888669950022611780949375373375365642151289535157575020855885093801431179294153895003268801388014603385462625386072478550081412162875464276823948296327358064121365774669924825633208130035645906008038843962988508424785832427605826235478552475790105014072409073577857517851574067599797130516570864206162062427465265253659127228009939041887596075845239430894994737994826996415868373970239984638020720710472436526027958724254547586542986783533247772162387103442266795745875759335905330486522597595512051191438947703227810518103927660150054560769; a=((2^(6048*2))-1); b=533382613945833573221243962086602384259629570437891726818853280842947366065471351560750189788300083919209666083839444033189126439947601806024975094234649030318675430710657994643517032160286925168684304743017004289246611555949220030929584532116367740679862292624908487117838663095526978972108422605736750948718806964186179869837928266153824012109285728325551445924526403455204553239288848757179991337051618880085145841970851163345009648264821965788316611977777662114756877491266178514095437103227821847257465520152122653126645584872193549823713867829136654312060757526625792908701419381341024932620312657518753277922477576364949238560040365021301206906648179670620301321831446295937119246652662584942557402334526373365970249791287930812036688231474327521068922076126802092283616083818481078468828053682366919146317393265044870945863507101354659232129677020326286721119158324323158615961988639141341973362542727236721131916929778293750568353199395431127479154569407893615510159662754884556689634673743191599363263858624919654553821039473673062425990917384650990654951779828491304736588873874522519563831065599516805372617159464922263358534830284071846575836727820131811009042609889795472820861007744117733660314167953829633790277702707889089168309969850514831527460308794247457217823666910958571564269834926888134971411300719161065133922865333124075803322710815931448794127282143541013507734381467234520531909776253206693033115334725516473752750597496319734515043472272017957991559594534295515221904048823284453333538445413026502878822856740651063031547495894667970940026049862864363103556163550110059432576394029582091048721103863431740328814644207912604705437940739070711034860087121567306967234771762517152374759398029629933603152765395449587185861316231547628714431726239762711185431416673529227324961146031701841171127178656762491186995307422837761125045648810754700433225046702749714727664527919896624578043163203963945371818067889582648631176786414557687948596305182435339337932219228711131752480449884033318368963454504379270818005033533170132664824203854857029445837511582336578921899746755223540267646839305721926784799630021934126963321459632959336351195107559290323959762412547454860260944834130621275130282719086801410039998824567613340332928337858258080365254716789122954844229859100805277308812115813080460138032615336029771233041578857660411802599211911337253977053601734106578309860785345062060010043575437511786837698094857074073375703881643558855048230999943229639601046700539339068606794863611445771725595638859679280559912719602684083637664166639850535559683056024511070077720739396784865047219151721059750990539238418437705188773603776442503032356596352431087533337770977036147586738967560559695061308705692124612548126697507912375865971723350945365753439589862827154322732651591973219885355206126828961619557575132291148785645783231199785410507243675730846401273827942253980345525772454063100625427102712125242759303428016835722769251362807671756853944998300453773031548836225698200462500344948077944362898557432271789139699612334155168062110173938202368256149572314509072894661551031402359011540621772435427844542884893562626839975030526904997565021677889975279877866837153787139736431328007170549751027359233316547289458197091769936822590407186607590257187361855040126565267512523313278296811032869517564490393332536226296492471372666924131812161063968833574776221743313155581358546622455092507201; d=36908148345776022749280107983609692993793777434044953106354403035231897449210478643871412823070148459476047072991757120730365781919121924464051221018403832233423061268210196474007309675590200851788680161808491602780491791172607323887077150656042927999964187910699094723814542389226524505407175324048834332504934667732429249839438566481862224909832956590257907065531261889599847606165131478606639427626775666846500672797362762724734071648666394661489838882760790271763111242555888955131860512334153692515598000812452871183394483969; gcd(c,b) Output: ? ? ? ? ? ? 5333826139458335732212439620866023842596295704378917268188532808429473660654713515607501897883000839192096660838394440331891264399476018060249750942346490303186754307106579946435170321602869251686843047430170042892466115559492200309295845321163677406798622926249084871178386630955269789721084226057367509487188069641861798698379282661538240121092857283255514459245264034552045532392888487571799913370516188800851458419708511633450096482648219657883166119777776621147568774912661785140954371032278218472574655201521226531266455848721935498237138678291366543120607575266257929087014193813410249326203126575187532779224775763649492385600403650213012069066481796706203013218314462959371192466526625849425574023345263733659702497912879308120366882314743275210689220761268020922836160838184810784688280536823669191463173932650448709458635071013546592321296770203262867211191583243231586159619886391413419733625427272367211319169297782937505683531993954311274791545694078936155101596627548845566896346737431915993632638586249196545538210394736730624259909173846509906549517798284913047365888738745225195638310655995168053726171594649222633585348302840718465758367278201318110090426098897954728208610077441177336603141679538296337902777027078890891683099698505148315274603087942474572178236669109585715642698349268881349714113007191610651339228653331240758033227108159314487941272821435410135077343814672345205319097762532066930331153347255164737527505974963197345150434722720179579915595945342955152219040488232844533335384454130265028788228567406510630315474958946679709400260498628643631035561635501100594325763940295820910487211038634317403288146442079126047054379407390707110348600871215673069672347717625171523747593980296299336031527653954495871858613162315476287144317262397627111854314166735292273249611460317018411711271786567624911869953074228377611250456488107547004332250467027497147276645279198966245780431632039639453718180678895826486311767864145576879485963051824353393379322192287111317524804498840333183689634545043792708180050335331701326648242038548570294458375115823365789218997467552235402676468393057219267847996300219341269633214596329593363511951075592903239597624125474548602609448341306212751302827190868014100399988245676133403329283378582580803652547167891229548442298591008052773088121158130804601380326153360297712330415788576604118025992119113372539770536017341065783098607853450620600100435754375117868376980948570740733757038816435588550482309999432296396010467005393390686067948636114457717255956388596792805599127196026840836376641666398505355596830560245110700777207393967848650472191517210597509905392384184377051887736037764425030323565963524310875333377709770361475867389675605596950613087056921246125481266975079123758659717233509453657534395898628271543227326515919732198853552061268289616195575751322911487856457832311997854105072436757308464012738279422539803455257724540631006254271027121252427593034280168357227692513628076717568539449983004537730315488362256982004625003449480779443628985574322717891396996123341551680621101739382023682561495723145090728946615510314023590115406217724354278445428848935626268399750305269049975650216778899752798778668[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.015s sys 0m0.017s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:28:53 2005 Input: c=322226786600448469988526949675172383162664450560269840101215606291701764770565355213211750680915487300495092625225621702078687282750984448016874692613736074368687345968184113117100135917659457286481778990144839381637061480389970324364798075007168190501534845502388603547862093233601920978231388537562689807500841111237911981439009112678995339086277305428888531759483698646053950871846107666583490811140310097105610801423587274990629424582626242889921428548921415892683059539770418324263571341447442037423429939628885002629877201554701195078279126542994050203887117727734016341481700241795596978880448334044457707746889474361783414382308487609438848811960789750955289039753980499860682133437162423487861889182316955595804458794679915946656557094807940831697437027549519470401683987699238195962943166728908475047932362649838817302127456833245216546623767860498789019689816930967023576707522894368891430845069547519849935037157594180492988149604766795837530532230031429439506086604230354717664704734799906065009788947388743937484540848534519105768050711346126353623598044232544219132508653181616869475809871634319440422056345564501087346204246789512187429000943926929083985157501699598313125002702224978750051954197777385921298690233812880528748811089744680105137194020464572459795918615201188957138799065830480779402660738504822950565351072466465435854482833523916348126566353736306147807602575123668135833512620097190265883611405881825865961469094465385419563100057212895401528193252191267553204814920265412808061268237107696236278877846849135004732341025707496773941346986673234093369559464103328696856767769626602471701289099979906893242875682334955324360515159341149567161822073306537422292401029316287163914259605466397904621246552384811056504523119616256688002926549256092443107857509766989037471799149180934914570835830336161847946904136889621503463514246071858447824610382902413186988146598153534517157358137651859406884423008448556811042623904030387566853308916568430751870705232857654703306934595315494704702348617167478275161769006831210836890494337282275695421837073542905261410929314252649523047919341093394604486006864831203115277564935125934973358979846778318613729914426454991812335721021977344403737970976002097638789733747546445420022227539048576869466813329901343744649697197508729099880346460990410403732379930498969196777623779689623239788836566732908039033969234303114045993239182445682666489251867367194616730714725731600011030232742762776490889830622568222907933534247884894322084226158939700930151919945047277662313982436216980533807516809984508687911412308127355226534863334633573943584324513254534484069803269854634952710535287723262682310692035665889370152174589129817292725663920937185253951869294849522411341169485360822074916110947358273591703195867214476037501628153985631684832986371257289808479081908702131113128083807903331392771282693428882789178173894362779050676133856188519638129065939231824321331207206192487908235999487799069016953328243509943187133847481540974052922006246670146194033620719515935805779823433665735223996163438569547033616886933883738503095711505612412637326598483750677445445115730554867640405390699866042354882321164323417220858794526868616416282611436450698798289919904246596745576581963210388668004429380385161350877854091168798241106989624716323389081459185815248715014432088030746767685530277577689897520931774397570497915947844057351646658809506780854370599936354627312593716058146065173906811352599242440003001704912598638885372905518657416849313143624796730054173472295247097720849552132285066349967592169036985950846992402634747332618960515447277545503650844861261729122404455847713976286648310714911442502288508149565672838741594292579660620717991047410513367777057020202945086172521166388769148287853744359763007260071399806400186887631257044604024270641289467553061292025352250359528842425487689303710942318255547085444349985432832970399874541503649925836851445531515104477825176755886108715916399735324930351057665208725926181338981128337040281705547186938821573618254222124553483245609684963721041395907930935068360109322762715263848112701058513260051670783198744053408407125111142238495505849085365548844104897287944758694460983469194784618994160659952563378775940778217442006582355808434121436468962719321381865284092932589455422859854979818780184871940951848122315517777619870831262492843314377036421158076522427263862272051648430036315925404222582770718815567870856855637173271289834157643355608275115868111163894469155265771727298506936016400031208966801633701344150843830398050788885824713475466007617384714480731551971559274278131771922297634390588604338102287476423144827701658101724439223081661603244289406418292318309379478838514230579662664421106903571346092596573593030362844806475039468208256818859360515331885137015539119949134745231244182679745974093460701511693969462776145016286878998601773567012696635144046679457292552092320660309934376598489619295159451050434830858246128578481428055308050318562845014186657077494234222065868728114521049361776646366502990083348876305264870301859972855409857380521614096493753501500572352320238821325600812349441771464995702717650226371466617714256080554338432347387589769673314617143476835610930499036728541724707810019388428683932649574740398974985050060819472013254544474175737316625984881044547520628707904517991476460503245346292210503422058331375502522390550747125303702613686438252123269981793837836879845610725752016848469310020124138516209630833719690689; a=((2^(6048*2))-1); b=533382613945833573221243962086602384259629570437891726818853280842947366065471351560750189788300083919209666083839444033189126439947601806024975094234649030318675430710657994643517032160286925168684304743017004289246611555949220030929584532116367740679862292624908487117838663095526978972108422605736750948718806964186179869837928266153824012109285728325551445924526403455204553239288848757179991337051618880085145841970851163345009648264821965788316611977777662114756877491266178514095437103227821847257465520152122653126645584872193549823713867829136654312060757526625792908701419381341024932620312657518753277922477576364949238560040365021301206906648179670620301321831446295937119246652662584942557402334526373365970249791287930812036688231474327521068922076126802092283616083818481078468828053682366919146317393265044870945863507101354659232129677020326286721119158324323158615961988639141341973362542727236721131916929778293750568353199395431127479154569407893615510159662754884556689634673743191599363263858624919654553821039473673062425990917384650990654951779828491304736588873874522519563831065599516805372617159464922263358534830284071846575836727820131811009042609889795472820861007744117733660314167953829633790277702707889089168309969850514831527460308794247457217823666910958571564269834926888134971411300719161065133922865333124075803322710815931448794127282143541013507734381467234520531909776253206693033115334725516473752750597496319734515043472272017957991559594534295515221904048823284453333538445413026502878822856740651063031547495894667970940026049862864363103556163550110059432576394029582091048721103863431740328814644207912604705437940739070711034860087121567306967234771762517152374759398029629933603152765395449587185861316231547628714431726239762711185431416673529227324961146031701841171127178656762491186995307422837761125045648810754700433225046702749714727664527919896624578043163203963945371818067889582648631176786414557687948596305182435339337932219228711131752480449884033318368963454504379270818005033533170132664824203854857029445837511582336578921899746755223540267646839305721926784799630021934126963321459632959336351195107559290323959762412547454860260944834130621275130282719086801410039998824567613340332928337858258080365254716789122954844229859100805277308812115813080460138032615336029771233041578857660411802599211911337253977053601734106578309860785345062060010043575437511786837698094857074073375703881643558855048230999943229639601046700539339068606794863611445771725595638859679280559912719602684083637664166639850535559683056024511070077720739396784865047219151721059750990539238418437705188773603776442503032356596352431087533337770977036147586738967560559695061308705692124612548126697507912375865971723350945365753439589862827154322732651591973219885355206126828961619557575132291148785645783231199785410507243675730846401273827942253980345525772454063100625427102712125242759303428016835722769251362807671756853944998300453773031548836225698200462500344948077944362898557432271789139699612334155168062110173938202368256149572314509072894661551031402359011540621772435427844542884893562626839975030526904997565021677889975279877866837153787139736431328007170549751027359233316547289458197091769936822590407186607590257187361855040126565267512523313278296811032869517564490393332536226296492471372666924131812161063968833574776221743313155581358546622455092507201; d=36908148345776022749280107983609692993793777434044953106354403035231897449210478643871412823070148459476047072991757120730365781919121924464051221018403832233423061268210196474007309675590200851788680161808491602780491791172607323887077150656042927999964187910699094723814542389226524505407175324048834332504934667732429249839438566481862224909832956590257907065531261889599847606165131478606639427626775666846500672797362762724734071648666394661489838882760790271763111242555888955131860512334153692515598000812452871183394483969; gcd(c,b) Output: ? ? ? ? ? ? 5333826139458335732212439620866023842596295704378917268188532808429473660654713515607501897883000839192096660838394440331891264399476018060249750942346490303186754307106579946435170321602869251686843047430170042892466115559492200309295845321163677406798622926249084871178386630955269789721084226057367509487188069641861798698379282661538240121092857283255514459245264034552045532392888487571799913370516188800851458419708511633450096482648219657883166119777776621147568774912661785140954371032278218472574655201521226531266455848721935498237138678291366543120607575266257929087014193813410249326203126575187532779224775763649492385600403650213012069066481796706203013218314462959371192466526625849425574023345263733659702497912879308120366882314743275210689220761268020922836160838184810784688280536823669191463173932650448709458635071013546592321296770203262867211191583243231586159619886391413419733625427272367211319169297782937505683531993954311274791545694078936155101596627548845566896346737431915993632638586249196545538210394736730624259909173846509906549517798284913047365888738745225195638310655995168053726171594649222633585348302840718465758367278201318110090426098897954728208610077441177336603141679538296337902777027078890891683099698505148315274603087942474572178236669109585715642698349268881349714113007191610651339228653331240758033227108159314487941272821435410135077343814672345205319097762532066930331153347255164737527505974963197345150434722720179579915595945342955152219040488232844533335384454130265028788228567406510630315474958946679709400260498628643631035561635501100594325763940295820910487211038634317403288146442079126047054379407390707110348600871215673069672347717625171523747593980296299336031527653954495871858613162315476287144317262397627111854314166735292273249611460317018411711271786567624911869953074228377611250456488107547004332250467027497147276645279198966245780431632039639453718180678895826486311767864145576879485963051824353393379322192287111317524804498840333183689634545043792708180050335331701326648242038548570294458375115823365789218997467552235402676468393057219267847996300219341269633214596329593363511951075592903239597624125474548602609448341306212751302827190868014100399988245676133403329283378582580803652547167891229548442298591008052773088121158130804601380326153360297712330415788576604118025992119113372539770536017341065783098607853450620600100435754375117868376980948570740733757038816435588550482309999432296396010467005393390686067948636114457717255956388596792805599127196026840836376641666398505355596830560245110700777207393967848650472191517210597509905392384184377051887736037764425030323565963524310875333377709770361475867389675605596950613087056921246125481266975079123758659717233509453657534395898628271543227326515919732198853552061268289616195575751322911487856457832311997854105072436757308464012738279422539803455257724540631006254271027121252427593034280168357227692513628076717568539449983004537730315488362256982004625003449480779443628985574322717891396996123341551680621101739382023682561495723145090728946615510314023590115406217724354278445428848935626268399750305269049975650216778899752798778668[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.009s sys 0m0.019s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:29:41 2005 Input: c=35725497937327068562692229836881559493123695844726082854574090097053409869663624513939173085797105579437508929596300931922964909634501740500347819471904610001107179671741959395751092404582209526511457928917339276866891373303005564036170370829183337060236499132441002625991144568629613286368282119024282368881471006377597740402323488533611646441630025749911982715620111463270390323428756282201683781125699069104682791661304954562110819274178169050379643892611816221979593569993588127859791885462008332929227658470657806508531070200026546274720038366069532572353979679988964610253031373191702178787426096351682079167417416213485149575252862631469232034076947013899593644888075027142834248684205161455126974875639323525771972283762652953770008541628855056352598232405401662483327415414201599600227108116106386639810117289762567220585208742424364111380562313962390748695847238177905608682700019642546333325131030147755423482843826265130616215477179655911713052113941750584656994852900927918620714887128030356419994681475610190074362441193606946838262820851162503108553159224267103224707404925679507574306873277045219309300457625951729217801243679061722228973745049051280010310201255092737261305206058503511110878600083137762607000021327693466311725003435586247101781198326456992559403729680442380507335513120479735419029696324659302341875920729683842230544826031092471235228080447664945302909075124525077090251448016613222404067503189670790400052672830033064669334646294560575087723235662525637513835691365221526185252607389138290703541562441610660307373002245364502376802169823306264137821192483912162685250363578295034462372411036345937169497991107540740497882429525717617173507501178383606816731573902265210228398765033494338789415564678058427144766421725789952705972381724428021235493706502417377441073830677408548722703858043741127315113484292150102110837199538481142029131758641379586768758647790441785648526662603366533445056254161948637528441449727563787718993297419943150988693510546378406624704025108438619492795546967563494957451592030594585050013902160333149095525276412561089688675088351712023505938822714979474153369167325299719818709692608596677950975668675388193174094773796021866789795910372028482658566937920747560774243049773356785879887335172268039890159409550583397651155824322686268792395491672750910114305820382225593223170666794795190583879699916784895221179677260513451224163388835495341538150624902887858265734027819240527693744358849990120805823781793456429723066617298625789371953290866039112302605648230787240247198185684269733333290973190145278493466070622242032433784510520052065393099760074613184540876266940790881870605546228351776584794288466391008084965386019538682349740442314950938057317997391685500145717939040410101638917572636120934873056425444615209769818499377067164648062839635108081415868636080831347910971553401560406972718925182358460954699868546799792956195876837869840404342345745635892448016073644750074441555829529105243670139420243090703789056413009817886540908808990606753429943556654482649280408079473251441176556203639449320010510208025869297353424956803082797285076538604338652780705610185876987350605025399076193056041339152402169183631641076601301795827033373123686612074095120428761312699593493733111646128153833265531208044254425797204376317751139607121971425374816853471417195917069677033331491516729213271668095366389734187129979381272950545424615137639517140485076053315439711423039978874552233947644369125307129318995916006633545744120497285813588807202072458013222622216925750818414066758128656920504085957649550467375198432954366795755698976009734812842297256014228425149793050503898919226144877520813298804183456108377108355232779784830464506404597152217169279716437987314712295596408543398411319855170781260681631779232263268962874330457342409999224148997892531812890185358964600404010117383053992040599842450555480643071063176887888831156341507531532521497964930467307502632549598754294552168343499487967465734291709319632907342318235645986526455688698439908584800467531608430681766559301608572418684258361578749332029077671050248518976053855851799138971373964089028610665078044803931236527442204458134642278487185680327338687034935014022674380970546505351063803292230303945796241402640059259895297358438945164992262699310905321365302464217760216051310269245549757889; a=((2^(6048*2))-1); b=533382613945833573221243962086602384259629570437891726818853280842947366065471351560750189788300083919209666083839444033189126439947601806024975094234649030318675430710657994643517032160286925168684304743017004289246611555949220030929584532116367740679862292624908487117838663095526978972108422605736750948718806964186179869837928266153824012109285728325551445924526403455204553239288848757179991337051618880085145841970851163345009648264821965788316611977777662114756877491266178514095437103227821847257465520152122653126645584872193549823713867829136654312060757526625792908701419381341024932620312657518753277922477576364949238560040365021301206906648179670620301321831446295937119246652662584942557402334526373365970249791287930812036688231474327521068922076126802092283616083818481078468828053682366919146317393265044870945863507101354659232129677020326286721119158324323158615961988639141341973362542727236721131916929778293750568353199395431127479154569407893615510159662754884556689634673743191599363263858624919654553821039473673062425990917384650990654951779828491304736588873874522519563831065599516805372617159464922263358534830284071846575836727820131811009042609889795472820861007744117733660314167953829633790277702707889089168309969850514831527460308794247457217823666910958571564269834926888134971411300719161065133922865333124075803322710815931448794127282143541013507734381467234520531909776253206693033115334725516473752750597496319734515043472272017957991559594534295515221904048823284453333538445413026502878822856740651063031547495894667970940026049862864363103556163550110059432576394029582091048721103863431740328814644207912604705437940739070711034860087121567306967234771762517152374759398029629933603152765395449587185861316231547628714431726239762711185431416673529227324961146031701841171127178656762491186995307422837761125045648810754700433225046702749714727664527919896624578043163203963945371818067889582648631176786414557687948596305182435339337932219228711131752480449884033318368963454504379270818005033533170132664824203854857029445837511582336578921899746755223540267646839305721926784799630021934126963321459632959336351195107559290323959762412547454860260944834130621275130282719086801410039998824567613340332928337858258080365254716789122954844229859100805277308812115813080460138032615336029771233041578857660411802599211911337253977053601734106578309860785345062060010043575437511786837698094857074073375703881643558855048230999943229639601046700539339068606794863611445771725595638859679280559912719602684083637664166639850535559683056024511070077720739396784865047219151721059750990539238418437705188773603776442503032356596352431087533337770977036147586738967560559695061308705692124612548126697507912375865971723350945365753439589862827154322732651591973219885355206126828961619557575132291148785645783231199785410507243675730846401273827942253980345525772454063100625427102712125242759303428016835722769251362807671756853944998300453773031548836225698200462500344948077944362898557432271789139699612334155168062110173938202368256149572314509072894661551031402359011540621772435427844542884893562626839975030526904997565021677889975279877866837153787139736431328007170549751027359233316547289458197091769936822590407186607590257187361855040126565267512523313278296811032869517564490393332536226296492471372666924131812161063968833574776221743313155581358546622455092507201; d=36908148345776022749280107983609692993793777434044953106354403035231897449210478643871412823070148459476047072991757120730365781919121924464051221018403832233423061268210196474007309675590200851788680161808491602780491791172607323887077150656042927999964187910699094723814542389226524505407175324048834332504934667732429249839438566481862224909832956590257907065531261889599847606165131478606639427626775666846500672797362762724734071648666394661489838882760790271763111242555888955131860512334153692515598000812452871183394483969; gcd(c,b) Output: ? ? ? ? ? ? 5333826139458335732212439620866023842596295704378917268188532808429473660654713515607501897883000839192096660838394440331891264399476018060249750942346490303186754307106579946435170321602869251686843047430170042892466115559492200309295845321163677406798622926249084871178386630955269789721084226057367509487188069641861798698379282661538240121092857283255514459245264034552045532392888487571799913370516188800851458419708511633450096482648219657883166119777776621147568774912661785140954371032278218472574655201521226531266455848721935498237138678291366543120607575266257929087014193813410249326203126575187532779224775763649492385600403650213012069066481796706203013218314462959371192466526625849425574023345263733659702497912879308120366882314743275210689220761268020922836160838184810784688280536823669191463173932650448709458635071013546592321296770203262867211191583243231586159619886391413419733625427272367211319169297782937505683531993954311274791545694078936155101596627548845566896346737431915993632638586249196545538210394736730624259909173846509906549517798284913047365888738745225195638310655995168053726171594649222633585348302840718465758367278201318110090426098897954728208610077441177336603141679538296337902777027078890891683099698505148315274603087942474572178236669109585715642698349268881349714113007191610651339228653331240758033227108159314487941272821435410135077343814672345205319097762532066930331153347255164737527505974963197345150434722720179579915595945342955152219040488232844533335384454130265028788228567406510630315474958946679709400260498628643631035561635501100594325763940295820910487211038634317403288146442079126047054379407390707110348600871215673069672347717625171523747593980296299336031527653954495871858613162315476287144317262397627111854314166735292273249611460317018411711271786567624911869953074228377611250456488107547004332250467027497147276645279198966245780431632039639453718180678895826486311767864145576879485963051824353393379322192287111317524804498840333183689634545043792708180050335331701326648242038548570294458375115823365789218997467552235402676468393057219267847996300219341269633214596329593363511951075592903239597624125474548602609448341306212751302827190868014100399988245676133403329283378582580803652547167891229548442298591008052773088121158130804601380326153360297712330415788576604118025992119113372539770536017341065783098607853450620600100435754375117868376980948570740733757038816435588550482309999432296396010467005393390686067948636114457717255956388596792805599127196026840836376641666398505355596830560245110700777207393967848650472191517210597509905392384184377051887736037764425030323565963524310875333377709770361475867389675605596950613087056921246125481266975079123758659717233509453657534395898628271543227326515919732198853552061268289616195575751322911487856457832311997854105072436757308464012738279422539803455257724540631006254271027121252427593034280168357227692513628076717568539449983004537730315488362256982004625003449480779443628985574322717891396996123341551680621101739382023682561495723145090728946615510314023590115406217724354278445428848935626268399750305269049975650216778899752798778668[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.011s sys 0m0.016s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:30:09 2005 Input: c=733753268907089300889644611649424295088518962645023876483960446382821771907399702383697288440268527371270351509089303702987672791838668684688147073225153481149027526921925559687975851028664332855762019481909771108845203244214143330515512109310026220872309956847786509845220087495757805349887636249180080454883976584209953610902132047685920728736114122935434263702082746160644548335739342836093617949598702709999078112936821903009619506332359352558005600369463056389897573511095583982976635859312754416159732714945935951030378863097506012896253842614573714099006380954622275864727033891739511196812130970795915367263112044298879178491407556019315731656603881778833691751176681189705715140272754091992356337683941067516945773661711201010131259227464864053057792466843978589957268260979989597311998245808173002791132317884260229073885087029331494973658028155550516396275095013774938372578926516580421692312592577259782359408252377700630271620453768720698577438709961813935561138989690838325080245994585394107067976486063340866809348846190596227944649532276130044066481590812461281139719403805136279928540159074982187202788897101577611489389115310974394771803780878270627130869405893502608204869752633862838171986362562136919466859346090261938784028896725921719672976149759182246802578151344004974257356391240044442017091629404010436886838401653125802192480064153556511461796676794623633091872916197634648106965631479020252034656869495201552301513869439103906106905359335497794949580538319159593371761135252920937555614890851640952753217354380260429464597322735321611959949416269262978175235041809707451791287092146109918879526374773342055864281271738282301694039635516589746219529305198446902315077256895769763781548248565050660370474510009296468870154664380100446721367937555537063941249958162066736656797069688955032197319929906222100025492399423296222433338074498866321924931563467058774613898241127964114412778464251811846289061937027169311793326543735469106092420505559864965086796994334615484035935615100778140141488999046782519951971654910256801082256055327992749734837689829877181884951433246099254832860917696520410727607925105964563605700174047168195112916498351302641056195397639186177557463875653014402549357704602482939877471558251555137005824551727954875641374005992022366575163812582192333010695460933852791101653926663134111748025675424571137678051202148064417739853303448120800075670374346850039042363086290358845963695065153686420502283522177897184949318752065434489064112966177307534730862248162677232751327829157789039779257197145816366896938301439900846011096835312416114550936463317856553940306765615686430511857468068184709376501518859121076060363064559830018429927950557573397797587280384796457882728565469123312594866766224853060036766407205595935634788409587999858900570982265070028999068492362943508338429485586629930051032747056117339936278488237125430525587170326652141953017204577936305248524636250182272007423106872285486910760334205509889771684580772983180577043888006655358484759355592233127767252347778137058116223561130795152131489367295333806622290594150481983336755784928043024687192325180338791096485411396244670595706634831098938801626217237358096860741594542829834862785412388353894507539208302637846243768441943936971453649501553098600359182840715563408867928235751933337588784597111395909228865690640975712870374965382071571440290661117575140852447402405607476380109132521266029240577976289829805719739497443997310360357542297601; a=((2^(6048*2))-1); b=533382613945833573221243962086602384259629570437891726818853280842947366065471351560750189788300083919209666083839444033189126439947601806024975094234649030318675430710657994643517032160286925168684304743017004289246611555949220030929584532116367740679862292624908487117838663095526978972108422605736750948718806964186179869837928266153824012109285728325551445924526403455204553239288848757179991337051618880085145841970851163345009648264821965788316611977777662114756877491266178514095437103227821847257465520152122653126645584872193549823713867829136654312060757526625792908701419381341024932620312657518753277922477576364949238560040365021301206906648179670620301321831446295937119246652662584942557402334526373365970249791287930812036688231474327521068922076126802092283616083818481078468828053682366919146317393265044870945863507101354659232129677020326286721119158324323158615961988639141341973362542727236721131916929778293750568353199395431127479154569407893615510159662754884556689634673743191599363263858624919654553821039473673062425990917384650990654951779828491304736588873874522519563831065599516805372617159464922263358534830284071846575836727820131811009042609889795472820861007744117733660314167953829633790277702707889089168309969850514831527460308794247457217823666910958571564269834926888134971411300719161065133922865333124075803322710815931448794127282143541013507734381467234520531909776253206693033115334725516473752750597496319734515043472272017957991559594534295515221904048823284453333538445413026502878822856740651063031547495894667970940026049862864363103556163550110059432576394029582091048721103863431740328814644207912604705437940739070711034860087121567306967234771762517152374759398029629933603152765395449587185861316231547628714431726239762711185431416673529227324961146031701841171127178656762491186995307422837761125045648810754700433225046702749714727664527919896624578043163203963945371818067889582648631176786414557687948596305182435339337932219228711131752480449884033318368963454504379270818005033533170132664824203854857029445837511582336578921899746755223540267646839305721926784799630021934126963321459632959336351195107559290323959762412547454860260944834130621275130282719086801410039998824567613340332928337858258080365254716789122954844229859100805277308812115813080460138032615336029771233041578857660411802599211911337253977053601734106578309860785345062060010043575437511786837698094857074073375703881643558855048230999943229639601046700539339068606794863611445771725595638859679280559912719602684083637664166639850535559683056024511070077720739396784865047219151721059750990539238418437705188773603776442503032356596352431087533337770977036147586738967560559695061308705692124612548126697507912375865971723350945365753439589862827154322732651591973219885355206126828961619557575132291148785645783231199785410507243675730846401273827942253980345525772454063100625427102712125242759303428016835722769251362807671756853944998300453773031548836225698200462500344948077944362898557432271789139699612334155168062110173938202368256149572314509072894661551031402359011540621772435427844542884893562626839975030526904997565021677889975279877866837153787139736431328007170549751027359233316547289458197091769936822590407186607590257187361855040126565267512523313278296811032869517564490393332536226296492471372666924131812161063968833574776221743313155581358546622455092507201; d=36908148345776022749280107983609692993793777434044953106354403035231897449210478643871412823070148459476047072991757120730365781919121924464051221018403832233423061268210196474007309675590200851788680161808491602780491791172607323887077150656042927999964187910699094723814542389226524505407175324048834332504934667732429249839438566481862224909832956590257907065531261889599847606165131478606639427626775666846500672797362762724734071648666394661489838882760790271763111242555888955131860512334153692515598000812452871183394483969; gcd(c,b) Output: ? ? ? ? ? ? 5333826139458335732212439620866023842596295704378917268188532808429473660654713515607501897883000839192096660838394440331891264399476018060249750942346490303186754307106579946435170321602869251686843047430170042892466115559492200309295845321163677406798622926249084871178386630955269789721084226057367509487188069641861798698379282661538240121092857283255514459245264034552045532392888487571799913370516188800851458419708511633450096482648219657883166119777776621147568774912661785140954371032278218472574655201521226531266455848721935498237138678291366543120607575266257929087014193813410249326203126575187532779224775763649492385600403650213012069066481796706203013218314462959371192466526625849425574023345263733659702497912879308120366882314743275210689220761268020922836160838184810784688280536823669191463173932650448709458635071013546592321296770203262867211191583243231586159619886391413419733625427272367211319169297782937505683531993954311274791545694078936155101596627548845566896346737431915993632638586249196545538210394736730624259909173846509906549517798284913047365888738745225195638310655995168053726171594649222633585348302840718465758367278201318110090426098897954728208610077441177336603141679538296337902777027078890891683099698505148315274603087942474572178236669109585715642698349268881349714113007191610651339228653331240758033227108159314487941272821435410135077343814672345205319097762532066930331153347255164737527505974963197345150434722720179579915595945342955152219040488232844533335384454130265028788228567406510630315474958946679709400260498628643631035561635501100594325763940295820910487211038634317403288146442079126047054379407390707110348600871215673069672347717625171523747593980296299336031527653954495871858613162315476287144317262397627111854314166735292273249611460317018411711271786567624911869953074228377611250456488107547004332250467027497147276645279198966245780431632039639453718180678895826486311767864145576879485963051824353393379322192287111317524804498840333183689634545043792708180050335331701326648242038548570294458375115823365789218997467552235402676468393057219267847996300219341269633214596329593363511951075592903239597624125474548602609448341306212751302827190868014100399988245676133403329283378582580803652547167891229548442298591008052773088121158130804601380326153360297712330415788576604118025992119113372539770536017341065783098607853450620600100435754375117868376980948570740733757038816435588550482309999432296396010467005393390686067948636114457717255956388596792805599127196026840836376641666398505355596830560245110700777207393967848650472191517210597509905392384184377051887736037764425030323565963524310875333377709770361475867389675605596950613087056921246125481266975079123758659717233509453657534395898628271543227326515919732198853552061268289616195575751322911487856457832311997854105072436757308464012738279422539803455257724540631006254271027121252427593034280168357227692513628076717568539449983004537730315488362256982004625003449480779443628985574322717891396996123341551680621101739382023682561495723145090728946615510314023590115406217724354278445428848935626268399750305269049975650216778899752798778668[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.008s sys 0m0.016s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:36:29 2005 Input: c=856593993037010096035237352196145276676103830279646813045132639423359800052897415862231458703253010723667879917155212292612637342570108385881243019520783648015678321244618397972411062770786415278513640781400173653937522141559578122317931308525950390109298229240696560213879314239913157805945748920555634655780805679553878467162285725143401664396220429759270737728139605155915398869722045365000820825411501702733173850916522675531226482010405294520125975415448648543535240673643264527006102952616845106125615967922349119136616411772853097122016655389243644019384288420251747321482276700708734824408915673614762058897307909158127433652067171569381364342555963828720807496863488486054819378221299974150919033303680660163020755488335157282506538385982744399318620823100543622032427835846439738992558654990042979711476910927024657148643385774711255272820829810788586185522952798127749185039065822554689088227633696216988446693461008400935722332507954026290455101727248906321722155827612126433254264320218313777571010726826997616023372001850661634032120236051853982111676992979910225856498021027737752001579952968560057084382813094698194537478725847370855460625134889823155847059576641798254505747830731596115165938056590007712681660913544301497590349497303257285499138586877729185738114857367025422532779310398185011969802200461712760519756236095937328097769230186645026522727309680033388601348302945092748066565287482243195117313033225732017371227745809416922988216819213119806276248945857507023452336811659569008059510317887682295605376899031948701986308105191777944439666541062108819032076346158229192082337087879907199674482083894960305992902148201435971344116582598895307331314081991877101640772213657975924515170639367144693615820801; a=((2^(6048*2))-1); b=733753268907089300889644611649424295088518962645023876483960446382821771907399702383697288440268527371270351509089303702987672791838668684688147073225153481149027526921925559687975851028664332855762019481909771108845203244214143330515512109310026220872309956847786509845220087495757805349887636249180080454883976584209953610902132047685920728736114122935434263702082746160644548335739342836093617949598702709999078112936821903009619506332359352558005600369463056389897573511095583982976635859312754416159732714945935951030378863097506012896253842614573714099006380954622275864727033891739511196812130970795915367263112044298879178491407556019315731656603881778833691751176681189705715140272754091992356337683941067516945773661711201010131259227464864053057792466843978589957268260979989597311998245808173002791132317884260229073885087029331494973658028155550516396275095013774938372578926516580421692312592577259782359408252377700630271620453768720698577438709961813935561138989690838325080245994585394107067976486063340866809348846190596227944649532276130044066481590812461281139719403805136279928540159074982187202788897101577611489389115310974394771803780878270627130869405893502608204869752633862838171986362562136919466859346090261938784028896725921719672976149759182246802578151344004974257356391240044442017091629404010436886838401653125802192480064153556511461796676794623633091872916197634648106965631479020252034656869495201552301513869439103906106905359335497794949580538319159593371761135252920937555614890851640952753217354380260429464597322735321611959949416269262978175235041809707451791287092146109918879526374773342055864281271738282301694039635516589746219529305198446902315077256895769763781548248565050660370474510009296468870154664380100446721367937555537063941249958162066736656797069688955032197319929906222100025492399423296222433338074498866321924931563467058774613898241127964114412778464251811846289061937027169311793326543735469106092420505559864965086796994334615484035935615100778140141488999046782519951971654910256801082256055327992749734837689829877181884951433246099254832860917696520410727607925105964563605700174047168195112916498351302641056195397639186177557463875653014402549357704602482939877471558251555137005824551727954875641374005992022366575163812582192333010695460933852791101653926663134111748025675424571137678051202148064417739853303448120800075670374346850039042363086290358845963695065153686420502283522177897184949318752065434489064112966177307534730862248162677232751327829157789039779257197145816366896938301439900846011096835312416114550936463317856553940306765615686430511857468068184709376501518859121076060363064559830018429927950557573397797587280384796457882728565469123312594866766224853060036766407205595935634788409587999858900570982265070028999068492362943508338429485586629930051032747056117339936278488237125430525587170326652141953017204577936305248524636250182272007423106872285486910760334205509889771684580772983180577043888006655358484759355592233127767252347778137058116223561130795152131489367295333806622290594150481983336755784928043024687192325180338791096485411396244670595706634831098938801626217237358096860741594542829834862785412388353894507539208302637846243768441943936971453649501553098600359182840715563408867928235751933337588784597111395909228865690640975712870374965382071571440290661117575140852447402405607476380109132521266029240577976289829805719739497443997310360357542297601; gcd(c,b) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.010s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:37:17 2005 Input: c=856593993037010096035237352196145276676103830279646813045132639423359800052897415862231458703253010723667879917155212292612637342570108385881243019520783648015678321244618397972411062770786415278513640781400173653937522141559578122317931308525950390109298229240696560213879314239913157805945748920555634655780805679553878467162285725143401664396220429759270737728139605155915398869722045365000820825411501702733173850916522675531226482010405294520125975415448648543535240673643264527006102952616845106125615967922349119136616411772853097122016655389243644019384288420251747321482276700708734824408915673614762058897307909158127433652067171569381364342555963828720807496863488486054819378221299974150919033303680660163020755488335157282506538385982744399318620823100543622032427835846439738992558654990042979711476910927024657148643385774711255272820829810788586185522952798127749185039065822554689088227633696216988446693461008400935722332507954026290455101727248906321722155827612126433254264320218313777571010726826997616023372001850661634032120236051853982111676992979910225856498021027737752001579952968560057084382813094698194537478725847370855460625134889823155847059576641798254505747830731596115165938056590007712681660913544301497590349497303257285499138586877729185738114857367025422532779310398185011969802200461712760519756236095937328097769230186645026522727309680033388601348302945092748066565287482243195117313033225732017371227745809416922988216819213119806276248945857507023452336811659569008059510317887682295605376899031948701986308105191777944439666541062108819032076346158229192082337087879907199674482083894960305992902148201435971344116582598895307331314081991877101640772213657975924515170639367144693615820801; a=((2^(6048*2))-1); b=227160077046482876543105891084100845157692694930009934810441010055051139162201195856634960442412185050869094038166182124779529982796045125692766957161108830913105184571961987588595741494542926781061234060443216412783969935039897967347195237994196604995375922805693159337042359654371720461376081998527986928395752881528032432466745586393443989599212137534592426860247658725277316759393738049797040088563242760615390818485698598069614719223176365753041408928343440145460743665870552476459349758310582326204348231674267297425103114129188708547180972683789088844416135358781896947211714597948746602920429521302343896983518170603245508599467298227465285705987521191637796174277677120755014928760806324225178921629608697466828180658297825590050050896790900545036199956049102442147769366943213222091321546468056496065355365054945541776966586154432493435362886628041774601070595259482762699111290746691681782636349839756724855670475493577472890811765832742448436806950857363717803928499911228901758034532049508461815465301214979811114936131367796261059222317617741910806260627393930621438477785424692796300217033762559890768601281; gcd(c,b) Output: ? ? ? ? ? 227160077046482876543105891084100845157692694930009934810441010055051139162201195856634960442412185050869094038166182124779529982796045125692766957161108830913105184571961987588595741494542926781061234060443216412783969935039897967347195237994196604995375922805693159337042359654371720461376081998527986928395752881528032432466745586393443989599212137534592426860247658725277316759393738049797040088563242760615390818485698598069614719223176365753041408928343440145460743665870552476459349758310582326204348231674267297425103114129188708547180972683789088844416135358781896947211714597948746602920429521302343896983518170603245508599467298227465285705987521191637796174277677120755014928760806324225178921629608697466828180658297825590050050896790900545036199956049102442147769366943213222091321546468056496065355365054945541776966586154432493435362886628041774601070595259482762699111290746691681782636349839756724855670475493577472890811765832742448436806950857363717803928499911228901758034532049508461815465301214979811114936131367796261059222317617741910806260627393930621438477785424692796300217033762559890768601281 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:38:00 2005 Input: c=9019518416950496514607021993442341214242630778291978921531924189540378811860382033077382435363030464213363952749413272911959521902752888406979964918875578335803432885755271009464277578935368200773357170822191216892304167237924423683233231466622302966021541728870433282433227362897752359174819625758350435817211379151705043042137077654094342408334652044070554765912281798811455678308021972218522966391011801585158863259904832121797839241326221247025778297157975463693446453777366777710954558320286838440302730852929930543135397574175903136623212863808422561573827176391074068989323337111790295402349880479956351794616502135536070009875034870415150933141426017159068960546796622916845109634425643791168101897485904382771759665699593361027951231175526153117215421198024431990833911488587253145354123301840971112502275518161541519477878175794029162824290947908702497689584102875944708021522699560117207558888948589267497176698947319331413820888216247551750236072826005747429048821542185392198214923229137441713961271604281270205241214704025698583344852398591264398644377288724721112203713372963383331232059201725993002347522673496503294267872982300208870195201; a=((2^(6048*2))-1); b=227160077046482876543105891084100845157692694930009934810441010055051139162201195856634960442412185050869094038166182124779529982796045125692766957161108830913105184571961987588595741494542926781061234060443216412783969935039897967347195237994196604995375922805693159337042359654371720461376081998527986928395752881528032432466745586393443989599212137534592426860247658725277316759393738049797040088563242760615390818485698598069614719223176365753041408928343440145460743665870552476459349758310582326204348231674267297425103114129188708547180972683789088844416135358781896947211714597948746602920429521302343896983518170603245508599467298227465285705987521191637796174277677120755014928760806324225178921629608697466828180658297825590050050896790900545036199956049102442147769366943213222091321546468056496065355365054945541776966586154432493435362886628041774601070595259482762699111290746691681782636349839756724855670475493577472890811765832742448436806950857363717803928499911228901758034532049508461815465301214979811114936131367796261059222317617741910806260627393930621438477785424692796300217033762559890768601281; gcd(c,b) Output: ? ? ? ? ? 227160077046482876543105891084100845157692694930009934810441010055051139162201195856634960442412185050869094038166182124779529982796045125692766957161108830913105184571961987588595741494542926781061234060443216412783969935039897967347195237994196604995375922805693159337042359654371720461376081998527986928395752881528032432466745586393443989599212137534592426860247658725277316759393738049797040088563242760615390818485698598069614719223176365753041408928343440145460743665870552476459349758310582326204348231674267297425103114129188708547180972683789088844416135358781896947211714597948746602920429521302343896983518170603245508599467298227465285705987521191637796174277677120755014928760806324225178921629608697466828180658297825590050050896790900545036199956049102442147769366943213222091321546468056496065355365054945541776966586154432493435362886628041774601070595259482762699111290746691681782636349839756724855670475493577472890811765832742448436806950857363717803928499911228901758034532049508461815465301214979811114936131367796261059222317617741910806260627393930621438477785424692796300217033762559890768601281 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:50:42 2005 Input: c=9504852159897593149328728605071978780049545226696791737968114608398771841834334458931828068733017242823251118994468257379658972430406179167898748547769683509951569795705054789471784343943275731077778411923896181509652140680165721637213815375848859174435410806573383364583458285405026709218488902080216453255051346733664183205457903056066413458075293132621536413153262296667561954574920577236589017143989175694650988585947029545559272117905541716871539793716256214451274555342175653405515895693612478734467125598909286726186677007420950369390304482826660776927788903266149628718678333001159657135729616885905856078436750463937253287487899455228683393964538269188074856268432709801310598740915088790760201214657746074582308011614402337811654454645321205195163784417940005519899975900904765054502608692394670496802583981561017366165924818737063864626028868895043592837247631372638968159666693434860443928135389542335670314583349548988156538137053659956746423054738922194937319368577087366420601452623281490677350991345368323710770380332147089568405515218168694921566078018835768150725356225284490960306337258249926010983919132388750172030234987362765047198721177328175528512469862325927178612649646294832033199468564614740243110865029415086610349762818170231509543659968205779930093618203628719965809231588842694169841825342649330968117471881587187171278560820624250733384257182182970435988470393430780641705595851440400304005578226371829509579922160219618603751924662426942023032467497307844347953747484762400604388574786415807450131170974180875382598477533315580200451529276927272267158873262477131341491816342043119101512195848724715194516714014693623783855356424640172633153042193010755950007771053540858580164893828234556598711717189973258587115690716865526649975929468383203489475626543020089951891543703204950845693199478428382028828178747515259930804795904944474043172450506201545816566275663473015885451710951010472394899137552538174016411905019173459312553984367947629698635513792653614436445179120161726170635706345028608943123966838330905589451574106117301713212237625780154887808990452799374270295217028067783610254760560681924732149221463649562935202174892461629366886608512005660236109547916312815174427322667677498330006600423062881976541812825609709557778567399350148897372310579887281291123575730241601377092203086635954823111663037713871422294023750998904774998671313951059560479807568464213252693154277721565752385107220415780584763023185386416244243952781796729619397238429419104546595755666262860823785291404815779466462049006825420232065757697964735827423136034788522825600367173244784652561561773144403028241923252326012781951773049512520515960149287824385605700885012097368261846995393248174682394643524930728634479726940211998305225225215584687596032572933126016807248119979988639027598239365054815058884992670542076160820994842142661505109193944453289535193922527056407941619531542987874677002205546172512796261402979485116350874973943197429642415323144866986314064088266994566504068449675303880474767352234827760533479317670023738220666982924724041115081527830508694003663340437891229355040825107187340527603691315873412851055835929990129257851379359915265455708184483116536547003725703201407216881857020556093183585755906408276805048345454764705435156081477774810732829956544988925312269370688630058720554925558707636448462795803821385081989843084116602114218945187440673468198622997756607964134077145321072443060331198321127175694253182311688620165997593002077860125791390438665233576764739652489099500727223648514762701578015823706835606324546877872273827895533043092961065554895950498568150631968366296946188763536873132764917384634585014723573639321392631226803986535891219330077908568849387014637392067554315517769124358134081224393020147315711361755746664448001; a=((2^(6048*2))-1); b=227160077046482876543105891084100845157692694930009934810441010055051139162201195856634960442412185050869094038166182124779529982796045125692766957161108830913105184571961987588595741494542926781061234060443216412783969935039897967347195237994196604995375922805693159337042359654371720461376081998527986928395752881528032432466745586393443989599212137534592426860247658725277316759393738049797040088563242760615390818485698598069614719223176365753041408928343440145460743665870552476459349758310582326204348231674267297425103114129188708547180972683789088844416135358781896947211714597948746602920429521302343896983518170603245508599467298227465285705987521191637796174277677120755014928760806324225178921629608697466828180658297825590050050896790900545036199956049102442147769366943213222091321546468056496065355365054945541776966586154432493435362886628041774601070595259482762699111290746691681782636349839756724855670475493577472890811765832742448436806950857363717803928499911228901758034532049508461815465301214979811114936131367796261059222317617741910806260627393930621438477785424692796300217033762559890768601281; gcd(c,b) Output: ? ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.008s sys 0m0.011s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:52:12 2005 Input: c=1964973040277098757534505342586186949603782276677969895251841205721058899235271423120979085438503638061192622776544644095218754739032195731939134141808525188856145735930824318493349434657095091546144007232962627873648603158600749096699607883483621166406881128917755390641781742570449002999465728425515398180109960036742287628584781625637789282296855511223151728508577554477503266212790062463935927503280691009037835881603981578059469271658093313612420987194696037192367273582164474328819581952789184336839733506554276174220826751768964026924117986126214073589649498897951057131898576097130920128343362873793622411934259535608025201406571243640944404240522862236559477711969802501695051100699211715269099607726129706618106186333372242083454007148137288480759044240297968371644076096734188726334211747054410103207750728854517173694620631117635133993386063774014870195893104042842462313902138771023631640624076519324940985954485839496191091984860210639167616856596378462482516863388140152534681349093262624614317812929458916094322543533052490346611943236320042112573820269220889420404070910626105489123244289725974708505750911318076856511610216909611290466063287729366946256814794473349214823547925624227017831481436079276041815863781186344623364428434351543359376680291464875968136361616244510549829877050605537768917211161417768052547883259668334131767076473199090707115173215137384799509031570450270990728009712693873188818746809208068701865146866944360816508546656795683607113313523727027895985884423276133678097905831511733727748429961305218563199647330193478859030089401047149645678726212955667601376610692915211596646406818436372575083869809111479762718339987431381116032151321259036499120773428467525864885719032376118739535722667784093995501554852945220494523673424679132452349895586363062230455478778708559274384825663099709383899417698605336545110572131817197373051207900196268907071660949302044792697373969804881731708454850632463010019489060667408508237616773742498717779843075753363573026244260061096785432892639207581359570601258002798518022392418461476796063144719038385629235765084535871619996994069089095189044391065316612421852525148474455852081696131561838761410501906228750963056907566564389886001379685712980324895697717821845913532389069196731498484792800253498468357098038640769069113984958217839396751012554442395449735125385398991600781850717864588694929107677545338468565452328508822866750979621983259890705744546142560333818176365173260667143162742741756562186694029536318711718646858914338786537533401505388950860583291179157190000025892316291279132313336992535466735127399099986175335990268087734553505725300028361115574147575985421744028616034438722038352923896434631018583811792071097674466674127958218003588356077983136524742805693414940827119773193639080584018692470252957292404615409343320787350331942591540163640227125485509234552529360554309789013846491229805901008388223044960618639013610369836762796247000972598666949545033199527069037221259851679969279919855240339325957131156986683753448249869038732538756335415419407821807671857846295931020055510715211660436628232345603003899138184412958528911338753209896994128350624577021305979576621329634137642270991142907895611028244160044230279680871258060742150999878075117856823339952204020107430492175096687176569395625723760814317995088718169721232779848409454948945434625232749530281380172861741220974686824907793437091093940563009657478899460618974829020715908012502595280006944204185617785791022759567645951527298541046595467681034022551232953538673093382990591401537907260039366554762292479648800772574001400777148230948559046076168480479431486885937656837786044467499369059332344559458904989291849277822416379359356370533210699256875804624385399835250563727713788810700969884345255880642359417020074859895483512770606479567915846083903841260312972321131184318968351778393003081055267343508928388244505110364611555667890325840746188814383257257224110492925048930098454842709816183314491738349337592181344298933395330233589989172401941019609015568197454021387692289961207304731187819535959517325235365804478437834131684669144422274092431067137231098694468835985098949270373071696750029375579303514607342391506957273069969056886529210135673828731455991891554144555599750203539334668254978505608929820505125521996833792004728647142497167739393553185371145838740546106004514849788665623415554505524495945208901607333531516445694334587848284795689335059025799202586422763407931323112983554112177992199751910703837583735301228277503232064223998285969535621770700596933038182675698398290878244083532018912833514159763202661749724339023163470972981479918041903151206779983904149525469834209595835110867004803; a=((2^(6048*2))-1); b=227160077046482876543105891084100845157692694930009934810441010055051139162201195856634960442412185050869094038166182124779529982796045125692766957161108830913105184571961987588595741494542926781061234060443216412783969935039897967347195237994196604995375922805693159337042359654371720461376081998527986928395752881528032432466745586393443989599212137534592426860247658725277316759393738049797040088563242760615390818485698598069614719223176365753041408928343440145460743665870552476459349758310582326204348231674267297425103114129188708547180972683789088844416135358781896947211714597948746602920429521302343896983518170603245508599467298227465285705987521191637796174277677120755014928760806324225178921629608697466828180658297825590050050896790900545036199956049102442147769366943213222091321546468056496065355365054945541776966586154432493435362886628041774601070595259482762699111290746691681782636349839756724855670475493577472890811765832742448436806950857363717803928499911228901758034532049508461815465301214979811114936131367796261059222317617741910806260627393930621438477785424692796300217033762559890768601281; gcd(c,b) Output: ? ? ? ? ? 227160077046482876543105891084100845157692694930009934810441010055051139162201195856634960442412185050869094038166182124779529982796045125692766957161108830913105184571961987588595741494542926781061234060443216412783969935039897967347195237994196604995375922805693159337042359654371720461376081998527986928395752881528032432466745586393443989599212137534592426860247658725277316759393738049797040088563242760615390818485698598069614719223176365753041408928343440145460743665870552476459349758310582326204348231674267297425103114129188708547180972683789088844416135358781896947211714597948746602920429521302343896983518170603245508599467298227465285705987521191637796174277677120755014928760806324225178921629608697466828180658297825590050050896790900545036199956049102442147769366943213222091321546468056496065355365054945541776966586154432493435362886628041774601070595259482762699111290746691681782636349839756724855670475493577472890811765832742448436806950857363717803928499911228901758034532049508461815465301214979811114936131367796261059222317617741910806260627393930621438477785424692796300217033762559890768601281 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.010s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:52:47 2005 Input: c=135153069332350411358248198404551973093631704736768755651786249820983960806535213299641979452084253176274321629000260343132472579131639295234075200323912715702350322520285400323955652034954783734317747728345799881823602613889396851839431540694158519351803941923534185745356826026618504490442602346875173332242232566527503244824497144629578822337501688488958443094279986009746098318967825112688318611760204145771555155940511582918609654880223733576865836913656915808137184350983269218691023667022644628791309415053911419547007931480302977234210138196164892967937434680997654985170346177301588282084858093437490601019450515491060151878819974648715461072632315276513525548990000839934204733001566058001965875323202861255052485597634936171003512387456858822171201893207386486312731992514012176484282152792635006061182517463324158643034980578453109185258337031397752287360765773548885763819084629819167639676015869411382836119426731243175009392741720498047449272821553920004002846121142429321690889828602415181640844941086478867191444475506556894728066796680432896926715992543086008563118202962671963257892878320880260132011000807289428217061023301576256537805671962380500264209978510253596364088238049861438197744614150526271387638268555126778644946257130388140824461561799735066645571146222049191428266820071898139058886426698315711897291286212549387897249825877063680330829898355751612316323019198001756169926104488709830964092521985240030114109057501394765557005537554854404245922088704620042091706049477716232443214182965907994351723043784157556883175270637828677276941889163687444897112452057361785614344517735607640830323538769714139088507615832857982075660481988689569914483134299701572365610330297828893652452039252299490072903368341606029484789764827352859415540135453374092964295204652621392022494647535462641795557967540925934613452289287478824532563232166871648634285832799277805482396875885482771853287230473733602265846835743467495517326555869943994154540388572296894152224273518443321563706305672641072710040046383765380377238456686409730028032604351567380717742438119052409862895480985825627037821167069237713784267778792219314818360046558942290091279861521698539137633307718924733774507495565810432323209944273732143637267138405853240841905060523388060770660445384892573044846332197374133735280061169662994929318277495026639257967512429196985156677620832084464806731394586645584004800120209390596199043214702383692014720025106664770174945246104271828750881876779961563878425912819249769237146877423586658588382371747117706103904717992143763432526906134340918158797429112104747798857792953798556664818765369589877611935981826123989653264519369173971213350475042988003563201289593575114503994965776303928583359335670439472472680724520021982775884433764832278044132394712015849375009412371356571800149778434881277050352255177966718573968166131022775740463572484707360634388082212835226408459654332510455498161694286292021078957712808140237777028562479131087210088132692812252703797967203941717754915849861153851179245614672468896570877849828876521554367726204207736007841015352238262547114437726671005190096135003395967191079606745936255581905267924656687990393244518754870143787023844073442539728720624871369329824913589099232130954313995572136022345885880961465813300921034149568874322884199451306385344163843132642227362760726706698817634094506564473285537795394273820915990438659768935090702293222287319110190843609450474457109902688627101463380956073149395010506044297357590279983039848214252363039814716187469642831184972573385553211218251214969812068265981070995732802951068305150870946646996114490332054014333814976825756060273596517054135019103776665977633682098964168388481910277583202336220652845525337189138372562439722020211458565847442341592084824237202422183956021062122603107944659497144987811220268840703860177391434611323558189517810776438917942356660870589229735263804978781907503398355084711487106341147404808318682305531045350268931898722706304935874153652050719683350607501338308123952811811839379795597433529837887157122530855713018419348789841888358137698895494556223222880864987540923392955831111721033529277203511809773287972064457414153793599483385425346404611284677466981919471547009095398723288485872909536411431104258613982796068207669330646775840099655743340304209641081975519087261960956472161500424533689452640752837671416551079898467049091772339743684866144800132396410600785183718576864397450517251483036252499106108246849673135704828263470520558565901281832765988329027203296872108292971003165974895638941853371950160249092123046110803164347046903419337214130981995715015524312237276190017911511231290241443379580537569540963382583893; a=((2^(6048*2))-1); b=227160077046482876543105891084100845157692694930009934810441010055051139162201195856634960442412185050869094038166182124779529982796045125692766957161108830913105184571961987588595741494542926781061234060443216412783969935039897967347195237994196604995375922805693159337042359654371720461376081998527986928395752881528032432466745586393443989599212137534592426860247658725277316759393738049797040088563242760615390818485698598069614719223176365753041408928343440145460743665870552476459349758310582326204348231674267297425103114129188708547180972683789088844416135358781896947211714597948746602920429521302343896983518170603245508599467298227465285705987521191637796174277677120755014928760806324225178921629608697466828180658297825590050050896790900545036199956049102442147769366943213222091321546468056496065355365054945541776966586154432493435362886628041774601070595259482762699111290746691681782636349839756724855670475493577472890811765832742448436806950857363717803928499911228901758034532049508461815465301214979811114936131367796261059222317617741910806260627393930621438477785424692796300217033762559890768601281; gcd(c,b) Output: ? ? ? ? ? 227160077046482876543105891084100845157692694930009934810441010055051139162201195856634960442412185050869094038166182124779529982796045125692766957161108830913105184571961987588595741494542926781061234060443216412783969935039897967347195237994196604995375922805693159337042359654371720461376081998527986928395752881528032432466745586393443989599212137534592426860247658725277316759393738049797040088563242760615390818485698598069614719223176365753041408928343440145460743665870552476459349758310582326204348231674267297425103114129188708547180972683789088844416135358781896947211714597948746602920429521302343896983518170603245508599467298227465285705987521191637796174277677120755014928760806324225178921629608697466828180658297825590050050896790900545036199956049102442147769366943213222091321546468056496065355365054945541776966586154432493435362886628041774601070595259482762699111290746691681782636349839756724855670475493577472890811765832742448436806950857363717803928499911228901758034532049508461815465301214979811114936131367796261059222317617741910806260627393930621438477785424692796300217033762559890768601281 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.009s sys 0m0.011s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:53:37 2005 Input: c=5797823745542894399993487984408732919807460200624973431074868080347645352260100952324738511950763724262121814980063504059562977955970970581874445554627116627444138926699214976790169964178061161439567059686233961727236180939873744234028207313892948365655868127645068240116546953224593732162610027320800194425045367703123128343893318374569037035627029663633410968825017631579344443351543267671413436221535075533934844319870944314641570712548742378141900257975072532629968012997437656844023150745255228381078006737330505750375699518695164395959424228740289690186497133584902191461985593809857504272011414930182772125582365213464036372477370110622258207397036389537708616060658094459019550126616878641069275248732480856893847779916560257861246295202130274212655050971961155090417913968255852450958009214217966027248188300086832767493242699946510625252384583732905164401388433509883135164475339102533895571876619167405209391249913398960791445787041332334410761993117151559521378152852405702101621115722294847138297153321885756389320255480526656716917626729030624894973016710698211512295405729598557044223451517347186312556775805726456531983227802392701151293624124335313811685898438945287476474121146663010518542517015594623627799676914552219065889333667812969877931515670702031943956550393464424152900640044266575396117130397594084848238654978874753888604085018963737305599498020494685441050277516966314451114328192214397965084832138700185754112181266414772663420940223707880581953673746498221530252071960778869737171900946587790929248983045950733854539713896350593165327179836287050958650956718174329098466154079001657622166511036408311058663618713605507360287438633636033199540265724323348306190653781383419572410108500377482307618865271400027003766023114724930694330579359674578223340706304003319978657914612649077336689029537168115250888090999419965875876763423571346087009816515777006798609964217986477279108027560968366962629095094310303955957554625281798041891827402183385275287386792434615484694191826718762503111837603867932751801229320338455236928171436299059702189628849858539310321113679628742955592688733612359563479377924251182481161685322763600450057048668941638674344013886960007454614023232199838373437859563027418113219816327306989869242205848028315420645208072793641330052178464989667270184893877125090941157319612844864624339046477165157443124603012830185955417244845208081335197980361605705297886972446586748402673417060901066885802635927427902224309633940198256783425246142132459750210067239654526128796807161731273051516653854066482065656853251012007985877801429029417347984118783140944475347207986340778070950880778436102683422612473474924765705052337651237765998939967979714062202177760555271270359887420978914352566630540089313318857382084201976665271004878041090016516211761458391823609016277074397368210383732056399063702465193729259823279291857265126362420663301138313517586532295161531272710810101938656474581000935530017492901572754456311921843255660109487053485391755134559553640592418221176748283883774718754947058378011620115891826507923478518124826949309434956138609001661304577460859514178001628724253768896483902688941069363161455449804523380324948313834113673547829030917966652004262765639608493376484583713882458735023637868211826217728360572301532930786704745522894747171137460605029519653478073131170979653331801900154715133339862631178167981678863645431760496550585658840130724512470114693039786987135253858205443844681950841797837716550385839189978562909486502003957460556810720955234423355119255826579106568196055562394140623236496978722308472521602175159833166601475531486865945434101231820892529537998095170393982884436694121486750190129079154407296208239783072469487394485244105237404588930652469736185125415719936611110294917602728429590491871694141075162281526296475697645370008529908792423207560148055577117649084585665090212447199213701223874362481445617172472369197163772960709808294256136944733486574194386781731023925301630343437611155765549297900159045143421909139582678213692239526293746722057704822724501553473399654617555741424998399849663015581623391569001224354313112085758299559586859302625876615043883662839750081669323473183708349980893624669789669337200100682471597045312877434383318451007297166943244939988340597543247684605555302464216048398165719273112225441292134892203745031295683988359176047259723587623006240274938517109508115690710171169507803637801260508711632465250333201127495013191158942484099767197276171260927052488463210556468309638725452670554539578237440307286945000027409457053406124158083828366269606759227276689263409429631117583789413389571971913525375055189019402438395752201987798444552502363; a=((2^(6048*2))-1); b=227160077046482876543105891084100845157692694930009934810441010055051139162201195856634960442412185050869094038166182124779529982796045125692766957161108830913105184571961987588595741494542926781061234060443216412783969935039897967347195237994196604995375922805693159337042359654371720461376081998527986928395752881528032432466745586393443989599212137534592426860247658725277316759393738049797040088563242760615390818485698598069614719223176365753041408928343440145460743665870552476459349758310582326204348231674267297425103114129188708547180972683789088844416135358781896947211714597948746602920429521302343896983518170603245508599467298227465285705987521191637796174277677120755014928760806324225178921629608697466828180658297825590050050896790900545036199956049102442147769366943213222091321546468056496065355365054945541776966586154432493435362886628041774601070595259482762699111290746691681782636349839756724855670475493577472890811765832742448436806950857363717803928499911228901758034532049508461815465301214979811114936131367796261059222317617741910806260627393930621438477785424692796300217033762559890768601281; gcd(c,b) Output: ? ? ? ? ? 227160077046482876543105891084100845157692694930009934810441010055051139162201195856634960442412185050869094038166182124779529982796045125692766957161108830913105184571961987588595741494542926781061234060443216412783969935039897967347195237994196604995375922805693159337042359654371720461376081998527986928395752881528032432466745586393443989599212137534592426860247658725277316759393738049797040088563242760615390818485698598069614719223176365753041408928343440145460743665870552476459349758310582326204348231674267297425103114129188708547180972683789088844416135358781896947211714597948746602920429521302343896983518170603245508599467298227465285705987521191637796174277677120755014928760806324225178921629608697466828180658297825590050050896790900545036199956049102442147769366943213222091321546468056496065355365054945541776966586154432493435362886628041774601070595259482762699111290746691681782636349839756724855670475493577472890811765832742448436806950857363717803928499911228901758034532049508461815465301214979811114936131367796261059222317617741910806260627393930621438477785424692796300217033762559890768601281 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.011s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 06:54:40 2005 Input: c=1376403141124393317479415948243413523100884877956080727967212222127149819550994722930651516028022452364068751255227317568406984541732756451837232116550147277736428951589324100788206872583314502971559206394742034508720240583124404190405951487230002666938330438057214700069716072691503404117737542764342050518643548286160949416951666498933472722981095483118799043106609158670051964658632970025921641683818299734296203411666209857616618680473794303530752111846521852001723383425455314283480950828940626280734193375044732889292031051253056008106285770579825763983341954560832421684513990419790858213490545722322220721615509066618072058934499467135784647354009654173287315260992139417077393935132962531004414419482316267976488179256672323139689918477090262548150312344617176422929781339831450601384282272270990890223024153408327101794389042704468576495979855554573157043106336119822233465576200523482703872553352017691307642704793950643278476038117099527774454447037707575140447569454729750189339614099978043218898515304570525758404409201904552671459947130223661836982203730020810315098130218165235420763624085828665762034192985304252786228276748730388892970404026401773515149106236001944140576965561273860281443661330532496714514415554384645962051281619121020735726930929958190384844550088587950297379891853872937756435212338740489849957508143625229688494778329529388022491894936892269509344246759569815582776805291645358755481050786063167911987345642455745546721686433847258802099884845539174715511302877467680231303660110717638118171020312245569804820629232212218070621122210644905494988601502682919557111689486873400208013339746150862362513599587697586890482587381046723722332378495962053067465763087538427477325322052956023491202742171122140936374594123539187952477062597727953691406458790322768549823246531499615094226698043435497041665194302068431399091196293699661615341989996782940117003422526176122231437813076312281160041513128304543580522733106299360374892788046683446653595106632494857568350159031568739474384341306199225856384376750600163839383148425378633587046993121036846490530277673398980463020431016504917275631391374056539099907087500029464409718226209321538327236046594915158509262769362956559586806015235371798614460512257814357265711858968327443604612740833094077020812795255800110313491736816559349473307379226191641410099459404547890942950770109022584585472530215691699755736111222341601976778157264579922308491381207742589563499384608950687951893902546688623161714427232843801818326429282174781073035664131271056028325932509556162678762430882199603294330104835970592548715005620345820937684525542428017968801963957862189064629661273451646365193623346136449693817502702865573323069669859543660782391476386082909475281405242437264305143479338227191441298469541301465870325096641710616422520556580184994089088809991646614411035764315479251190976747777623070216724627460301561836427925996782810134375367985981845681232590951338945129817494682183576740004148963206688812104063616335458758417227835500965188668178884025244845925528075538403320316167438465898945944794411435220839087096718669081211879413841269577739407785119339052021534091336797178291629905066084971436698619447438313476962963332235220678944347919779629862751335766971556179588418726990034633649625600526271918212526668594184497451784060926394208281383802820596610953079228637185959263664193678926459683089569740477841162771998483318231748805871846449429464647118463560641741438301400170407770591020477876634421733599378883417358943784831249098051988148951740655084832056504593105304231592345534155947893934487182687382710361490778977225260366606506982070367576737905328730505842222123430094003505172739814976458229083083894439614318445182796698743022927556324807142416731657801425288677257356231060453089716475158169198599973620946481989385471603013866122678677983519673612571020870216074432619772114905245130250695691788585382613631034089595503311172216223527461386617564443035002325120549046573323667107706805487104973312407071642737302745357300157902228144356305469490835329217153264563331692515398195395604366336183086577727196307414201910539087239402113374547505994618836447492134909362457747797067604651350981848461207125580701569785340853968426915129736348586146293648798401023588824853997992509724764226913346501712790585863318709056154539515840688140827322627023453093842117720984810024619123259092181277335796155723339217395373565885878249198438718426596985268071704960882654314266465334657207319339692637624494392467817633270129188655342319672014469357610008240731042246818235157075213334004981356595961036431783007537596572033983773690558040912810055254135239789652788219; a=((2^(6048*2))-1); b=227160077046482876543105891084100845157692694930009934810441010055051139162201195856634960442412185050869094038166182124779529982796045125692766957161108830913105184571961987588595741494542926781061234060443216412783969935039897967347195237994196604995375922805693159337042359654371720461376081998527986928395752881528032432466745586393443989599212137534592426860247658725277316759393738049797040088563242760615390818485698598069614719223176365753041408928343440145460743665870552476459349758310582326204348231674267297425103114129188708547180972683789088844416135358781896947211714597948746602920429521302343896983518170603245508599467298227465285705987521191637796174277677120755014928760806324225178921629608697466828180658297825590050050896790900545036199956049102442147769366943213222091321546468056496065355365054945541776966586154432493435362886628041774601070595259482762699111290746691681782636349839756724855670475493577472890811765832742448436806950857363717803928499911228901758034532049508461815465301214979811114936131367796261059222317617741910806260627393930621438477785424692796300217033762559890768601281; gcd(c,b) Output: ? ? ? ? ? 227160077046482876543105891084100845157692694930009934810441010055051139162201195856634960442412185050869094038166182124779529982796045125692766957161108830913105184571961987588595741494542926781061234060443216412783969935039897967347195237994196604995375922805693159337042359654371720461376081998527986928395752881528032432466745586393443989599212137534592426860247658725277316759393738049797040088563242760615390818485698598069614719223176365753041408928343440145460743665870552476459349758310582326204348231674267297425103114129188708547180972683789088844416135358781896947211714597948746602920429521302343896983518170603245508599467298227465285705987521191637796174277677120755014928760806324225178921629608697466828180658297825590050050896790900545036199956049102442147769366943213222091321546468056496065355365054945541776966586154432493435362886628041774601070595259482762699111290746691681782636349839756724855670475493577472890811765832742448436806950857363717803928499911228901758034532049508461815465301214979811114936131367796261059222317617741910806260627393930621438477785424692796300217033762559890768601281 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.014s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 08:37:46 2005 Input: Mod(452,1147)^2 Output: ? Mod(138, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.331s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 08:38:01 2005 Input: Mod(452,1147)^4 Output: ? Mod(692, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 08:38:14 2005 Input: Mod(452,1147)^8 Output: ? Mod(565, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 08:38:26 2005 Input: Mod(452,1147)^16 Output: ? Mod(359, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 08:38:39 2005 Input: Mod(452,1147)^32 Output: ? Mod(417, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 08:38:51 2005 Input: Mod(452,1147)^64 Output: ? Mod(692, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 08:39:28 2005 Input: Mod(452,1147)^128 Output: ? Mod(565, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 08:39:44 2005 Input: Mod(452,1147)^256 Output: ? Mod(359, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 08:39:56 2005 Input: Mod(452,1147)^512 Output: ? Mod(417, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 08:43:21 2005 Input: Mod(149703,1147) Output: ? Mod(593, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 08:43:54 2005 Input: Mod(335045,1147) Output: ? Mod(121, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 08:44:15 2005 Input: Mod(50457,1147) Output: ? Mod(1136, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.249.105 (168.122.249.105) Time: Thu Mar 24 08:44:49 2005 Input: Mod(513472,1147) Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '60.35.3' ************** PARI ***************** Host 60.35.34.62 (60.35.34.62) Time: Thu Mar 24 11:17:19 2005 Input: factor(208985912004232692112989418962913512143454946422920593821299571281505741429255867900662632079343171630051175697271076302567705286976144762874932292328157121848234881) Output: ? [208985912004232692112989418962913512143454946422920593821299571281505741429255867900662632079343171630051175697271076302567705286976144762874932292328157121848234881 1] ? Errors (if any) and Timing Info: Timing: real 0m0.125s user 0m0.089s sys 0m0.006s '60.35.3' ************** PARI ***************** Host 60.35.34.62 (60.35.34.62) Time: Thu Mar 24 11:17:31 2005 Input: factor(59865091562028169565031261511383796403314949997486501394077091779336886690231729006236862939) Output: ? [59865091562028169565031261511383796403314949997486501394077091779336886690231729006236862939 1] ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.025s sys 0m0.007s '60.35.3' ************** PARI ***************** Host 60.35.34.62 (60.35.34.62) Time: Thu Mar 24 11:56:58 2005 Input: factor(5379067687293838489899471787387056657106736549649316523287796764105644846345909489590917706708507493649123048981220179322840142144660751937074891608289707032413433507208827489006772472139145809) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 25382 Killed /usr/bin/gp -q -emacs Timing: real 0m21.028s user 0m20.985s sys 0m0.017s '60.35.3' ************** PARI ***************** Host 60.35.34.62 (60.35.34.62) Time: Thu Mar 24 11:58:25 2005 Input: factor(5379067687293838489899471787387056657106736549649316523287796764105644846345909489590917706708507493649123048981220179322840142144660751937074891608289707032413433507208827489006772472139145809) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 25401 Killed /usr/bin/gp -q -emacs Timing: real 0m21.039s user 0m20.980s sys 0m0.022s '67.67.9' ************** PARI ***************** Host 67.67.9.194 (67.67.9.194) Time: Thu Mar 24 15:14:22 2005 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.006s sys 0m0.007s '67.67.9' ************** PARI ***************** Host 67.67.9.194 (67.67.9.194) Time: Thu Mar 24 15:15:05 2005 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.007s sys 0m0.005s '67.67.9' ************** PARI ***************** Host 67.67.9.194 (67.67.9.194) Time: Thu Mar 24 15:15:32 2005 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: ? 366,378,582,594,846,1026,1374,1386, ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.009s sys 0m0.004s '67.67.9' ************** PARI ***************** Host 67.67.9.194 (67.67.9.194) Time: Thu Mar 24 15:18:31 2005 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: ? 366,378,582,594,846,1026,1374,1386, ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '67.67.9' ************** PARI ***************** Host 67.67.9.194 (67.67.9.194) Time: Thu Mar 24 15:20:29 2005 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 15:23:47 2005 Input: c=9019518416950496514607021993442341214242630778291978921531924189540378811860382033077382435363030464213363952749413272911959521902752888406979964918875578335803432885755271009464277578935368200773357170822191216892304167237924423683233231466622302966021541728870433282433227362897752359174819625758350435817211379151705043042137077654094342408334652044070554765912281798811455678308021972218522966391011801585158863259904832121797839241326221247025778297157975463693446453777366777710954558320286838440302730852929930543135397574175903136623212863808422561573827176391074068989323337111790295402349880479956351794616502135536070009875034870415150933141426017159068960546796622916845109634425643791168101897485904382771759665699593361027951231175526153117215421198024431990833911488587253145354123301840971112502275518161541519477878175794029162824290947908702497689584102875944708021522699560117207558888948589267497176698947319331413820888216247551750236072826005747429048821542185392198214923229137441713961271604281270205241214704025698583344852398591264398644377288724721112203713372963383331232059201725993002347522673496503294267872982300208870195201; a=((2^(6048*2))-1); b=227160077046482876543105891084100845157692694930009934810441010055051139162201195856634960442412185050869094038166182124779529982796045125692766957161108830913105184571961987588595741494542926781061234060443216412783969935039897967347195237994196604995375922805693159337042359654371720461376081998527986928395752881528032432466745586393443989599212137534592426860247658725277316759393738049797040088563242760615390818485698598069614719223176365753041408928343440145460743665870552476459349758310582326204348231674267297425103114129188708547180972683789088844416135358781896947211714597948746602920429521302343896983518170603245508599467298227465285705987521191637796174277677120755014928760806324225178921629608697466828180658297825590050050896790900545036199956049102442147769366943213222091321546468056496065355365054945541776966586154432493435362886628041774601070595259482762699111290746691681782636349839756724855670475493577472890811765832742448436806950857363717803928499911228901758034532049508461815465301214979811114936131367796261059222317617741910806260627393930621438477785424692796300217033762559890768601281; gcd(c,b) Output: ? ? ? ? ? 227160077046482876543105891084100845157692694930009934810441010055051139162201195856634960442412185050869094038166182124779529982796045125692766957161108830913105184571961987588595741494542926781061234060443216412783969935039897967347195237994196604995375922805693159337042359654371720461376081998527986928395752881528032432466745586393443989599212137534592426860247658725277316759393738049797040088563242760615390818485698598069614719223176365753041408928343440145460743665870552476459349758310582326204348231674267297425103114129188708547180972683789088844416135358781896947211714597948746602920429521302343896983518170603245508599467298227465285705987521191637796174277677120755014928760806324225178921629608697466828180658297825590050050896790900545036199956049102442147769366943213222091321546468056496065355365054945541776966586154432493435362886628041774601070595259482762699111290746691681782636349839756724855670475493577472890811765832742448436806950857363717803928499911228901758034532049508461815465301214979811114936131367796261059222317617741910806260627393930621438477785424692796300217033762559890768601281 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.008s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.176 (128.197.60.176) Time: Thu Mar 24 16:54:23 2005 Input: factor(6653) Output: ? [6653 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 17:39:30 2005 Input: c=1552494403116096590440671964995233552299547535037006842840371728072619365348308060972256171809040564305486225726849098236609896874679392779405645645296960600062685900168308854798981543625775610536762330356886484853623027212983664641; a=((2^(6048*2))-1); b=51001264246554923426512935206051621120025607714695965533761488057718965836780582760080565615420773495226910862271611985727454588863218335227397686595581846602653852094611868252256902497185121570561; gcd(c,b) Output: ? ? ? ? ? 51001264246554923426512935206051621120025607714695965533761488057718965836780582760080565615420773495226910862271611985727454588863218335227397686595581846602653852094611868252256902497185121570561 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 17:39:47 2005 Input: c=1552494403116096590440671964995233552299547535037006842840371728072619365348308060972256171809040564305486225726849098236609896874679392779405645645296960600062685900168308854798981543625775610536762330356886484853623027212983664641; a=((2^(6048*2))-1); b=51001264246554923426512935206051621120025607714695965533761488057718965836780582760080565615420773495226910862271611985727454588863218335227397686595581846602653852094611868252256902497185121570561; b/c gcd(c,b) Output: ? ? ? ? 1/30440312138359703439668535634817281 ? 51001264246554923426512935206051621120025607714695965533761488057718965836780582760080565615420773495226910862271611985727454588863218335227397686595581846602653852094611868252256902497185121570561 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 17:40:02 2005 Input: c=1552494403116096590440671964995233552299547535037006842840371728072619365348308060972256171809040564305486225726849098236609896874679392779405645645296960600062685900168308854798981543625775610536762330356886484853623027212983664641; a=((2^(6048*2))-1); b=51001264246554923426512935206051621120025607714695965533761488057718965836780582760080565615420773495226910862271611985727454588863218335227397686595581846602653852094611868252256902497185121570561; c/b gcd(c,b) Output: ? ? ? ? 30440312138359703439668535634817281 ? 51001264246554923426512935206051621120025607714695965533761488057718965836780582760080565615420773495226910862271611985727454588863218335227397686595581846602653852094611868252256902497185121570561 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 17:44:36 2005 Input: c=1965971958187633597535416240487262504016735365972853497345878700361134631200015789357474967113225609488346196642242734189414464888538284879288609670301166040041572354960009110185090480750662352867424968770473044005432652375051048186129055571477004565285979750216000861428883194571895943012315295938330428032180623753846841056780750972412648880946006153056430441664563040283077703382814150741532298000331540559680440737843796202294651924407003332793162032840248447186585337013865930289; a=((2^(6048*2))-1); b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; c/b gcd(c,b) Output: ? ? ? ? 2471256853011621119922157195546386510921469951135168798701747802379149509612541743659666166929504836642035468657978532825019720368239155939811744601737074578347198207554210017644650446484267402115811943592802484336237755653769746410354085771567944773868184706603362772952592261904433504279676287223371884154418143902065022821660473900760882745535119 ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 17:45:10 2005 Input: c=5504900545319378881963669959626048407940196811271133436242631249772527826414660817761386094610862183316670802750775677472316926066572394549327130593623639503462960022594003412189630531307627230651212742380186394426881; a=((2^(6048*2))-1); b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; c/b gcd(c,b) Output: ? ? ? ? 5504900545319378881963669959626048407940196811271133436242631249772527826414660817761386094610862183316670802750775677472316926066572394549327130593623639503462960022594003412189630531307627230651212742380186394426881/795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 17:45:36 2005 Input: c=5504900545319378881963669959626048407940196811271133436242631249772527826414660817761386094610862183316670802750775677472316926066572394549327130593623639503462960022594003412189630531307627230651212742380186394426881; a=((2^(6048*2))-1); b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 17:45:56 2005 Input: c=5526446061971807490121430550987003612992514350641740022450848825408149971512720851212882390047004284478729272954734797647577798774788972706754439254531209229055276354325464792618800428422407819952525408935662074462721; a=((2^(6048*2))-1); b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 17:58:38 2005 Input: c=5526446061971807490121430550987003612992514350641740022450848825408149971512720851212882390047004284478729272954734797647577798774788972706754439254531209229055276354325464792618800428422407819952525408935662074462721; a=((2^(6048*2))-1); b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 6946827316925268800938223490149102474198424275692237475352753209803191224399782591 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 18:21:46 2005 Input: c=5504900545319378881963669959626048407940196811271133436242631249772527826414660817761386094610862183316670802750775677472316926066572394549327130593623639503462960022594003412189630531307627230651212742380186394426881; a=((2^(6048*2))-1); b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b Output: ? ? ? ? 1 ? 5504900545319378881963669959626048407940196811271133436242631249772527826414660817761386094610862183316670802750775677472316926066572394549327130593623639503462960022594003412189630531307627230651212742380186394426881/795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 18:25:35 2005 Input: c=30422535940226736991509627739466313462398936196548531143404341177712044584323079983854699055717286475957489668260496255023637598331061177965894193851904738922918114174742194995486875185421377031387482763445719476257231856135897340426943759633846214073768481351525269018069742309973055082931934997141602248278577436505802992799139046856236576191741951990954580177375065643077463753751426175477160046073159594885460375387746426794803201; a=((2^(6048*2))-1); b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 38241593485181469888230596512551961883348139659746591067470075405758110254380635352463849854742592132005032257311476047829037900745550897565634878325695705990230480323930151902193376508780817993909483119484034989475639188409612489380803042791621706880450990321341936186332019539968752719270446228671 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 18:25:56 2005 Input: c=5504900545319378881963669959626048407940196811271133436242631249772527826414660817761386094610862183316670802750775677472316926066572394549327130593623639503462960022594003412189630531307627230651212742380186394426881; a=((2^(6048*2))-1); b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b Output: ? ? ? ? 1 ? 5504900545319378881963669959626048407940196811271133436242631249772527826414660817761386094610862183316670802750775677472316926066572394549327130593623639503462960022594003412189630531307627230651212742380186394426881/795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 18:26:24 2005 Input: c=5526446061971807490121430550987003612992514350641740022450848825408149971512720851212882390047004284478729272954734797647577798774788972706754439254531209229055276354325464792618800428422407819952525408935662074462721; a=((2^(6048*2))-1); b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 6946827316925268800938223490149102474198424275692237475352753209803191224399782591 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 18:31:37 2005 Input: c=3671549673397374468724111447436967120664276627159906795709663861859176263933242223404854138560601051534715254054759950628856445042453562376646290906017450216124878302916216047129534437122545363369517111779007431331595310739585757928523108227973505876167812502196158768385409878792547969627352100612109324195338918155379466840430450012390189220529000341958627292126191681301734921865161006062800198089926204596019635680677221210761; a=((2^(6048*2))-1); b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b Output: ? ? ? ? 1 ? 3671549673397374468724111447436967120664276627159906795709663861859176263933242223404854138560601051534715254054759950628856445042453562376646290906017450216124878302916216047129534437122545363369517111779007431331595310739585757928523108227973505876167812502196158768385409878792547969627352100612109324195338918155379466840430450012390189220529000341958627292126191681301734921865161006062800198089926204596019635680677221210761/795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 18:31:58 2005 Input: c=87117970594172345251077962474330593587605161988644077984517179654642393084780705852042907579746122650953666983092623921827640855555739747597286416721768222755459081773248548220828153022829183072529782550603162142124250861831206705017641607675087762280901997233113199483118126916075307456975776323554844448045714322529392598872476267041257576251091525619812636978837769418586052288533152142464512113141091065119857921608615331339113; a=((2^(6048*2))-1); b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 109508622925518758374779330634226928144809083282897561331625081782758231287690505391037887273680676731802564646027918396520877649291899968507104413182367929574460426673978563751578369965668831497957651000233004311320112725774763624237273938790777277676842174416017275106145008497510274212379195223 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 18:45:27 2005 Input: c=46713459698496361911039025290217844357941649030880971950435423799280919971943575170922962693577353707052593978416329607074677100216558187016776654376026006277427800726204776467107934913116488166482884682955209998613085253083587955950612489433865105475760164844882396468411693586222819501915623746790669300472643801015154790350167423855496950060158052202773843724391682400166209310079047035769548932785877735238566952371906441562723224375834806190498323062317143353600454192786468369596929; a=((2^(6048*2))-1); b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 58719534084409129430470377123377689886005047508922745825952229532330971497903604371097327792411964423451404770782227918455293575669730584285866863481874629056107776609695584229254539258912677741673807591708579830313345312089222944456423432018225935771881936813602502848126544735111244495189388260714539339393129517256967007265474520355979334916659962559 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 18:49:56 2005 Input: c=30422535940226736991509627739466313462398936196548531143404341177712044584323079983854699055717286475957489668260496255023637598331061177965894193851904738922918114174742194995486875185421377031387482763445719476257231856135897340426943759633846214073768481351525269018069742309973055082931934997141602248278577436505802992799139046856236576191741951990954580177375065643077463753751426175477160046073159594885460375387746426794803201; a=((2^(6048*2))-1); b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 38241593485181469888230596512551961883348139659746591067470075405758110254380635352463849854742592132005032257311476047829037900745550897565634878325695705990230480323930151902193376508780817993909483119484034989475639188409612489380803042791621706880450990321341936186332019539968752719270446228671 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 18:56:57 2005 Input: c=30422535940226736991509627739466313462398936196548531143404341177712044584323079983854699055717286475957489668260496255023637598331061177965894193851904738922918114174742194995486875185421377031387482763445719476257231856135897340426943759633846214073768481351525269018069742309973055082931934997141602248278577436505802992799139046856236576191741951990954580177375065643077463753751426175477160046073159594885460375387746426794803201; a=((2^(6048*2))-1); b=3032439252874850892655549311808025559552817118945260647114694548761484146747722246839292990651932207379790258924796716413356726448028778354929959918595296062381366280741601473736900500127465700209513923300255285539688167227131565809214601721168543734214139243940182308814799111008893861877653978030487830697771055105061189783007160508792624501734586408444846820690885599357894652773386146403500815679993731490224562140278471041961287181776835797741847725346069209740322500693733962156171039713212944468296419274264547391846890978075292050257663855655742723435816446311229484859569453346291018446485271226803170253635042349404578164772933389313448554543835543429681211527641509929664173753734389482031832124838357233597235780545505623007907671884908600199750379391634354142317495769991909463870651602278747479870586131579987198470935431741683007686315405060047386787250686698496126963356747613310633029095590456750864644563021075067207617676624392288591710564352955018115225136716561051421414729511285420126684335899213208012223357602029848860233317934526832795662762238328096664445488272766651550316496151629024802253538973977584117575026653298772209991438499613378717430668007426702744786616172961510600678856556449035281853232617964583200525089103211148406948198039255574978071481; gcd(c,b) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 18:57:19 2005 Input: c=145298250842732500377305328082818709008515987975368766033273809112073090531715104442708645166722681591009095687751054559144204868878846572569116947972836654427136822276999508072880542501141359385824976631419001192006058776957272713187414059340807225209795657811138833858142423204773004990056907580926168033036374963591829679740545420531179677586007314866054364801768192782286447364634531429940621746764078669169034160092911080947774534817288950180046841706856738262749179456136108433184152061601762176496920783136210743389393204020856895767582139351922785511862195422056460515639882975133574895283623349874016471; a=((2^(6048*2))-1); b=3032439252874850892655549311808025559552817118945260647114694548761484146747722246839292990651932207379790258924796716413356726448028778354929959918595296062381366280741601473736900500127465700209513923300255285539688167227131565809214601721168543734214139243940182308814799111008893861877653978030487830697771055105061189783007160508792624501734586408444846820690885599357894652773386146403500815679993731490224562140278471041961287181776835797741847725346069209740322500693733962156171039713212944468296419274264547391846890978075292050257663855655742723435816446311229484859569453346291018446485271226803170253635042349404578164772933389313448554543835543429681211527641509929664173753734389482031832124838357233597235780545505623007907671884908600199750379391634354142317495769991909463870651602278747479870586131579987198470935431741683007686315405060047386787250686698496126963356747613310633029095590456750864644563021075067207617676624392288591710564352955018115225136716561051421414729511285420126684335899213208012223357602029848860233317934526832795662762238328096664445488272766651550316496151629024802253538973977584117575026653298772209991438499613378717430668007426702744786616172961510600678856556449035281853232617964583200525089103211148406948198039255574978071481; gcd(c,b) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 18:57:29 2005 Input: c=148334421519665118824430541267506583249081933160894787624316330189887374358587786574824639188015244264268656682550638767336391730835627721683310786126063759206243120093210337688638083209140833257436028075207143821340347701954933902050987098754709498689664912936272736331594886559232859042939889784131479618529360254851390777606261835242612722671794961758423350763464136140006613076277405584949498697724552913898330094229873736337317586321381262103602025913266740247091245532297265498355690818017551080325392069318090100346112384780612585684050581100487844518771337113071855515422021981916811297725335767698864102205257411882919993795509636879441761450483261996380633910461690949989308537861608107372194376056866249750929133054336234134091754770724406981669815815388070732192501355595686656598250864071436517628132471583922946329438471999569721047613113937665410239840733889223084657906533329045458551778909510105838022264855134332504437832059285283098455524540428373264234488801714443379270629464036979671041303819262544405907369140718621883811355856221743109589356179325334639029355108643185576161871289827104691588226600951073502935613042370699851022868091227698544890649803731037555906039626024174629178000475278329456451022358960857933854059460108310522403055716910000012827918741669841948569271710154404440504851422118801480339724048772716770509234991005933619943359257638811127436835559867186748407498045676675283973257068258833410060325508834633879913431018755384410047370548558263126307786737798931201278448020048055712441172709564665490622217448709851770718799020822178067478714191047362154858731378689009732480759501503621280279886852887766754459887094343782430912862175613398814916612135272802168380209571277052603955384543110064407754574319505092970823025956469981853985537857452591556676303847317078622698018027864156842904059551240321641996562951745601278349473973684770114424455301660244050824725389711240963439627951788969415425125070639163661640038559409931435597996545968126800059651015217425045991224598383037049049694531015588688611228536339205878839572128642088678477800436073882981984282980239066289981137922670635573085045263762089470072356982286247121250410503821717135214372270314772003459012052206627303403845932393822784648723583724039632471270155494033980207280651135992635389607085464817411264428785609016401335067085913597498982146460766295938406923372779721044192707828301983084069655455746820661546865731063652768480019126724525129116876782206985156985407905179584439963704590489684087847908940022988587467158242267987932930035721737469930131401283907144499292630164871466925064528500716096603704536386676195863559223927811260773020499981038855657852573916951204961053031011085663671520871498784255634786355459297558480290698431962722054451152784850586231136255033911374680932941755908662235612788788377787427061415109486676979468005113408652082619517459302321182960022530287123231685896526797861200143979534499936095216417489178675220757921292640710117270138191300686540653054663088209521406192192431762257698703761343069836981712878467976400950860413623625386395040078036882010583230623137003372230847590577757567033584143054636828154977569076071008477850225740069611381605598351942925863653738783491943117885932607058975348272209775464444761674845493869303765167795560803633220675769561170954956611557710077660178514994287337773051437137356098630364098683713535136938713244387897678818134795040760604063503575149895533641830060354074460031614059451021145082759596255794109528970763464579560298246623848964150753583797467145255307543791174677262924782993614103420670497967490866820440303707806406867753798305933858761190843856795907646435375171170570970010310640899010997039340805309860938983443879895033186367260849030458598062390756013022481807838636287666243355328670165630038285875903324602475109852330131229699408450530444640305615191997983653855232020439680583506233471330485788887402486680270506541357906759236483562533359069586855438774629726795603898699615294561959109859398204865043872308186759009463059996920598323766042269314577817539955184095019301761538021917928489034564666199112790539832851669682657346794408166592056574801502764450208138897073003265425237617235915625971640439787486896409357990163250067557376247723957512050031759067466288798828126119640179804137995289333688431467697741618822819142714532720326329528296159556472259376215987919634589507521538100703935114034757819606389191260335633234357827816526031458442735348644718282505087408562440449030598957063653960721147543438464474916645427639758382087474284269767439552262323876586946211189296611664679530195212139927419217548875458481205817007769659251734076919839850707983057531088366782240049051214940948105184195696472962594733543046040138657711282427129912121030872152914101403001145793591959864865073; a=((2^(6048*2))-1); b=3032439252874850892655549311808025559552817118945260647114694548761484146747722246839292990651932207379790258924796716413356726448028778354929959918595296062381366280741601473736900500127465700209513923300255285539688167227131565809214601721168543734214139243940182308814799111008893861877653978030487830697771055105061189783007160508792624501734586408444846820690885599357894652773386146403500815679993731490224562140278471041961287181776835797741847725346069209740322500693733962156171039713212944468296419274264547391846890978075292050257663855655742723435816446311229484859569453346291018446485271226803170253635042349404578164772933389313448554543835543429681211527641509929664173753734389482031832124838357233597235780545505623007907671884908600199750379391634354142317495769991909463870651602278747479870586131579987198470935431741683007686315405060047386787250686698496126963356747613310633029095590456750864644563021075067207617676624392288591710564352955018115225136716561051421414729511285420126684335899213208012223357602029848860233317934526832795662762238328096664445488272766651550316496151629024802253538973977584117575026653298772209991438499613378717430668007426702744786616172961510600678856556449035281853232617964583200525089103211148406948198039255574978071481; gcd(c,b) Output: ? ? ? ? 3032439252874850892655549311808025559552817118945260647114694548761484146747722246839292990651932207379790258924796716413356726448028778354929959918595296062381366280741601473736900500127465700209513923300255285539688167227131565809214601721168543734214139243940182308814799111008893861877653978030487830697771055105061189783007160508792624501734586408444846820690885599357894652773386146403500815679993731490224562140278471041961287181776835797741847725346069209740322500693733962156171039713212944468296419274264547391846890978075292050257663855655742723435816446311229484859569453346291018446485271226803170253635042349404578164772933389313448554543835543429681211527641509929664173753734389482031832124838357233597235780545505623007907671884908600199750379391634354142317495769991909463870651602278747479870586131579987198470935431741683007686315405060047386787250686698496126963356747613310633029095590456750864644563021075067207617676624392288591710564352955018115225136716561051421414729511285420126684335899213208012223357602029848860233317934526832795662762238328096664445488272766651550316496151629024802253538973977584117575026653298772209991438499613378717430668007426702744786616172961510600678856556449035281853232617964583200525089103211148406948198039255574978071481 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.013s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 18:57:59 2005 Input: c=70916683057053523202175420792264102267405320836163970936265701760715715741596743245496270329483951469281910185762556437094807631983462698924291685091244307668664683269517325095205537302622450625045968843445946199418846218572548330598846777111885320891319536346480092167459968297617124878677026823742943827461281061111587817791117850632986002206532653385337131680627651326446686165306084128397561172652778133445883876647450476441497381038440212141872554878713855113745180468988520319107453228435168498733597436596313267900177880786287257210468303228868445077167303747913647065425780117341384322751897430729761971525396940391127286004257950728051152387652480309430180358954468146684618916411943821642140630310772413514827114348544605774132761656091785362940408291837122609769806111505130741308302022343002820998915046427873218599882094740994263132133276900211847435751591755389923961406630853256209304162845054697316906994312574931110945197928481948093217977105796256671527754951753937060374449432704855340777603205055235940432576704499056411924612701305798689566851387524752807996222739401232737576973046899208796162139280650942401239329998622053276250592574706074087848221615047601699192711775260330704392110831993557052045250602457015689933080463867331617965893522350504464079373718400511508078572991418244112439126359292291363134276226769891523643674471597693813178767105434059182954732823888042786532609471354072442862629415774705145383636316892192198013655940748219653715140204384986502731721948254002269496321920622251409023251082953151969973455068542444125957417719230344279089886753285069403106894712732404305012474007223971856701583018483331111137735290517969171232958371369306912501193067260828357195826973333618250334226737953430209508333300164153852124706418479138610819771180297087587488299242984627995353734175213715270649213186360618681287646891423513927620453328722392743283280455314387126719747794656674392780468975543641359998891191681427739346150606984484698716215598937908161395559717799988307669589079592325250100123587630947958052068643088376150782836276358413587767130229124116535409088554492868891094239063203229376256948276182311689387651055493363047772060604880185634733127805008500477106700856853725263389858157749534256843313689921562095852569286303294809631838489096570138589017874809042279541348897650813295088183192247640129902147857681419827113908415468137483037714105092385933656316573728591715536094314396012172699148060878300337590498990385081574713340014232165190006781358203584333883876130610089620012417878975980712219717024227800102072604623163844978676010546741501253643808696954011013329092336439135112111934280196968505646664517011709763778433889812123713912138874604703224255046590686997326951301440573742154020478609180425721091703117238110757561360839055013613327163355060417628807875738264235777399881909438186800000062187692670506791988086852292365380687586789330367259173813866795930746063877470678038043558432283203466238050251516729614405047564585989517759143811240409691844211870374500544767700096074459803588368561887303392376850959901354511145227684994730399086873796685205477892360368627996822349939859954751269608175324376066305142153843912302636681578584231373352707273656465546206082602792030020735863427530124790876361313478946959195441159721958394485532616642084052752259113460882187216479239898731462987985110001757469281556172290162755527440116314511741439328658539235724725252193185595121409289882495415585246395458284252142154326770484703510926199234593573739041653595202061247912906586464234902635177375212180233799305259293808328326853580983935703659977756875977557307670232889336438804563578493290506116649886802192694233261624747428412746896313226651100069168885647681517131576479482137667183448162003268182990296060014812356243616641469299311159862004200551384636776253221549131475083210922729066374368216808865980769581229925483025305864778205924269732609886395482857610725828334912669686900672877981443866297800495249686241710373816942973642459193075719218733196794599405440328372469391248742893813583607520292276852597904576862003197694343608044391147010560214985643057696781690388392976291174944080260674753053586673786448874971122343475778940892165750374968266867632915503175697197235832774750301526277098157239230569664153973185172546413881529769988496460626158205407984468046106916314027326222113954402645407878753141348388237975397292797493636772169725679370144475756832954283117542062141134258741686012082582885702487884158499878706179642171758349343448325488755367057604603056715902572637169022213474895562702776580074973334880830485046931478135826675549325352416924042140795076455423524558275873668487144782180052130201796685334713; a=((2^(6048*2))-1); b=3032439252874850892655549311808025559552817118945260647114694548761484146747722246839292990651932207379790258924796716413356726448028778354929959918595296062381366280741601473736900500127465700209513923300255285539688167227131565809214601721168543734214139243940182308814799111008893861877653978030487830697771055105061189783007160508792624501734586408444846820690885599357894652773386146403500815679993731490224562140278471041961287181776835797741847725346069209740322500693733962156171039713212944468296419274264547391846890978075292050257663855655742723435816446311229484859569453346291018446485271226803170253635042349404578164772933389313448554543835543429681211527641509929664173753734389482031832124838357233597235780545505623007907671884908600199750379391634354142317495769991909463870651602278747479870586131579987198470935431741683007686315405060047386787250686698496126963356747613310633029095590456750864644563021075067207617676624392288591710564352955018115225136716561051421414729511285420126684335899213208012223357602029848860233317934526832795662762238328096664445488272766651550316496151629024802253538973977584117575026653298772209991438499613378717430668007426702744786616172961510600678856556449035281853232617964583200525089103211148406948198039255574978071481; gcd(c,b) Output: ? ? ? ? 3032439252874850892655549311808025559552817118945260647114694548761484146747722246839292990651932207379790258924796716413356726448028778354929959918595296062381366280741601473736900500127465700209513923300255285539688167227131565809214601721168543734214139243940182308814799111008893861877653978030487830697771055105061189783007160508792624501734586408444846820690885599357894652773386146403500815679993731490224562140278471041961287181776835797741847725346069209740322500693733962156171039713212944468296419274264547391846890978075292050257663855655742723435816446311229484859569453346291018446485271226803170253635042349404578164772933389313448554543835543429681211527641509929664173753734389482031832124838357233597235780545505623007907671884908600199750379391634354142317495769991909463870651602278747479870586131579987198470935431741683007686315405060047386787250686698496126963356747613310633029095590456750864644563021075067207617676624392288591710564352955018115225136716561051421414729511285420126684335899213208012223357602029848860233317934526832795662762238328096664445488272766651550316496151629024802253538973977584117575026653298772209991438499613378717430668007426702744786616172961510600678856556449035281853232617964583200525089103211148406948198039255574978071481 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.014s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 18:58:23 2005 Input: c=45065201773556146134687670269980609818760853329754154661746743027224730959730803093760912668142284522114039250281900194067765206805039164772218768610988926799515493780956445402176147726595440704283814597837212753807793697696335234127575835265637049435764992246853086233325942783034006377750083886593456531616555737108420239215280794040430780004445141632482769964403853779453466231338103233870922784963086109698516625726695925269093094184823394604248446691191958766502348819460623298136182396425482362606395159732508654195399320902201452925445303785370511340590954558737845544165110061122305049573026207256579476525623807844442173052620323399434553958922512104887888617570385658103149366405796653670742579290257284638773579485147762316846886296989861720961136101652849784974667505368329876879100251303743331601461264859246809387014424157508538303058275648629445471613285037879525848579623256433834513210493014701963955116716617857270273888890621818781750484223940012789661017917831629082585812205092043445803919635923274592338726714113450053357165484411895543007480195332849830930282080915647838504944735866940354428006322643199194577958718658804182101450373824684413042178708782676415405403435791864432365458365499280148285786639299459009009002592742148371427379042783408256875002182085663231267599582803313072097253920397807552997069679391668459545246601916956534611301502425897604556790050690859764886118297036080755902266455932711195112024394694820347664926110850505980094643617420161314366201837257523148575615384170620017125728262351573664681874174682178754777306375771212595088511501424115012468917070870029399952992162053394367877682927659036574902180742103837086500525940983485473861524630059296552625580095772333864435680632632350246665276652238186831681317657245816576994459077384215621701802347509037926982683157920869471943904913657521684355533617507943938596779179342549031606327921699906885504722808050938699721014851910078308025012754202231028037328896158513702258976098571398464015227538789894726381974888935305050144913456891756727334891221792616997442247738633548621699892377717576887800252719853389168727680157717669472128032403969833364067893457917432146830637472507685359204301316257139189964519333121333729413420136503306773461911686915231563097872220556475070626943237902004341512240644009161643650862654842516629392573249239780748970353606351527145301644608738471625149678116908207659844340946543161626035019511244040525507482212894790914056638235632454229176575643564748802061037767073606785474364134248932743609240372181836878467020584794834942786061572086245793137374649594494226854963542411723502771179020404650973796905401483837842466669302657834473088107497434949836013139857699717155571834040593229709013862993989978849544668851807206424450942629431276267896827962771841578779820794821911518294826112484841094022674573521158565756781272343387529989137954190734838022642646136091574848114288090105899887451687232125055633178198767503985779878006968861999435794996741927430071633776932784609455498473182289384410141292134112538578261995077675050865848065393535263795120518619918421950253830007864013406983732503936656698912595318060176163715070824177074617493208009431081828058056003847027872144488229096729067019658627685689407035470486508869182451766326075432118156669918900275526517430662233557098569037459997672734750530786817022446787733255159357993755911149136666109696838507982733122648068817626180636298086139069851472405418476159704623625557882426924455947137214776740980158922860702557151259759733261363089400210451985245541045265479871779638636684529460483870372904059046142080634048696161925639760842115201388651483440819550224535650489314379098595372708456273221981031698634208442303897929369393518730845975916660267465232699336121337827284076209275025079015873209189164150383431616841877028864147686720195950021257618992350486678179298841378196989908839291638766031336079818443111805968288451839046692061765423928719426255937333294128416989891882679076870332171850323932339655776781989370584847418087591731799506992660647686691806816169507376309537706082772720383755333178659027442660893569129663115850371766284421927518039664978538124664653734579811774365839672225296646749940363225772008872156033549016283319951567272907899587148364962189348289647507526192153850927667345845390599050396081756772374389737166956791573292971095746406245717154786662258408572612014464153275271006136341866260880607619657154052945526005593864381962372897516761479303665951985642471537616188787185538819661649687254844176224558879866118759560546652548166023636427856952967039341989797321531738027447327579353304193; a=((2^(6048*2))-1); b=3032439252874850892655549311808025559552817118945260647114694548761484146747722246839292990651932207379790258924796716413356726448028778354929959918595296062381366280741601473736900500127465700209513923300255285539688167227131565809214601721168543734214139243940182308814799111008893861877653978030487830697771055105061189783007160508792624501734586408444846820690885599357894652773386146403500815679993731490224562140278471041961287181776835797741847725346069209740322500693733962156171039713212944468296419274264547391846890978075292050257663855655742723435816446311229484859569453346291018446485271226803170253635042349404578164772933389313448554543835543429681211527641509929664173753734389482031832124838357233597235780545505623007907671884908600199750379391634354142317495769991909463870651602278747479870586131579987198470935431741683007686315405060047386787250686698496126963356747613310633029095590456750864644563021075067207617676624392288591710564352955018115225136716561051421414729511285420126684335899213208012223357602029848860233317934526832795662762238328096664445488272766651550316496151629024802253538973977584117575026653298772209991438499613378717430668007426702744786616172961510600678856556449035281853232617964583200525089103211148406948198039255574978071481; gcd(c,b) Output: ? ? ? ? 3032439252874850892655549311808025559552817118945260647114694548761484146747722246839292990651932207379790258924796716413356726448028778354929959918595296062381366280741601473736900500127465700209513923300255285539688167227131565809214601721168543734214139243940182308814799111008893861877653978030487830697771055105061189783007160508792624501734586408444846820690885599357894652773386146403500815679993731490224562140278471041961287181776835797741847725346069209740322500693733962156171039713212944468296419274264547391846890978075292050257663855655742723435816446311229484859569453346291018446485271226803170253635042349404578164772933389313448554543835543429681211527641509929664173753734389482031832124838357233597235780545505623007907671884908600199750379391634354142317495769991909463870651602278747479870586131579987198470935431741683007686315405060047386787250686698496126963356747613310633029095590456750864644563021075067207617676624392288591710564352955018115225136716561051421414729511285420126684335899213208012223357602029848860233317934526832795662762238328096664445488272766651550316496151629024802253538973977584117575026653298772209991438499613378717430668007426702744786616172961510600678856556449035281853232617964583200525089103211148406948198039255574978071481 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.009s sys 0m0.012s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:10:03 2005 Input: c=6403508165719011069024097426864024654043146987629657902284962206477487930447170619681899096231372289592812776354355826387841550079575689217643889919932788419517450666918893740811727035640872414813615329028646395094183726907209036766440079829566423975653488707708769967345335886938070104779296519177400432639807935930846023777592577255441731387646319606221659197055875617410738479418128618629667212177235730016430270516076872311083819743982636600975069399398323795452381354137856425862847937795880366564081179151246311301175476937387629420223514946458128201315311471142212435489782729621966998427778903529658885638914643742617155503577058081319698898452670000466355015880374078903408819154165998208505692590942482367711381205686455169940528111960974051986233502966335391119688898592950344310538986989358977567640142748544350200148362053879769996237408034189363875343101907831005524899246750550626115739158759987047542657775307800422097343539748736425824890114812811086690084691435169674679481475950616100220979391062601711601999751792558850522780209045359833973622665080696272993433083298213046599960056168008416399814138842059937093182036335853456263059383458284489424636891747630791851438231417665893150832256072857015707417739104991192521458599231582951005621225163761361834354093472415330826351436292491787498961510832746533512931276410435203991189366785180476859585493511262548737578464832197233945249410876683311027639610200383634220360749216929458994549212691483108210060313816636201329458510227190757597729718449286303934429113995479395491307729060089438053659247768193232021045293552090125893291544564396345193255691091384405428282282155700447923374644699302355128108748504279316819829524759253028092466559126740076467587645569802596984893402806631289022240027546849613271140866003074424475131935390489149558860906417272700924745925324431768579455868703897517593702722469307989213870899706718110845672861377901570581289188579931587382664298121583042538842255345580623637217048677071101977582880020028812584788868910233153274020336148664223866901652557611988702484097277070894098746010748161617286719394495332529968205014972162792477115414202721094868355312172321628903330933359401754211490846122472678687769065523947407943198206106223902021234765662588890974859182407475636163622314619900611173123773138147197816675322905659286523710965258351140780473057243738046763933411655431150677239945410363167124727574592033551351489087555429689780795670103031320236539139273765732760789123216416098584994178765979069066154185401550982436509530441103622496543374900759111367534073902099308280478589956395533259641070620837088251615582877633434838893032737926307122099445721927043959422297857970522853893505358013946532583716460468779504665675443801129678502143463342265006244249393089074522506973990064470046766813066884031834827385958828831309180968146492568768225529105953037817537164510214929638450247126000589154227947128761440122019706512036997901242875514058430953162068091504740455937752639586785761174477957328125923491476924348221633180487983375942754321675657134708496396527746352775203568857162781448007794443583605901756864339384864765339371525097602614000798505993896060995209360718749094503869834039646232739865162521596053316724249842154696613480954103691839182682759401870502906913241632915246610777561080530978034252478354723833285234968244380814023313128597384565857445146955587425525295171811388073872374968517673787534336651166354454065270861333658620275837373905501520584915677981157184555424290434497948561603661289619858215535555117954924229540463817225662783933634908552541244584005835957475905686984143095826081984308439290463778981778619863314743063503842839605291134378018026003061070795984268490919136212328426361765036281018836934041803557627391678336974560216838485021990916678516061770147; a=((2^(6048*2))-1); b=3032439252874850892655549311808025559552817118945260647114694548761484146747722246839292990651932207379790258924796716413356726448028778354929959918595296062381366280741601473736900500127465700209513923300255285539688167227131565809214601721168543734214139243940182308814799111008893861877653978030487830697771055105061189783007160508792624501734586408444846820690885599357894652773386146403500815679993731490224562140278471041961287181776835797741847725346069209740322500693733962156171039713212944468296419274264547391846890978075292050257663855655742723435816446311229484859569453346291018446485271226803170253635042349404578164772933389313448554543835543429681211527641509929664173753734389482031832124838357233597235780545505623007907671884908600199750379391634354142317495769991909463870651602278747479870586131579987198470935431741683007686315405060047386787250686698496126963356747613310633029095590456750864644563021075067207617676624392288591710564352955018115225136716561051421414729511285420126684335899213208012223357602029848860233317934526832795662762238328096664445488272766651550316496151629024802253538973977584117575026653298772209991438499613378717430668007426702744786616172961510600678856556449035281853232617964583200525089103211148406948198039255574978071481; gcd(c,b) Output: ? ? ? ? 3032439252874850892655549311808025559552817118945260647114694548761484146747722246839292990651932207379790258924796716413356726448028778354929959918595296062381366280741601473736900500127465700209513923300255285539688167227131565809214601721168543734214139243940182308814799111008893861877653978030487830697771055105061189783007160508792624501734586408444846820690885599357894652773386146403500815679993731490224562140278471041961287181776835797741847725346069209740322500693733962156171039713212944468296419274264547391846890978075292050257663855655742723435816446311229484859569453346291018446485271226803170253635042349404578164772933389313448554543835543429681211527641509929664173753734389482031832124838357233597235780545505623007907671884908600199750379391634354142317495769991909463870651602278747479870586131579987198470935431741683007686315405060047386787250686698496126963356747613310633029095590456750864644563021075067207617676624392288591710564352955018115225136716561051421414729511285420126684335899213208012223357602029848860233317934526832795662762238328096664445488272766651550316496151629024802253538973977584117575026653298772209991438499613378717430668007426702744786616172961510600678856556449035281853232617964583200525089103211148406948198039255574978071481 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.008s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 24 19:15:11 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 24 19:16:08 2005 Input: mod(1789,6912)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(1789,6912)^(-1) ^------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.033s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 24 19:16:17 2005 Input: Mod(1789,6912)^(-1) Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 24 19:19:00 2005 Input: Mod(5192,7081)^(85) Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 24 19:19:25 2005 Input: Mod(2604,7081)^(85) Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Thu Mar 24 19:19:39 2005 Input: Mod(4222,7081)^(85) Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:21:18 2005 Input: c=364734282154381048030646304603682112959882982161584526270323421996095779484427461600729746905742353254019726895950866331910971847042309928299420838880157948579391832466734526688430078280802494935415075524491569784851150934886720051265716490918446764819423781300153890997617834816879469662535671402554251031274132013398722464847555965345953400482388126994264878374364899755826217734914475252631078192765982935282984768019533048363560927940312388639214424319865838703637133056077359986850571987628745625696591418626960580350093834614838092493281272638185618435125866331753520481789624166993271484683201851198773036164858010880295276111040673378292205621095920605529273855303602187918173767508055089559137229503868004797023063133584218915187154690098225716834975591680220328623790110005088764362884045295075890343260716997094572182630847408530545679863931550199581216025375065212369992423679224961180309396723974325579774449281211887560739946162342609009078519560243266417539624655991758021386840591112261814754252995616501779221161934685114841620598431391634070150791255590212601246371627236221228371126121826669228762487035842464004455032271706512733130320871109099764474918745651638254138033367395313097615595099148540818796031517519717217283499550273127173966204230335874801799307582220052579005185114483347507217440828488127742914173226887056143543652613633095356820691562102242606594336899766853531598064077276091820626697060526076768381577453236904887961770438424974799665976132795350684172460562779743413438035612453124324254123915143232844790404656645372407637458245724933420115012307694538045786300789589974336929792001; a=((2^(6048*2))-1); b=4310239366457002491199828598990528604412882140024786774268282214392381352364790262545992598059778748262167112465659490686930900374688399866917464854586279576885390584727616191876941597484930773812210250504807361444564809390960209083713933383285373397186338281445669872963137731239532149175312842517629757776380016018156214775941513126230735694393262019475875509722589204433657447758984659109005161602241905820011591160278728348586314939370561732900907987592987534917310643027609917085762139342817765230679466498396379520406617204736063900480371226719750851607397902196274673813205329638214995380337698920825715079213676959571192581992339066224433443972969216330775468464364744268684437907634977105779887575272005450427408737186976496578691188382656244040479920098598430679208349766075635748874076946088383513256319873939822931482427331048400862159356241; gcd(c,b) Output: ? ? ? ? 4310239366457002491199828598990528604412882140024786774268282214392381352364790262545992598059778748262167112465659490686930900374688399866917464854586279576885390584727616191876941597484930773812210250504807361444564809390960209083713933383285373397186338281445669872963137731239532149175312842517629757776380016018156214775941513126230735694393262019475875509722589204433657447758984659109005161602241905820011591160278728348586314939370561732900907987592987534917310643027609917085762139342817765230679466498396379520406617204736063900480371226719750851607397902196274673813205329638214995380337698920825715079213676959571192581992339066224433443972969216330775468464364744268684437907634977105779887575272005450427408737186976496578691188382656244040479920098598430679208349766075635748874076946088383513256319873939822931482427331048400862159356241 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:21:46 2005 Input: c=28156561133497208453712904778853620574318825745825027392103905384867409813661929826135370294859915564586433017792121431627836216103403382345947027720211322196702645849700845694092949833623441034972152006748295467133160430352774488362935290265149329474319231942270292586246074865523115737892073462945921969665188917146269328243430244895228331500878093960512826664678333452783153406544167888454272158068608646774486755398326264704039503546391469899462791171034086252571785345856673195437174943474344521501196494795294872210503152832463124423862291953207223534891788407888068779064913405584877882184611834505110063968153728996430362582512019193283827217658459967878601866133603239621104102995999200983913120110904160250992951542896972277026849038436422954116296110745048619175700585710393146765296906239899840847512706877462483132437400483902402105785078290927158996134354704686708919663320134267752875452658475058327099626783449066520848601476512885125829104970538975567583902771666738145114244873455131373279234363122538720165150161682891861101934504190678942981017281849660145468656525743397173064558729456234098423444424948746195787272674962758880293342801101947851672991093454029031470999533661011695514447776487950540466445961836713042416907869115295964239057049293033078930120008526461133592985601; a=((2^(6048*2))-1); b=4310239366457002491199828598990528604412882140024786774268282214392381352364790262545992598059778748262167112465659490686930900374688399866917464854586279576885390584727616191876941597484930773812210250504807361444564809390960209083713933383285373397186338281445669872963137731239532149175312842517629757776380016018156214775941513126230735694393262019475875509722589204433657447758984659109005161602241905820011591160278728348586314939370561732900907987592987534917310643027609917085762139342817765230679466498396379520406617204736063900480371226719750851607397902196274673813205329638214995380337698920825715079213676959571192581992339066224433443972969216330775468464364744268684437907634977105779887575272005450427408737186976496578691188382656244040479920098598430679208349766075635748874076946088383513256319873939822931482427331048400862159356241; gcd(c,b) Output: ? ? ? ? 4310239366457002491199828598990528604412882140024786774268282214392381352364790262545992598059778748262167112465659490686930900374688399866917464854586279576885390584727616191876941597484930773812210250504807361444564809390960209083713933383285373397186338281445669872963137731239532149175312842517629757776380016018156214775941513126230735694393262019475875509722589204433657447758984659109005161602241905820011591160278728348586314939370561732900907987592987534917310643027609917085762139342817765230679466498396379520406617204736063900480371226719750851607397902196274673813205329638214995380337698920825715079213676959571192581992339066224433443972969216330775468464364744268684437907634977105779887575272005450427408737186976496578691188382656244040479920098598430679208349766075635748874076946088383513256319873939822931482427331048400862159356241 ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:25:10 2005 Input: c=10088386292792229115694538847914838375254853381267053658011282689383146458060125574769524814361253988573711336651209804910881697057982008406208359030991827554193883006088412751065646040501259494630230575530787506882969150581087733517587015839270132126450675767866023229947211566636420693928151249369419564716841656467174980649503003566460620492964482734527607800759959513854879874168703489669488051131269986991073016837119403047097037867703192397167178579102918137522664555259942949107261594715892784200725592474161749521526912795270082938436111306992811418617441777091836357999884219013527628386153295644851274513942134431396194009152273075437897; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:25:40 2005 Input: c=12928493344617089603798784043495321491795550781331933682786351298074241360050443809225451451477178033291217625168334865309627676946514850728663772715527813777931293011353151984580130615520755925883453680709791472736473545677092860213512014104534001534377108780212424327381583442722988768870504583866938470156460114824720023041; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:25:52 2005 Input: c=780321884683696101459628548176861383069403947259780455893277580411841536042758563620882590988806530903786675090451824204804054002036190817294108468512117807084847700080029225573952358297349115030567153769033679679056099945443130923432731729592835092108469893972759070412660823292739629881995785364893116568795931007718217; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Thu Mar 24 19:26:56 2005 Input: Mod(5^13,23) Output: ? Mod(21, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Thu Mar 24 19:27:17 2005 Input: Mod(28^749,1147) Output: ? Mod(289, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 24 19:28:02 2005 Input: Mod(784^2,1147) Output: ? Mod(1011, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 24 19:28:10 2005 Input: Mod(1011^2,1147) Output: ? Mod(144, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 24 19:28:25 2005 Input: Mod(1043^2,1147) Output: ? Mod(493, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:29:02 2005 Input: c=2546142228132597513869883422145250603841633238170263628471986078613020660384861629858371055117579580469970588138801914211933414282766132504706663410453822955627350410555084266316826891481698764038635023196531632369932084246494819968395353562762015760322543786806574536539577802104870145543162214780531376903371150881984261883986174938089261777046376669225770211933381; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:29:11 2005 Input: c=394084245522141626953485431836389151723559284453923018207583827853088848961345600136226457938568714191417465503877379385115981547433628245884286861389966518821587519018427381484935621512343404690876613960452907137615128342099279874712555836750713786108988193618211890497487555141204017965601253543733286235379007377343972969937252463051371460556657752820793900696326269864854480730383338902850290961623835199761114816063278188123510498992044700855009053163113604344853551148134630802743582739354528816628076129317511197687774191784754595722808330993687417349545067158089250301046533483013230881732586237210154838160098075738786496366602539101973176856161418093964998236189070605945588346726091269124326463024672498122338455430258817444003282495539942889881601; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:29:27 2005 Input: c=167800129208013146881347264657367506695613976290614903493701664972509875036914068685141506237270737591946540662519572685082695267165414745820463635762487067708906856040268569288474890591657449174184625162803588601984425881615232271598024834454580107659254090046915564383711969987863585402106939730761555619935227272018521453143183458320939500659478241323397700550040406593948216947048045143672594754466413693622517489051807030882365030853507199142081681306218837381414479547638631072501082104909444679610668779622732379791557140523727289515007839369211432325863909078368514142612074214852005042946887766460811248990399521997412894954229758063758540801; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '170.224' ************** PARI ***************** Host 170.224.224.154 (170.224.224.154) Time: Thu Mar 24 19:29:59 2005 Input: Mod(1043*453,1147) Output: ? Mod(1062, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Thu Mar 24 19:30:36 2005 Input: Mod(71*144,1147) Output: ? Mod(1048, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:30:44 2005 Input: c=1443688700076602897284233351847796841424643902331979857504827803954671105528434586651389321841034656712472362562769686545589780854999071800253979736750530920473094825309119144228008348705944824194640936654001244836571797705394677752987076333659097066963807974477203376181216216503010858280124429145258842278606141872633562850995201104775276388240761417783765723886603084993772608635652633035923091921641264430043673535868362447019400185328231760453977470715620976650239512352105416884128913746819789693541318251372668330957132271781453552952355981356229566040028815172279290821562211560760223217389041779335335651347165458850550179080132553192551222911078804916025169703749420780633444831413990698519512833179699470919543753810232046474268205383740409800065933357206624600819841920219367523290616158320201869979594068114205174235522212555232278654304509426389504689606468521841484409944763634184348637626372420084007473729; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.002s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Thu Mar 24 19:30:56 2005 Input: Mod(784*28,1147) Output: ? Mod(159, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:31:03 2005 Input: c=167800129208013146881347264657367506695613976290614903493701664972509875036914068685141506237270737591946540662519572685082695267165414745820463635762487067708906856040268569288474890591657449174184625162803588601984425881615232271598024834454580107659254090046915564383711969987863585402106939730761555619935227272018521453143183458320939500659478241323397700550040406593948216947048045143672594754466413693622517489051807030882365030853507199142081681306218837381414479547638631072501082104909444679610668779622732379791557140523727289515007839369211432325863909078368514142612074214852005042946887766460811248990399521997412894954229758063758540801; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Thu Mar 24 19:31:14 2005 Input: Mod(1062*1048,1147) Output: ? Mod(386, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Thu Mar 24 19:31:52 2005 Input: Mod(386*159,1147) Output: ? Mod(583, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Thu Mar 24 19:32:33 2005 Input: Mod(1032*583,1147) Output: ? Mod(628, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:32:39 2005 Input: c=128137428986907803811605022311111055996423832129489143435178705268940561547142444851684605122864633667911683334487385404537378377381046520074974626907499011557560228651329863386147292838499597361871691249285960289423059958007266776049091094681605423669944792080435323398548925935112212932430722052640644137746483328275060648712448184310472724553835043313597562038382539520348757022850574822733725741848020385413707806206084103339868506092694243605279217285329384779658432508990506653846665212826341867490808211292264607178594516391246939261188657882222538790537433310045443153851849233473695433321611925317108318846402871012767160883001827162178455683610682143740332937473441087451276776979340688439382501065789364146527697570130883080394495610166759289913167064237383026704971391303277347329; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:33:03 2005 Input: c=54560610795027780264227935866872905503343113066120870651246968752785861486786851145998055729875607323389996732125503603542031670302516846587252641718797594971448072545154490571615147323821320437916671744317472284494790616344448051882499305367374242418910933877218854099063570130618940839440463912358955637834370913671939804084964294339878346427399355169003109309181073088157949503153849414791414357291505981413490546271071469205419911531294394071343161093684633207545765616266299384215622241700902904930150518166250030207476473840300573204614451960990672700262740422289371504309946951442665967747110679743930387233207757790685207902400022164104757250693384186885654018861887989744129; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:33:33 2005 Input: c=167800129208013146881347264657367506695613976290614903493701664972509875036914068685141506237270737591946540662519572685082695267165414745820463635762487067708906856040268569288474890591657449174184625162803588601984425881615232271598024834454580107659254090046915564383711969987863585402106939730761555619935227272018521453143183458320939500659478241323397700550040406593948216947048045143672594754466413693622517489051807030882365030853507199142081681306218837381414479547638631072501082104909444679610668779622732379791557140523727289515007839369211432325863909078368514142612074214852005042946887766460811248990399521997412894954229758063758540801; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.004s '170.224' ************** PARI ***************** Host 170.224.224.154 (170.224.224.154) Time: Thu Mar 24 19:35:44 2005 Input: Mod(7^7386,7387) Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '170.224' ************** PARI ***************** Host 170.224.224.154 (170.224.224.154) Time: Thu Mar 24 19:35:48 2005 Input: Mod(7^7386,7387) Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Thu Mar 24 19:37:55 2005 Input: Mod(452^151,1147) Output: ? Mod(917, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:39:10 2005 Input: c=17942620888106281838166262249032794933906282574205536082656532582100771059436896084477566426251415371641719860305852232449190996928945240530700231861065863783187000558858677834707519753963211390407796019713912267256789734642346258603792945163251541117588206801055605560287582377245658486493169528215282226441350805812460819910517315130010536593814838507739718327337727671450124646345498178756105725208188524104633927858221311406685680574644523986316126926638308491922228744531025559530353741325644374631871436427944788440700864570640164820463822636095590868735976263160913265632067238541311911842157386490092665947628452734907912031699572057149580451065994608218576537784085119154365207114143251239994805752510458514466116954216403599710673027581762215742760772734959852347260624717292720869741788170739624199861216426997113122221543193393445864197584427021839617073813618952537640448379230405056149629667211200644852865759728430660003268099662072133904637448806134482200595094007820808553441637708305548241569483412771191575370475991435149883075199049; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.005s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:39:33 2005 Input: c=940214483107390402446739754206711945893387066826873504468285660877207514615491934583448115229327030862553844309351824044185314907267813833473622677332411997536761625471194236724198647645663813018837870020066424971593269140885734013005119760567020140059548805823709589048550879632726111258109766551508572394239886076178961751045868758559138407661157093280290843882073498953217303343803665768241052436648032629457287538743802442037959371264951973065495337469211356305849321248515422604929258344316065626672127748649894197063642882488221303859296121109944941210894110026816314203414821254536994633866197804169393960879832601999709993174470417915092649106913346227815679668081192807796829163391557526105329473308899624633052189723481073981741610161499657381398808847479283854363692047363218496066274097470703634933388317788511934708494390412584421274646629503502014222401; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Thu Mar 24 19:40:56 2005 Input: Mod(917^329,1147) Output: ? Mod(236, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:42:37 2005 Input: c=12928493344617089603798784043495321491795550781331933682786351298074241360050443809225451451477178033291217625168334865309627676946514850728663772715527813777931293011353151984580130615520755925883453680709791472736473545677092860213512014104534001534377108780212424327381583442722988768870504583866938470156460114824720023041; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:42:52 2005 Input: c=2091671735412778357621761066865852219937389830607486842752574128957931215851033988599835291357560503915249721; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:43:08 2005 Input: c=27042164110407782971543176066843209261956529852118411861189470057768767372243686527803471776892822266104387731332441167789463985678002379910607316101903948860255444375235509049369798544197721724404417504553538020068204602496064157546577745444769238663327650167223192699936147065430446768422230700269158405282439864623202682532849783881430881833400931246323375004872292121399374938957536828238605485444369813356534644664514614388821561; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:43:19 2005 Input: c=1535488684778860345925363096721961011533088844851184129; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:43:33 2005 Input: c=41522937003464146671935085527229038746032556261695138046615996924354230497886130346251387123828627581884000082273170731923407895848907232965977616482542319333503141236039726305383372015228042129753910453452533804898617441246992457383872362435486626354079375899696352402594747472705752315111950671449003995091916619395080510424020630270786592215131563031850677937352510615043990432093428231230016843280178308732681302911374391266767317695213373983822250412872988860890192732085431736205369; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:43:42 2005 Input: c=19851555241898344194024677386685159656733700909763716290055242607800732852259753933996737693213885201217459994132499498406250252651723813397871790398504745605672059210769705810600179881620969795969361895394281829724056385350873832529232271517452146035914296631496639025584789286377516171475858692316820980385007287299541866805730431177450449140991644752279354167629504547555115009; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:45:06 2005 Input: c=167800129208013146881347264657367506695613976290614903493701664972509875036914068685141506237270737591946540662519572685082695267165414745820463635762487067708906856040268569288474890591657449174184625162803588601984425881615232271598024834454580107659254090046915564383711969987863585402106939730761555619935227272018521453143183458320939500659478241323397700550040406593948216947048045143672594754466413693622517489051807030882365030853507199142081681306218837381414479547638631072501082104909444679610668779622732379791557140523727289515007839369211432325863909078368514142612074214852005042946887766460811248990399521997412894954229758063758540801; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '216.148' ************** PARI ***************** Host 216.148.246.90 (216.148.246.90) Time: Thu Mar 24 19:45:11 2005 Input: Mod(-151,1147) Output: ? Mod(996, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Thu Mar 24 19:46:44 2005 Input: Mod(452^996,1147) Output: ? Mod(667, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Thu Mar 24 19:47:00 2005 Input: Mod(667^329,1147) Output: ? Mod(963, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:47:43 2005 Input: c=1839666051061286901410927116724998399084733692877640774589760863798518178240773498903698908791216102320935604373551965738483386877928387470709985661282830129467359721823138314943541725445505884750909381420651925288771401917916831025082550212566953488359847121498695989179233144880049387556363851064104044411033527100944115022806627960977588008060751904526380254116512018279476765883527608418076158355186068830441941717314262423594017355702799717641297006671212060208748433318063947850403548786340935944077391466242425246353288479414122106920286281614375840712187058909352899341576453609368133384815837611564155191287782637445420713562275583748413872070325915111721503878641947710859045854302232288372514973902229534408768009149203113006132829075962889012115998619443806102706414807499138962680824902891132712529162567550884720658459588535674647634676026252964245242892403490943110309661878967385209814886174503407326355035089100139283873801; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:48:03 2005 Input: c=394084245522141626953485431836389151723559284453923018207583827853088848961345600136226457938568714191417465503877379385115981547433628245884286861389966518821587519018427381484935621512343404690876613960452907137615128342099279874712555836750713786108988193618211890497487555141204017965601253543733286235379007377343972969937252463051371460556657752820793900696326269864854480730383338902850290961623835199761114816063278188123510498992044700855009053163113604344853551148134630802743582739354528816628076129317511197687774191784754595722808330993687417349545067158089250301046533483013230881732586237210154838160098075738786496366602539101973176856161418093964998236189070605945588346726091269124326463024672498122338455430258817444003282495539942889881601; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:49:32 2005 Input: c=394084245522141626953485431836389151723559284453923018207583827853088848961345600136226457938568714191417465503877379385115981547433628245884286861389966518821587519018427381484935621512343404690876613960452907137615128342099279874712555836750713786108988193618211890497487555141204017965601253543733286235379007377343972969937252463051371460556657752820793900696326269864854480730383338902850290961623835199761114816063278188123510498992044700855009053163113604344853551148134630802743582739354528816628076129317511197687774191784754595722808330993687417349545067158089250301046533483013230881732586237210154838160098075738786496366602539101973176856161418093964998236189070605945588346726091269124326463024672498122338455430258817444003282495539942889881601; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:52:17 2005 Input: c=12979093907943917255578001641825735384593395854771928322872885994990160268999203188706140135916819028522683766779485191998505830215867961864052906156762055485242271795431126108971549575559807830303423468640337194101740110392555596649456626858317626087040179746448901618173787473828138263827235897974267207888782720451377103361; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:52:41 2005 Input: c=12979093907943917255578001641825735384593395854771928322872885994990160268999203188706140135916819028522683766779485191998505830215867961864052906156762055485242271795431126108971549575559807830303423468640337194101740110392555596649456626858317626087040179746448901618173787473828138263827235897974267207888782720451377103361; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) c/b Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? 5598607713200226649 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:56:58 2005 Input: c=835468003951784192514174371902764921983525328638393803328968613729896792142794465780783365147171097328639181804313189774040882013287419112913172750386133887159399837927212610639144926457963224314552704206026373233177121597231456175280452945422012913757350318587175517731063684495140332681063614266168941523222093200903575962717882293672022918377397665222840398884699932032049; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) c/b Output: ? ? ? ? 1 ? 835468003951784192514174371902764921983525328638393803328968613729896792142794465780783365147171097328639181804313189774040882013287419112913172750386133887159399837927212610639144926457963224314552704206026373233177121597231456175280452945422012913757350318587175517731063684495140332681063614266168941523222093200903575962717882293672022918377397665222840398884699932032049/2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:57:23 2005 Input: c=19851555241898344198329297250781597311250545333776875160899623230836077678104939301417193539261932443625795598852285702220985397517722365541929897721924927292794499548988498841396722597567664172938086804639392654393521586271816630180838842436172448843788400919949877476807804207289029444834752538578440219533280156546669868450139601179940936563565345923359910717899355085013516289; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:57:31 2005 Input: c=5844668700872821475211655685785558016801834030487829716461262953921464814293952654299747734116205320623435821839335216566328902623434869097657929247251160457177; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:57:45 2005 Input: c=116025763585971044649281225056516605211131737996689111880647996893885307341330085576171176170275582030538911238001617742668552228201001459490843086107214738907964711366048959759161790222995637960664547422832416019709163472169701868479758173745186610733645761270258222806771037455628532364424347655811270053599605167892297468357073718562652758275247492571160002413842690377904946714657671650587997994269788465175525378050272666625225742593550056891580964155373604525309160903717275851056100930159824726447492601082289090069458835369576456153; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:57:53 2005 Input: c=71587896132544134548606515859870745415268282343957182030359814083527234629600662800497615697060034112842508233846998147226496724800017900505850184128151493906214226912852208171402824567588308621730025759887600684160553862328706052852010793200780138822659434703749323471777730110122804468849822503635553623070956388589547537976314484353156751855827702916405721489340939963167352122943783408412794762464459483013299158257018235307764283180220385102105454883865513992115752277593559200101614273908611856218102934867772368572856101423028673446401; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:58:10 2005 Input: c=23276974558706675732669323862520567413370554196638492834781552531551364931525323649223967731949298208893436971053005892034135772227343605129675961902910669993178866280739088688351847561565963865061643623440047422341123243413182918425983465944242931706099452591456686094387480764898285162383332705462145508055322266459933634763586254243800774632367231787788879429165843645507468930600501239928017908320441999352166785173593658137270871289406271833342227602805660565934336888560409434108594779712378351907992987950452066717524230431288071876131440849286191276307470846641046529; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:58:18 2005 Input: c=4203730336031677396989105882818718142822006110464634495401868037311687210523220392676395071158005345897567777137950017780665822654443254086269804405080388318729596610215127427555657431632848313890977800397539725403393575396103664410277647691186919069936147856182635104100510621678735828330451134876660375153279416968233319191368341612231941481579761765449729; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 19:58:40 2005 Input: c=4203730336031677396989105882818718142822006110464634495401868037311687210523220392676395071158005345897567777137950017780665822654443254086269804405080388318729596610215127427555657431632848313890977800397539725403393575396103664410277647691186919069936147856182635104100510621678735828330451134876660375153279416968233319191368341612231941481579761765449729; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) c/b Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? 1813303551884773431693556514731500391847373008867161 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Thu Mar 24 19:59:27 2005 Input: Mod(329^(-151),1147) Output: ? Mod(793, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Thu Mar 24 19:59:45 2005 Input: Mod(329^(996),1147) Output: ? Mod(1025, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Thu Mar 24 20:00:02 2005 Input: Mod(452^(-151),1147) Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Thu Mar 24 20:00:11 2005 Input: Mod(452^(-151),1147) Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Thu Mar 24 20:02:02 2005 Input: Mod(763^(329),1147) Output: ? Mod(452, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Thu Mar 24 20:03:13 2005 Input: Mod(23^(640),1279) Output: ? Mod(23, 1279) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:03:29 2005 Input: c=835468003951784192514174371902764921983525328638393803328968613729896792142794465780783365147171097328639181804313189774040882013287419112913172750386133887159399837927212610639144926457963224314552704206026373233177121597231456175280452945422012913757350318587175517731063684495140332681063614266168941523222093200903575962717882293672022918377397665222840398884699932032049; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) c/b Output: ? ? ? ? 1 ? 835468003951784192514174371902764921983525328638393803328968613729896792142794465780783365147171097328639181804313189774040882013287419112913172750386133887159399837927212610639144926457963224314552704206026373233177121597231456175280452945422012913757350318587175517731063684495140332681063614266168941523222093200903575962717882293672022918377397665222840398884699932032049/2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:03:43 2005 Input: c=19851555241898344198329297250781597311250545333776875160899623230836077678104939301417193539261932443625795598852285702220985397517722365541929897721924927292794499548988498841396722597567664172938086804639392654393521586271816630180838842436172448843788400919949877476807804207289029444834752538578440219533280156546669868450139601179940936563565345923359910717899355085013516289; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) c/b Output: ? ? ? ? 1 ? 19851555241898344198329297250781597311250545333776875160899623230836077678104939301417193539261932443625795598852285702220985397517722365541929897721924927292794499548988498841396722597567664172938086804639392654393521586271816630180838842436172448843788400919949877476807804207289029444834752538578440219533280156546669868450139601179940936563565345923359910717899355085013516289/2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:03:52 2005 Input: c=5844668700872821475211655685785558016801834030487829716461262953921464814293952654299747734116205320623435821839335216566328902623434869097657929247251160457177; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) c/b Output: ? ? ? ? 1 ? 5844668700872821475211655685785558016801834030487829716461262953921464814293952654299747734116205320623435821839335216566328902623434869097657929247251160457177/2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.011s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:04:11 2005 Input: c=23276974558706675732669323862520567413370554196638492834781552531551364931525323649223967731949298208893436971053005892034135772227343605129675961902910669993178866280739088688351847561565963865061643623440047422341123243413182918425983465944242931706099452591456686094387480764898285162383332705462145508055322266459933634763586254243800774632367231787788879429165843645507468930600501239928017908320441999352166785173593658137270871289406271833342227602805660565934336888560409434108594779712378351907992987950452066717524230431288071876131440849286191276307470846641046529; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) c/b Output: ? ? ? ? 1 ? 23276974558706675732669323862520567413370554196638492834781552531551364931525323649223967731949298208893436971053005892034135772227343605129675961902910669993178866280739088688351847561565963865061643623440047422341123243413182918425983465944242931706099452591456686094387480764898285162383332705462145508055322266459933634763586254243800774632367231787788879429165843645507468930600501239928017908320441999352166785173593658137270871289406271833342227602805660565934336888560409434108594779712378351907992987950452066717524230431288071876131440849286191276307470846641046529/2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:04:21 2005 Input: c=15100225973479294853331062983588773457367169559309743050267720708922574478940838856114854186785189096760459977920084292548365017432872457111959319084898143776955148024749374043086259293799899934922389590819863186493485381479922326402367505595027110155205343501189577774378704371913300248257685574897634739838965388253952773980462518644473472835935640352048821218639626956630632326545453605971724901164235372099302154444556482439602876503441170654570078068781266251577805259751088402787310891486757015661207945834441735681; a=((2^(6048*2))-1); b=2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489; gcd(c,b) c/b Output: ? ? ? ? 2318271715544956860688509132692025669730751361521542498097015714107616729828038420650876143410664732782559744326911159090462184041662793831858082991897461075821360912094946076269801143838885560327915837492683292919714443410040675519743108217538214610000509604493101531897564191863485609145771044129464928489 ? 6513570377547258298197043700902349083834065623235476792383608939806211613389524544456412810822105777005815838666976744829505711618470043621069328170124084417152497553644637430422065768510310381591160155422357085529 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Thu Mar 24 20:04:24 2005 Input: Mod(23^(2),1279) Output: ? Mod(529, 1279) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:05:54 2005 Input: c=5515483943889989217132475992564218247094195896489129331928784189500417490875118678587196351434773182462285636934244245103120694078723592604734009202359425900381275523057399211115887819752460724132338537272234808934401; a=((2^(6048*2))-1); b=35045282158487636123259014292004089245227471550191132494367732831303373727594575532334779423274207863833033604171200909745257231922557618156366994601; gcd(c,b) c/b Output: ? ? ? ? 1 ? 5515483943889989217132475992564218247094195896489129331928784189500417490875118678587196351434773182462285636934244245103120694078723592604734009202359425900381275523057399211115887819752460724132338537272234808934401/35045282158487636123259014292004089245227471550191132494367732831303373727594575532334779423274207863833033604171200909745257231922557618156366994601 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:06:05 2005 Input: c=325750435249020339359419117903384803732908450280506614265047263707036952931491954404106200879050645031363205046798869472500848439043294704837824393363704018915331876430278122735879301958562938966749093384445957927925498638604667940498883906300381770129495222670846337311555164377551; a=((2^(6048*2))-1); b=35045282158487636123259014292004089245227471550191132494367732831303373727594575532334779423274207863833033604171200909745257231922557618156366994601; gcd(c,b) c/b Output: ? ? ? ? 35045282158487636123259014292004089245227471550191132494367732831303373727594575532334779423274207863833033604171200909745257231922557618156366994601 ? 9295129477795534387880853241866138898045348901394541125114469051512289012190765141738842745389671388999468438682273146852587637312951 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:07:33 2005 Input: c=9745314011400033702663774894832773257816370709432338472830583336283555203155952901399168705085029318327683231749875967628107752118618061360287411950482515442439504545700501294621528918959408839149593252799521233627680999253385814008764591971124128132622239125598312561350452712139705548801; a=((2^(6048*2))-1); b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) c/b Output: ? ? ? ? 313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753 ? 31052098873669991221403987178479263664518962358782811542250110182017 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:11:11 2005 Input: c=9745314011400033702663774894832773257816370709432338472830583336283555203155952901399168705085029318327683231749875967628107752118618061360287411950482515442439504545700501294621528918959408839149593252799521233627680999253385814008764591971124128132622239125598312561350452712139705548801; a=((2^(6048*2))-1); b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) (b-1)/(c/b) Output: ? ? ? ? 313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753 ? 313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970752/31052098873669991221403987178479263664518962358782811542250110182017 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:11:43 2005 Input: c=9745314011400033702663774894832773257816370709432338472830583336283555203155952901399168705085029318327683231749875967628107752118618061360287411950482515442439504545700501294621528918959408839149593252799521233627680999253385814008764591971124128132622239125598312561350452712139705548801; a=((2^(6048*2))-1); b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753 ? 215424 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:15:00 2005 Input: c=9745314011400033702663774894832773257816370709432338472830583336283555203155952901399168705085029318327683231749875967628107752118618061360287411950482515442439504545700501294621528918959408839149593252799521233627680999253385814008764591971124128132622239125598312561350452712139705548801; a=((2^(6048*2))-1); b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) gcd(b-1,c-1) gcd(2^215424-1,b) Output: ? ? ? ? 313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753 ? 215424 ? 313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:21:58 2005 Input: c=409878152396304564097055177920055367547978096241020896529339074541711365871187708774486932400786985227659597003254354407340295169569741323028881688415464673874098878974637; a=((2^(6048*2))-1); b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) gcd(b-1,c-1) gcd(2^215424-1,b) Output: ? ? ? ? 1 ? 612 ? 313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 24 20:27:21 2005 Input: GCD(23,1279) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: GCD(23,1279) ^------------ Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 24 20:27:34 2005 Input: gcd(23,1279) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:30:40 2005 Input: c=1552518184837998334099521669977458790031299981415713329039206952615921927750800579306927040595042411208066545131577395102121223464558492072919344800045301285085106862372574116492663540550382992252291576959373402905435367687837450241; b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 19584 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:31:04 2005 Input: 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b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 128 ? ? Errors (if any) and Timing Info: Timing: real 0m0.583s user 0m0.392s sys 0m0.189s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:31:42 2005 Input: c=501345835233645442908941039500988418948097571594511263665954258557540602401198305327289353890465943308881346544635302894398771796992550818651991400332644201816576777207515050223374628808376572803605797556989505615625832899781598945019456709251777787624781530860787461916495924804888226101037144332431948229615695403300970637665539542170734656365897369275093281753947812539638162855026062773040866813344231227761451421281324689674744783536760896891892933145191887071681215131333863000683714548393343820581684558051790351519809948863802410989196226535647532301903116306327780309892334566100844133432683913032723490308335815886061689149621681088324981059366429252954327722931240308211653192998196138544733996540575746586058176570358376224075823697522847193255662679480746712984378380809679168675461890072188776611900525615483821916995461986769406578709470092496233853892975799955900730542946073975740695641246890566060688408568228217056989389973381593682694773474657240928747661117396278598077401361598662923780769586985269624843979271222404816539736028163037324240066307555056073549320871459014879983846525245929989321218346439903692149878505955664664551974320292512537091271663519225132582194138942947650497211966496449235418217426032474724013384886699506626996721350491276506216538253762362444088273577612944531806632629578556714489981876168170215413731691583321704493593661882648919221223072876570087322647014562896598373705769346326686021670168129778937324040219181659130464875379428140027903763922433871443740549716741952726571449225482336509979995015457782017078491702360811783835327779930214019337039877851206174142616958678016017564473544306309216452018999629359255451085449268371392533194333562907629027727235051582996224547172563036659545115407313662226017955940464658302607994835903753406677811510722410690777927180769080031771190670667847392167140134387778094159600906856638976358412080213691574251982973998971421941335437475831405229975246896772526361506123575545499452313703808595683502511274557638455296041188081112945749075696873568410857305546286444591680857459894964549201750606980967262077565820201193068058469645909157946934645156454230790440294386765003233477206072309892349820806388952438252785009918409066067968929989847036403413500908835446035877019175852395799568137178530228035533338431465801184784699398859134515538226401737219575120101071986333322121155920674923271549755854270316945189248792916453313476297426728443755976825259771843650212210702404998310313379682730038254510245897850227731215874594946826784451774943220892307863096010777508393613014053905793092708846974035970268732089980024998597196836995830943397054711735644106251480255059011564796149419614856698203362934611364509414198695975597099563938382691528962003175452655004395851198996692708800401342267239171772094206772266867948466868932585404363698721278671815236800219238114391161394482639439586954126722770461181625224663115377960808447937209203908800573075204692645186190846940142680165119082252997612164050238411670262275177491642108601134534091683856502108108259494009685594216551608810585809923856348653062681862359572355505525968309696754898361825657011050001034074969660174937877082455577510846333767269020046231076744133969902505697240209598700141228203035183254361178474478520055450709484734544415895964296918266025252281042423770193834539649398177358676630708590061256950812566141336642012804775880459823690889583390218444120934776291064984141599904267224480301215923582778842723099829419543066880022859502155459968215474530810175467178246476111335885665303636592554168708476763623634885198877547035858018827320357610806692329100506006269891556416270387451981546385959321544011842972957747235481414121720113952802945410292739068135480049985282451732156000295754418553093674157834008438296027329819761947825401453295849543194945318027327614162622314093354738761292745082057924582268051967100737923481950227435378264869034318389738231166561547047989843138852828978350662269662521833972706571936305468911460514342886114573729974451802944481246300303804096864422520332845255288130135642427585299892839900793357786626084132869971236591232815393369825515523805863796698363933918692809072381011285283866669206201241534641136967485665603256745053834676456301877286824196787041930041739526118359342032374006398493617746372458323168028218478317743604505233173909586454560896072107213104553810826043231337608391966292634832585442858035098590568425055742858204017237581706902135082715207939954484261823400912137512834101047496539651269111075774812766493344653775800556921616691818972497069374804105829760656466078915299437313307254152517564301818692673167822229279933079226576408919567499279206167584740268168214067249160664100391207213219111382382900676785434770501045536772910087919650071052400154931580750367037557028114156687411410738117259714063882540586659206418233994829022962881230741440440794117727259561578171358636043879061536379713449222405454468976048268766609462085963531393903346856159187134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b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753 ? 6 ? ? Errors (if any) and Timing Info: Timing: real 0m0.809s user 0m0.444s sys 0m0.244s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:32:28 2005 Input: c=272137216161128550228672444314570157533550760583204536394017533984969787566842266319836715692081706632532387281077241833916431341678215172269603262184699357243083326869626998539397556295815271200393073079198433409827621528867396100270911571983681200383917199210770126702266153167953711705136708033536439911643799789594385896617637120649667570552658783225123375670976683548892637209182940936338344058446268983022946926251995900022074437436974661620437124626477114376997686788136701340628236171599280675033669797411220492895875613401210134243592952718849751059483263494224349098927898079457561357183276850686818741360330118578112941240565905384066039745132826042530638350457600801652124429620181913866235297363462689005566208388574029715378977863063870757774082206466481835224231801490020033850131753666647325559564773815175661219278901190111818486077283274636070244241044338317800046962971054773825709775316742962863373727541877220901383822985787650710788968570746575246899200895312360635164671856498415324980154505039493810090851635065990716299897564866048069790278299794144626413010482279985601597053702617282279045156713694939775855041238598238664477959297537870711162268893488440921819426061787816388801489666881277133281102714170714093578206681380439195383727262924034290075561680134904127285521548872706672625233665377821119625930446947476839321238809281596570778460994049364852329642146141353927787246081935975881615903862776235908277129180444593466186263549871145760908715346818083993903300875213539775285109029456981010734821192934263784182551084422067675510763544060870153854916086860364954987922478302741016668281756197444049003943389138674688825878746280609758341893374284005244498854124115224906205271999047752361297498361048420343070627399574486687098773192148345889328284176109567013672430990888547560286726108732485425061842476121925762387907513801399850717734970661063749500211210029026428605478053097926039819766044164734095593325620139545652552891036567883398044348116306302228995406462132470097888489488196098436018391197927020109894017476386850722670632888706608691604638397052980889531988010362833016650653155432191208409660839845056551297737566821619517093963797969054331079260899824934248028783224128472900574718374229010849352876154857224162977754126104463139987012706982298955983351310479404351336755403859612050457181231249914289878787567926842395005183652683935061803189364742825044765143170554567491560837020348651973164930377088512750953507779616653578165411067412255922031361036862002172957894285426240123870092043507505339541894865158864246576967088725746341103305784576886661721328685792357866091214503650720815892316860792468854733225348614681394627292462252709860921180156543170064112376298887330667468748291735593698472149915200958694146970875034986165006156461358226778525528270641344798430990822205653257362853515098421267332732202479004331322671701256040494063957857739521194554680275951624884457407232467741160148608422328669918323584820097699266700077834917352890072908968289064354144655946207941029734174244841500807999366594636581195378205796196136080646021583419805291245018100227352256447603071093649074209414720129745841113997892622254816494938735530027201214615975405743186868729713307491795179598744295045472459080746643512168756360723092204826003834769935480840102744371279386438882809544394257587660014721669555231504055239616577779056172305883954285333197232390176767143278063604332315485486255580674141183510483236858035017518020479096973410575949737281468710376006969388608525437945623509068186049796826803922193291295707914167305084613874223596743999256663052066853856912911019028990177394182564011065921064210799724971372420818399815267255859430523011904894091206068389437003084764295571999372849980331635647067157183981063510696766525885807821357121035054716331333760460365621462539537096599488238748071922341760377319229694901145004726233612544041922872867391869900815858872015173834926545682121446609990399430804555311805176740761290355751679170473766884865281194750914375312966609219246154237530336635766802001509571153599820339738997432333247998321050001574628700025594188016275116971739826838999076103177662641740857847018188802346022322997410949543894295006916305917794229861920504301179165435913876840427395018059890270487522506579114841904110565614753869271312171246868296286919359904762459915387324734414504131639873738279652881620304410982607256478197782072221823285496320863287371460391341226723027117465634567902032943896502794414637804596316636295503601680660706430483368111022032219261906474632771669065894643544080261520273191494321431959341942937726870542628022556400369487965647303996270765035272416212206320263975858182245756020251677555548872538336111251811879572341180948607840786994022176010832199989527055354936804760063907148595980463835452440708473038812924544358736146232762537515596309924564789274137032216686381392853924872731332983170135124774628337384310969753796897222853702409438133586367621347621366714509486068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b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753 ? 64 ? ? Errors (if any) and Timing Info: Timing: real 0m0.817s user 0m0.444s sys 0m0.255s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:32:42 2005 Input: c=17034834443239860950065618625187262772884553525798439952983762253704705103649784280496129033483832339176066600096204887426910459693091728324504490099524163564976292108509177836165122099427433602256803603476421464829838624283136249612212483707110054716831542574115069085472028260560033978825660557071943839882958916253072035433611117644811862089; b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 792 ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:33:02 2005 Input: c=206978476703774724724960445571179443557867028483443728891191392204317072741121962725828384606018829748395827916283834028527394548148646757937075476994973976413137402634137995870456233442653537036896984611796958759123112128062679163343324459455578675899287436819309684465801810240493406183624032659968972516856090702348660346515481310430669782339486015482240465877971820841983838084481088593734454269745129865965461411989942230680693161085045656746505122315659849592080880801697595194517955119639668302934782789504723898723806426278751789726674273795228942247603043042754365107313719699663334739982924227484121781759736680399889114408138475613441823540009040085799221055261964999220302305168498080960136516932424171524553288156898288692838533360525432759777623415015243508927771558925821653105173540944105356834369014998878413400183721051763573577573742678740749155197562528092066476978086449273853490979672806102972777394976819302661402282755706995477027086611740166664299016583975309343056392175950880723789240560557113798818905520928814785120489890733964614486030032604729782693712648734177809489341016465992348526362147043163748391703983046861361860762693146168137686063072335948602766747099683118908416166666771174389272564980283394755355258255338269590355164994268144031159616267955627145230239742070174815723565273857999717793536540669035380161756882081420138714231212051343651218859436192091781688694950489016562938918283741977641619942401144535987094695373953700673365052648019640189498833730760279460298479246893487980974245592958565539019559806418730604489772857652324927400903690723543675987530607482166263233940282879945244773675638679037112055661480483602476393312219878869024298124998523652373995578721128987343855834846099947475389655303400903783399969398179608636960295632266953896569288419398059243116004211213058345822056820915215300309366874720809661231108703940038223913671340316073507147325841226938953129190494926171995049560412436130823917354523006318850507760039482248072403609782907355008919332594337668805211239053834657930283228542571212981190789070523431933404446648483049296713073112268243114464090645420248770527023115726954171080239423705712487698192846918501165166383676045434769249071034710180045439340485419342165821379289725693044209941031170495216287243103012393508263678365041367476564041002421215515100111965607628565398113287405729047714035622774163582053815632066254492706542563401392909932335386767352672924978933988258077902111563611401856001280018628368235470688628237238117187416289207828734886554151450725758162752911091071634892976435379077001055172028326655152803252499571011175098794288232427523179974867099925301685216434779190569835239869121435563630070824099801227329718199695691762128358485035928290651765815503899211484946767981330118798273560492483841599183942411384658122370449919720687279881729954519503163603670731944344298118045533902175045517046750537505114767474298945107162765250351863620944469028466008680735158462084315558940428667250397038868286655547094495021830591808493848209942729843846584817489872978689885905088728848981805800515237665306056885414286702062651608038332858214796927548149293772491294033442020274704597875048088562543249492890488728510042141880555095976060856088901790252802117888008527663792912608469062982034418008999688780560116172005816657686586440479671455936724266037075627087872561220873994731455813569294623135884949827857207142165688206432276630817198695264162668654599686216191827368409525124364114766419922384438639649366117229306612738937812780948658332121795182727344940777347168795558103524615406626325332611777260534340041196282754120840421765032866151323871360375576729628320365385075240063327262880596694315656929519544058859853847723234421873346173326361509561785852646380635186631427017705666573018629285820430599378895214662236767451854937702380434079307339170908242262897627867339858709559126671961501781556989583238138613128162689207225097281608758142830825834363672509060945878702225285429804086012523749000891961213201496124813746263811908370792949451681419004786389080153601341655921909514722083379802007431616472376586601447609723192004950535457339504287253832183772844396653784693856229172898196834042360358574487884950537582190751618625467885210188480743958706599385645896304667423701839553464984549729508898695205691629331117557421369718536759134012579139963434213533819354580131031862214302352831987015110410692877382419996400960914532868676151144296143504547078789575324466038990022131501685723496103475387116881343858273072311180413156180207751253160882468839292729346043587252367552014867228209790772421092088777006010213162845028071487591048396944806031653059283844748409202201051608039399718480070073357413429430875242261640175794700693769866756526407935358886969254422839272982681443540002055837054776601756583931922119355250453004424604983393073776602018439458961776729489721964691450987454488957187297683788219876520290947477020935280678635261706449902088109017166743540164427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b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753 ? 16 ? ? Errors (if any) and Timing Info: Timing: real 0m0.680s user 0m0.461s sys 0m0.199s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:33:24 2005 Input: c=509968154854762361447582288979869055571142328949159585711776984128537710528350294618403224962749293686278770378632670198317440754264548307103816086110729024130743311941055283928497975553806808506896622963288714091463375041138062700314485861004481115208426341779395129581537577064492014454369078436859818579794544245779411815121113595518830170803532039193603204067041872562924374723968313783622040302923516162223029506225582568930325350898674468401524231462815620189843932605722895453391658127997801315931396167573831298870815671187903923044209693096928979440216047409224962672440107292965720333085641931205596695545338035145779448320347829086645544982461862153982847828682763576875976196603818568252560389956804727395814626065504950643229139763823420512204067636983722336220352801712890453001890251259297447508524155316996868270278829412176304342103406124299742396284207605049910863564804710948909084580136453850193283396039653052138787531632522367618982362259904275505583887547481407349677476011264110556483694914320113542741115549729360877306073146083045597861267891178566031658069517518842928205318907216030926479166306986911433570141140285061668047467329254702704383214505270725333463314912690352489481826829624291850275359847347402592527597306141530973490354250814612056542175042447747697610074045587773608381538569611037803202349694284786638592673315571015122037504111344492020705087737561117204737736191549742302203954624163892358080208498187992623681806326715369392913867450340684834342784394619645845027284881585138647525511851429794688021716324650209650506308993272238065762450785706422130617640890939480741447776671000245214006314553610957261911669608304969581594549846911308092839786276260657009701143571809873688411712364114685917393151413450087961920952254011106586910383069263943667747639098467212769283146314179130697041040181675758641312681803466347832490013736406284371937852098897206934684186280913342468246278388418095663989540991138785242287578554200450468547726441973016465092410589109477365360700533632313448395177402726874019169391180824178250324549905291512156294480048684746521652132223785776431139249154653474425971745109843668461126265693070422165622638062617858221868967702563297314839334970082890527461801137123845861186346378538056319663705525768656307932198444876162511502607058392985858151016715511777219116429280483921370536232560170886997449366291627301260042449356662030083209655224689928212497478679381335539571676647865954042565242215272050536773811314937608241087217151125444440195717349924838820424023677177410184770311782010518817045866181445147560742893086453310211484741691484371415721255997502069902099596920835773650916156283994673014752365769873961999564750121944848551060160630979221132774265772935804017997582314483260144086618719999543223699644574690547005312446317012217829402490866022883337365569691755906502839087000433222346959630047891483477279400723385656026623288789015305341788515205924851706785069316523842819958426273940951076932235563381828578054005951952694135436879721680830150665756843219599711660616605884300717498682328561463682029759323679127048762212397048869556198960984857156000166544906001643708021181077366513062339141394803504683331522177654531584277983561638515937594282745535067164601678271986948348355325405626935523833946426583903346030946677902880561887597108047447147079096090498261596963998546073699943820904562792976714274844682409917082668504420665338184064102888067081415689969591842079191636130565437592390361737216527344948539465410614477732602934573192911369613115507617573368870285623844699540911479368545891451458328897015383830634350495086214500338539185625035289205607342185973459710311735556343440919360008390255312018424865800533672374400566879640510833217069151767940838432068535579447123201378321301065133213162478744648795017675068679793970780925229221551425765703125837003864460633672284634453697989012218813479896936514185146840222415066202615212878337443304649659159920477874217523255374786056847587511303909533956657521613088574414316529602280381178884312842318469630454188252851789533046424099056903489097933361598820198994516587685544422501664988047490696382513193977301962307830691818918152345856595945843244912723303469835613676725504629063336801695816132618136892199140071426809986810842114093670721233326965703454918187763148194549372703211055133004616941901016140069697168197554803590957267912758765839647520468597096323772147079179483983466513383843983820309058771039241580606961752259586018279674088698407977962613838574809555576881886982951591198273032122110881684945200937878005580503206801162666844182672683035730352278305803389087937512547112994241181996654733186541630848322886592190535501014869177579415791694705301724951238696862385699458134579023818209324232926950238600381782166134349859523929444733531710669154122127581591804881476418908967314684270075873635622195536667515908208252551106542777122996605233371480122968385319246766551109956175880890107589405403505008237462128447877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b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753 ? 816 ? ? Errors (if any) and Timing Info: Timing: real 0m0.788s user 0m0.450s sys 0m0.224s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:33:37 2005 Input: c=437418729288104567334590844915492692716772673899259734623310963774863048759280452149927121518826178577227248865282356065885752144627208590549933526953166537387861966688305810024600684105248286702450986599749659103392780475488619641284715623073590472274405318660174011461729419382972086173051763295726945279800612909906270149350135759184817375859180106638437635928199421700412334326378446079558517849758911142185877595146888656276416359135693930544461853630214737007830624898011951103131175445389952178042422635978467578099727427046561539015329403464952215758224612825532712174445897237955500386646323157399167113848978318617896971383740922205101615317592752946481274360743535989629585673184519201875245422810941028712791792188892203616978223135228843117172493873642724273712284483446264609184448788709829501978787107019896501; b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 204 ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:33:55 2005 Input: c=116585806850276254871576866199163694056251203074189391498302319933876476274818486205759902115629774447847216660967067994191049054579479856607389220173231586920643427460823963495540003485135426537863322735841640435855043119972947214662511056982886936308443712698054947743391358256964396922394208261305978658477398202519699930810479107590284140511162714176380114637357094919623658396136289496622558672656720297155805625224470615135432416182414518121829271990843691118403862327072555817978660332839275799706159535400494250444571983199774399494594626753478092073692813892510537180797788972262792777850344056477580640502964935176615135055810412370314028894791005024114315917380166051916133735436051114980873232617377026683541141242891307608792587230457042275005108007846053726022946693563047961650552214944955872875534113824437371148806054547071160976699374427213219897340551850233108908822343795378691507855362202253650134638833069070841815470805124677581496400921832588663971297859699542904465481979575647374185016155809304717863040684771151987260731370253160021024649456438962534284947362059635457264897600933870462650091296599097246373943375486671902803277691966185972085175929809914814011395487002873731343315703796609924256047658439263394261509479952572071741373953495935081359504924213062192847420886399148009539992760147179583626978819945515453157603177213213174003027205340140643191791976335112028083036657525505835522271720526069800134909559424738931898566392998055053213023366815135285311823799224594341283595132581261130760903420468432158173202090290735237300770256267983836017967593043486962272674352955513532085931579937685095739165581384999682091515729031184246065148687550657384180238557810954884213798071587044161458892027987870525617313690097840919397502980067842159609718763382135085480738563911392591377930918511136231829952999131387251098076590831052248357460210545781193919756734439591317324285237006978040838139969589719211380727074422697013554756951606748510381976928904577508307850493732128377183865539288699511949140220020024350324009859785821993000454451908138002184669615362391124955402355758950972690716837987036406126023995641632852811570368007943681338709947393979475866545321951779445518781653156102734818826168181060323273267646720175636393899262304066820518800539284312423194880405392154991166699893614078183424470431111024239768683343777776752443115349030124834045622687151265044925168445046699195717967026384305409723097780386027464448606217892434022688177404719597861286151742061588374677356425316580082715877107286706837756110965216927913852247934317589761079392406601855648571616425149822737032045708743137326302388788008732338077269426401840191764844468357125407399103517483325980830839497512578309051126794659038707837486133672390276468984331315863716702369304092537166018157708685940365033331198146164429599197773454310118677459301355709076058263390828103133899483584755921787338920199725904780341302647864563517054753987939293645420915344668363412570084218767943834951979179983894537555507108527664508450997816670139691688033631640837064811915206174799632627446758582618851917514957229393351872195734887022335570754482797949840336963643325336572327290686500644171454235836991362637002191685908781034749579344808046495765296832437431421042558034070446198434326028625317636385001426832800657579024074956265536624164094215004075984181262564107975899719537504324825368649243022330178734418943202065432510405381257406462327980105323044256106692755478812781133067820688232600700354615402422591195412819724415861315369412290618010753592732297621076102392614870060184758453109566542489670917607811039912967669613192377702297383276381657963050110548830235884631035792421806157380392314863983607164368753839405940062206450540308717687063992752064134134545449475695273013525118357936173664579789380684153971346231700744341245390757874605134520788736687566710930122904983755707497193660572199846044851115728749727462677840864669979992321939735762692022293361889006610678868783952536246943182237749440312945970472542638841648207994140739495651806687287588118083466358176983162937575828390357549620821920995941741889515566434134545088317050612098832298952304287489773991373123834444981882217008393042971276940428698739602120124314748580431375088786966410211075226057500200806398147617537487918497007970191318479159852908990268766022670042014334809812877798694336390042967705886632290044458878896979142877654212320152045245627725981945911885669279594172744613611739268729069405208523667730002796080886455534359501229469491021830264125104868295606921880844776768974029263420533957439222281496056088224778366362459884346828282098457547022249376375283654134672170279364604949211410862329758766529487395495414135437031002085993977230197851531095266723883248698535871143210871725651788824913675752357603370283737673806584996121404026390795976225960852944023792326786219743764773314878155598264361882214172320058146339868352202346049730375861999034868347200162820737805224412840999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b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753 ? 612 ? ? Errors (if any) and Timing Info: Timing: real 0m0.640s user 0m0.454s sys 0m0.183s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:34:30 2005 Input: c=158755735153810408976516379083281203918276108646928267323836804418570741967329391367221446256629769537830411571607423816162255728800563687897000022839074940478028905913008591227042684335958801934883215812899945249752899952925725373486407682856816748498612817521892931781947073030920077204436384082246980511377668877065656291181920617650979211381356255916880916542316177841554910038992046999989889744357407070931443629972880628344463827688000500298432245476263986189798896360556223405058956115625413053670478135701806462457658988731716553694432239340228714768596647709994502203760358060932423336838806551366174112616363348819905728870207394602670768741196003430178729027570449953598160799799796952058156844249397431691586700062685588240525371006292336410146619418775091034413977014200762271865390416038230414089812200803284092507831026459497299188358811854166749447809825582492435824489496947655961082934238492883436180888736521459854598937920975347709239568087556024253577029227983920242111361511855210186312434169892271882916876921251494857777881413040402742169705502126747587158059363856631662437259488166845126335444837343179727939364329937396941253119726523724389467543652600455044409768862151878266103415151890248806898045024166732000721657810897142190617472403017813288517612247301510428981674493022993146494139315021839276025849516910163521927394639585013535424869190452760324203004021885811604576738238816688505267791080851978730162382133085585348403363814904953979154910364115305680387942004411755716797659310007488155819242513655126726884614612461974755617019208496948380656709788029084689551093694617830889918489833230625153768839872502826827856312960172033376397555087433994856344821589140769916954931298316442801130460932824042000471040661974761193699802150348601263818065113052227701409611221562913881131570695358466680371092742361576906139744743071424492962367529283030627658287657308123020942990667774430560445248602526420244753759179696516719925431581334651686787177288347300087055536120494567000183460903112380281943714157823364050576150948499396168606157157333209757664385683387324301596661138801588908150559606211805700572144694964773099550495967856409899266409744069058094296104539964524272736280701628850944051163458507985107917851438662308090756393111916303954596441132659215159056872650080790987054790023799400045897136984651152348363139949799358643036757533494475192015723775414621828014729421459972616947870288450301959869473967452724069465928939881251701707741795068242517625373709425591354416729948329763996388646455287885851253566297570142838809412197780827580812544877890983517751620569082694216371710421406111464391480967434618768564384315617172051137637436116634104513261173145209210950204327908246789970397067060442018440749469832586382467668272224042720155511315114474295312216447910644726167628239072563752838223776042506223420800810918059589155670304709224533222696786972473701926602612672719355163453193443154473806923111646969294231511497874153823336126677865312089561728447349813139200968739350955536346485212551402461159451914616002626528484502405575586999391817384264965861754033083939161230146009332336905304218235781824248022633323771403075760653092184490200257490876031798935563235856603897562703627459498243559359937556027252726520654751170032954032944242880426354670642569689012403272176373203173701917184324516649188312784606423032324484921543917705582870202375214918112346178440790868863462508918498665612562776751402770084166080782346947524488030337291436060498811756462014651621345418752918548604616050503113027895196826198285441016957189834281456504021892402090792794203660502143926695858343202653787058765050138514839512910522768968687221593986784341080998411101799534205356727448174840770264752346479565665464323248483949951667459136063044967864707603906610203763336298124283496992741919040317285800443411239998869867561386782210790401395980647825961253308816894872969949133234501190389966362137935377408866546133367688833433589008878243722796984720638016613707822277403891897530955618016324005049397772904598256435495224821296475348615644841821601078574547664567284319197233147415213312543909477472366942256089303483041180396425705543717364874264632951404044734938396206117860872034319605359953763568766766054299362767456429381295317381982367032123412109057193702812786979355131199367514651190882437141105781619023776264492013176164695379135511300217998377594173544123587581059316884191829161095463270512088353048101859155452155914379657824797400889654791316706693804688455565382366966716853511749193115024972520717081778846501982002389946481195570225261138891569688852280217603437989914270825248761757631165397578501683338306546765169863075589385594544871132530404022603120493716031819244029847151820981730070130450666209369379099372737970742475550379148898864674294210435077783723748092904827630574439351611183486760445791793338483400836479995708324721846675842379527261504539428680154016299648745992084180025739799904686647279314362827405424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081877621998538279551144689977910016143723171460322697508008477304748314799415678267628304450960071007183802809796613767105616585881585003811634626206477910050407867686773510547651011209518801134724256885643764313764936350254839931619623961845902029162644351367889924667419295711449018647943633906784301817900868295388640993547610729565658988346046900165284233744135180237806553997039852475735328126074319054279022737636477238362684238366934714130330276561367934252536986047995296664899001864888523399601391162332000910682076090634960557431873988967906465868171684869417891354007747509794529010602760998960059005132773299298792467141576564024636037287771640317062179315349266618366815592462685249919541957360612219945648734298809567018979435291442468085893582431061834640509668314214594464857999949472488045034607135115905658207153175733749032338009860624342660413379840849055743349077169588934984031753298766267179766733113858588677186648535533551628564250810814378793462674242960893458052228379671904775999185193780085843969; b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 128 ? ? Errors (if any) and Timing Info: Timing: real 0m0.737s user 0m0.398s sys 0m0.214s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:34:54 2005 Input: c=499727682740979118102799668152664769073128210793925719147375447600871023621742214309581886957271075796530402194139827086446976388920003973963084938215004869533111333314394955614098710364880006742173866358895351297645878515359862673940652181925483415414612835601824997539703097970769933875015685047485263158155595448796648679756373043802271972202339212472367053979963581279847119544539226193863226133908835377149809863466464575777176267394769346019129090681266907412582858129232594117934878051454859907625184986522790028044914043194537274139805145760584719643869851437678743276215123874795552015045917908061590537619657766521769031589611463446665189517531431566264835884786369256462405442929504364123537820298810364756741026783545078425333318798573388973711554747763011280168196240373899088489862219836666450821428665737821536631625068164223421792200689817712957641567840857246015876278798924230885381579908151573291106342687922809701750555580377084226833181739050487477239179827694359314115634498987432901974777903860117852062378015525760492614076415833193775663964875724614028182461839583254727019625034557559103440334713651280822387876356066559466234231080024855130551650308701068591075894598541049305986099252752534219149171574147033971814558943126199526258092219651188544876743396027936292157280233664346878680897544813523537026932764124278860881105386363241999614277236315422511277408768843521213879715737483063664791909035488321822812881690316833967850920196522032156667231956537880188539079437753731291007566913180408069742482852445029821198848429900873156306998047887282639566456352436919542804187465909636371558681887682613822129323206279289555173507317775070555310908543816376606373564203937644075915323160423578964532412606645320592789003339646526770342059302032589982184015382238769269451625037346527215714469324895253179294965756873416969991059492923443017113066596819968936008915452000514193432300801354071589917024914083490952428890073782884622652615224036568976679404615476409579697464691825903891980380325932707692503379300018519521039630579583274248378395107710450991423333777477203397223800111755700626360175837967253610546797142678673413960533444242533200023301759134684310078652702125871548458971653678140952963147951289517581472897265511167931193794983898840778832546828650841807680478375657178451763207664623990148735650332217584594786485992413692758226579052730694087626075092781427607359833605527270741254104114451470033548010810496967950316970626956115976823820040493854732282678420039756485637464351811009578546455936570117573075749935764473586557960493171434202176313239779274812122285604757544815945284547663629536363809769861428016490368713199028052126420748127554904953274883568878312290082983442090112526174019201226758133336332277119218904233152483718160579411328963760606185647172451509842749624737887218439713417706225343012536127456316162837363428982786921951169277217130183202504292136468200945177805579388620717627689820145544948386262542365814558439432104859983736794217952625365006525273993521061158249616918393930050571168561536337463265709811217138658642175521226499046189968859511624506760904568867911341681783510084468746613124332270738321787237305516153137888970900690282388546502966989533819203689379570222753294035613924618522030731138988271530368772662138225262150686806931677655762869767737286568333126651877729645991882482305024420150121282894130669274566373707180030306457962126700534969521815586822644155763537456661576827535954152375101129707511265833715856734530860480198378865020228401604381322580802915038211324464017030984702730498946491427971764305365789133173586091108245636985474777404382211690843378747466198608562038608408230600743920581520731044623581657354633590700129251788633849554323991889453878466260279984507936884622764171953530827728420326492650769728376529100115303555793598048882484610945217133828812602661733276953715202014355000219087863462757807092554409982884294078672510379266394206661466934138680715059441215254336944044641741801414577701327380201267370060276614865007916869209422499430620694777854228049305920493722644656971896927105130089226821830819666213486551783906036873145279032239448119486145095798053135705206967946119447166315782112952433753749641903340150441029501926363590721493785676946350335953941592682065329773187931356597706787110190397253356800316727977179514473568604026867831628430608685383319438115080782655398780345491076508230588936380818921059829427840037584579227504066588369935649319218939934097860608114515427728667020140407487689164991842432092863972504461278037633854370080551503402565292442234387106791421917795040582679118764638800914861590187844148270756288299094196269047034683834872097305166482290876393398927171080166449073726024502908441030380957532603889390800221438995461196118840364066606435795150603074230553891870115245016466432946797441271082187326768947119219892274819633368767468209489793399419783869737978187626214843721244805373516555064910967045290646421332744533582751043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78880757577132004649569197024421901692749883638403174426595209886621064804891103571316020032905859183574209846620572791656759997089077975970774135672961908531126794584573787279774158046873052425356229118492893500183796876907972940928709796163160574096970560354611231106506227787953130944013408236313533161638111385309822341939856780351196942016651022258430714346221339017819982716962664720035497837540327001253145931239096423024589568245367999066333795961893393814861662549034456296138510919390162620559584521013906492759783211785763882441819119454901803591813103022227376095329724094366394381356809016076127879120760230885579639473649409306954178450812307100298562291566352839086982518157634031408488968348244455533757825881804179727345667736733934894791790573350882976490877859180178102983035182878393839107546567804980441824975114855839117551407967338051971687725314688329879837844689902667333298563413282899015209116781842527163828661800035463373799481496998685907002768863473692909901489421247870583998233594921292342463363099243245928400696951174195203354491281484041968520234903317619782865350863651886538899139272938190476409263474301132317025011597649151459725626303185793893347342894519008103636625434899864184050772220632890378021169427190396366094337; b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 128 ? ? Errors (if any) and Timing Info: Timing: real 0m0.649s user 0m0.396s sys 0m0.233s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:35:17 2005 Input: c=76488058293387470058869903147467393301583234037975419005361430418748468850019972193944075727626681363968259941189196363674329358118517177906816522787053159013215287275745388011019939029694165929760236906114059831466718463023190969727589024230923666690307570753138939588456290219098235516022513080888710170418206831414335751000874067074212581229833989028424686518266797650591645802014498975857069637977459969420985180408340346971541453162062763672499498463635022311113823277744260830144450901664905865923215950208317872106399305723942823355560329513947348268779900503732291444480211447412520000062455937228114972343973761429418554194098896123774251569525065468971516640101731037848911220091554351993485947284539652045751002365344774519148892671840422842601074202165726200739098340130082288453191193098162832973229921794508947386203078088256739768610447267368427023830599493542787569231774277989678460974821417875385427635107788097352942948020198012142787273305519358847101977755926025633090017074913383075636395596176100659114778318526354257802485315189069110397723099445486827076158882247204218173012694981065914673112229295686382435000075874445484173829959815270444377404756160189048289844297102936931442833463932650753127082980418729329144738719701637717296166158108488189817562239389350778158162448415631847724730534547374905424431639475023354067960529560547124446626465183813167138481979905148132261616348755218750436682386818860415704965194845549557431852336632273782702856473915625762338563305492998138047272195534479095542544926585433997312416575270532045500052165928576361373075992196167155700178363527383969763104156630040479860175914646727187121034480248338501935668493063515601034880206717133845067610992456531647985633929063695632321959076997371135287172446586215653773983842220272073707325090344158405507418277864190160701067046187643242192236620411134870157217155598838549254551699890551341206715576423426470360331542673830466441462059102844282487930197988125575695492622091922105878560754227004741196071369071343765466361553861050759982817671334806989278024267545738019471834045540188262616535441959382236718895073665816632968192655590916058936504836741399558079984805359039929459598589602969663571492178779744035708335660700221120342813048711379647744107308860323879471942354773518585431265391345082048667470072011477000217266675636434295957170433892681877473619539026004111004190127259476756881229162611760420706338286629759144001173034639608162408707944259007362175835150601402635379723349118074107371805069626659324214719698511589035366085062106607407897064474169710339633605921997318513818510186987773576187294920052878837434892150743449562896624664892160849442282758949659323835739509663920553174014394315274855400883124127756312983421903713880054289527919164364107964675828063591169819754537089958411813959333747334427444664404180850444110872697155753105350603053613721887762079128814371505677226152301426586258599627119422843587341331443655648191115024811773059072830249101074016014714333780052222353667173789080014300762776601618464636182019996606180544470621724452415470061890123622196585871705224044777757592755365560992044545096599167435162070072692801; b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 107712 ? ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:35:59 2005 Input: c=304422472668573833125574886370311471504577950904723314357244909748444519373141437976690231209545623258643167932714923171426814892361616146943244910892612676351666640463967646655198727411780976134967360665740179020956098864179914982414568399105811113746186214180959257095279374089809820837235560181742551965370353379411620418561154289253004518080130958813344730740943807366365507461371669020624087786902535348946780463245460997320169638078161049113480934093501762861560447376046723495184063788581975881036261622025916059986319298900549179316367626860050616569703254741723820060965811915526594973289494418725727916180186773205186385591263197120961188100212922321526029579504650261251705078642567001156321188300452613085737598753819514315876753396226351732017210335208975660266952167939664675258168763045342329766713152465890269596359660848818198216185463659200037148003767324567733898164935144009868601276299854724945376195748594840729884797035377260959145260772510720232363779399307481534595130937901458329124061864089279636993932800317116013054661977492406060414585889823395490057448270489341127667592449902006170708427318255716841393981560625921841722323357660759157123453031220921774514234346296446755490181580579603917492547554871209720344354943477680453995285168954246769368940873452655426408931634829911649541338682530122328004539801399771091492871123008870367128853273005639827015545240285171584581928555878593778319476234360035259509420958211119913230355976947887535105734789597117649035054162508153376164357941824818180509959547196860628274453704189464288344209932599530725142936896302831114681269974768351171435428535664431191771817034392857223453636297223286445749089111745231558470971876823896615225157952007613399021432307204886221026774710838040295974699895126033015614393218541486769661122039841352169251587498562391451592324761305333136466406866262563348507092540460553134891986380403306438224018736247529885464124405453879150207417623075903240785248694643383364126080628165109042684413248093289753521312305210800088919623105525718281943785921211302615886881216805266970454347470980818809176607852491069533915248357591039791201843599987269954735181774578191637548903261788155580237465198272009193053787310173690906802484712226548596720454889128735611215049719334607406961400132763237140833096037839033548811468331404721408341011932656416423916590558560800269237589871006909190098447362530243145713465579068721304146030279700724949424280150544447583002685300500934942885488769929730461010070166709677199985359987740510023820992539784425366119234750968461889310097508405083871120460508051559983956013853982990649823472280188326868987129681772726347323456773355340219554647326550896138649124884389260462862331877098140699350327997963279761604216666343717907904350836874660553563955103181877738850001915240274895510697867465154828679384447941304495160286104349671028708025714130148037302307655533662389155492386610327527079080324887701132350269513305765955452662652869837775069339322108786769921; b=313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 313837529986205815615686559295823544576085657676648298233395913068570322970900149058863246475303661233148542134676518742693542775896151014490861952020952436207096978287454032687555034029695698261318685010949988362246970753 ? 19584 ? ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:36:56 2005 Input: c=304422472668573833125574886370311471504577950904723314357244909748444519373141437976690231209545623258643167932714923171426814892361616146943244910892612676351666640463967646655198727411780976134967360665740179020956098864179914982414568399105811113746186214180959257095279374089809820837235560181742551965370353379411620418561154289253004518080130958813344730740943807366365507461371669020624087786902535348946780463245460997320169638078161049113480934093501762861560447376046723495184063788581975881036261622025916059986319298900549179316367626860050616569703254741723820060965811915526594973289494418725727916180186773205186385591263197120961188100212922321526029579504650261251705078642567001156321188300452613085737598753819514315876753396226351732017210335208975660266952167939664675258168763045342329766713152465890269596359660848818198216185463659200037148003767324567733898164935144009868601276299854724945376195748594840729884797035377260959145260772510720232363779399307481534595130937901458329124061864089279636993932800317116013054661977492406060414585889823395490057448270489341127667592449902006170708427318255716841393981560625921841722323357660759157123453031220921774514234346296446755490181580579603917492547554871209720344354943477680453995285168954246769368940873452655426408931634829911649541338682530122328004539801399771091492871123008870367128853273005639827015545240285171584581928555878593778319476234360035259509420958211119913230355976947887535105734789597117649035054162508153376164357941824818180509959547196860628274453704189464288344209932599530725142936896302831114681269974768351171435428535664431191771817034392857223453636297223286445749089111745231558470971876823896615225157952007613399021432307204886221026774710838040295974699895126033015614393218541486769661122039841352169251587498562391451592324761305333136466406866262563348507092540460553134891986380403306438224018736247529885464124405453879150207417623075903240785248694643383364126080628165109042684413248093289753521312305210800088919623105525718281943785921211302615886881216805266970454347470980818809176607852491069533915248357591039791201843599987269954735181774578191637548903261788155580237465198272009193053787310173690906802484712226548596720454889128735611215049719334607406961400132763237140833096037839033548811468331404721408341011932656416423916590558560800269237589871006909190098447362530243145713465579068721304146030279700724949424280150544447583002685300500934942885488769929730461010070166709677199985359987740510023820992539784425366119234750968461889310097508405083871120460508051559983956013853982990649823472280188326868987129681772726347323456773355340219554647326550896138649124884389260462862331877098140699350327997963279761604216666343717907904350836874660553563955103181877738850001915240274895510697867465154828679384447941304495160286104349671028708025714130148037302307655533662389155492386610327527079080324887701132350269513305765955452662652869837775069339322108786769921; b=4992679136035358713351811618087572638282077725057974536974435415747267082108779566637963573792109263527472593560542218809703059254171528599079386231114709983130799215279414032993750509003444564997721564444772755382147484900856453623495527973681621555062694932406510900408023434790438448371983901256717295420157790349918864636101157965764597331016239088656195277238290412412670590677702415342797257584972352196979735070980626903991450748490607417716928638934371532413976448460067743454183873; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 4032 ? ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 24 20:37:19 2005 Input: c=1250704829118797703570514291919423575290792709618770457090264295749276233159765165842816475541998117757746754425472104697933956820301747903420199388155522977357488643096788797895235823576680691421766285464210477063781831442687670360631003105095364296391118702702696296439218585973683422416444371010793915481896273316354500270755690674490880064766301187204551662680052084067748968322038615036691507009522540993889274053828749863007791799903606035772850871556295224622087564237796922814176754357974940594132736897474753; b=4992679136035358713351811618087572638282077725057974536974435415747267082108779566637963573792109263527472593560542218809703059254171528599079386231114709983130799215279414032993750509003444564997721564444772755382147484900856453623495527973681621555062694932406510900408023434790438448371983901256717295420157790349918864636101157965764597331016239088656195277238290412412670590677702415342797257584972352196979735070980626903991450748490607417716928638934371532413976448460067743454183873; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 4992679136035358713351811618087572638282077725057974536974435415747267082108779566637963573792109263527472593560542218809703059254171528599079386231114709983130799215279414032993750509003444564997721564444772755382147484900856453623495527973681621555062694932406510900408023434790438448371983901256717295420157790349918864636101157965764597331016239088656195277238290412412670590677702415342797257584972352196979735070980626903991450748490607417716928638934371532413976448460067743454183873 ? 12096 ? ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.005s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Thu Mar 24 20:45:09 2005 Input: Mod(23^640,1279) Output: ? Mod(23, 1279) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '170.224' ************** PARI ***************** Host 170.224.224.154 (170.224.224.154) Time: Thu Mar 24 21:31:15 2005 Input: factor(6653) Output: ? [6653 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 24 21:33:30 2005 Input: factor(12250) Output: ? [2 1] [5 3] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 21:58:02 2005 Input: factor(8800) Output: ? [2 5] [5 2] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Thu Mar 24 22:00:38 2005 Input: mod(1011*28,1147) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(1011*28,1147) ^----------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '66.119.' ************** PARI ***************** Host 66.119.33.154 (66.119.33.154) Time: Thu Mar 24 22:00:51 2005 Input: Mod(1011*28,1147) Output: ? Mod(780, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 24 22:01:21 2005 Input: Mod(386*780,1147) Output: ? Mod(566, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 24 22:01:40 2005 Input: Mod(1032*566,1147) Output: ? Mod(289, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:07:03 2005 Input: nextprime(1105665) Output: ? 1105669 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:08:46 2005 Input: nextprime(82398688) Output: ? 82398703 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:09:32 2005 Input: nextprime(82398600) Output: ? 82398629 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:09:42 2005 Input: nextprime(82398629) Output: ? 82398629 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:09:47 2005 Input: nextprime(82398629) Output: ? 82398629 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:09:55 2005 Input: nextprime(82398630) Output: ? 82398637 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:10:01 2005 Input: nextprime(82398638) Output: ? 82398653 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:10:20 2005 Input: nextprime(82398654) Output: ? 82398671 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:10:50 2005 Input: nextprime(82398672) Output: ? 82398703 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:11:14 2005 Input: nextprime(82398671) Output: ? 82398671 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:11:42 2005 Input: nextprime(1105660) Output: ? 1105661 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:12:00 2005 Input: nextprime(1105662) Output: ? 1105669 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:13:04 2005 Input: Mod(1105665,19) Mod(82398688,19) Output: ? Mod(17, 19) ? Mod(1, 19) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:25:43 2005 Input: pi Output: ? pi ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:26:00 2005 Input: pi(32) Output: ? ? ? ? Errors (if any) and Timing Info: *** obsolete function: pi(32) ^------ For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: pi ===> Pi Pi=Pi(): the constant pi, with current precision. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:26:15 2005 Input: Pi(32) Output: ? ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: Pi(32) ^--- Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:26:25 2005 Input: Pi Output: ? 3.1415926535897932384626433832795028841 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:27:47 2005 Input: precision=32 Pi Output: ? ? 3.1415926535897932384626433832795028841 ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: precision=32 ^--- Timing: real 0m0.012s user 0m0.009s sys 0m0.001s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:35:15 2005 Input: for (n=1,20,print(fibonacci(n))) Output: ? 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:36:11 2005 Input: for (n=1,30,print(fibonacci(n))) Output: ? 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:36:28 2005 Input: for (n=1,40,print(fibonacci(n))) Output: ? 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040 1346269 2178309 3524578 5702887 9227465 14930352 24157817 39088169 63245986 102334155 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.011s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:37:12 2005 Input: Mod(9,4) Output: ? Mod(1, 4) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:37:32 2005 Input: Mod(9,4)^1 Output: ? Mod(1, 4) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:37:44 2005 Input: Mod(4,9)^1 Output: ? Mod(4, 9) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:37:56 2005 Input: factorial(4) Output: ? 24.000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:38:03 2005 Input: Mod(9,4)^1 Output: ? Mod(1, 4) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:38:14 2005 Input: Mod(12,4)^1 Output: ? Mod(0, 4) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:38:54 2005 Input: Mod(614656,1147)^1 Output: ? Mod(1011, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:40:32 2005 Input: Mod(18496,1147)^1 Output: ? Mod(144, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:41:54 2005 Input: precision=100 f=5006 c=19 factorial(f)/(factorial(f-c)*factorial(c)) Output: ? ? 5006 ? 19 ? 1.5501654791140266289309379737332059425 E53 ? Errors (if any) and Timing Info: *** expected character: '(' instead of: precision=100 ^---- Timing: real 0m0.025s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:42:18 2005 Input: Mod(20736,1147)^1 Output: ? Mod(90, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:42:35 2005 Input: precision=200 f=5006 c=19 factorial(f)/(factorial(f-c)*factorial(c)) Output: ? ? 5006 ? 19 ? 1.5501654791140266289309379737332059425 E53 ? Errors (if any) and Timing Info: *** expected character: '(' instead of: precision=200 ^---- Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:42:49 2005 Input: Mod(8100,1147)^1 Output: ? Mod(71, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:44:50 2005 Input: (precision=200) f=5006 c=19 factorial(f)/(factorial(f-c)*factorial(c)) Output: ? ? 5006 ? 19 ? 1.5501654791140266289309379737332059425 E53 ? Errors (if any) and Timing Info: *** expected character: '(' instead of: (precision=200) ^----- Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:45:01 2005 Input: Mod(5041,1147)^1 Output: ? Mod(453, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 22:45:29 2005 Input: precision=10 f=5006 c=19 factorial(f)/(factorial(f-c)*factorial(c)) Output: ? ? 5006 ? 19 ? 1.5501654791140266289309379737332059425 E53 ? Errors (if any) and Timing Info: *** expected character: '(' instead of: precision=10 ^--- Timing: real 0m0.014s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:45:49 2005 Input: Mod(205209,1147)^1 Output: ? Mod(1043, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:46:47 2005 Input: Mod(10816,1147)^1 Output: ? Mod(493, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:47:39 2005 Input: Mod(243049,1147)^1 Output: ? Mod(1032, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:51:22 2005 Input: (-115)*(-104)*453*71*144*1011*28 Output: ? 1568048204136960 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:52:02 2005 Input: Mod(1568048204136960,1147)^1 Output: ? Mod(289, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:53:21 2005 Input: 7^7386 Output: ? 7836525394947970685765064676824624881230843694638653432597293697270900348717161274111722972468270718930712577924994374650698495363358801523185551274561566929222651989785236373702460086634634940103775721791690379940686820484234683151915000605720616895085768755138746929720910704204836021228053171447520320588006367036893856646530014282413149363430471445537761787686028318686003461552188028475934931546480878063771110043350814118031022864718663032984583510480981567089557643496281453541983057917469183789450304777645053241291541744557797093545928964311564444915089899253342265105336315340761896970130573560253210922903045498127224571279679253933490311683526849908297452473886243431616837896438333457152401748652912392357437587922066344164793484849687123175524202171959149799699848686904006085376984584739707761858054562412031377021615051176965455988056793836470956658798217507375350352917508531930305085230711643655136072274902922220403119532770292330451209753098003284637094853555284524325942248185110784504778993102684450493660780770373940728555790026570684550108901235483750186600502144506194894659542082454708256820848020692333528269863628499182468946823427734100122287570660746486502607745826614460946661646852333068028886106155535688564852728770116870189546914823146684972123764164077867785008596847424980892967443638305071840033774662993790587984154581146773544765254984497258149323228318486246568806284560001555977603800557884391543437643178525437084402609028655562062472989345075227797815830905648986773972086161214487405614679532825266121993110079079302201901735944164432298040062643877559644334998478705112462240056447834269603854855654279446214329597279009697888384952269822953987574035741284524192509017370584183628078608704527588844366974735773761599098517020577814348375808668347291322014575553809958211427253166622890243207068547357670097157892911487650229437600540479900516238100881300970154316089182070287032502634219444706180244875076964243805193228860352050305925417074962808786746470833706363076932232404741716322939102390253573793568137599367923917213784885064376948089957436403057911701881101514842822857357533871084485405565391621717530550054529402629765344279818901973303180311300650040425589566786273149546332150406923900786525349239562824189074087924075702338377532893700116219987197470503110559192856153904451944774013991475021246351524614741931034931006348622370527837923962721599910900181774989306614786976007925930294108263277425847368311267218064884261148854892429724507036223427707359324480656493695298462686252347545012748538349382713581699498025290360226843595283207598524991213819237608753432741910231371845150666682636389190110224157289894165110413163801844039835576745991781732628223521965288300361611548799601830368005210706903879142712525315969041882657841162575000441664701208585535945469892978628403465795905067382888933473810491520262948523493834420016375284935631742135453182777210045765582786281879130098505375922869449139835957364032471734291454024536166849382206978467102401675813174674858113085510054465424892254427390779720478644753951040277933756403338895257591518034328895284028616942721212818945987783947048282257968819417409413832046363531[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.016s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:54:38 2005 Input: Mod(7836525394947970685765064676824624881230843694638653432597293697270900348717161274111722972468270718930712577924994374650698495363358801523185551274561566929222651989785236373702460086634634940103775721791690379940686820484234683151915000605720616895085768755138746929720910704204836021228053171447520320588006367036893856646530014282413149363430471445537761787686028318686003461552188028475934931546480878063771110043350814118031022864718663032984583510480981567089557643496281453541983057917469183789450304777645053241291541744557797093545928964311564444915089899253342265105336315340761896970130573560253210922903045498127224571279679253933490311683526849908297452473886243431616837896438333457152401748652912392357437587922066344164793484849687123175524202171959149799699848686904006085376984584739707761858054562412031377021615051176965455988056793836470956658798217507375350352917508531930305085230711643655136072274902922220403119532770292330451209753098003284637094853555284524325942248185110784504778993102684450493660780770373940728555790026570684550108901235483750186600502144506194894659542082454708256820848020692333528269863628499182468946823427734100122287570660746486502607745826614460946661646852333068028886106155535688564852728770116870189546914823146684972123764164077867785008596847424980892967443638305071840033774662993790587984154581146773544765254984497258149323228318486246568806284560001555977603800557884391543437643178525437084402609028655562062472989345075227797815830905648986773972086161214487405614679532825266121993110079079302201901735944164432298040062643877559644334998478705112462240056447834269603854855654279446214329597279009697888384952269822953987574035741284524192509017370584183628078608704527588844366974735773761599098517020577814348375808668347291322014575553809958211427253166622890243207068547357670097157892911487650229437600540479900516238100881300970154316089182070287032502634219444706180244875076964243805193228860352050305925417074962808786746470833706363076932232404741716322939102390253573793568137599367923917213784885064376948089957436403057911701881101514842822857357533871084485405565391621717530550054529402629765344279818901973303180311300650040425589566786273149546332150406923900786525349239562824189074087924075702338377532893700116219987197470503110559192856153904451944774013991475021246351524614741931034931006348622370527837923962721599910900181774989306614786976007925930294108263277425847368311267218064884261148854892429724507036223427707359324480656493695298462686252347545012748538349382713581699498025290360226843595283207598524991213819237608753432741910231371845150666682636389190110224157289894165110413163801844039835576745991781732628223521965288300361611548799601830368005210706903879142712525315969041882657841162575000441664701208585535945469892978628403465795905067382888933473810491520262948523493834420016375284935631742135453182777210045765582786281879130098505375922869449139835957364032471734291454024536166849382206978467102401675813174674858113085510054465424892254427390779720478644753951040277933756403338895257591518034328895284028616942721212818945987783947048282257968819417409413832046363531,7387)^1 Output: ? Mod(1363, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:56:04 2005 Input: 7^7392 Output: ? 9219593761902338032095740941637402926519275298305429376916390061902241551262253067379700959879195818114794040802976631832800272810037996404012569219008937876561157839462432741297207267324781660682691098930705815096418637431497262381396479062624248570899456082733184375347354234389947530614592275676293181968583610755235253406076096503116246094582315350960721365594735456650896212481533693621652687615119288233246073254901799301722318090112859871676032654245770003865193671996940167277607647809323320036450389067851628687847085947054802702585849967222912453798154115572564641473777121635252964166388918487902300118686203998091698435864829845460212016792552503648612869861002426534862893616780734929005229133272664900484601747814431833246437886990808403544772468613288220147848874981655694119385168594100418784748382612132130794752159891559188089315388937380669715799509514915252025936703919612730684629723079941643831037670700538963082066099108921223852543762422269884342695724259256690024227795567300986862027437595377229161286971968537237527738601408360144666357621214534277257033624767990093231618004664587139717067159487864323472674211860293003182891248294494891452870104006661633905452986887553647159137960905301331205304215030926182239663586870754796609300049820283843402853887301395970670384764105027015770767267766029533969081335553265564688857478023173367607680874836711179240097284884415884225734905721996230592091095318345407806938952823103391475428825496122982210878847234587554751852346902186976449710419647807232287831614323573597339863674076936008247515373320950012954321153299895510145963682360211777760700804010312539846239199128703225676696627902782119468706012495924007136840977309263829867244933846318586196598202354789662999509302106890472783723414289539592802720655140223904767436927993301877736162049078000164142230684075280825292605289431436105618431042659869198158348963305841778376851335761813871990869024132834502373996293079297663194371781821915583664418193934522994909519355471147199096380002101854581836774624571109427032394978204280368809362845779429388835658354024353833602538146097121197432663452565023992186234793627589034457516833653296899892629891764139982571458604442101766060301869428382497709764311632241900036339208126853267030203773701795823044077783674109249731652737952072204541784803336507048668507179720830447746120105193997734443285979659090732702296039162902335079174954856457169339230729403564777731715430663258735170344522769381155684399016292394646585283046500463431171658247558267581688365749024363232048527882665268701733642431773855903279221414740907588666913146194854322326086529968106662101307845454885518272777618809987586310749983081231494426157685891871290619778691356942032492432371047243557409654450344565344772609858908984418084528123549357862269614104324888797184485874390426530393474224352725295001342603305168674156308405261256805065358973921388304939315005559846742750492232767977769590589719496678218525605479210562670676552745326554936629672688096761304547577441873223821463971723978027731488411280978433345920766575859376586285070964176881603845052207602012706827546942079669361765167935862833593677736356388001279264226231[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.015s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:56:54 2005 Input: Mod(9219593761902338032095740941637402926519275298305429376916390061902241551262253067379700959879195818114794040802976631832800272810037996404012569219008937876561157839462432741297207267324781660682691098930705815096418637431497262381396479062624248570899456082733184375347354234389947530614592275676293181968583610755235253406076096503116246094582315350960721365594735456650896212481533693621652687615119288233246073254901799301722318090112859871676032654245770003865193671996940167277607647809323320036450389067851628687847085947054802702585849967222912453798154115572564641473777121635252964166388918487902300118686203998091698435864829845460212016792552503648612869861002426534862893616780734929005229133272664900484601747814431833246437886990808403544772468613288220147848874981655694119385168594100418784748382612132130794752159891559188089315388937380669715799509514915252025936703919612730684629723079941643831037670700538963082066099108921223852543762422269884342695724259256690024227795567300986862027437595377229161286971968537237527738601408360144666357621214534277257033624767990093231618004664587139717067159487864323472674211860293003182891248294494891452870104006661633905452986887553647159137960905301331205304215030926182239663586870754796609300049820283843402853887301395970670384764105027015770767267766029533969081335553265564688857478023173367607680874836711179240097284884415884225734905721996230592091095318345407806938952823103391475428825496122982210878847234587554751852346902186976449710419647807232287831614323573597339863674076936008247515373320950012954321153299895510145963682360211777760700804010312539846239199128703225676696627902782119468706012495924007136840977309263829867244933846318586196598202354789662999509302106890472783723414289539592802720655140223904767436927993301877736162049078000164142230684075280825292605289431436105618431042659869198158348963305841778376851335761813871990869024132834502373996293079297663194371781821915583664418193934522994909519355471147199096380002101854581836774624571109427032394978204280368809362845779429388835658354024353833602538146097121197432663452565023992186234793627589034457516833653296899892629891764139982571458604442101766060301869428382497709764311632241900036339208126853267030203773701795823044077783674109249731652737952072204541784803336507048668507179720830447746120105193997734443285979659090732702296039162902335079174954856457169339230729403564777731715430663258735170344522769381155684399016292394646585283046500463431171658247558267581688365749024363232048527882665268701733642431773855903279221414740907588666913146194854322326086529968106662101307845454885518272777618809987586310749983081231494426157685891871290619778691356942032492432371047243557409654450344565344772609858908984418084528123549357862269614104324888797184485874390426530393474224352725295001342603305168674156308405261256805065358973921388304939315005559846742750492232767977769590589719496678218525605479210562670676552745326554936629672688096761304547577441873223821463971723978027731488411280978433345920766575859376586285070964176881603845052207602012706827546942079669361765167935862833593677736356388001279264226231,7393) Output: ? Mod(3809, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:57:54 2005 Input: 7^7386 Output: ? 7836525394947970685765064676824624881230843694638653432597293697270900348717161274111722972468270718930712577924994374650698495363358801523185551274561566929222651989785236373702460086634634940103775721791690379940686820484234683151915000605720616895085768755138746929720910704204836021228053171447520320588006367036893856646530014282413149363430471445537761787686028318686003461552188028475934931546480878063771110043350814118031022864718663032984583510480981567089557643496281453541983057917469183789450304777645053241291541744557797093545928964311564444915089899253342265105336315340761896970130573560253210922903045498127224571279679253933490311683526849908297452473886243431616837896438333457152401748652912392357437587922066344164793484849687123175524202171959149799699848686904006085376984584739707761858054562412031377021615051176965455988056793836470956658798217507375350352917508531930305085230711643655136072274902922220403119532770292330451209753098003284637094853555284524325942248185110784504778993102684450493660780770373940728555790026570684550108901235483750186600502144506194894659542082454708256820848020692333528269863628499182468946823427734100122287570660746486502607745826614460946661646852333068028886106155535688564852728770116870189546914823146684972123764164077867785008596847424980892967443638305071840033774662993790587984154581146773544765254984497258149323228318486246568806284560001555977603800557884391543437643178525437084402609028655562062472989345075227797815830905648986773972086161214487405614679532825266121993110079079302201901735944164432298040062643877559644334998478705112462240056447834269603854855654279446214329597279009697888384952269822953987574035741284524192509017370584183628078608704527588844366974735773761599098517020577814348375808668347291322014575553809958211427253166622890243207068547357670097157892911487650229437600540479900516238100881300970154316089182070287032502634219444706180244875076964243805193228860352050305925417074962808786746470833706363076932232404741716322939102390253573793568137599367923917213784885064376948089957436403057911701881101514842822857357533871084485405565391621717530550054529402629765344279818901973303180311300650040425589566786273149546332150406923900786525349239562824189074087924075702338377532893700116219987197470503110559192856153904451944774013991475021246351524614741931034931006348622370527837923962721599910900181774989306614786976007925930294108263277425847368311267218064884261148854892429724507036223427707359324480656493695298462686252347545012748538349382713581699498025290360226843595283207598524991213819237608753432741910231371845150666682636389190110224157289894165110413163801844039835576745991781732628223521965288300361611548799601830368005210706903879142712525315969041882657841162575000441664701208585535945469892978628403465795905067382888933473810491520262948523493834420016375284935631742135453182777210045765582786281879130098505375922869449139835957364032471734291454024536166849382206978467102401675813174674858113085510054465424892254427390779720478644753951040277933756403338895257591518034328895284028616942721212818945987783947048282257968819417409413832046363531[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.012s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Thu Mar 24 22:58:46 2005 Input: Mod(7836525394947970685765064676824624881230843694638653432597293697270900348717161274111722972468270718930712577924994374650698495363358801523185551274561566929222651989785236373702460086634634940103775721791690379940686820484234683151915000605720616895085768755138746929720910704204836021228053171447520320588006367036893856646530014282413149363430471445537761787686028318686003461552188028475934931546480878063771110043350814118031022864718663032984583510480981567089557643496281453541983057917469183789450304777645053241291541744557797093545928964311564444915089899253342265105336315340761896970130573560253210922903045498127224571279679253933490311683526849908297452473886243431616837896438333457152401748652912392357437587922066344164793484849687123175524202171959149799699848686904006085376984584739707761858054562412031377021615051176965455988056793836470956658798217507375350352917508531930305085230711643655136072274902922220403119532770292330451209753098003284637094853555284524325942248185110784504778993102684450493660780770373940728555790026570684550108901235483750186600502144506194894659542082454708256820848020692333528269863628499182468946823427734100122287570660746486502607745826614460946661646852333068028886106155535688564852728770116870189546914823146684972123764164077867785008596847424980892967443638305071840033774662993790587984154581146773544765254984497258149323228318486246568806284560001555977603800557884391543437643178525437084402609028655562062472989345075227797815830905648986773972086161214487405614679532825266121993110079079302201901735944164432298040062643877559644334998478705112462240056447834269603854855654279446214329597279009697888384952269822953987574035741284524192509017370584183628078608704527588844366974735773761599098517020577814348375808668347291322014575553809958211427253166622890243207068547357670097157892911487650229437600540479900516238100881300970154316089182070287032502634219444706180244875076964243805193228860352050305925417074962808786746470833706363076932232404741716322939102390253573793568137599367923917213784885064376948089957436403057911701881101514842822857357533871084485405565391621717530550054529402629765344279818901973303180311300650040425589566786273149546332150406923900786525349239562824189074087924075702338377532893700116219987197470503110559192856153904451944774013991475021246351524614741931034931006348622370527837923962721599910900181774989306614786976007925930294108263277425847368311267218064884261148854892429724507036223427707359324480656493695298462686252347545012748538349382713581699498025290360226843595283207598524991213819237608753432741910231371845150666682636389190110224157289894165110413163801844039835576745991781732628223521965288300361611548799601830368005210706903879142712525315969041882657841162575000441664701208585535945469892978628403465795905067382888933473810491520262948523493834420016375284935631742135453182777210045765582786281879130098505375922869449139835957364032471734291454024536166849382206978467102401675813174674858113085510054465424892254427390779720478644753951040277933756403338895257591518034328895284028616942721212818945987783947048282257968819417409413832046363531,7387) Output: ? Mod(1363, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 23:01:14 2005 Input: isprime(3) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 23:02:14 2005 Input: for(n=1,5006,print n, print(isprime(n)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: for(n=1,5006,printn *** ,print(isprime(n)) ^------------------ Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 23:02:43 2005 Input: for(n=1,5006,print(n," ",isprime(n)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...,print(n," ",isprime(n)) ^ Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 23:02:59 2005 Input: for(n=1,5006,print(n) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: for(n=1,5006,print(n) ^ Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 23:03:12 2005 Input: for(n=1,5006,print(n,ismprime(n))) Output: ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: print(n,ismprime(n))) ^-- Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 23:03:35 2005 Input: for(n=1,5006,print(n)) Output: ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 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1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 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1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 2131 2132 2133 2134 2135 2136 2137 2138 2139 2140 2141 2142 2143 2144 2145 2146 2147 2148 2149 2150 2151 2152 2153 2154 2155 2156 2157 2158 2159 2160 2161 2162 2163 2164 2165 2166 2167 2168 2169 2170 2171 2172 2173 2174 2175 2176 2177 2178 2179 2180 2181 2182 2183 2184 2185 2186 2187 2188 2189 2190 2191 2192 2193 2194 2195 2196 2197 2198 2199 2200 2201 2202 2203 2204 2205 2206 2207 2208 2209 2210 2211 2212 2213 2214 2215 2216 2217 2218 2219 2220 2221 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.007s sys 0m0.021s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 23:04:07 2005 Input: for(n=1,5006,isprime(n)) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.028s sys 0m0.001s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 23:04:25 2005 Input: for(n=1,5006,print(isprime(n))) Output: ? 0 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 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0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.047s user 0m0.027s sys 0m0.018s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 23:05:22 2005 Input: for(n=1,5006,print(nextprime(n))) Output: ? 2 2 3 5 5 7 7 11 11 11 11 13 13 17 17 17 17 19 19 23 23 23 23 29 29 29 29 29 29 31 31 37 37 37 37 37 37 41 41 41 41 43 43 47 47 47 47 53 53 53 53 53 53 59 59 59 59 59 59 61 61 67 67 67 67 67 67 71 71 71 71 73 73 79 79 79 79 79 79 83 83 83 83 89 89 89 89 89 89 97 97 97 97 97 97 97 97 101 101 101 101 103 103 107 107 107 107 109 109 113 113 113 113 127 127 127 127 127 127 127 127 127 127 127 127 127 127 131 131 131 131 137 137 137 137 137 137 139 139 149 149 149 149 149 149 149 149 149 149 151 151 157 157 157 157 157 157 163 163 163 163 163 163 167 167 167 167 173 173 173 173 173 173 179 179 179 179 179 179 181 181 191 191 191 191 191 191 191 191 191 191 193 193 197 197 197 197 199 199 211 211 211 211 211 211 211 211 211 211 211 211 223 223 223 223 223 223 223 223 223 223 223 223 227 227 227 227 229 229 233 233 233 233 239 239 239 239 239 239 241 241 251 251 251 251 251 251 251 251 251 251 257 257 257 257 257 257 263 263 263 263 263 263 269 269 269 269 269 269 271 271 277 277 277 277 277 277 281 281 281 281 283 283 293 293 293 293 293 293 293 293 293 293 307 307 307 307 307 307 307 307 307 307 307 307 307 307 311 311 311 311 313 313 317 317 317 317 331 331 331 331 331 331 331 331 331 331 331 331 331 331 337 337 337 337 337 337 347 347 347 347 347 347 347 347 347 347 349 349 353 353 353 353 359 359 359 359 359 359 367 367 367 367 367 367 367 367 373 373 373 373 373 373 379 379 379 379 379 379 383 383 383 383 389 389 389 389 389 389 397 397 397 397 397 397 397 397 401 401 401 401 409 409 409 409 409 409 409 409 419 419 419 419 419 419 419 419 419 419 421 421 431 431 431 431 431 431 431 431 431 431 433 433 439 439 439 439 439 439 443 443 443 443 449 449 449 449 449 449 457 457 457 457 457 457 457 457 461 461 461 461 463 463 467 467 467 467 479 479 479 479 479 479 479 479 479 479 479 479 487 487 487 487 487 487 487 487 491 491 491 491 499 499 499 499 499 499 499 499 503 503 503 503 509 509 509 509 509 509 521 521 521 521 521 521 521 521 521 521 521 521 523 523 541 541 541 541 541 541 541 541 541 541 541 541 541 541 541 541 541 541 547 547 547 547 547 547 557 557 557 557 557 557 557 557 557 557 563 563 563 563 563 563 569 569 569 569 569 569 571 571 577 577 577 577 577 577 587 587 587 587 587 587 587 587 587 587 593 593 593 593 593 593 599 599 599 599 599 599 601 601 607 607 607 607 607 607 613 613 613 613 613 613 617 617 617 617 619 619 631 631 631 631 631 631 631 631 631 631 631 631 641 641 641 641 641 641 641 641 641 641 643 643 647 647 647 647 653 653 653 653 653 653 659 659 659 659 659 659 661 661 673 673 673 673 673 673 673 673 673 673 673 673 677 677 677 677 683 683 683 683 683 683 691 691 691 691 691 691 691 691 701 701 701 701 701 701 701 701 701 701 709 709 709 709 709 709 709 709 719 719 719 719 719 719 719 719 719 719 727 727 727 727 727 727 727 727 733 733 733 733 733 733 739 739 739 739 739 739 743 743 743 743 751 751 751 751 751 751 751 751 757 757 757 757 757 757 761 761 761 761 769 769 769 769 769 769 769 769 773 773 773 773 787 787 787 787 787 787 787 787 787 787 787 787 787 787 797 797 797 797 797 797 797 797 797 797 809 809 809 809 809 809 809 809 809 809 809 809 811 811 821 821 821 821 821 821 821 821 821 821 823 823 827 827 827 827 829 829 839 839 839 839 839 839 839 839 839 839 853 853 853 853 853 853 853 853 853 853 853 853 853 853 857 857 857 857 859 859 863 863 863 863 877 877 877 877 877 877 877 877 877 877 877 877 877 877 881 881 881 881 883 883 887 887 887 887 907 907 907 907 907 907 907 907 907 907 907 907 907 907 907 907 907 907 907 907 911 911 911 911 919 919 919 919 919 919 919 919 929 929 929 929 929 929 929 929 929 929 937 937 937 937 937 937 937 937 941 941 941 941 947 947 947 947 947 947 953 953 953 953 953 953 967 967 967 967 967 967 967 967 967 967 967 967 967 967 971 971 971 971 977 977 977 977 977 977 983 983 983 983 983 983 991 991 991 991 991 991 991 991 997 997 997 997 997 997 1009 1009 1009 1009 1009 1009 1009 1009 1009 1009 1009 1009 1013 1013 1013 1013 1019 1019 1019 1019 1019 1019 1021 1021 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1033 1033 1039 1039 1039 1039 1039 1039 1049 1049 1049 1049 1049 1049 1049 1049 1049 1049 1051 1051 1061 1061 1061 1061 1061 1061 1061 1061 1061 1061 1063 1063 1069 1069 1069 1069 1069 1069 1087 1087 1087 1087 1087 1087 1087 1087 1087 1087 1087 1087 1087 1087 1087 1087 1087 1087 1091 1091 1091 1091 1093 1093 1097 1097 1097 1097 1103 1103 1103 1103 1103 1103 1109 1109 1109 1109 1109 1109 1117 1117 1117 1117 1117 1117 1117 1117 1123 1123 1123 1123 1123 1123 1129 1129 1129 1129 1129 1129 1151 1151 1151 1151 1151 1151 1151 1151 1151 1151 1151 1151 1151 1151 1151 1151 1151 1151 1151 1151 1151 1151 1153 1153 1163 1163 1163 1163 1163 1163 1163 1163 1163 1163 1171 1171 1171 1171 1171 1171 1171 1171 1181 1181 1181 1181 1181 1181 1181 1181 1181 1181 1187 1187 1187 1187 1187 1187 1193 1193 1193 1193 1193 1193 1201 1201 1201 1201 1201 1201 1201 1201 1213 1213 1213 1213 1213 1213 1213 1213 1213 1213 1213 1213 1217 1217 1217 1217 1223 1223 1223 1223 1223 1223 1229 1229 1229 1229 1229 1229 1231 1231 1237 1237 1237 1237 1237 1237 1249 1249 1249 1249 1249 1249 1249 1249 1249 1249 1249 1249 1259 1259 1259 1259 1259 1259 1259 1259 1259 1259 1277 1277 1277 1277 1277 1277 1277 1277 1277 1277 1277 1277 1277 1277 1277 1277 1277 1277 1279 1279 1283 1283 1283 1283 1289 1289 1289 1289 1289 1289 1291 1291 1297 1297 1297 1297 1297 1297 1301 1301 1301 1301 1303 1303 1307 1307 1307 1307 1319 1319 1319 1319 1319 1319 1319 1319 1319 1319 1319 1319 1321 1321 1327 1327 1327 1327 1327 1327 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1361 1367 1367 1367 1367 1367 1367 1373 1373 1373 1373 1373 1373 1381 1381 1381 1381 1381 1381 1381 1381 1399 1399 1399 1399 1399 1399 1399 1399 1399 1399 1399 1399 1399 1399 1399 1399 1399 1399 1409 1409 1409 1409 1409 1409 1409 1409 1409 1409 1423 1423 1423 1423 1423 1423 1423 1423 1423 1423 1423 1423 1423 1423 1427 1427 1427 1427 1429 1429 1433 1433 1433 1433 1439 1439 1439 1439 1439 1439 1447 1447 1447 1447 1447 1447 1447 1447 1451 1451 1451 1451 1453 1453 1459 1459 1459 1459 1459 1459 1471 1471 1471 1471 1471 1471 1471 1471 1471 1471 1471 1471 1481 1481 1481 1481 1481 1481 1481 1481 1481 1481 1483 1483 1487 1487 1487 1487 1489 1489 1493 1493 1493 1493 1499 1499 1499 1499 1499 1499 1511 1511 1511 1511 1511 1511 1511 1511 1511 1511 1511 1511 1523 1523 1523 1523 1523 1523 1523 1523 1523 1523 1523 1523 1531 1531 1531 1531 1531 1531 1531 1531 1543 1543 1543 1543 1543 1543 1543 1543 1543 1543 1543 1543 1549 1549 1549 1549 1549 1549 1553 1553 1553 1553 1559 1559 1559 1559 1559 1559 1567 1567 1567 1567 1567 1567 1567 1567 1571 1571 1571 1571 1579 1579 1579 1579 1579 1579 1579 1579 1583 1583 1583 1583 1597 1597 1597 1597 1597 1597 1597 1597 1597 1597 1597 1597 1597 1597 1601 1601 1601 1601 1607 1607 1607 1607 1607 1607 1609 1609 1613 1613 1613 1613 1619 1619 1619 1619 1619 1619 1621 1621 1627 1627 1627 1627 1627 1627 1637 1637 1637 1637 1637 1637 1637 1637 1637 1637 1657 1657 1657 1657 1657 1657 1657 1657 1657 1657 1657 1657 1657 1657 1657 1657 1657 1657 1657 1657 1663 1663 1663 1663 1663 1663 1667 1667 1667 1667 1669 1669 1693 1693 1693 1693 1693 1693 1693 1693 1693 1693 1693 1693 1693 1693 1693 1693 1693 1693 1693 1693 1693 1693 1693 1693 1697 1697 1697 1697 1699 1699 1709 1709 1709 1709 1709 1709 1709 1709 1709 1709 1721 1721 1721 1721 1721 1721 1721 1721 1721 1721 1721 1721 1723 1723 1733 1733 1733 1733 1733 1733 1733 1733 1733 1733 1741 1741 1741 1741 1741 1741 1741 1741 1747 1747 1747 1747 1747 1747 1753 1753 1753 1753 1753 1753 1759 1759 1759 1759 1759 1759 1777 1777 1777 1777 1777 1777 1777 1777 1777 1777 1777 1777 1777 1777 1777 1777 1777 1777 1783 1783 1783 1783 1783 1783 1787 1787 1787 1787 1789 1789 1801 1801 1801 1801 1801 1801 1801 1801 1801 1801 1801 1801 1811 1811 1811 1811 1811 1811 1811 1811 1811 1811 1823 1823 1823 1823 1823 1823 1823 1823 1823 1823 1823 1823 1831 1831 1831 1831 1831 1831 1831 1831 1847 1847 1847 1847 1847 1847 1847 1847 1847 1847 1847 1847 1847 1847 1847 1847 1861 1861 1861 1861 1861 1861 1861 1861 1861 1861 1861 1861 1861 1861 1867 1867 1867 1867 1867 1867 1871 1871 1871 1871 1873 1873 1877 1877 1877 1877 1879 1879 1889 1889 1889 1889 1889 1889 1889 1889 1889 1889 1901 1901 1901 1901 1901 1901 1901 1901 1901 1901 1901 1901 1907 1907 1907 1907 1907 1907 1913 1913 1913 1913 1913 1913 1931 1931 1931 1931 1931 1931 1931 1931 1931 1931 1931 1931 1931 1931 1931 1931 1931 1931 1933 1933 1949 1949 1949 1949 1949 1949 1949 1949 1949 1949 1949 1949 1949 1949 1949 1949 1951 1951 1973 1973 1973 1973 1973 1973 1973 1973 1973 1973 1973 1973 1973 1973 1973 1973 1973 1973 1973 1973 1973 1973 1979 1979 1979 1979 1979 1979 1987 1987 1987 1987 1987 1987 1987 1987 1993 1993 1993 1993 1993 1993 1997 1997 1997 1997 1999 1999 2003 2003 2003 2003 2011 2011 2011 2011 2011 2011 2011 2011 2017 2017 2017 2017 2017 2017 2027 2027 2027 2027 2027 2027 2027 2027 2027 2027 2029 2029 2039 2039 2039 2039 2039 2039 2039 2039 2039 2039 2053 2053 2053 2053 2053 2053 2053 2053 2053 2053 2053 2053 2053 2053 2063 2063 2063 2063 2063 2063 2063 2063 2063 2063 2069 2069 2069 2069 2069 2069 2081 2081 2081 2081 2081 2081 2081 2081 2081 2081 2081 2081 2083 2083 2087 2087 2087 2087 2089 2089 2099 2099 2099 2099 2099 2099 2099 2099 2099 2099 2111 2111 2111 2111 2111 2111 2111 2111 2111 2111 2111 2111 2113 2113 2129 2129 2129 2129 2129 2129 2129 2129 2129 2129 2129 2129 2129 2129 2129 2129 2131 2131 2137 2137 2137 2137 2137 2137 2141 2141 2141 2141 2143 2143 2153 2153 2153 2153 2153 2153 2153 2153 2153 2153 2161 2161 2161 2161 2161 2161 2161 2161 2179 2179 2179 2179 2179 2179 2179 2179 2179 2179 2179 2179 2179 2179 2179 2179 2179 2179 2203 2203 2203 2203 2203 2203 2203 2203 2203 2203 2203 2203 2203 2203 2203 2203 2203 2203 2203 2203 2203 2203 2203 2203 2207 2207 2207 2207 2213 2213 2213 2213 2213 2213 2221 2221 2221 2221 2221 2221 2221 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.119s user 0m0.097s sys 0m0.021s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 23:09:35 2005 Input: forprime(n=1,5006,print(n)) Output: ? 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 1999 2003 2011 2017 2027 2029 2039 2053 2063 2069 2081 2083 2087 2089 2099 2111 2113 2129 2131 2137 2141 2143 2153 2161 2179 2203 2207 2213 2221 2237 2239 2243 2251 2267 2269 2273 2281 2287 2293 2297 2309 2311 2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 2389 2393 2399 2411 2417 2423 2437 2441 2447 2459 2467 2473 2477 2503 2521 2531 2539 2543 2549 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 2671 2677 2683 2687 2689 2693 2699 2707 2711 2713 2719 2729 2731 2741 2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 2857 2861 2879 2887 2897 2903 2909 2917 2927 2939 2953 2957 2963 2969 2971 2999 3001 3011 3019 3023 3037 3041 3049 3061 3067 3079 3083 3089 3109 3119 3121 3137 3163 3167 3169 3181 3187 3191 3203 3209 3217 3221 3229 3251 3253 3257 3259 3271 3299 3301 3307 3313 3319 3323 3329 3331 3343 3347 3359 3361 3371 3373 3389 3391 3407 3413 3433 3449 3457 3461 3463 3467 3469 3491 3499 3511 3517 3527 3529 3533 3539 3541 3547 3557 3559 3571 3581 3583 3593 3607 3613 3617 3623 3631 3637 3643 3659 3671 3673 3677 3691 3697 3701 3709 3719 3727 3733 3739 3761 3767 3769 3779 3793 3797 3803 3821 3823 3833 3847 3851 3853 3863 3877 3881 3889 3907 3911 3917 3919 3923 3929 3931 3943 3947 3967 3989 4001 4003 4007 4013 4019 4021 4027 4049 4051 4057 4073 4079 4091 4093 4099 4111 4127 4129 4133 4139 4153 4157 4159 4177 4201 4211 4217 4219 4229 4231 4241 4243 4253 4259 4261 4271 4273 4283 4289 4297 4327 4337 4339 4349 4357 4363 4373 4391 4397 4409 4421 4423 4441 4447 4451 4457 4463 4481 4483 4493 4507 4513 4517 4519 4523 4547 4549 4561 4567 4583 4591 4597 4603 4621 4637 4639 4643 4649 4651 4657 4663 4673 4679 4691 4703 4721 4723 4729 4733 4751 4759 4783 4787 4789 4793 4799 4801 4813 4817 4831 4861 4871 4877 4889 4903 4909 4919 4931 4933 4937 4943 4951 4957 4967 4969 4973 4987 4993 4999 5003 ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 23:09:42 2005 Input: forprime(n=1,5006,print(n)) Output: ? 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 1999 2003 2011 2017 2027 2029 2039 2053 2063 2069 2081 2083 2087 2089 2099 2111 2113 2129 2131 2137 2141 2143 2153 2161 2179 2203 2207 2213 2221 2237 2239 2243 2251 2267 2269 2273 2281 2287 2293 2297 2309 2311 2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 2389 2393 2399 2411 2417 2423 2437 2441 2447 2459 2467 2473 2477 2503 2521 2531 2539 2543 2549 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 2671 2677 2683 2687 2689 2693 2699 2707 2711 2713 2719 2729 2731 2741 2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 2857 2861 2879 2887 2897 2903 2909 2917 2927 2939 2953 2957 2963 2969 2971 2999 3001 3011 3019 3023 3037 3041 3049 3061 3067 3079 3083 3089 3109 3119 3121 3137 3163 3167 3169 3181 3187 3191 3203 3209 3217 3221 3229 3251 3253 3257 3259 3271 3299 3301 3307 3313 3319 3323 3329 3331 3343 3347 3359 3361 3371 3373 3389 3391 3407 3413 3433 3449 3457 3461 3463 3467 3469 3491 3499 3511 3517 3527 3529 3533 3539 3541 3547 3557 3559 3571 3581 3583 3593 3607 3613 3617 3623 3631 3637 3643 3659 3671 3673 3677 3691 3697 3701 3709 3719 3727 3733 3739 3761 3767 3769 3779 3793 3797 3803 3821 3823 3833 3847 3851 3853 3863 3877 3881 3889 3907 3911 3917 3919 3923 3929 3931 3943 3947 3967 3989 4001 4003 4007 4013 4019 4021 4027 4049 4051 4057 4073 4079 4091 4093 4099 4111 4127 4129 4133 4139 4153 4157 4159 4177 4201 4211 4217 4219 4229 4231 4241 4243 4253 4259 4261 4271 4273 4283 4289 4297 4327 4337 4339 4349 4357 4363 4373 4391 4397 4409 4421 4423 4441 4447 4451 4457 4463 4481 4483 4493 4507 4513 4517 4519 4523 4547 4549 4561 4567 4583 4591 4597 4603 4621 4637 4639 4643 4649 4651 4657 4663 4673 4679 4691 4703 4721 4723 4729 4733 4751 4759 4783 4787 4789 4793 4799 4801 4813 4817 4831 4861 4871 4877 4889 4903 4909 4919 4931 4933 4937 4943 4951 4957 4967 4969 4973 4987 4993 4999 5003 ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.004s '170.224' ************** PARI ***************** Host 170.224.224.154 (170.224.224.154) Time: Thu Mar 24 23:10:54 2005 Input: Mod(7^8,7387) Output: ? Mod(2941, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '170.224' ************** PARI ***************** Host 170.224.224.154 (170.224.224.154) Time: Thu Mar 24 23:11:03 2005 Input: Mod(7^8^2,7387) Output: ? Mod(6262, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '170.224' ************** PARI ***************** Host 170.224.224.154 (170.224.224.154) Time: Thu Mar 24 23:11:14 2005 Input: Mod(7^16,7387) Output: ? Mod(6691, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 23:11:21 2005 Input: for(n=1,5006(print(forprime(i=1,5006))) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: for(n=1,5006(print(forprime(i=1, ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 23:11:27 2005 Input: for(n=1,5006(print(forprime(i=1,5006)))) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: for(n=1,5006(print(forprime(i=1, ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Thu Mar 24 23:12:07 2005 Input: Mod(4476941,7387) Output: ? Mod(419, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Thu Mar 24 23:12:20 2005 Input: Mod(44769481,7387) Output: ? Mod(4261, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 24 23:13:55 2005 Input: Mod(4261^2,7387) Output: ? Mod(6262, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 24 23:14:05 2005 Input: Mod(6262^2,7387) Output: ? Mod(2448, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 24 23:14:19 2005 Input: Mod(2448^2,7387) Output: ? Mod(1847, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 24 23:14:31 2005 Input: Mod(1847^2,7387) Output: ? Mod(6002, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 24 23:14:44 2005 Input: Mod(6002^2,7387) Output: ? Mod(4992, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 24 23:14:57 2005 Input: Mod(4992^2,7387) Output: ? Mod(3713, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Thu Mar 24 23:15:06 2005 Input: Mod(3713^2,7387) Output: ? Mod(2227, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Thu Mar 24 23:15:09 2005 Input: for(n=1,1000,print(isprime(n))) Output: ? 0 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.012s sys 0m0.006s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Thu Mar 24 23:17:29 2005 Input: Mod(2227*3713,7387) Output: ? Mod(2798, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Thu Mar 24 23:17:55 2005 Input: Mod(4992*2448,7387) Output: ? Mod(2318, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Thu Mar 24 23:18:11 2005 Input: Mod(6262*6691,7387) Output: ? Mod(7365, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '216.148' ************** PARI ***************** Host 216.148.244.90 (216.148.244.90) Time: Thu Mar 24 23:18:28 2005 Input: Mod(2941*49,7387) Output: ? Mod(3756, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Thu Mar 24 23:19:00 2005 Input: Mod(2798*2318,7387) Output: ? Mod(7365, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Thu Mar 24 23:19:24 2005 Input: Mod(7365*3756,7387) Output: ? Mod(6012, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Thu Mar 24 23:19:45 2005 Input: Mod(7365*6012,7387) Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Thu Mar 24 23:20:01 2005 Input: Mod(7^7386,7387) Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.239.19 (168.122.239.19) Time: Thu Mar 24 23:20:42 2005 Input: Mod(1789,6912)^(-1) Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.239.19 (168.122.239.19) Time: Thu Mar 24 23:22:20 2005 Input: Mod(5192,7081)^85 Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.239.19 (168.122.239.19) Time: Thu Mar 24 23:23:03 2005 Input: Mod(2604,7081)^85 Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.239.19 (168.122.239.19) Time: Thu Mar 24 23:23:34 2005 Input: Mod(4222,7081)^85 Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 24 23:26:59 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 24 23:30:05 2005 Input: Mod(329,1080)^(-1) Output: ? Mod(929, 1080) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 24 23:32:17 2005 Input: Mod(452,1147)^929 Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 24 23:55:21 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 24 23:57:47 2005 Input: Mod(1789,6912)^(-1) Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.005s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Thu Mar 24 23:58:11 2005 Input: factor(97) Output: ? [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 24 23:59:16 2005 Input: Mod(5192,7081)^85 Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Mar 25 00:00:51 2005 Input: Mod(2604,7081)^85 Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Mar 25 00:01:33 2005 Input: Mod(4222,7081)^85 Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 25 00:01:57 2005 Input: factor(8800) Output: ? [2 5] [5 2] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.006s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 25 00:04:01 2005 Input: phi(8800) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: phi(8800) ^--------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: phi(x) ===> eulerphi(x) eulerphi(x): Euler's totient function of x. Timing: real 0m0.024s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 25 00:04:18 2005 Input: phi (8800) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: phi(8800) ^--------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: phi(x) ===> eulerphi(x) eulerphi(x): Euler's totient function of x. Timing: real 0m0.012s user 0m0.005s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 25 00:04:31 2005 Input: eulerphi (8800) Output: ? 3200 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 25 00:04:45 2005 Input: phi (8800) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: phi(8800) ^--------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: phi(x) ===> eulerphi(x) eulerphi(x): Euler's totient function of x. Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 25 00:14:45 2005 Input: eulerphi(2) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:42:51 2005 Input: c=273192012459800687704824585888975043054622734855695668338266611608673527130783133063624073697432427385052572315643911766753586272309802904388296180130498649440113431463001632487477771588508516477635112637417763025475438135218777422322151487031543337728325638692545670939087782166213214447837400906590805492070642943481749018222759125188566460028662197974877689143389752173304082262237493902628036995784309011824799502575811492438895860111863784965566285605021539888881400235451101366767116902735437187204260760828362508698007467559899278931007128268175759258906751496775069703900326610772353746016247785298560272036036627105150257802617628097922799983980365463590565438472445247860823578404918874245163188829046738877286263863743359540815775562404655499582436573855288909937607167857462303208876763044604428313297077599651202337576220282029684991697270260840553164841047072666811863911709058652357331151920195277944232995901201222460884207149431295194266599154292022311958008684093063376756769219591443535480449248514733105328213120411173757071991310403039710780908560311399075090228256164739665700602493543159197254858563197444575826074972023659669320641715825429348216122128710456794252181203605093713516137420339358548568657988631227564456966645556779697127014138295201164331755062661145969365128243182843151800106373026691963216521904130687524473312244626682158279752884820593507903791859662682674288961337032401045187728279735288536916049535991080873701313700702568779510234168083246292111595561714168474055978571241013455852515164493243126837027241730919077315706825975860197390308318181557716185881870424188919998830646780507492022642764658235527329323323067011912639358342594100816730308148226935403863867795251441920904558475297134100098524050697841985829613889625919462045670807016853356819852693775556446682517832011894868760830269100649759616979260520486287283304685341151378182748754621401623108701830903105240272525316839605355589150530114781463041892221601983555323379866783748805886739427691486047731049965910777840422204088030067204607635526558196368174684939241147220619265859026658011948110373814344782256278647660992591353807851267074091747911016698656787190176679277848925636939285944859187473050273652288832695053551749152986007817825316560679538828816530806563715528386579556842389444954755020130633892944830143929369147184877052863059994722630308498037385638062695084594455154267993814036565724614059558083420891759607124584993141757803916098671469250349039234507385242070228789303836295838814444134704897557383653844956393361588501661723198866446644202693229251984505033609347853232914733209693698747728722050984302561531150798484654326547591925528448706742336558595544023330615184970562431703121724752828645633147753383083576958245047548321222428953454715134159394427785061225808154094792714602855344346134098364419488412112235393048696726469609392717950787490792790511784218981625798444836162243276991288460238537692351694224377612804925306470386574982740259208381021647929662257004141182879758728519705113734998791046760623251829141091797483145297679498094266014303171475597514129693435359959916836456750182258580489044524981324291382421414520723329386419872919903566781172900031451190472267588141942763854470876837544165151837969648211648007395398442040264535589420009661503366565314618974425189393396150514143533164160212790236728448804031750600181602936915610900769725984525275097075193866152141944616215692882039737789612648059435994509255189084027789129784465351084061487296995784251363427322609057055944336878146154905403409962559109796598838238783423348284329005168181093955179019055812347307054807827260511405757170825874296949718280835748653457; b=1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441 ? 149688 ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.011s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:43:24 2005 Input: c=27079852469069910604302894412028075690402263873585956057997540484240718344825030004546507471959541721994391352413198794609045152033560164083320301151028652273004470093528428814889719002333347992913775347207499185181200974368667068396377088859127430678504560631084282364642941314581819524269749435490259475850503316580658230867571673291571110731440352665741263696713208388784522035488946016066505340929550073877138540124290045587112579222936433771271987551687117047248660862912711518124611101723430821541745400226560673589767911748840794892525238101961456777147526250519492544277221319476650125688216965560131647558184200913683219016807562778336783837149587586848739933180492094620368626658156227303949341222246414102127185815576250636000037393505424176820442374109794461575565642064331535877036473604890553960682890903316114268765998274438607581065847279924148951429176538202914793948531748301919692267136219482385959554217771361020546127734974475916090749222672213597029148926533939085342102175727231271759336608432396752722237810689020824850250987274910384156221927858527072895324121823261380919535702213072086709525995782236386814395290724751514942419142531604551706769935612310972747926395060437812617834395707525363686932414365611820534591862095374654744563914255825865470921401993393704829855956875406023242129203523922814175172493074734114769108462821990021439761745306745629688302646881358067990500601179255404791740943306117422356311492537938691400370499273935810328808881731171068975763141964441774789332745085802891425833741764848116402616444946888056005826120405416224742829154946044025756641357132336769572874551834686993572976471709018451908555001794406685518137118104788447684997696096911053819923154274005643468343382978904198063522543961803680380009174497678682416636135416428853980016382118723002046064913072153494284479875450201731381321532619023934020389737528442620263418477226592672673603171293262517402351468235780579765078184903033666464865841331071570691250503696673254526733368198330162267346605837727465860155386331759283413322606134796328224013430120129463866821948874708086887236058580656363802120902659117643197528778409101846961427859306166380002308311188417485779904334837196056889312661136863153890971900359726270467662158522065918329376632083059619384820930377775077117206310620725044386800558931923716293200063421597899769313580971239122844870772067349194093619314976098790223731142635730563561402281999438877465276630475848530755000557018304005785005989332197899552257619384123190049678968287420927785330902681348491839827376772833829567505980653625040121658067879263305475888793108091806988735208255317301516179578833887399862517214400531449779757698725872844068475821109941284188163856689747976652292365981930605819670376572586583877063492828951263712536501114817912695240775898631293295348425790404854708444432125773188064138459552286363655622789321626631039872946043451224222337968301363191418939199362959339308538013000368167324722784742373181786287718702810624500489727487437543206276134825481; b=1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441 ? 83160 ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:45:36 2005 Input: c=83532498605224898768543686442060809618041224732451717652248951422594345057471816626571924969125914686033007930087167903840244811338207278067020319763687572286822666137814628374722275291997433438596069383969666295093019038093312246668446425912211485674950153350485038543774776755410150386481627113812917384616741065544743626441617061662814591098871368835752251325040252090511912078116698375726410667760941476514454825348339399210580012279230536605194399075599764424676475750234010982084463931799268156675998551782926550460089668428762254611641884408699451773123538636080550994502340570544948119733517221013466975547802409700576361015277800413758034260454025063999747310349619315706822487139157105952845508167290733447144197539302209213128257111033106425072292934386441474636305812550259113524040917470844216451933898986021670365002423778511677216902704618501600289110319520497621542562594247378990217182949464979419926817282758879674196786229199730613283310373234469448147602418234995286973138779266625376886627579243137254603914157971469735105200262200388167365854831338725023220933326299467823041162654829723140722147675644091731517740586338985878045176874040942161752634864810196616966364527909557608559843009522887259975982680241452176955164022518630189007866990277949474271023830208107557099628154667630633514137328949641906399036677505413466477055198519701275930026872104027289993808998030572673960202781680469919310181011859770738180202702395673638047364130180588649331853618128063153757424033957030588704946345417224521868609221939200527995643061249949363577048894150020186555426597860214443473195633326456155400167729248410843534276309127498451450209015161043891947659134843751512378665835530096103215934634711796518805131490833709067795323895156087741525571366882204579015689132797426788172324625099518972904928471076827887732545585243938599151962046049506266309263430698137125528263795115997111992002604835838763791487935705115671794709875030304825570556859778190933960004486754834328503427188888210374489651221706805897329531895975918658351774410868799182741597597430825553986363972589035822086284599645101308557240388023195212105277401963740899993909646587037633046016239203750853612995932206433284870518924177099956915389022312873299866910820554400955908371692892249708045497253693980230584679717074067889298214072212746182757656076360852450393591174434064634919870666158996467143068925035921292260511014838568238962245397218474152577692015934056528596853895202804629009712951944524431431938455519294599034710379058369937921716747732669255375178924558270750975948377713203195542527803506407662698233716404743549067261268245330362418073559690681524911499044970244832006255467209530904074111764851122278572063932964982910658425009590606510165253092583744576228682304518795907809251194959317252629136312824548941099240719420001570261792128757620322633341000796784812361194617650028425543506684394592845609490434149312916167639726205868983472273668844850880029461805479134406853847124086325981575195012719772405156495363359038428161909323277922901908973487442522044092377551303743049780412203226758653803010770047127275844567037649299799179239483995161170746830517936463679730590251048972849949106155242774944656126779254139155398177570404092773408493423569058919508963742833726097370221005357185900489477800041734780578724736567293148371335181224924392237801565912109564092059392060121568682197813433521087448792409628989267721587961223753049634113258033226220187664640211475445068083688493837648044793766081954947677743457783225032862326263755672884013182051006741339002540427076228100008507099344165282595677273062830904103946414942828486108778767830608031470939464606401145566769914906593750085312591342717293181148712296107921727096007211856906239170255197007840374949103808464038416118571619049664242024339406439868127574961459623189272584916327353134643349690828727999945169179493781229278927622209651010203525793693275400398669128038088535485719742390931725172238716059229216421954379464693308921681676254548914980643272455405168961843610808778354123094149571908967468539539024471559501989903601968642622791313355054854332484206937250002186391931574494757783827318204307188618697662030338212906991633680026108769279298700941887125512614637157932073166495022702876951676429502328711894238741322096393410495487612946634162830892908530815507654227999325898554137228193513195000523748190386779692941187220832649124612970873545221102974273844468613563133344434612384776097534659607978138888244068625196952254579121351097542652672650093711845545520093962366458750428313327716664606721; b=1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441 ? 7560 ? ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.012s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:46:40 2005 Input: c=4544002743243864838594347337091321891127539948854786051470388550887066776766315852247259217809393564695579435326105184416412400467328951708690530364110584036137406705524106153164217774831662154572504828498169652402732962503093924865484345683795660336435240348373112144729847080770624395910879489279324867749611004078931931420099152529261425929656738338916140603522001747898566800267796236082412139350880411793681890126343472553736154841240630335332264028468323272971764330116258169033437455443198526734768469234858153607173958207923804706459441564484567403753395997645859734384974132516976559857488249412870953004775397218639964238030939008152749932133545418755901874938112181807669078579609015635319799319793534407745902426845643299242388794929476634924554667532935020438992220022973170489273247199720905456135070291714998448480905271950999750466900696248560920790801135959667081732443456772564659489049888608058046427420824679933191887017516490732966236343733339207114797558442519923145595342429464480325646312350545555740924168831799053101378431465933759509418852083659500815975766584788114859598121275103366927940062481663095629715105009669531279810233659324366348878759366841027858796529959563523736913913712504550738342488324903208079612726215545916702313626162264080966330081957242840908450178068860230143891169302552967424180408831405725594564602564875604338667129733220931816963770001769400921448293918859926584607484476837054234524651932139648172273950783785826509593724917728635576692168977991764228973091575451776811194884731016112928680274111710377012992151636456482663192998256313849493319773150765534306340550147900181114812617104560431526068634832573609142930447312367678884675215429458616572467713038417233470405521119617231486938750535257205750303967826147918412205642533111321883984609855568830377670319099853847352098889865951107451709216040237248416383206831279370873313660035617773197167037553411349461452913594993155879514340767399160074775793321905792475693777324214093888314136900792487431910554082993967819742520596204107814238801713242480191849534594398001720560249033190402712732919847653996763268682746545289771987885990125243368043003940748758341334208706428461180119211143120842865239245201658520154216825726243661616268033888490353782769339705356905574280383653977768959463637932440249832833541351359783977197025126060020271276892221509921247855835317896807342059572580939541108870197697505652629601539692637545303222190926857552536469202548041055569587561338731354115452490709108687000649292546561071962314403159690783301548139441966745607033023396482148258272224024282842823070757476835291270971833874021904505947631231195255413466096497314687339245283979119683740058122371615364926518023647813798862816146582020829135546489875871226892660782812276826473207517348923368867027058687221989292942509248458095389350758662811292578972651369013029077675448334356484582506914321381905532959886592426196100959147597436885730034072833784322622521939901687918731413001533070014072320749880294839026931468255156754234891480769446547674103779867537155736303091801926615904651153613452519190910342213296740785125781506969274277584014366938563815387723191137684321746276756026271248846223127651125226793564933991191414094438872098970520949158704341307007662286455720020458823020699785496080878057401614175180358171501749387119476819340007504288957460107732820601649717356112502852300608900689651699575708576964801515619706966958654627175172598896672441560034634216595705012184581194718210930879452927886656956446011522155294204994541574917907245673246828476425684680552013244342962356135756492623955326772758242618590824086211959022346767181164664165141007352950281; b=1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441 ? 83160 ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.013s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:47:50 2005 Input: c=27079852469069910604302894412028075690402263873585956057997540484240718344825030004546507471959541721994391352413198794609045152033560164083320301151028652273004470093528428814889719002333347992913775347207499185181200974368667068396377088859127430678504560631084282364642941314581819524269749435490259475850503316580658230867571673291571110731440352665741263696713208388784522035488946016066505340929550073877138540124290045587112579222936433771271987551687117047248660862912711518124611101723430821541745400226560673589767911748840794892525238101961456777147526250519492544277221319476650125688216965560131647558184200913683219016807562778336783837149587586848739933180492094620368626658156227303949341222246414102127185815576250636000037393505424176820442374109794461575565642064331535877036473604890553960682890903316114268765998274438607581065847279924148951429176538202914793948531748301919692267136219482385959554217771361020546127734974475916090749222672213597029148926533939085342102175727231271759336608432396752722237810689020824850250987274910384156221927858527072895324121823261380919535702213072086709525995782236386814395290724751514942419142531604551706769935612310972747926395060437812617834395707525363686932414365611820534591862095374654744563914255825865470921401993393704829855956875406023242129203523922814175172493074734114769108462821990021439761745306745629688302646881358067990500601179255404791740943306117422356311492537938691400370499273935810328808881731171068975763141964441774789332745085802891425833741764848116402616444946888056005826120405416224742829154946044025756641357132336769572874551834686993572976471709018451908555001794406685518137118104788447684997696096911053819923154274005643468343382978904198063522543961803680380009174497678682416636135416428853980016382118723002046064913072153494284479875450201731381321532619023934020389737528442620263418477226592672673603171293262517402351468235780579765078184903033666464865841331071570691250503696673254526733368198330162267346605837727465860155386331759283413322606134796328224013430120129463866821948874708086887236058580656363802120902659117643197528778409101846961427859306166380002308311188417485779904334837196056889312661136863153890971900359726270467662158522065918329376632083059619384820930377775077117206310620725044386800558931923716293200063421597899769313580971239122844870772067349194093619314976098790223731142635730563561402281999438877465276630475848530755000557018304005785005989332197899552257619384123190049678968287420927785330902681348491839827376772833829567505980653625040121658067879263305475888793108091806988735208255317301516179578833887399862517214400531449779757698725872844068475821109941284188163856689747976652292365981930605819670376572586583877063492828951263712536501114817912695240775898631293295348425790404854708444432125773188064138459552286363655622789321626631039872946043451224222337968301363191418939199362959339308538013000368167324722784742373181786287718702810624500489727487437543206276134825481; b=1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441 ? 83160 ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.015s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:49:58 2005 Input: c=963638367452796313185376259724602368701212859210233285855940565711034929282173543938702457998663811539206363657953169969001496020115466071272968595978586135722946101494363806063859037800806645894750711138385607087584087029840901594626752094319159441589878690950809359829841690988091197113435496167578220582374045113344290117135597451223381717957494461991139874578311414706432192429024857934373523073473588068829119973894562246726650228171191230885925051304142317985551819087469244260261588266522493391685689062435308114256202947643952995857799383137214183722422434777029971233001838314853250212631704123229739512147970800366280633021056039729501511417786105394516989810406731247331112715557527689650503153183707421369329404037302759578463843212026443097319768331366438894764386671436269991095992993931718243039814158418450534409018167243435139702722464794162128838626995820404465021589895519830848991979513978690435079338549893635031029229717659810231141893887183216967709006568515457556740515097375471376850542456012152511516031289958721019435070172889307412874127556033712095383552511182380749718029985763384507896613092193244660275309295883712477385385002237206793103935676911428499891924363392502050778438286927604921201559127950023139844155347756819785590644897318274994107735980780647637920813901493611265314526086932052418515557176243164541905891720907473779834706443991820677325128611996199814603517542230222785068942977179098189678859176859690080259835857435374070298555554377863301855175381387064453055566365852313026570416351111776853644711003164611288397778768128129699147742339802932125909531431031772180088997519557757564922309224509217037804011699117416163516990723402387648611010105347314219273996410601009531525496841; b=1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 83160 ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:50:12 2005 Input: c=28101675258790910774092980592310457268797412868026234459958400564004474796899671238755659926828984690548404927086175305162901098247695172747253867550639564929283281537814973092930693136154811838038963407967545405741453706900915192861399568433767141689052940260528137095703535595518275324603708773861629466963805420444757509074950233364601241995235456508388525004588962762374602189371270188168955220637057561454250713157230533023584731784595856801696191790390663284175912972738625995615887320181263332649016845716932416912061029114198785075007005555135915818745764205470117908360919268291521870318069401965630075965410993609287079483998483714458204721240481627467774445635630898925323721169877462199199477265738883439399567838571712358797736069001747855844439301390786541650512321990847218053566766350975643195633419322612800042598149912631924073597197591470536562981102315082557854056025753055487017481001894338788427478959263439147902932165777836372196170640431584785188224824828794921403103298359557683752593100569403522845928407116313659065132413428737855455190618624485329728713432817509121112367042965815244763150412019959856787007443025970669037906436187494208141477215413564703836475680488633683636916464766033376017436623583246140379386909524394327042087933325986521715443892005816602095255041; b=1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441 ? 249480 ? ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:52:07 2005 Input: c=5125268459763805560786623597631591177110478385657; b=1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 1944 ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:53:40 2005 Input: c=50960571918381248856416248832764534260257953905163966272273095428490488040312180664746508499470589; b=1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 756 ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:53:57 2005 Input: c=82484243660824572580832787314940528498740852099165200413024025659473775728342951; b=1412354174998074095011912937318791269898968061614785004245124645839783127053249544348715912597686452820895880646462956002709930459834079341059553583374460012819776826528694618379040789459225671416212185514497232627710390221108963807328010772197666329955181612453242127704190667122494641100630920966674474273095727531233118398146955042300689336449260574497151645617860434464209397505662636025240734194341700933520195388654552224887356424827004437899530022675293930091289672924582197032850298322683719963911765322512866994161872274369419403558274813718161625657590113036864188362424910927581954043774094528772671073691033123396462384479268022920198465163843705210671964131425149788571617998654856955648895223650068702853758280741733190112078161819713954561515794240097784024881114852996931942655207140556503010156532783014806895410046698604836879586184129328687633162633254612757479079131795180836188282395713662470472964926778425458517676491923709403399338711486991831162033642109102262584704155906409162797834493426582649712416126489454922132354798173937289747635087053622235078049951869676280410482302469839450426452173270695024262948146072039004151790093698599252817605102312905861936115274945034881287728774621274290403498765011043456668641293513496441; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 110 ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:54:23 2005 Input: c=82484243660824572580832787314940528498740852099165200413024025659473775728342951; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 110 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:54:46 2005 Input: c=912658308018835919042251464095648899502624125705028038109326899714055640784774788694892421380271208256284377773104758639340693950775459815125457481103525899255122029628911; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 810 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:55:04 2005 Input: c=28301479621116288723240373870524716203; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 54 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:55:14 2005 Input: c=25177713911815836211; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 30 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:55:43 2005 Input: c=912658308018835919042251464095648899502624125705028038109326899714055640784774788694892421380271208256284377773104758639340693950775459815125457481103525899255122029628911; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 810 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:58:49 2005 Input: c=21587506073480580678262968214137021504159716833077625089009844755627304694025438780920615088486586187388818197411751929320652645034052591934872910276510926156183885616900100940596842814739074437047650960800119169110732877959967539367500632917510433324676728199581166623132406087876631636434210325441; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 990 ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:59:01 2005 Input: c=912658308018835919042251464095648899502624125705028038109326899714055640784774788694892421380271208256284377773104758639340693950775459815125457481103525899255122029628911; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b-1,c-1) Output: ? ? ? ? 1 ? 810 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:59:42 2005 Input: c=912658308018835919042251464095648899502624125705028038109326899714055640784774788694892421380271208256284377773104758639340693950775459815125457481103525899255122029628911; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b,(gcd(b-1,c-1)*c)+1) Output: ? ? ? ? 1 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 00:59:51 2005 Input: c=21587506073480580678262968214137021504159716833077625089009844755627304694025438780920615088486586187388818197411751929320652645034052591934872910276510926156183885616900100940596842814739074437047650960800119169110732877959967539367500632917510433324676728199581166623132406087876631636434210325441; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b,(gcd(b-1,c-1)*c)+1) Output: ? ? ? ? 1 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:00:20 2005 Input: c=4993189211487079345128855523420269746545514198797136986145670471292604683519796894667602873344120809462127; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b,(gcd(b-1,c-1)*c)+1) Output: ? ? ? ? 1 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:00:29 2005 Input: c=3088453301742325219637346889791143653091546397400889969228127960338674275246575660137025936884613369451486760470692749551599689; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b,(gcd(b-1,c-1)*c)+1) Output: ? ? ? ? 1 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:00:37 2005 Input: c=119352786619210251178268004659349901971719684049048622826986032253381529701011725646916651783; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b,(gcd(b-1,c-1)*c)+1) Output: ? ? ? ? 1 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:00:44 2005 Input: c=12070547024921759102281429662292243780325032202023650799035719482762121489697379310169197425278743673518863782306064864993647363243274434417891453748661373942907332930578639238887978977690478953671567650545894466843717711628631665112292486277626370426341645607131357899492963830272548585868570555283790392366568050088569314245804995220408222869993459479519199864516070376894742869364728383727008922805283230279514679612624859199081; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b,(gcd(b-1,c-1)*c)+1) Output: ? ? ? ? 1 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:00:52 2005 Input: c=907631175481686734207589229341820542593038092094559255712085980047510764475132263429041296022031375172259330762563016216257529463396808468190810297888243141704939584163254438684994731904888641953458243200826136011614664274855569590046401527888074445126596926114476296598179913175313010819518755378307619789087257615820860426255416532863839352802967511882886909127667463246927069062279367271423045979616013179003058177356317604615604534527010686801233092871564117821601264536988903031106384354272950039974131214269832214571414744548690558014641462063296974157981686527682861132005509586454657671542721963596141815036893261459532129511529127566462817185446570217555078044533993747185801952025358917328405061940089562798288554626202643228218401288623717618221959977626945912441690879530556852015634563458256323505803692511233749366481; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b,(gcd(b-1,c-1)*c)+1) Output: ? ? ? ? 1 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:01:24 2005 Input: c=1229792061534775859990144743470740480960160901482629918917810317546521297651241695779625769140520768226248954083079384353647391027731585530589413245638384160822636213533352882909229510326662077426719311350729329408805610568691152026817390633259382731866955490539735169925694080137867451669299446511423657522999639793070392745559674079191641591156898230011385414137042636837670572401999831518778203739687204237732565681840899424913339444976402490182991837913210205029798368181292122977049682886830771360714418824021302835071803967564017953589578981519272460134102724135985054688905616723689858408143222012899548542001299713769276967262124486318476021705697643850275211103096632450834255645388136261324375850597065279664753577837412960943950028969883801017825327837010987766144814682074392388989256437593351521633521914791758506958981570182533084751133568967813099427553255340336233516403734995029131125793316237267477745448401789640000081931077982178397381432859811934180513960468773113808227429872213758440346321147215474982021951845300773550589306914724404204657285173189882872393; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b,(gcd(b-1,c-1)*c)+1) Output: ? ? ? ? 1 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.011s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:02:50 2005 Input: c=28062289621746599308218083084731385754583973507295366791300087545463870741914957943579374811140503; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b,(gcd(b-1,c-1)*c)+1) Output: ? ? ? ? 1 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:06:30 2005 Input: c=763637120918784792412328089479737354635175670906304097568286927501314026130079652671307755152517605469624983151029017342330718121156625564161; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b,(gcd(b-1,c-1)*c)+1) Output: ? ? ? ? 1 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:06:38 2005 Input: c=408767438707291447099913962563276239771524088019084834245595569884005015823131367889667133674411758426963188867095097037656628310039325455586010126824805870992502631389037148041589368161665738122823238732240121929310577999249230667816322077712684206756562703018268959589144120873807971972235751795822007281159932310244360435649037733217727482757244032396238230388593627091566891497976120922425729554193797231560915317464280342627910791840537686647568439625648643609761008054562400580213086814610475704469610159898265044549471039384086516220669961111890336434058216199264830360138177326602982436228621306530438329565295804898418148864247126853921891738675517942386217908051787839295799373163510213973305701943331019670745972661584147634727243167867297816572355535493038838898313775024686277151567422400902701788469308491529061840381067393469181825422833016664419531438430029447009319229136246834229630322262671153869038444276410971438280211639814637558562740027688828529731534488004227779439687916075790992770657688480208518582764807023594427361715677987861221522452166135436426650594259868296414951014403960748817900214857044762477703763651016473330382867474545595958926418160394691840644370170345163801421823343916010621129758474488901359753352411983663488957309099764139898312199595853540816385206985202868035513923970278901308843500087822689271825213155097917224858619642718395355741434144081197391485707804648931733189712791952121977597227015734992447236820332969200507454744895293611787849364922300925008357822689429557081449655891619120332319699638056198794352010125332397719943872412657410473022712655555130043071560320725345291102073701025434074650003712144894541209950715343089189862879723910378046203615724864779439665057815807073745444255672206827685404216246944127398555332637881261407624074779354419392877769195096875205110722111713314997958295048616872853595376116951935931709448692864171467613976734913179412822016592757604645870652739261209513479167684916431124572246132802067356914999367494271515494052913327708519950547665536843422134033149702999494384918017291346201309539835432632290598664590724368495985889595995202446698615476417975833468991162637128089371395718420521496711298801430606952398868817197781991315578409932347713358720169018759104176942822992468134638141879241486601919423363009438238988004885702429584855105172926543221032410495848414454689830183552252076236837693421836542700264397546845572232985073232927506201628360489612906276753761764034809981658017654739578968080264064345236785887845594888373887899308739531833599198810723450299592931951; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b,(gcd(b-1,c-1)*c)+1) Output: ? ? ? ? 1 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:06:48 2005 Input: c=85481528145337704321393909384439586221014285049795295346258789056726763643492298110999242648130134568607868948701432306912533009543122555802438699736286751183502227645259146079004141707244822544325988175465261788724956575637408143993768132712636720654815093241532341643976131784709266022108644348189136538415919975342736135015649317887039848497005938180856927022217328267994655847130674279743360683381202205094244612546680496687602247882322663913731519736419821955618913867690784608390219827332396952490027442443965396520891450770846803946176269699812687241027655880406135413425258031631655955248493625451647057533648586357022162882016218334907151588780032921228324939635592743254946216451; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b,(gcd(b-1,c-1)*c)+1) Output: ? ? ? ? 1 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:06:58 2005 Input: c=1329323763481361479949493796224541085617048201606811474099172501063111671653513565551270950293851869616234712299728973259455437386748804880770891530690044494161827265281610283266654513636386205427309026850617755307392912699328415498706785471809265406887859500948705394629408272005083811684675608742859668803015990069697676216120533; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b,(gcd(b-1,c-1)*c)+1) Output: ? ? ? ? 1 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:07:06 2005 Input: c=5332694855232257203442227001736786000133230595141824227666788900219556340172564467730364361884169187757591368062944654396963194681448398280036705930558176643677013628540141425411357894177721857995927910428313507240698141273558026606750813496441869236687078519273957805126412223441750378981568912592564172786450153593710825487660238318836749752087186463727744851021393282981627787064336042692685577856001393822704327520904648665482162056825439870731540880658328634626806127577162725682704017511230935737560334879810388260721636949095280879874951878446473136197564486537205252309287363527335433043924961659119269843606488554978397418931772919806428019002505628866402360328494242987833872447447628316503564130720675543391142242361583862634723038859396198236363943650175415341780241464402851264469; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b,(gcd(b-1,c-1)*c)+1) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:07:39 2005 Input: c=8762521446391916258068777673878458022285405457708781368626659492264781827360559450026338563813912205189336375362996906403596899796901707349825849926252571122207297890219081335785962959155425761447683242376626821455964666326675595667041519331644987447779229958355177641709485023411245691614520929596564497312252285920079231985654032418444108607974074198288586874366556698151406545776717143465405302963580950977609796259935703476719822524422215695630616478329135191125964830172456952896425406064719265657288554931010245047716691428001950512767122054215253975280186818638605060654361331572259585322672556018649643509347839850942409254934596521615934157174439892198711658485134129029540574806117592021190312999223897455055974743087751080942402209150907385148402590889213919642749483905700877142320944371382924736268407431981754269241701650548829238357; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) gcd(b,(gcd(b-1,c-1)*c)+1) Output: ? ? ? ? 1 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:19:00 2005 Input: c=39096187556642394531977525045534720382003169681; b=363733969145146151488695111649569937234008802011844981015524350652536000247938783447228179028384822892286372553222453042873503460511691821673187641021460648025949263768749783586241987879773576684481; gcd(c,b) gcd(b,(gcd(b-1,c-1)*c)+1) Output: ? ? ? ? 39096187556642394531977525045534720382003169681 ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:19:48 2005 Input: c=39096187556642394531977525045534720382003169681; d=9303566201133291683996856107555769425055550895006840647160549767261729682167365769152925654455501900038403139609404401697463216287510105466508432170801; b=363733969145146151488695111649569937234008802011844981015524350652536000247938783447228179028384822892286372553222453042873503460511691821673187641021460648025949263768749783586241987879773576684481; gcd(c,b) gcd(c-1,d-1) Output: ? ? ? ? 39096187556642394531977525045534720382003169681 ? 23760 ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:41:41 2005 Input: c=2750912780407702350765641644771132981627387611432057348735180977907096689784951978183689535609711639795803624831838415261346031593694541966528035; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:42:00 2005 Input: c=2750912780407702350765641644771132981627387611432057348735180977907096689784951978183689535609711639795803624831838415261346031593694541966528035; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 3457939485 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:42:53 2005 Input: c=2489513828423260045941757144589260616857364354237155971706046133852576189850635274374379670235033158186247624282206710643752064790673793634867; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 3129357 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:43:31 2005 Input: c=3970516472764370089221303260907911669628970261941237594427505795618143843461938236641753860023976328845689990880712457167068683876672717121; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 4991 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:45:21 2005 Input: c=3970516472764370089221303260907911669628970261941237594427505795618143843461938236641753860023976328845689990880712457167068683876672717121; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b (3^2970-1)/b Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 4991 ? 11223453650493410314182733418347281276649722965448867334278125048131481929453355421645306716818458087013380829030649531030974923308653676581323337592208989223635914429355659115271313937363675036413230181607202504512293725179740302511198496437215872944110975136711012064692929516253121746708058314679178063163994652669514642692175746359247391067610879547041450057998741039273937425136784144854725397079596640541426803761436058366158296763418485986927063129787628997948420584100440245876942610347414264719996609550647106466666431487615061920187833695879514055897563602693513848713104893302025445049441906540274076923337745869294930705108363278042692804984935365106291363510675285534736832495520680268696610309777037485330421123378523692223233923337716417564588819445256292746468088750712673363857928761824491600247141374695076313631678455771225735743635776276978484151255361590671929658684027979358217541335867094597106060594300036120247096547456225830154954554184503611330399919224748206660269237944954750581217831325684080649278987831138430493188792833132696218584901913666603595376770329589271131823316375593107807760857231817080411903686838042855681965309290883044193271379922878582873868141602511199780018260468302377548900459881625625088200878621308652277924448824105233367598982440712730847017451420143941299400686113347387770096799649892361576002348453378249756913011938712570962753053390190483168336470911247848/795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:45:44 2005 Input: c=3970516472764370089221303260907911669628970261941237594427505795618143843461938236641753860023976328845689990880712457167068683876672717121; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b (3^1485-1)/b Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 4991 ? 3350142332870860326394087024458408218357150634882818245036677965610979518992059489876070439777641399217569977695693378639012654693780638773833405904539160639972696912452856303242903430344312694375585149082907474193532001735245921059069084529218960274655804558452054982099065802497395888097479687842026756328586703217040240484605459647890912722686748983209336083487438562600206893785513849892191180735170130475334969879001021886867494782038694172499630407813112970213669085043476769840339696255399912316041095306750757958008723521746000296101665316132102212787783404926305244657081711083768195919225955011942443989727987531272853724704505495490792061440065189685511085506034669825519452393092004817508397561042/795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:46:03 2005 Input: c=3970516472764370089221303260907911669628970261941237594427505795618143843461938236641753860023976328845689990880712457167068683876672717121; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b gcd((3^1485-1),b) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 4991 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:46:22 2005 Input: c=3970516472764370089221303260907911669628970261941237594427505795618143843461938236641753860023976328845689990880712457167068683876672717121; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b gcd((3^4455-1),b) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 4991 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:46:36 2005 Input: c=3970516472764370089221303260907911669628970261941237594427505795618143843461938236641753860023976328845689990880712457167068683876672717121; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b gcd((3^5940-1),b) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 4991 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:46:58 2005 Input: c=3970516472764370089221303260907911669628970261941237594427505795618143843461938236641753860023976328845689990880712457167068683876672717121; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b gcd((3^5940-1),b-1) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 4991 ? 110 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:47:10 2005 Input: c=3970516472764370089221303260907911669628970261941237594427505795618143843461938236641753860023976328845689990880712457167068683876672717121; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b gcd((3^1485-1),b-1) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 4991 ? 22 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:47:26 2005 Input: c=3970516472764370089221303260907911669628970261941237594427505795618143843461938236641753860023976328845689990880712457167068683876672717121; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b gcd((3^7425-1),b-1) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 4991 ? 22 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:47:38 2005 Input: c=3970516472764370089221303260907911669628970261941237594427505795618143843461938236641753860023976328845689990880712457167068683876672717121; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b gcd((3^7425-2),b-1) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 4991 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:47:45 2005 Input: c=3970516472764370089221303260907911669628970261941237594427505795618143843461938236641753860023976328845689990880712457167068683876672717121; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b gcd((3^7425-2),b) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 4991 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:48:40 2005 Input: c=3970516472764370089221303260907911669628970261941237594427505795618143843461938236641753860023976328845689990880712457167068683876672717121; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b gcd((3^7425),b) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 4991 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:54:25 2005 Input: c=2489513828423260045941757144589260616857364354237155971706046133852576189850635274374379670235033158186247624282206710643752064790673793634867; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b gcd((3^7425-2),b) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 3129357 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Fri Mar 25 01:54:59 2005 Input: c=4692733566577845186600212217550756262776131807737039006665896962312106117868447492195705678393037503181076771771959649563472642130420101001724295; b=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; gcd(c,b) c/b gcd((3^7425-2),b) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 5898837945 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.006s '217.245' ************** PARI ***************** Host 217.245.62.144 (217.245.62.144) Time: Fri Mar 25 06:10:58 2005 Input: isprime(5); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '217.245' ************** PARI ***************** Host 217.245.62.144 (217.245.62.144) Time: Fri Mar 25 06:11:08 2005 Input: x=isprime(5); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '217.245' ************** PARI ***************** Host 217.245.62.144 (217.245.62.144) Time: Fri Mar 25 06:11:25 2005 Input: ls=[]; forstep(a=10^10+1,10^10+137,2,if(isprime(a^2-2),ls=concat(ls,a))); print(ls) Output: ? ? ? [10000000015, 10000000099, 10000000101, 10000000107] ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.007s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Fri Mar 25 08:45:04 2005 Input: Mod(329,1080)^-1 Output: ? Mod(929, 1080) ? Errors (if any) and Timing Info: Timing: real 0m0.306s user 0m0.003s sys 0m0.012s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Fri Mar 25 08:49:51 2005 Input: Mod(452,1147)^929 Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Fri Mar 25 09:00:30 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Fri Mar 25 09:03:49 2005 Input: Mod(1789,6912) Output: ? Mod(1789, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Fri Mar 25 09:03:58 2005 Input: Mod(1789,6912)^-1 Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Fri Mar 25 09:04:35 2005 Input: Mod(5192,7081)^85 Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Fri Mar 25 09:06:05 2005 Input: Mod(2604,7081)^85 Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.168.97 (168.122.168.97) Time: Fri Mar 25 09:06:35 2005 Input: Mod(4222,7081)^85 Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '134.157' ************** PARI ***************** Host 134.157.51.198 (134.157.51.198) Time: Fri Mar 25 09:37:07 2005 Input: factor(x^2+2*x+1) Output: ? [x + 1 2] ? Errors (if any) and Timing Info: Timing: real 0m0.042s user 0m0.005s sys 0m0.009s '134.157' ************** PARI ***************** Host 134.157.51.198 (134.157.51.198) Time: Fri Mar 25 09:37:31 2005 Input: factor(x^2+2*x+1) initell([1,0,1,1,0,0]) Output: ? [x + 1 2] ? ? Errors (if any) and Timing Info: *** obsolete function: initell([1,0,1,1,0,0 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: initell(x) ===> ellinit(x) ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '134.157' ************** PARI ***************** Host 134.157.51.198 (134.157.51.198) Time: Fri Mar 25 09:37:58 2005 Input: factor(x^2+2*x+1) ellinit([1,0,1,1,0,0]) Output: ? [x + 1 2] ? [1, 0, 1, 1, 0, 1, 3, 1, -2, -71, -109, -214, 357911/214, [-0.16820947738419271508722568091901170643, -0.040895261307903642456387159540494146783 + 1.2184291676328063597571463481032775501*I, -0.040895261307903642456387159540494146783 - 1.2184291676328063597571463481032775501*I]~, 3.4346780132399337533924115784969537938, -1.7173390066199668766962057892484768969 + 1.6374661587345328841074947777034643171*I, -0.97278698641326839186044431847848802833 + 0.E-39*I, 0.48639349320663419593022215923924401416 - 1.3784402512399743014136196205980353056*I, 5.6241690128299514023877203271605983534] ? Errors (if any) and Timing Info: Timing: real 0m0.088s user 0m0.009s sys 0m0.008s '70.22.2' ************** PARI ***************** Host 70.22.255.216 (70.22.255.216) Time: Fri Mar 25 09:51:40 2005 Input: Mod(452, 1147)^929 Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '70.22.2' ************** PARI ***************** Host 70.22.255.216 (70.22.255.216) Time: Fri Mar 25 09:52:37 2005 Input: Mod(763, 1147)^329 Output: ? Mod(452, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:21:14 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:21:45 2005 Input: 30*36 Output: ? 1080 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:23:46 2005 Input: 329*3 Output: ? 987 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:24:05 2005 Input: 1080-987 Output: ? 93 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:24:19 2005 Input: 329/93 Output: ? 329/93 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:24:28 2005 Input: 93*5 Output: ? 465 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:24:32 2005 Input: 93*4 Output: ? 372 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:24:36 2005 Input: 93*3 Output: ? 279 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:24:44 2005 Input: 329-279 Output: ? 50 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.237.145 (168.122.237.145) Time: Fri Mar 25 10:25:44 2005 Input: Mod(5192, 7081)^85 Mod(2604, 7081)^85 Mod(4222, 7081)^85 Output: ? Mod(1615, 7081) ? Mod(2823, 7081) ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:26:18 2005 Input: 6*7 Output: ? 42 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:28:55 2005 Input: 7+6 Output: ? 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '128.197' ************** PARI ***************** Host 128.197.150.199 (128.197.150.199) Time: Fri Mar 25 10:30:05 2005 Input: Mod(7,7387)^7386 Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:31:24 2005 Input: 329*151-46*1080 Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:32:46 2005 Input: Mod(7^151,1147) Output: ? Mod(441, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:34:27 2005 Input: Mod(441^329,1147) Output: ? Mod(164, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:34:32 2005 Input: Mod(441^329,1147) Output: ? Mod(164, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:36:10 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:46:42 2005 Input: Mod(-151,1147) Output: ? Mod(996, 1147) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:47:58 2005 Input: Mod(452^151,1147) Output: ? Mod(917, 1147) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:48:23 2005 Input: Mod(917^329,1147) Output: ? Mod(236, 1147) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:48:38 2005 Input: Mod(452^996,1147) Output: ? Mod(667, 1147) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:48:49 2005 Input: Mod(667^329,1147) Output: ? Mod(963, 1147) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:49:24 2005 Input: Mod(329,1080)^(-1) Output: ? Mod(929, 1080) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:50:49 2005 Input: Mod(452^929,1147) Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 10:51:01 2005 Input: Mod(763^329,1147) Output: ? Mod(452, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.244.46 (128.197.244.46) Time: Fri Mar 25 11:01:56 2005 Input: Mod(7,7387)^7386 Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.244.46 (128.197.244.46) Time: Fri Mar 25 11:02:18 2005 Input: Mod(7,7393)^7392 Output: ? Mod(1, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.244.46 (128.197.244.46) Time: Fri Mar 25 11:04:24 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.244.46 (128.197.244.46) Time: Fri Mar 25 11:06:02 2005 Input: Mod(329,1080)^(-1) Output: ? Mod(929, 1080) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.002s sys 0m0.011s '128.197' ************** PARI ***************** Host 128.197.244.46 (128.197.244.46) Time: Fri Mar 25 11:06:36 2005 Input: Mod(452,1147)^(929) Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:13:45 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:14:38 2005 Input: Mod(1789,6912)^(-1) Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:15:36 2005 Input: Mod(5192^85,7081) Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:17:08 2005 Input: Mod(2604^85,7081) Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Mar 25 11:20:26 2005 Input: factor(250) Output: ? [2 1] [5 3] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:21:08 2005 Input: Mod(4222^85,7081) Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.244.46 (128.197.244.46) Time: Fri Mar 25 11:24:38 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:28:49 2005 Input: Mod(2^6,9) Output: ? Mod(1, 9) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.244.46 (128.197.244.46) Time: Fri Mar 25 11:29:04 2005 Input: Mod(1789,6912)^(-1) Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.244.46 (128.197.244.46) Time: Fri Mar 25 11:29:35 2005 Input: Mod(5192,7081)^(85) Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.244.46 (128.197.244.46) Time: Fri Mar 25 11:30:44 2005 Input: Mod(2604,7081)^(85) Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.244.46 (128.197.244.46) Time: Fri Mar 25 11:31:17 2005 Input: Mod(2604,7081)^(85) Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.244.46 (128.197.244.46) Time: Fri Mar 25 11:31:26 2005 Input: Mod(4222,7081)^(85) Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:32:09 2005 Input: factor(975) Output: ? [3 1] [5 2] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.244.46 (128.197.244.46) Time: Fri Mar 25 11:32:36 2005 Input: Mod(4222,7081)^(85) Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.244.46 (128.197.244.46) Time: Fri Mar 25 11:32:53 2005 Input: Mod(2604,7081)^(85) Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.244.46 (128.197.244.46) Time: Fri Mar 25 11:36:25 2005 Input: Mod(4222,7081)^(85) Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:40:37 2005 Input: factor(91) Output: ? [7 1] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:40:46 2005 Input: factor(63) Output: ? [3 2] [7 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 11:49:37 2005 Input: 7^7386 Output: ? 7836525394947970685765064676824624881230843694638653432597293697270900348717161274111722972468270718930712577924994374650698495363358801523185551274561566929222651989785236373702460086634634940103775721791690379940686820484234683151915000605720616895085768755138746929720910704204836021228053171447520320588006367036893856646530014282413149363430471445537761787686028318686003461552188028475934931546480878063771110043350814118031022864718663032984583510480981567089557643496281453541983057917469183789450304777645053241291541744557797093545928964311564444915089899253342265105336315340761896970130573560253210922903045498127224571279679253933490311683526849908297452473886243431616837896438333457152401748652912392357437587922066344164793484849687123175524202171959149799699848686904006085376984584739707761858054562412031377021615051176965455988056793836470956658798217507375350352917508531930305085230711643655136072274902922220403119532770292330451209753098003284637094853555284524325942248185110784504778993102684450493660780770373940728555790026570684550108901235483750186600502144506194894659542082454708256820848020692333528269863628499182468946823427734100122287570660746486502607745826614460946661646852333068028886106155535688564852728770116870189546914823146684972123764164077867785008596847424980892967443638305071840033774662993790587984154581146773544765254984497258149323228318486246568806284560001555977603800557884391543437643178525437084402609028655562062472989345075227797815830905648986773972086161214487405614679532825266121993110079079302201901735944164432298040062643877559644334998478705112462240056447834269603854855654279446214329597279009697888384952269822953987574035741284524192509017370584183628078608704527588844366974735773761599098517020577814348375808668347291322014575553809958211427253166622890243207068547357670097157892911487650229437600540479900516238100881300970154316089182070287032502634219444706180244875076964243805193228860352050305925417074962808786746470833706363076932232404741716322939102390253573793568137599367923917213784885064376948089957436403057911701881101514842822857357533871084485405565391621717530550054529402629765344279818901973303180311300650040425589566786273149546332150406923900786525349239562824189074087924075702338377532893700116219987197470503110559192856153904451944774013991475021246351524614741931034931006348622370527837923962721599910900181774989306614786976007925930294108263277425847368311267218064884261148854892429724507036223427707359324480656493695298462686252347545012748538349382713581699498025290360226843595283207598524991213819237608753432741910231371845150666682636389190110224157289894165110413163801844039835576745991781732628223521965288300361611548799601830368005210706903879142712525315969041882657841162575000441664701208585535945469892978628403465795905067382888933473810491520262948523493834420016375284935631742135453182777210045765582786281879130098505375922869449139835957364032471734291454024536166849382206978467102401675813174674858113085510054465424892254427390779720478644753951040277933756403338895257591518034328895284028616942721212818945987783947048282257968819417409413832046363531[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.018s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:49:55 2005 Input: factor(62) Output: ? [2 1] [31 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 11:49:58 2005 Input: Mod(7836525394947970685765064676824624881230843694638653432597293697270900348717161274111722972468270718930712577924994374650698495363358801523185551274561566929222651989785236373702460086634634940103775721791690379940686820484234683151915000605720616895085768755138746929720910704204836021228053171447520320588006367036893856646530014282413149363430471445537761787686028318686003461552188028475934931546480878063771110043350814118031022864718663032984583510480981567089557643496281453541983057917469183789450304777645053241291541744557797093545928964311564444915089899253342265105336315340761896970130573560253210922903045498127224571279679253933490311683526849908297452473886243431616837896438333457152401748652912392357437587922066344164793484849687123175524202171959149799699848686904006085376984584739707761858054562412031377021615051176965455988056793836470956658798217507375350352917508531930305085230711643655136072274902922220403119532770292330451209753098003284637094853555284524325942248185110784504778993102684450493660780770373940728555790026570684550108901235483750186600502144506194894659542082454708256820848020692333528269863628499182468946823427734100122287570660746486502607745826614460946661646852333068028886106155535688564852728770116870189546914823146684972123764164077867785008596847424980892967443638305071840033774662993790587984154581146773544765254984497258149323228318486246568806284560001555977603800557884391543437643178525437084402609028655562062472989345075227797815830905648986773972086161214487405614679532825266121993110079079302201901735944164432298040062643877559644334998478705112462240056447834269603854855654279446214329597279009697888384952269822953987574035741284524192509017370584183628078608704527588844366974735773761599098517020577814348375808668347291322014575553809958211427253166622890243207068547357670097157892911487650229437600540479900516238100881300970154316089182070287032502634219444706180244875076964243805193228860352050305925417074962808786746470833706363076932232404741716322939102390253573793568137599367923917213784885064376948089957436403057911701881101514842822857357533871084485405565391621717530550054529402629765344279818901973303180311300650040425589566786273149546332150406923900786525349239562824189074087924075702338377532893700116219987197470503110559192856153904451944774013991475021246351524614741931034931006348622370527837923962721599910900181774989306614786976007925930294108263277425847368311267218064884261148854892429724507036223427707359324480656493695298462686252347545012748538349382713581699498025290360226843595283207598524991213819237608753432741910231371845150666682636389190110224157289894165110413163801844039835576745991781732628223521965288300361611548799601830368005210706903879142712525315969041882657841162575000441664701208585535945469892978628403465795905067382888933473810491520262948523493834420016375284935631742135453182777210045765582786281879130098505375922869449139835957364032471734291454024536166849382206978467102401675813174674858113085510054465424892254427390779720478644753951040277933756403338895257591518034328895284028616942721212818945987783947048282257968819417409413832046363531,7387) Output: ? Mod(1363, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:50:01 2005 Input: factor(53) Output: ? [53 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:50:35 2005 Input: 53^2=62^2 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 53^2=62^2 ^----- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:50:41 2005 Input: 53^2+62^2 Output: ? 6653 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:51:02 2005 Input: factor(6653) Output: ? [6653 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:51:21 2005 Input: factor(11-2i) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: factor(11-2i) ^-- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 11:52:09 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:53:04 2005 Input: 63^2+62^2 Output: ? 7813 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:53:10 2005 Input: 53^2+62^2 Output: ? 6653 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 11:53:53 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 11:55:36 2005 Input: Mod(131,1008)^-1 Output: ? Mod(731, 1008) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 11:55:37 2005 Input: Mod(131,1008)^-1 Output: ? Mod(731, 1008) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 11:56:02 2005 Input: Mod(329,1080)^-1 Output: ? Mod(929, 1080) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.52.10 (168.122.52.10) Time: Fri Mar 25 11:57:04 2005 Input: factor(97) Output: ? [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 11:57:35 2005 Input: Mod(1789,6912)^(-1) Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 11:58:27 2005 Input: Mod(452,1147)^929 Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:00:23 2005 Input: Mod(5192,7081)^(85) Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 12:01:54 2005 Input: factor(70810 Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: factor(70810 ^ Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 12:02:07 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:02:31 2005 Input: Mod(2604,7081)^(85) Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 12:03:25 2005 Input: Mod(1789,6912)^-1 Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:03:42 2005 Input: Mod(4222,7081)^(85) Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 12:04:24 2005 Input: Mod(5192,7081)^85 Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 12:05:25 2005 Input: Mod(2604,7081)^85 Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 12:05:37 2005 Input: Mod(4222,7081)^85 Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Mar 25 12:07:54 2005 Input: factor(6778) Output: ? [2 1] [3389 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '219.178' ************** PARI ***************** Host 219.178.24.119 (219.178.24.119) Time: Fri Mar 25 12:08:45 2005 Input: 1*242*33 Output: ? 7986 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:10:41 2005 Input: 2^2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:10:50 2005 Input: 2^3 Output: ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:10:55 2005 Input: 2^4 Output: ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:11:01 2005 Input: 2^5 Output: ? 32 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:11:11 2005 Input: 2^6 Output: ? 64 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:11:16 2005 Input: 2^7 Output: ? 128 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:12:10 2005 Input: Mod(2,9)^(64) Output: ? Mod(7, 9) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:12:15 2005 Input: Mod(2,9)^(6) Output: ? Mod(1, 9) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:13:00 2005 Input: Mod(2,15)^(4) Output: ? Mod(1, 15) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:14:44 2005 Input: 3^4 Output: ? 81 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:14:56 2005 Input: 3^5 Output: ? 243 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:15:06 2005 Input: 3^6 Output: ? 729 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:15:24 2005 Input: 728/16 Output: ? 91/2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:15:35 2005 Input: 242/16 Output: ? 121/8 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:15:46 2005 Input: 80/16 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:16:33 2005 Input: Mod(3,16)^(4) Output: ? Mod(1, 16) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:16:39 2005 Input: Mod(3,10)^(4) Output: ? Mod(1, 10) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:19:19 2005 Input: 91/7 Output: ? 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:19:29 2005 Input: 63/7 Output: ? 9 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:19:48 2005 Input: 91/7 Output: ? 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:21:23 2005 Input: (13*13)+(9*9) Output: ? 250 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:21:41 2005 Input: factor250 Output: ? factor250 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:21:47 2005 Input: factor(250) Output: ? [2 1] [5 3] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 12:26:53 2005 Input: factor(975) Output: ? [3 1] [5 2] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:28:06 2005 Input: 975^(1/2) Output: ? 31.224989991991991029234465604698972305 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:28:23 2005 Input: 975/25 Output: ? 39 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Mar 25 12:29:12 2005 Input: gcd(1,1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 25 12:29:33 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Mar 25 12:29:34 2005 Input: gcd(92416,281961) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 12:31:01 2005 Input: factor(53) Output: ? [53 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 12:31:08 2005 Input: factor(62) Output: ? [2 1] [31 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:32:45 2005 Input: 975/4 Output: ? 975/4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:33:19 2005 Input: (975)/(4) Output: ? 975/4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 25 12:34:52 2005 Input: Mod(329, 1080)^(-1) Output: ? Mod(929, 1080) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:36:46 2005 Input: (53*53)+(62*62) Output: ? 6653 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:37:03 2005 Input: factor(6653) Output: ? [6653 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:37:53 2005 Input: 6653/4 Output: ? 6653/4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:38:59 2005 Input: (53*53)+(62*62) Output: ? 6653 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Mar 25 12:39:09 2005 Input: factor(6653) Output: ? [6653 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Mar 25 12:39:59 2005 Input: factor(377) Output: ? [13 1] [29 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Mar 25 12:42:39 2005 Input: factor(281961) Output: ? [3 4] [59 2] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Mar 25 12:42:44 2005 Input: factor(281961) Output: ? [3 4] [59 2] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 25 12:44:56 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 25 12:48:51 2005 Input: Mod(1784, 6984)^(-1) Output: ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(8, 6984). Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 25 12:49:34 2005 Input: Mod(1789, 6984)^(-1) Output: ? Mod(6781, 6984) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 12:51:16 2005 Input: i^2 Output: ? i^2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 12:51:16 2005 Input: i^2 Output: ? i^2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 12:51:18 2005 Input: i^2 Output: ? i^2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 12:51:26 2005 Input: (i)^2 Output: ? i^2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.170.101 (168.122.170.101) Time: Fri Mar 25 12:51:30 2005 Input: (i)^2 Output: ? i^2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Mar 25 12:52:11 2005 Input: gcd(137) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: gcd(137) ^- Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Mar 25 12:52:27 2005 Input: factor(137) Output: ? [137 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 12:56:12 2005 Input: factor(1734251) Output: ? [1171 1] [1481 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 12:57:25 2005 Input: factor(64027) Output: ? [43 1] [1489 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 12:58:25 2005 Input: factor(52633) Output: ? [7 1] [73 1] [103 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:01:56 2005 Input: Mod(2*3*4*5*67*8*9*10*11*12*13*14*15*16*17*18*19*20*21*22*23*24,25)^1 Output: ? Mod(0, 25) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:02:54 2005 Input: Mod(7,7387)^7386 Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:04:33 2005 Input: Mod(7,7387)^7386 Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:04:34 2005 Input: Mod(7,7387)^7386 Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:05:59 2005 Input: Mod(7,7393)^7392 Output: ? Mod(1, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 25 13:07:08 2005 Input: Mod(5192, 7081)^(6781) Output: ? Mod(5557, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:07:36 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 25 13:07:46 2005 Input: Mod(2604, 7081)^(6781) Output: ? Mod(414, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Mar 25 13:08:11 2005 Input: Mod(4222, 7081)^(6781) Output: ? Mod(5072, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:08:43 2005 Input: Mod(13,1020096)^(-1) Output: ? Mod(78469, 1020096) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:08:53 2005 Input: Mod(5,23)^5 Output: ? Mod(20, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:09:16 2005 Input: Mod(5,23)^13 Output: ? Mod(21, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:09:22 2005 Input: Mod(5,23)^13 Output: ? Mod(21, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:09:23 2005 Input: Mod(329,1080)^(-1) Output: ? Mod(929, 1080) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:10:47 2005 Input: Mod(452,1147)^929 Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:11:18 2005 Input: Mod(28,1147)^2 Output: ? Mod(784, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:11:42 2005 Input: Mod(784,1147)^2 Output: ? Mod(1011, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:12:37 2005 Input: Mod(23,1279)^.5 Output: ? ? Errors (if any) and Timing Info: *** incorrect type in glog. Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:12:47 2005 Input: Mod(23,1279)^1/2 Output: ? Mod(651, 1279) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:12:52 2005 Input: Mod(23,1279)^(1/2) Output: ? Mod(699, 1279) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:12:55 2005 Input: Mod(23,1279)^(1/2) Output: ? Mod(699, 1279) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:13:04 2005 Input: Mod(1011,1147)^2 Output: ? Mod(144, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:13:25 2005 Input: Mod(144,1147)^2 Output: ? Mod(90, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:13:36 2005 Input: Mod(90,1147)^2 Output: ? Mod(71, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:13:58 2005 Input: Mod(71,1147)^2 Output: ? Mod(453, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:14:55 2005 Input: Mod(453,1147)^2 Output: ? Mod(1043, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:15:15 2005 Input: Mod(1043,1147)^2 Output: ? Mod(493, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:15:39 2005 Input: Mod(493,1147)^2 Output: ? Mod(1032, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:16:24 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:17:42 2005 Input: Mod(28,1147)^3 Output: ? Mod(159, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:18:02 2005 Input: Mod(1032*1043,1147)^1 Output: ? Mod(490, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:18:25 2005 Input: Mod(453*71,1147)^1 Output: ? Mod(47, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:18:45 2005 Input: Mod(490*47,1147)^1 Output: ? Mod(90, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:18:59 2005 Input: Mod(90*159,1147)^1 Output: ? Mod(546, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:19:23 2005 Input: Mod(28,1147)^749 Output: ? Mod(289, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:19:43 2005 Input: Mod(28,1147)^512 Output: ? Mod(1032, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:19:47 2005 Input: Mod(1789,6912)^(-1) Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:19:55 2005 Input: Mod(28,1147)^128 Output: ? Mod(1043, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:20:03 2005 Input: Mod(28,1147)^64 Output: ? Mod(453, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:20:13 2005 Input: Mod(28,1147)^32 Output: ? Mod(71, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:20:19 2005 Input: Mod(28,1147)^3 Output: ? Mod(159, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:20:34 2005 Input: Mod(1032*1043,1147)^1 Output: ? Mod(490, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:20:52 2005 Input: Mod(453*71,1147)^1 Output: ? Mod(47, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:21:11 2005 Input: Mod(490*47,1147)^1 Output: ? Mod(90, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:21:30 2005 Input: Mod(90*159,1147)^1 Output: ? Mod(546, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:22:06 2005 Input: Mod(5192,7081)^85 Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:22:08 2005 Input: Mod(5192,7081)^85 Output: ? Mod(1615, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:22:33 2005 Input: Mod(2604,7081)^85 Output: ? Mod(2823, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.35.54 (168.122.35.54) Time: Fri Mar 25 13:22:53 2005 Input: Mod(4222,7081)^85 Output: ? Mod(1130, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:22:57 2005 Input: Mod(28,1147)^13 Output: ? Mod(1061, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:23:28 2005 Input: Mod(90*1061,1147)^1 Output: ? Mod(289, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:23:44 2005 Input: Mod(28,1147)^749 Output: ? Mod(289, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:25:23 2005 Input: Mod(49,7387)^2 Output: ? Mod(2401, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:25:39 2005 Input: Mod(2401,7387)^2 Output: ? Mod(2941, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:25:57 2005 Input: Mod(2941,7387)^2 Output: ? Mod(6691, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:26:16 2005 Input: Mod(6691,7387)^2 Output: ? Mod(4261, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:26:33 2005 Input: Mod(4261,7387)^2 Output: ? Mod(6262, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:26:47 2005 Input: Mod(6262,7387)^2 Output: ? Mod(2448, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:27:07 2005 Input: Mod(2448,7387)^2 Output: ? Mod(1847, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:27:44 2005 Input: Mod(1847,7387)^2 Output: ? Mod(6002, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:28:10 2005 Input: Mod(6002,7387)^2 Output: ? Mod(4992, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:28:35 2005 Input: Mod(4992,7387)^2 Output: ? Mod(3713, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:29:01 2005 Input: Mod(3713,7387)^2 Output: ? Mod(2227, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.002s sys 0m0.010s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:29:34 2005 Input: Mod(7,7387)^4096 Output: ? Mod(2227, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:33:17 2005 Input: Mod(3713*2227*4992*2448*6262,7387)^1 Output: ? Mod(2589, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:34:01 2005 Input: Mod(2589*6691*2941*49,7387)^1 Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:34:23 2005 Input: Mod(7,7387)^7386 Output: ? Mod(702, 7387) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:35:46 2005 Input: Mod(49,7393)^2 Output: ? Mod(2401, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:36:01 2005 Input: Mod(2401,7393)^2 Output: ? Mod(5654, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:37:07 2005 Input: Mod(7,7393)^8 Output: ? Mod(5654, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:37:11 2005 Input: Mod(7,7393)^16 Output: ? Mod(384, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:37:19 2005 Input: Mod(7,7393)^32 Output: ? Mod(6989, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:37:27 2005 Input: Mod(7,7393)^64 Output: ? Mod(570, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:37:33 2005 Input: Mod(7,7393)^128 Output: ? Mod(7001, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:37:41 2005 Input: Mod(7,7393)^256 Output: ? Mod(5804, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:37:50 2005 Input: Mod(7,7393)^512 Output: ? Mod(3908, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:37:53 2005 Input: Mod(7,7393)^512 Output: ? Mod(3908, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:38:00 2005 Input: Mod(7,7393)^1024 Output: ? Mod(5919, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:38:17 2005 Input: Mod(7,7393)^2048 Output: ? Mod(6527, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:38:32 2005 Input: Mod(7,7393)^4096 Output: ? Mod(3263, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:40:58 2005 Input: Mod(3263*6527*5919,7393)^1 Output: ? Mod(2843, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:41:24 2005 Input: Mod(7001*570*6989,7393)^1 Output: ? Mod(1230, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:41:38 2005 Input: Mod(7001*570*6989*2843,7393)^1 Output: ? Mod(1, 7393) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:42:02 2005 Input: factor(7393) Output: ? [7393 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:43:36 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:44:38 2005 Input: Mod(1789,7081)^-1 Output: ? Mod(3871, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:45:30 2005 Input: Mod(5192,7081)^3871 Output: ? Mod(5995, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:46:53 2005 Input: Mod(2604,7081)^3871 Output: ? Mod(2214, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.150.178 (128.197.150.178) Time: Fri Mar 25 13:47:09 2005 Input: Mod(4222,7081)^3871 Output: ? Mod(5122, 7081) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '24.63.8' ************** PARI ***************** Host 24.63.83.241 (24.63.83.241) Time: Fri Mar 25 14:22:06 2005 Input: (3+4)/2 Output: ? 7/2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '24.63.8' ************** PARI ***************** Host 24.63.83.241 (24.63.83.241) Time: Fri Mar 25 14:23:02 2005 Input: prime(51651318165135489145613245613) Output: ? ? Errors (if any) and Timing Info: *** impossible assignment I-->S Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Mar 25 16:11:21 2005 Input: 12345678*89009090 Output: ? 1098877564213020 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Mar 25 16:11:32 2005 Input: 12345678*8900909022222 Output: ? 109887756695647656516 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Mar 25 16:11:42 2005 Input: 2*8 Output: ? 16 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Mar 25 16:12:08 2005 Input: 11111111111111111111111111*8888888888888888888888888888888888888 Output: ? 98765432098765432098765431111111111101234567901234567901234568 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Fri Mar 25 17:26:49 2005 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Fri Mar 25 17:26:58 2005 Input: decimalcycle(p0,q0)= local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans decimalcycle(7,17) Output: ? ? ? ? ? ? ? ? ? [0] ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Fri Mar 25 17:27:42 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Fri Mar 25 17:28:05 2005 Input: decimalcycle(p0,q0)= local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans decimalcycle(7,17) Output: ? ? ? ? ? ? ? ? ? [0] ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Fri Mar 25 17:29:28 2005 Input: decimalcycle(p0,q0)= { local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans } decimalcycle(7,17) Output: ? ? [4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Fri Mar 25 17:29:55 2005 Input: decimalcycle(p0,q0)= { local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans } decimalcycle(1,17) Output: ? ? [0, 5, 8, 8, 2, 3, 5, 2, 9, 4, 1, 1, 7, 6, 4, 7] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Fri Mar 25 17:30:31 2005 Input: decimalcycle(p0,q0)= { local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans } for(j=1,6,print(decimalcycle(j,17))) Output: ? ? [0, 5, 8, 8, 2, 3, 5, 2, 9, 4, 1, 1, 7, 6, 4, 7] [1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9, 4] [1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9, 4, 1] [2, 3, 5, 2, 9, 4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8] [2, 9, 4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5] [3, 5, 2, 9, 4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 18:58:02 2005 Input: cos(2) Output: ? -0.41614683654714238699756822950076218977 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:11:31 2005 Input: gadd(3,4) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: gadd(3,4) ^--------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:11:35 2005 Input: gadd(3,4) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: gadd(3,4) ^--------- Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:12:08 2005 Input: gsub(3,4) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: gsub(3,4) ^--------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:12:13 2005 Input: (1+x)^{3} Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (1+x)^{3} ^--- Timing: real 0m0.019s user 0m0.007s sys 0m0.008s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:12:21 2005 Input: exp(1+x,e) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: exp(1+x,e) ^--- Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:12:33 2005 Input: gmul(3,4) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: gmul(3,4) ^--------- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:13:05 2005 Input: gmod(13,5) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: gmod(13,5) ^---------- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:13:24 2005 Input: Mod(13,5) Output: ? Mod(3, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:13:34 2005 Input: Mod(13,5) Output: ? Mod(3, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:13:41 2005 Input: Mod(130,5) Output: ? Mod(0, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:13:53 2005 Input: (1+x)^(3) Output: ? x^3 + 3*x^2 + 3*x + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:14:16 2005 Input: 3>4 Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:14:21 2005 Input: 3<4 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:15:11 2005 Input: Pol(1+x+x^(3),{3=x}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: Pol(1+x+x^(3),{3=x}) ^------ Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:15:30 2005 Input: Pol(1+x,{3=x}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: Pol(1+x,{3=x}) ^------ Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:15:34 2005 Input: Pol(1+x,{v=x}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: Pol(1+x,{v=x}) ^------ Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:16:42 2005 Input: norml2([1,2,3]) Output: ? 14 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:17:16 2005 Input: random(N=3) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:17:18 2005 Input: random(N=3) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:17:20 2005 Input: random(N=3123) Output: ? 2268 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:17:21 2005 Input: random(N=3123) Output: ? 2268 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:17:22 2005 Input: random(N=3123) Output: ? 2268 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:17:23 2005 Input: random(N=3123) Output: ? 2268 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:17:24 2005 Input: random(N=3123) Output: ? 2268 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:17:24 2005 Input: random(N=3123) Output: ? 2268 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:17:25 2005 Input: random(N=3123) Output: ? 2268 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:17:26 2005 Input: random(N=3123) Output: ? 2268 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:19:34 2005 Input: E=[0,0,0,0,1]; E.disc Output: ? ? ? Errors (if any) and Timing Info: *** incorrect type in .disc: E.disc ^---- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:19:40 2005 Input: E=[0,0,0,0,1], E.disc Output: ? [0, 0, 0, 0, 1] ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,. *** incorrect type in .disc: E.disc ^---- Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:20:59 2005 Input: E=ellinit([0,0,0,0,1]), E.disc Output: ? [0, 0, 0, 0, 1, 0, 0, 4, 0, 0, -864, -432, 0, [-1.0000000000000000000000000000000000000, 0.50000000000000000000000000000000000000 - 0.86602540378443864676372317075293618346*I, 0.50000000000000000000000000000000000000 + 0.86602540378443864676372317075293618346*I]~, 4.2065463159763627835250572371508824064, -2.1032731579881813917625286185754412032 + 1.2143253239437908059099708448904656242*I, -1.2935547796148952674767575125656058188 + 3.359966980742911939 E-39*I, 0.64677738980744763373837875628280290940 - 1.1202513003332802196552063208342852345*I, 5.1081157178325565351221945057517738028] ? -432 ? Errors (if any) and Timing Info: *** Warning: unused characters: ,. Timing: real 0m0.014s user 0m0.008s sys 0m0.007s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:21:10 2005 Input: E=ellinit([0,0,0,0,1]) E.disc Output: ? [0, 0, 0, 0, 1, 0, 0, 4, 0, 0, -864, -432, 0, [-1.0000000000000000000000000000000000000, 0.50000000000000000000000000000000000000 - 0.86602540378443864676372317075293618346*I, 0.50000000000000000000000000000000000000 + 0.86602540378443864676372317075293618346*I]~, 4.2065463159763627835250572371508824064, -2.1032731579881813917625286185754412032 + 1.2143253239437908059099708448904656242*I, -1.2935547796148952674767575125656058188 + 3.359966980742911939 E-39*I, 0.64677738980744763373837875628280290940 - 1.1202513003332802196552063208342852345*I, 5.1081157178325565351221945057517738028] ? -432 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.008s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:21:30 2005 Input: E=ellinit([0,0,0,0,0]) E.disc Output: ? ? ? Errors (if any) and Timing Info: *** singular curve in ellinit. *** incorrect type in .disc: E.disc ^---- Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:22:25 2005 Input: E=ellinit([0,1,0,0,0]) E.disc Output: ? ? ? Errors (if any) and Timing Info: *** singular curve in ellinit. *** incorrect type in .disc: E.disc ^---- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:22:28 2005 Input: E=ellinit([0,1,0,0,0]) E.disc Output: ? ? ? Errors (if any) and Timing Info: *** singular curve in ellinit. *** incorrect type in .disc: E.disc ^---- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:22:37 2005 Input: E=ellinit([0,1,0,1,0]) E.disc Output: ? [0, 1, 0, 1, 0, 4, 2, 0, -1, -32, 224, -48, 2048/3, [0.E-38, -0.50000000000000000000000000000000000000 - 0.86602540378443864676372317075293618346*I, -0.50000000000000000000000000000000000000 + 0.86602540378443864676372317075293618346*I]~, 3.3715007096251920857424073155981539789, 1.6857503548125960428712036577990769894 + 2.1565156474996432354386749988003220288*I, -0.68725727892872625375798565691639628604 + 1.762849871799412534 E-39*I, -0.34362863946436312687899282845819814302 - 1.3713993048429847626983511310753992616*I, 7.2706940358628777611249866685015359950] ? -48 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:22:43 2005 Input: E=ellinit([0,1,0,0,0]) E.disc Output: ? ? ? Errors (if any) and Timing Info: *** singular curve in ellinit. *** incorrect type in .disc: E.disc ^---- Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:23:12 2005 Input: E=ellinit([0,1,0,0,0]) E.disc E.roots Output: ? ? ? ? Errors (if any) and Timing Info: *** singular curve in ellinit. *** incorrect type in .disc: E.disc ^---- *** incorrect type in .roots: E.roots ^----- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:23:18 2005 Input: E=ellinit([0,1,0,0,1]) E.disc E.roots Output: ? [0, 1, 0, 0, 1, 4, 0, 4, 4, 16, -928, -496, -256/31, [-1.4655712318767680266567312252199391080, 0.23278561593838401332836561260996955401 - 0.79255199251544784832589830065336124351*I, 0.23278561593838401332836561260996955401 + 0.79255199251544784832589830065336124351*I]~, 4.2937936508150131204218658628252572580, -2.1468968254075065602109329314126286290 + 1.1612202913947208330297532728286682426*I, -1.3024196978106162623868501074069662681 - 5.980032510762160970 E-39*I, 0.65120984890530813119342505370348313408 - 1.0838873995997173394444077028570833910*I, 4.9860403143882117295726646417544620660] ? -496 ? [-1.4655712318767680266567312252199391080, 0.23278561593838401332836561260996955401 - 0.79255199251544784832589830065336124351*I, 0.23278561593838401332836561260996955401 + 0.79255199251544784832589830065336124351*I]~ ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.007s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:25:49 2005 Input: polydegree(x^(3)+x^(2)+3*x+2 Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...ydegree(x^(3)+x^(2)+3*x+2 ^ Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:25:58 2005 Input: polydegree(x^(3)+x^(2)+3*x+2) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: polydegree(x^(3)+x^(2)+3*x+2) ^----------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:26:36 2005 Input: pol = x^(3)+2*x+3 polydegree(pol) Output: ? x^3 + 2*x + 3 ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: polydegree(pol) ^ Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:26:42 2005 Input: pol = x^(3)+2*x+3 factor(pol) Output: ? x^3 + 2*x + 3 ? [x + 1 1] [x^2 - x + 3 1] ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.008s sys 0m0.005s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:26:59 2005 Input: pol = x^(3)+2*x+3 roots(pol) Output: ? x^3 + 2*x + 3 ? ? Errors (if any) and Timing Info: *** obsolete function: roots(pol) ^---------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: roots(x) ===> polroots(x) polroots(x,{flag=0}): complex roots of the polynomial x. flag is optional, and can be 0: default, uses Schonhage's method modified by Gourdon, or 1: uses a modified Newton method. Timing: real 0m0.024s user 0m0.004s sys 0m0.009s '68.110.' ************** PARI ***************** Host 68.110.203.203 (68.110.203.203) Time: Fri Mar 25 21:27:03 2005 Input: pol = x^(3)+2*x+3 root(pol) Output: ? x^3 + 2*x + 3 ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: root(pol) ^ Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Fri Mar 25 23:56:30 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Fri Mar 25 23:57:39 2005 Input: isprime(1104587) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.003s sys 0m0.010s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Fri Mar 25 23:57:57 2005 Input: isprime(4) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Fri Mar 25 23:58:58 2005 Input: isprime(70785) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Fri Mar 25 23:59:17 2005 Input: isprime(5) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Fri Mar 25 23:59:35 2005 Input: isprime(19) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Fri Mar 25 23:59:49 2005 Input: isprime(83550368) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:00:00 2005 Input: isprime(53) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:00:09 2005 Input: isprime(5022) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:01:16 2005 Input: nextprime(1104587) Output: ? 1104589 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.006s sys 0m0.007s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:01:29 2005 Input: lastprime(1104587) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: lastprime(1104587) ^------------------ Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:01:53 2005 Input: isprime(1104583) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:03:41 2005 Input: gcd(1104587,70785) Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:03:58 2005 Input: gcd(70785,19) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:04:16 2005 Input: gcd(1104587,70785,19) Output: ? ? Errors (if any) and Timing Info: *** invalid flag in gcd. Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:04:32 2005 Input: gcd(11,19) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:05:09 2005 Input: lcm(19,53) Output: ? 1007 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:05:35 2005 Input: lcm(53,5022) Output: ? 266166 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:06:40 2005 Input: factor(1104587) Output: ? [11 1] [100417 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:08:26 2005 Input: factor(70785) Output: ? [3 2] [5 1] [11 2] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:10:15 2005 Input: factor(19) Output: ? [19 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:10:30 2005 Input: factor(83550368) Output: ? [2 5] [11 1] [97 1] [2447 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:11:57 2005 Input: factor(53) Output: ? [53 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:12:12 2005 Input: factor(5022) Output: ? [2 1] [3 4] [31 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:17:36 2005 Input: Mod(1104587,19) Output: ? Mod(3, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:18:09 2005 Input: Mod(83550368,19) Output: ? Mod(15, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:19:14 2005 Input: fibonacci(1104587) Output: ? 4798392847902424919131609835958247495987325090641191937339036628862987075778240738045095463866410438920703956740219188362881284529938406030148420838985585431455754572289726191648450693026304571005701668814652144899461011177933819115645645049313181454391359833496275343670036143532672634970384310208715331070520586756267820141842430106939629902050663976167822920517151065154505691487548148630845588487764110093910128196969757792924316890288114687459256974794502246064159068782431922934042068857157854688970476523940395379220133684405704029338516839206409365235531048000070008051647598002593512831832916889240799576646152481136473515930029590403642357868156769752981091274313235771483147083732080224470352826457201514540814796191359643011949310730259805211310053837543473271496425850156831595079809549188893200429563487730023883312567425522519532803950891653677301505620700041780586369917977948991066603924638929866975180973093587241552186636566055690380251466640914384009659283553324204939137007543504369765603032881486095089837217772834291035869248996106422853687351789401273013617999917101936497377651076705619678030849254554303602015575736013269081124871147963572491897068197428481639776421058901986308061618494612609912679217390651178999153610224400020152346065816238124231154739570369282320197320134571032197391175091484081291966009231634280703274709920476987115604441595048516325565094488329476637295740902037936209105916588360346677541437846435463334216434180449280396867283372409729295681288053228472835249343472965827181551356022634566827098735893129443141825925761466482298624837108390099652920026765285606835601517549358870776475047502236127337839752230073539879329938923799168195780688957776229507317409426401329567866403552306126790723275832631144258714763691074859072803829664967538929857594467110601893303082542360153303019419642056525846363731864612038620045421834626285755225280385052268067642603388449157055463199987896759007158718256839111746340030128832510691041077412993856117585529873320615746980099639278705945654085612159375061123720636691821711085825187809233658201063072821926614665520464937277826893826571843719631265705784257264912236318676512202607871070358165682429967646747089584583550461102098940448074762271513136922127634472687390502253749984870537534601360511902356141484382467064881741811626330542691059725005490260895567388151924716981764829309690065652521160692085120680577083395698714853344675494627550931924030863967330624298455366591381097223515370889044218918969394159517201099328956573569493912563601838667620519418768441748439905515276879654799001626744477756935963242367463929507440920180448960926032893183469795062750931242770334617592621494172764236711761085729549099565702850343918804869162919638158669599109566173719413073717120393151830535354875410221729100335099747291741422645082044768432695181669729725899618479653071349754455775818366879859378807406149404737630054187153114300542080840281267563861287937313661143815526750953160055644033506244074950388035914731559991692125425214342158227920120024701295446573398127370280595736085844062789565055783499601009808074452277766750930885776769834595083189954132874830077356337289541419341968486[+++] ? Errors (if any) and Timing Info: Timing: real 0m11.738s user 0m11.714s sys 0m0.009s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:19:45 2005 Input: fibonacci(21) Output: ? 10946 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:20:13 2005 Input: fibonacci(24) Output: ? 46368 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:20:23 2005 Input: fibonacci(22) Output: ? 17711 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:20:34 2005 Input: fibonacci(30) Output: ? 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:20:41 2005 Input: fibonacci(35) Output: ? 9227465 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:20:50 2005 Input: fibonacci(34) Output: ? 5702887 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:20:56 2005 Input: fibonacci(33) Output: ? 3524578 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:21:03 2005 Input: fibonacci(32) Output: ? 2178309 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:21:11 2005 Input: fibonacci(31) Output: ? 1346269 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:21:17 2005 Input: fibonacci(30) Output: ? 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:21:31 2005 Input: fibonacci(28) Output: ? 317811 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:21:42 2005 Input: fibonacci(24) Output: ? 46368 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:21:49 2005 Input: fibonacci(25) Output: ? 75025 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:22:00 2005 Input: fibonacci(5) Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.010s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:22:05 2005 Input: fibonacci(8) Output: ? 21 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:22:15 2005 Input: fibonacci(7) Output: ? 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:22:29 2005 Input: fibonacci(16) Output: ? 987 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:22:35 2005 Input: fibonacci(19) Output: ? 4181 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:22:40 2005 Input: fibonacci(17) Output: ? 1597 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:22:49 2005 Input: fibonacci(20) Output: ? 6765 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:22:55 2005 Input: fibonacci(219) Output: ? 2623059926317798754175087863660165740874359106 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:22:59 2005 Input: fibonacci(19) Output: ? 4181 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:24:06 2005 Input: binomial(5022,19) Output: ? 164723985354502666838838046473883141714609911299601540 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:24:33 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:24:55 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:25:01 2005 Input: pi(1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: pi(1) ^----- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: pi ===> Pi Pi=Pi(): the constant pi, with current precision. Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:25:18 2005 Input: Pi Output: ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:26:52 2005 Input: prime(5022) Output: ? 48823 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:27:28 2005 Input: prime(10) Output: ? 29 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:28:35 2005 Input: nextprime(83550368) Output: ? 83550371 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:29:59 2005 Input: isprime(83550359) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:30:09 2005 Input: isprime(83550359) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:30:16 2005 Input: isprime(83550357) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:30:21 2005 Input: isprime(83550357) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:30:33 2005 Input: isprime(83550353) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:30:48 2005 Input: isprime(83550349) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:31:22 2005 Input: isprime(83550367) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:31:33 2005 Input: isprime(83550363) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.006s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:31:40 2005 Input: isprime(83550361) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:31:56 2005 Input: isprime(83550351) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:32:05 2005 Input: isprime(83550347) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:32:26 2005 Input: isprime(1104583) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:32:33 2005 Input: isprime(1104581) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:32:39 2005 Input: isprime(1104579) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:32:45 2005 Input: isprime(1104577) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:32:53 2005 Input: isprime(1104573) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:33:00 2005 Input: isprime(1104571) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:33:08 2005 Input: isprime(1104569) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:33:13 2005 Input: isprime(1104567) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:33:24 2005 Input: isprime(1104563) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:33:30 2005 Input: isprime(1104561) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '139.168' ************** PARI ***************** Host 139.168.207.105 (139.168.207.105) Time: Sat Mar 26 00:33:40 2005 Input: isprime(1104559) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.001s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:20:10 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=80190; c=12959429; gcd(2^80190-1,a); Output: ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:20:28 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=80190; c=12959429; gcd(2^80190-1,a) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:21:26 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=80190; c=12959429; gcd(2^80190-1,a) gcd(2^c-1,a) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.058s user 0m0.049s sys 0m0.011s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:22:12 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=80190; c=12959429; gcd(2^80190-1,a) gcd((2^c-1),a) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.046s sys 0m0.012s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:22:19 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=80190; c=12959429; gcd(2^80190-1,a) gcd((2^c-1),a+1) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.061s user 0m0.050s sys 0m0.011s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:22:27 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=80190; c=12959429; gcd(2^80190-1,a) gcd((2^c)-1),a+1) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: gcd((2^c)-1),a+1) ^------ Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:22:35 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=80190; c=12959429; gcd(2^80190-1,a) gcd((2^c)-1,a+1) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.062s user 0m0.051s sys 0m0.011s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:22:41 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=80190; c=12959429; gcd(2^80190-1,a) gcd((2^c)-1,a) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.049s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:22:50 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=80190; c=12959429; gcd(2^80190-1,a) gcd((2^c)-1,a-1) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.062s user 0m0.050s sys 0m0.012s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:23:14 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=80190; c=2111; gcd(2^80190-1,a) gcd((2^c)-1,a-1) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:23:18 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=80190; c=2111; gcd(2^80190-1,a) gcd((2111^c)-1,a-1) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 10 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:23:26 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=80190; c=2111; gcd(2^80190-1,a) gcd((2111^c)-1,a) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.011s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:23:46 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=80190; c=12959429; gcd(2^80190-1,a) gcd((2111^c)-1,a) Output: ** WARNING: Computation used more memory than allowed. ** ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m5.443s user 0m5.426s sys 0m0.014s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:24:02 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=80190; c=12959429; gcd(2111^80190-1,a) gcd((2111^c)-1,a) Output: ** WARNING: Computation used more memory than allowed. ** ? ? ? ? 1 ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m5.509s user 0m5.487s sys 0m0.013s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:24:31 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=80190; c=12959429; gcd(80190^2-1,a) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:24:37 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=80190; c=12959429; gcd(80190^2-1,a-1) Output: ? ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:25:40 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; (a-1)/2 Output: ? ? 397767629008652583572560935775186502667698884185657943741485253017245426113197579306927856143455853420726306439662638465945570414413215 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 04:27:06 2005 Input: a=35045282158487636123259014292004089245227471550191132494367732831303373727594575532334779423274207863833033604171200909745257231922557618156366994601; (a-1)/2 Output: ? ? 17522641079243818061629507146002044622613735775095566247183866415651686863797287766167389711637103931916516802085600454872628615961278809078183497300 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '155.207' ************** PARI ***************** Host 155.207.120.6 (155.207.120.6) Time: Sat Mar 26 04:39:21 2005 Input: > R := PolynomialRing(Integers()); > K := NumberField(x^4 - 10*x^2 + 1); > UnitEquation(2*a,a^4-9*a^2,2*a); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: >R:=PolynomialRin ^-------------------- *** unexpected character: >K:=NumberField(x ^-------------------- *** unexpected character: >UnitEquation(2*a,a^ ^-------------------- Timing: real 0m0.013s user 0m0.005s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 05:55:27 2005 Input: b=17034834443239860950065618625187262772884553525798439952983762253704705103649784280496129033483832339176066600096204887426910459693091728324504490099524163564976292108509177836165122099427433602256803603476421464829838624283136249612212483707110054716831542574115069085472028260560033978825660557071943839882958916253072035433611117644811862089; a=30422419887462074119077577127953460242214304136101975431515900040706213604527812103392409810995250478407582966274166740155395822756752231402398100389410334562544609491379815062098203057753553771268411989775966876313005627306153999872252208593537342797842209873152047665265154032714681733197619680560980460649235647668708709727122181464806104386471687729025680174178047098011560219910444967111098858792854459778009269974583894815539201; gcd(a,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 05:55:42 2005 Input: b=414493686737811922516747674949449891953471618588769851321728772158159677026849; a=30422419887462074119077577127953460242214304136101975431515900040706213604527812103392409810995250478407582966274166740155395822756752231402398100389410334562544609491379815062098203057753553771268411989775966876313005627306153999872252208593537342797842209873152047665265154032714681733197619680560980460649235647668708709727122181464806104386471687729025680174178047098011560219910444967111098858792854459778009269974583894815539201; gcd(a,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 05:55:52 2005 Input: b=631144085771921355170916503458656270472461769656615428703704982072789188511880363; a=30422419887462074119077577127953460242214304136101975431515900040706213604527812103392409810995250478407582966274166740155395822756752231402398100389410334562544609491379815062098203057753553771268411989775966876313005627306153999872252208593537342797842209873152047665265154032714681733197619680560980460649235647668708709727122181464806104386471687729025680174178047098011560219910444967111098858792854459778009269974583894815539201; gcd(a,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 05:56:00 2005 Input: b=3764599310028560534111530318189217; a=30422419887462074119077577127953460242214304136101975431515900040706213604527812103392409810995250478407582966274166740155395822756752231402398100389410334562544609491379815062098203057753553771268411989775966876313005627306153999872252208593537342797842209873152047665265154032714681733197619680560980460649235647668708709727122181464806104386471687729025680174178047098011560219910444967111098858792854459778009269974583894815539201; gcd(a,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 05:56:14 2005 Input: b=1535488684778860345925363096721961011533088844851184129; a=30422419887462074119077577127953460242214304136101975431515900040706213604527812103392409810995250478407582966274166740155395822756752231402398100389410334562544609491379815062098203057753553771268411989775966876313005627306153999872252208593537342797842209873152047665265154032714681733197619680560980460649235647668708709727122181464806104386471687729025680174178047098011560219910444967111098858792854459778009269974583894815539201; gcd(a,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sat Mar 26 05:56:28 2005 Input: b=5449639725060582758664927054574208493106756731939660151305124879434176631701057541080594777921916243304233479540319344071503000552916453576824791398930896744045553524014400948938472964181822882502374539766629335154411658208601410904334850436328293346251449306174503958897410005233777306381438536578902975462164665212811513; a=30422419887462074119077577127953460242214304136101975431515900040706213604527812103392409810995250478407582966274166740155395822756752231402398100389410334562544609491379815062098203057753553771268411989775966876313005627306153999872252208593537342797842209873152047665265154032714681733197619680560980460649235647668708709727122181464806104386471687729025680174178047098011560219910444967111098858792854459778009269974583894815539201; gcd(a,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.002s '66.42.1' ************** PARI ***************** Host 66.42.170.105 (66.42.170.105) Time: Sat Mar 26 09:55:37 2005 Input: factor(123456) Output: ? [2 6] [3 1] [643 1] ? Errors (if any) and Timing Info: Timing: real 0m0.333s user 0m0.006s sys 0m0.006s '66.42.1' ************** PARI ***************** Host 66.42.170.105 (66.42.170.105) Time: Sat Mar 26 09:56:17 2005 Input: factor(643) Output: ? [643 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '66.42.1' ************** PARI ***************** Host 66.42.170.105 (66.42.170.105) Time: Sat Mar 26 09:56:55 2005 Input: 6^12345 Output: ? 1893154186034792119159455093360841878669508296792676884637785340931698435300470143425047283833714670645892573749367902901058987464092702498691227388164287695966926263502721510924208978381678802251230500483644821599166713702228753452829375973434048783146491331196646610121083972876828022164261462668826065369096268965844848894210608862393116437989338763124674170897431529091304381246130800648064300808368984710411641578466024066588311520688727964268632763597480597386084981759064325474824725739978541033984867130313914792430456557122640827809307611183080380318049993054729694754014200019280847725484651219013763154306663425971479779763860626504316619882961074331185734345438305443893332785177588889021569022110297449679081688727458405519747888034019699112900495027610109959139998166817690704126565717123769755515168091569327288319449815706986436090062514879098796742156412498273987612070672050303606800377732652161155274223320228953397246288753340334870426593563790626543279416322863731334594768886802241140712078735248070803624459629158549725207603922097693885557683407521683115561544047274383403768221537848361584064515865736483886177936263479126194603432752502885476402823304559738224872715616813412920201785824845106794589454640298284337241888794486361481490292057586102978291903963291456619316648155920343916627365463422083282124722144425082154435335723104109149908817694527656663403783326213281324441860060696190076789834202398634545073912234070545530981715862700600156313605690226302874860377918131016723051942362467472520108092544601210363599523300588834544863289379503324484112052057009957037469082375447536810155168865010473581696058798675245060915813217155886775293309111933619696860489914985405313169754016795566243211634330249561263087154019262777298614506568369154083846759149367495813438735914684396204571819702822958943905849459401704474961565401126780086388885174071755193077143625286525985931947760101580455311356226722952882045337910667351238329226701383722714324255952075302312195073210954761233054778896488743669777719547030574573880302788049660505323533092801076287026200759764442697405338158448615392956322759681148370418906144519607979787215667725670934344821870327037463306739544733071905891022490981844693580101478518883927423103084730877363965467805544713063609013872340190902390376770478549921867224474504210535479313316818906842043349903847840126385786970028266471291870262718059959394988635378611634287663453179673839344122991669473755604373508758340483108527340451123365562168673536103375968484597952884690680375865719248371052564938212099281963981216747978457087324500562748797311003563172468504975319286988293611459226863929603370878178166582900399407457672298640857686286434202756671980558331332889825030632393945918175675741312967086984161360437268254866946502908539194749177134136523252538596998361505460324083768446587979561970543353084248855759844029319106638541752354650883398990326336660270208713916412249479500535980427647858233994727629645625646228517124358492715951448285758255099939517545937072245560018646162488353189905711475179859748652988522588717371766131822032695620700145395505535990061086332363661520788650798807537719385885639285101875948[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.042s user 0m0.026s sys 0m0.009s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Sat Mar 26 11:19:56 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.049s user 0m0.004s sys 0m0.009s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Sat Mar 26 11:20:08 2005 Input: for(n=1,8, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, 8: 761/280, ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Sat Mar 26 11:20:31 2005 Input: for(n=1,12, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, 8: 761/280, 9: 7129/2520, 10: 7381/2520, 11: 83711/27720, 12: 86021/27720, ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Sat Mar 26 11:21:25 2005 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.007s sys 0m0.007s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Sat Mar 26 11:22:49 2005 Input: decimalcycle(p0,q0)= { local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans } decimalcycle(7,17) Output: ? ? [4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Sat Mar 26 11:23:53 2005 Input: decimalcycle(p0,q0)= { local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans } decimalcycle(7,13) Output: ? ? [5, 3, 8, 4, 6, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Sat Mar 26 11:24:51 2005 Input: decimalcycle(p0,q0)= { local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans } for(j=1,12,print(decimalcycle(j,13))) Output: ? ? [0, 7, 6, 9, 2, 3] [1, 5, 3, 8, 4, 6] [2, 3, 0, 7, 6, 9] [3, 0, 7, 6, 9, 2] [3, 8, 4, 6, 1, 5] [4, 6, 1, 5, 3, 8] [5, 3, 8, 4, 6, 1] [6, 1, 5, 3, 8, 4] [6, 9, 2, 3, 0, 7] [7, 6, 9, 2, 3, 0] [8, 4, 6, 1, 5, 3] [9, 2, 3, 0, 7, 6] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.006s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Sat Mar 26 11:26:53 2005 Input: decimalcycle(p0,q0)= { local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans } for(j=1,6,print(decimalcycle(j,7))) Output: ? ? [1, 4, 2, 8, 5, 7] [2, 8, 5, 7, 1, 4] [4, 2, 8, 5, 7, 1] [5, 7, 1, 4, 2, 8] [7, 1, 4, 2, 8, 5] [8, 5, 7, 1, 4, 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Sat Mar 26 11:27:42 2005 Input: decimalcycle(p0,q0)= { local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans } for(j=1,10,print(decimalcycle(j,11))) Output: ? ? [0, 9] [1, 8] [2, 7] [3, 6] [4, 5] [5, 4] [6, 3] [7, 2] [8, 1] [9, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Sat Mar 26 11:28:27 2005 Input: decimalcycle(p0,q0)= { local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans } for(j=1,15,print(decimalcycle(j,31))) Output: ? ? [0, 3, 2, 2, 5, 8, 0, 6, 4, 5, 1, 6, 1, 2, 9] [0, 6, 4, 5, 1, 6, 1, 2, 9, 0, 3, 2, 2, 5, 8] [0, 9, 6, 7, 7, 4, 1, 9, 3, 5, 4, 8, 3, 8, 7] [1, 2, 9, 0, 3, 2, 2, 5, 8, 0, 6, 4, 5, 1, 6] [1, 6, 1, 2, 9, 0, 3, 2, 2, 5, 8, 0, 6, 4, 5] [1, 9, 3, 5, 4, 8, 3, 8, 7, 0, 9, 6, 7, 7, 4] [2, 2, 5, 8, 0, 6, 4, 5, 1, 6, 1, 2, 9, 0, 3] [2, 5, 8, 0, 6, 4, 5, 1, 6, 1, 2, 9, 0, 3, 2] [2, 9, 0, 3, 2, 2, 5, 8, 0, 6, 4, 5, 1, 6, 1] [3, 2, 2, 5, 8, 0, 6, 4, 5, 1, 6, 1, 2, 9, 0] [3, 5, 4, 8, 3, 8, 7, 0, 9, 6, 7, 7, 4, 1, 9] [3, 8, 7, 0, 9, 6, 7, 7, 4, 1, 9, 3, 5, 4, 8] [4, 1, 9, 3, 5, 4, 8, 3, 8, 7, 0, 9, 6, 7, 7] [4, 5, 1, 6, 1, 2, 9, 0, 3, 2, 2, 5, 8, 0, 6] [4, 8, 3, 8, 7, 0, 9, 6, 7, 7, 4, 1, 9, 3, 5] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '68.161.' ************** PARI ***************** Host 68.161.12.136 (68.161.12.136) Time: Sat Mar 26 15:03:50 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '24.4.98' ************** PARI ***************** Host 24.4.98.22 (24.4.98.22) Time: Sat Mar 26 16:18:46 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 16:42:24 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) A=a^p*Mod(1, w^37) Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 + O(37^2) ? ? Errors (if any) and Timing Info: *** forbidden division t_INT % t_POLMOD. Timing: real 0m0.067s user 0m0.047s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 16:43:19 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) A=a^p*Mod(1, p^2) Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 + O(37^2) ? Mod(1045, 1369) ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.048s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 16:44:25 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) a^p A=a^p*Mod(1, p^2) (q-A)/w^p Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Mod(1045, 1369) ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(0, 1369). Timing: real 0m0.058s user 0m0.052s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 16:45:07 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) a^p A=a^p*Mod(1, p^2) (q-a^p)/w^p Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Mod(1045, 1369) ? Mod((8 + O(37))*x^35 + (17 + O(37))*x^34 + (10 + O(37))*x^33 + (22 + O(37))*x^32 + (24 + O(37))*x^31 + (12 + O(37))*x^30 + (18 + O(37))*x^29 + (17 + O(37))*x^28 + (1 + O(37))*x^27 + (21 + O(37))*x^26 + (35 + O(37))*x^25 + (10 + O(37))*x^24 + (27 + O(37))*x^23 + (17 + O(37))*x^22 + (15 + O(37))*x^21 + (15 + O(37))*x^20 + (15 + O(37))*x^19 + (5 + O(37))*x^18 + (5 + O(37))*x^17 + (5 + O(37))*x^16 + (3 + O(37))*x^15 + (30 + O(37))*x^14 + (10 + O(37))*x^13 + (22 + O(37))*x^12 + (36 + O(37))*x^11 + (19 + O(37))*x^10 + (3 + O(37))*x^9 + (2 + O(37))*x^8 + (8 + O(37))*x^7 + (33 + O(37))*x^6 + (35 + O(37))*x^5 + (10 + O(37))*x^4 + (3 + O(37))*x^3 + (12 + O(37))*x^2 + (20 + O(37))*x + (10 + O(37)), x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.052s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 16:53:42 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-lift(d))/w^(p-1) (q-lift(d))/w^p a=lift(d)+O(p^2) a^p A=a^p*Mod(1, p^2) (q-a^p)/w^p Output: ? 37 ? 32 ? ? ? ? ? ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Mod(1045, 1369) ? Mod((8 + O(37))*x^35 + (17 + O(37))*x^34 + (10 + O(37))*x^33 + (22 + O(37))*x^32 + (24 + O(37))*x^31 + (12 + O(37))*x^30 + (18 + O(37))*x^29 + (17 + O(37))*x^28 + (1 + O(37))*x^27 + (21 + O(37))*x^26 + (35 + O(37))*x^25 + (10 + O(37))*x^24 + (27 + O(37))*x^23 + (17 + O(37))*x^22 + (15 + O(37))*x^21 + (15 + O(37))*x^20 + (15 + O(37))*x^19 + (5 + O(37))*x^18 + (5 + O(37))*x^17 + (5 + O(37))*x^16 + (3 + O(37))*x^15 + (30 + O(37))*x^14 + (10 + O(37))*x^13 + (22 + O(37))*x^12 + (36 + O(37))*x^11 + (19 + O(37))*x^10 + (3 + O(37))*x^9 + (2 + O(37))*x^8 + (8 + O(37))*x^7 + (33 + O(37))*x^6 + (35 + O(37))*x^5 + (10 + O(37))*x^4 + (3 + O(37))*x^3 + (12 + O(37))*x^2 + (20 + O(37))*x + (10 + O(37)), x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.061s user 0m0.057s sys 0m0.002s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 16:56:38 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d)*Mod(1, sum(n=0, p-1, x^n); (q-D)/w^(p-1) (q-D)/w^p a=lift(d)+O(p^2) a^p A=a^p*Mod(1, p^2) (q-a^p)/w^p Output: ? 37 ? 32 ? ? ? ? ? ? ? Mod((-620425891761235030215584285/37*D + 341645695252746528126542794902960287713953976909959/37)*x^35 + (-1528688954895722868636909041/37*D + 742498522545873947959952690159777840568737692520683/37)*x^34 + (-2698660114751957008975094417/37*D + 1100753173352828116288318335869473387397248546720400/37)*x^33 + (-4096681431227141071140838641/37*D + 1325423081206980089712248871262410942931728359582301/37)*x^32 + (-5682534376422501884429792723/37*D + 1359448435447001939707538745546832832962913973139871/37)*x^31 + (-7410596848464652074327727813/37*D + 1194187752783768451796907260168234305931395954745281/37)*x^30 + (-9231155636311999368372296806/37*D + 871612578523686312698390910929906354515796444535023/37)*x^29 + (-11091836578323382148014154858/37*D + 473647906406532787441154388888260091550830523320418/37)*x^28 + (-12939111271530842228199900221/37*D + 101365532292985834894742667559503322733394060900756/37)*x^27 + (-14719836986334044121085615940/37*D - 150685334110913279388927697406845031522609608384778/37)*x^26 + (-16382785486074303787646728041/37*D - 218490888113701680750006514287436630307637490834740/37)*x^25 + (-17880116770132579573891618394/37*D - 84830427518645171828988815500438038725572450243500/37)*x^24 + (-19168755343645695016540459447/37*D + 216350062966944821629071389010343254831898554648233/37)*x^23 + (-20211629421066770589642838381/37*D + 608559234715596007798836451665324328988002367063706/37)*x^22 + (-20978737413939577409772897641/37*D + 992187030515891505099070256994329013134640690502946/37)*x^21 + (-21448011021975225596595567894/37*D + 1269802823448844669838965430945961818210759186728435/37)*x^20 + (-21605950097872273267942309730/37*D + 1370900035167554589120585851869762126004586933087685/37)*x^19 + (-21448011021975225596595567894/37*D + 1269802823448844669838965430945961818210759186728435/37)*x^18 + (-20978737413939577409772897641/37*D + 992187030515891505099070256994329013134640690502946/37)*x^17 + (-20211629421066770589642838381/37*D + 608559234715596007798836451665324328988002367063706/37)*x^16 + (-19168755343645695016540459447/37*D + 216350062966944821629071389010343254831898554648233/37)*x^15 + (-17880116770132579573891618394/37*D - 84830427518645171828988815500438038725572450243500/37)*x^14 + (-16382785486074303787646728041/37*D - 218490888113701680750006514287436630307637490834740/37)*x^13 + (-14719836986334044121085615940/37*D - 150685334110913279388927697406845031522609608384778/37)*x^12 + (-12939111271530842228199900221/37*D + 101365532292985834894742667559503322733394060900756/37)*x^11 + (-11091836578323382148014154858/37*D + 473647906406532787441154388888260091550830523320418/37)*x^10 + (-9231155636311999368372296806/37*D + 871612578523686312698390910929906354515796444535023/37)*x^9 + (-7410596848464652074327727813/37*D + 1194187752783768451796907260168234305931395954745281/37)*x^8 + (-5682534376422501884429792723/37*D + 1359448435447001939707538745546832832962913973139871/37)*x^7 + (-4096681431227141071140838641/37*D + 1325423081206980089712248871262410942931728359582301/37)*x^6 + (-2698660114751957008975094417/37*D + 1100753173352828116288318335869473387397248546720400/37)*x^5 + (-1528688954895722868636909041/37[+++] ? Mod((-393155596797403749679491227282/1369*D + 21266509997286420210125736280651244772079420741484557/1369)*x^35 + (-763355435599641803241005836019/1369*D + 29892129270221218879569389149892958898742544337300631/1369)*x^34 + (-1099949541065903806780931428784/1369*D + 23686193933310303015176875894632423569778670455519917/1369)*x^33 + (-1393254713617485147128344162637/1369*D + 4224836516542082922634833748113153008159894968349674/1369)*x^32 + (-1634833097459484677175624360202/1369*D - 23549307490829760186592638207944807108234633594710906/1369)*x^31 + (-1817734922329255857131213256733/1369*D - 52582389605082411745645835512526377155783029859401576/1369)*x^30 + (-1936698435733467480060578554934/1369*D - 75500826460795424252005667858099801703165259443492416/1369)*x^29 + (-1988301273987327253110294800394/1369*D - 86483981868885397611720395281855092048170307149803710/1369)*x^28 + (-1971058917386765863313262297930/1369*D - 82742444408640690536917371390069470663471615771174619/1369)*x^27 + (-1885467397137528450549357217035/1369*D - 65226459106194746217897113809119848832527775283018034/1369)*x^26 + (-1733989025440572567748680654537/1369*D - 38384591746804534670381052724415337894111799031296691/1369)*x^25 + (-1520981559253227077285242944302/1369*D - 9033918889311152272505075415128937800649791128926754/1369)*x^24 + (-1252572835555725382730744291006/1369*D + 15371316926165139295293247039038514404275810271567303/1369)*x^23 + (-936484484638238416798238518749/1369*D + 28632874593674601105143341926307058747574984491067239/1369)*x^22 + (-581809792856171654660944725934/1369*D + 27382692906483969026712129495341303347098317651194674/1369)*x^21 + (-198752105337811040178838740499/1369*D + 11938282774682403548172266267202374633196032844070229/1369)*x^20 + (201668705677868557215706044297/1369*D - 13777911695638429025743718397146967868522636323397309/1369)*x^19 + (607933262501738918450080277025/1369*D - 43234702999551528613079658635676921758612932106157097/1369)*x^18 + (1008354073517418515844625061821/1369*D - 68950897469872361186995643300026264260331601273624635/1369)*x^17 + (1391411761035779130326731047256/1369*D - 84395307601673926665535506528165192974233886080749080/1369)*x^16 + (1746086452817845892464024840071/1369*D - 85645489288864558743966718959130948374710552920621645/1369)*x^15 + (2062174803735332858396530612328/1369*D - 72383931621355096934116624071862404031411378701121709/1369)*x^14 + (2330583527432834552951029265624/1369*D - 47978695805878805366318301617694951826485777300627652/1369)*x^13 + (2543590993620180043414466975859/1369*D - 18628022948385422968442324308408551733023769398257715/1369)*x^12 + (2695069365317135926215143538357/1369*D + 8213844411004788579073736776295959205392206853463628/1369)*x^11 + (2780660885566373338979048619252/1369*D + 25729829713450732898093994357245581036336047341620213/1369)*x^10 + (2797903242166934728776081121716/1369*D + 29471367173695439972897018249031202421034738720249304/1369)*x^9 + (2746300403913074955726364876256/1369*D + 18488211765605466613182290825275912076029691013938010/1369)*x^8 + (2627336890508863332796999578055/1369*D - 4430225090107545893177541520297512471352538570152830/1369)*x^7 + (2444435065639092152841[+++] ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Mod(1045, 1369) ? Mod((8 + O(37))*x^35 + (17 + O(37))*x^34 + (10 + O(37))*x^33 + (22 + O(37))*x^32 + (24 + O(37))*x^31 + (12 + O(37))*x^30 + (18 + O(37))*x^29 + (17 + O(37))*x^28 + (1 + O(37))*x^27 + (21 + O(37))*x^26 + (35 + O(37))*x^25 + (10 + O(37))*x^24 + (27 + O(37))*x^23 + (17 + O(37))*x^22 + (15 + O(37))*x^21 + (15 + O(37))*x^20 + (15 + O(37))*x^19 + (5 + O(37))*x^18 + (5 + O(37))*x^17 + (5 + O(37))*x^16 + (3 + O(37))*x^15 + (30 + O(37))*x^14 + (10 + O(37))*x^13 + (22 + O(37))*x^12 + (36 + O(37))*x^11 + (19 + O(37))*x^10 + (3 + O(37))*x^9 + (2 + O(37))*x^8 + (8 + O(37))*x^7 + (33 + O(37))*x^6 + (35 + O(37))*x^5 + (10 + O(37))*x^4 + (3 + O(37))*x^3 + (12 + O(37))*x^2 + (20 + O(37))*x + (10 + O(37)), x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...d)*Mod(1,sum(n=0,p-1,x^n); ^- Timing: real 0m0.060s user 0m0.052s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 16:57:19 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d)*Mod(1, sum(n=0, p-1, x^n)); (q-D)/w^(p-1) (q-D)/w^p a=lift(d)+O(p^2) a^p A=a^p*Mod(1, p^2) (q-a^p)/w^p Output: ? 37 ? 32 ? ? ? ? ? ? ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Mod(1045, 1369) ? Mod((8 + O(37))*x^35 + (17 + O(37))*x^34 + (10 + O(37))*x^33 + (22 + O(37))*x^32 + (24 + O(37))*x^31 + (12 + O(37))*x^30 + (18 + O(37))*x^29 + (17 + O(37))*x^28 + (1 + O(37))*x^27 + (21 + O(37))*x^26 + (35 + O(37))*x^25 + (10 + O(37))*x^24 + (27 + O(37))*x^23 + (17 + O(37))*x^22 + (15 + O(37))*x^21 + (15 + O(37))*x^20 + (15 + O(37))*x^19 + (5 + O(37))*x^18 + (5 + O(37))*x^17 + (5 + O(37))*x^16 + (3 + O(37))*x^15 + (30 + O(37))*x^14 + (10 + O(37))*x^13 + (22 + O(37))*x^12 + (36 + O(37))*x^11 + (19 + O(37))*x^10 + (3 + O(37))*x^9 + (2 + O(37))*x^8 + (8 + O(37))*x^7 + (33 + O(37))*x^6 + (35 + O(37))*x^5 + (10 + O(37))*x^4 + (3 + O(37))*x^3 + (12 + O(37))*x^2 + (20 + O(37))*x + (10 + O(37)), x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.055s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 17:03:11 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d)*Mod(1, sum(n=0, p-1, x^n)); (q-D)/w^(p-1) (q-D)/w^p a=lift(d)+O(p^2) a^p A=Truncate(a^p, p^2) (q-a^p)/w^p Output: ? 37 ? 32 ? ? ? ? ? ? ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? ? Mod((8 + O(37))*x^35 + (17 + O(37))*x^34 + (10 + O(37))*x^33 + (22 + O(37))*x^32 + (24 + O(37))*x^31 + (12 + O(37))*x^30 + (18 + O(37))*x^29 + (17 + O(37))*x^28 + (1 + O(37))*x^27 + (21 + O(37))*x^26 + (35 + O(37))*x^25 + (10 + O(37))*x^24 + (27 + O(37))*x^23 + (17 + O(37))*x^22 + (15 + O(37))*x^21 + (15 + O(37))*x^20 + (15 + O(37))*x^19 + (5 + O(37))*x^18 + (5 + O(37))*x^17 + (5 + O(37))*x^16 + (3 + O(37))*x^15 + (30 + O(37))*x^14 + (10 + O(37))*x^13 + (22 + O(37))*x^12 + (36 + O(37))*x^11 + (19 + O(37))*x^10 + (3 + O(37))*x^9 + (2 + O(37))*x^8 + (8 + O(37))*x^7 + (33 + O(37))*x^6 + (35 + O(37))*x^5 + (10 + O(37))*x^4 + (3 + O(37))*x^3 + (12 + O(37))*x^2 + (20 + O(37))*x + (10 + O(37)), x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: *** expected character: ',' instead of: A=Truncate(a^p,p^2) ^------- Timing: real 0m0.060s user 0m0.051s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 17:03:30 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d)*Mod(1, sum(n=0, p-1, x^n)); (q-D)/w^(p-1) (q-D)/w^p a=lift(d)+O(p^2) a^p A=Truncate(a^p: p^2) (q-a^p)/w^p Output: ? 37 ? 32 ? ? ? ? ? ? ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? ? Mod((8 + O(37))*x^35 + (17 + O(37))*x^34 + (10 + O(37))*x^33 + (22 + O(37))*x^32 + (24 + O(37))*x^31 + (12 + O(37))*x^30 + (18 + O(37))*x^29 + (17 + O(37))*x^28 + (1 + O(37))*x^27 + (21 + O(37))*x^26 + (35 + O(37))*x^25 + (10 + O(37))*x^24 + (27 + O(37))*x^23 + (17 + O(37))*x^22 + (15 + O(37))*x^21 + (15 + O(37))*x^20 + (15 + O(37))*x^19 + (5 + O(37))*x^18 + (5 + O(37))*x^17 + (5 + O(37))*x^16 + (3 + O(37))*x^15 + (30 + O(37))*x^14 + (10 + O(37))*x^13 + (22 + O(37))*x^12 + (36 + O(37))*x^11 + (19 + O(37))*x^10 + (3 + O(37))*x^9 + (2 + O(37))*x^8 + (8 + O(37))*x^7 + (33 + O(37))*x^6 + (35 + O(37))*x^5 + (10 + O(37))*x^4 + (3 + O(37))*x^3 + (12 + O(37))*x^2 + (20 + O(37))*x + (10 + O(37)), x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: *** expected character: ',' instead of: A=Truncate(a^p:p^2) ^----- Timing: real 0m0.060s user 0m0.054s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 19:41:24 2005 Input: bern(2) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: bern(2) ^------- Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 19:41:33 2005 Input: bernfrac(2) Output: ? 1/6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 19:41:46 2005 Input: bernfrac(9) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 19:41:55 2005 Input: bernfrac(32) Output: ? -7709321041217/510 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 19:42:06 2005 Input: numerator(bernfrac(32)) Output: ? -7709321041217 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 19:42:22 2005 Input: numerator(bernfrac(12)) Output: ? -691 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 19:42:31 2005 Input: numerator(bernfrac(32)) Output: ? -7709321041217 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 19:42:36 2005 Input: numerator(bernfrac(12)) Output: ? -691 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 19:42:57 2005 Input: factor(numerator(bernfrac(32))) Output: ? [-1 1] [37 1] [683 1] [305065927 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 19:43:09 2005 Input: factor(bernfrac(32)) Output: ? [-1 1] [2 -1] [3 -1] [5 -1] [17 -1] [37 1] [683 1] [305065927 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 19:43:31 2005 Input: factor(numerator(bernfrac(6))) Output: ? [;] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 19:43:37 2005 Input: factor(numerator(bernfrac(8))) Output: ? [-1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 19:43:43 2005 Input: factor(numerator(bernfrac(10))) Output: ? [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 22:14:42 2005 Input: for(x=1, 10, print(x)) Output: ? 1 2 3 4 5 6 7 8 9 10 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 22:15:16 2005 Input: p=13 for(x=1, (p-3)/2, print(x)) Output: ? ? 13 ? 1 2 3 4 5 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 22:19:08 2005 Input: p=13 for(x=1, (p-3)/2, print(x)) 3>6 Output: ? 13 ? 1 2 3 4 5 ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 22:19:14 2005 Input: p=13 for(x=1, (p-3)/2, print(x)) 3<6 Output: ? 13 ? 1 2 3 4 5 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 22:19:20 2005 Input: p=13 for(x=1, (p-3)/2, print(x)) 3=6 Output: ? 13 ? 1 2 3 4 5 ? ? Errors (if any) and Timing Info: *** unexpected character: 3=6 ^-- Timing: real 0m0.014s user 0m0.008s sys 0m0.002s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 22:19:33 2005 Input: p=13 for(x=1, (p-3)/2, print(x)) 3 eq 6 Output: ? 13 ? 1 2 3 4 5 ? 3.0000000000000000000000000000000000000 ? Errors (if any) and Timing Info: *** Warning: unused characters: q6. Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 22:19:56 2005 Input: p=13 for(x=1, (p-3)/2, print(bernfrac(x))) Output: ? 13 ? -1/2 1/6 0 -1/30 0 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 22:22:18 2005 Input: p=13 for(x=1, (p-3)/2, if(valuation((bernfrac(x)), p)>0, return(x), next{1}) Output: ? 13 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...c(x)),p)>0,return(x),next{1}) ^---- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 22:22:43 2005 Input: p=13 for(x=1, (p-3)/2, if(valuation(bernfrac(x)), p)>0, return(x), next{1}) Output: ? 13 ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...,if(valuation(bernfrac(x) *** ),p)>0,return(x),nex ^-------------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 22:24:21 2005 Input: p=13 for(x=1, (p-3)/2, if (valuation(bernfrac(x), p)>0, return(x), next{1}) Output: ? 13 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...ac(x),p)>0,return(x),next{1}) ^---- Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 22:24:43 2005 Input: p=13 for(x=1, (p-3)/2, if (valuation(bernfrac(x), p)>0, return(x), return(x)) Output: ? 13 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...p)>0,return(x),return(x)) ^ Timing: real 0m0.015s user 0m0.007s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 22:25:01 2005 Input: p=13 for(x=1, (p-3)/2, valuation(bernfrac(x), p)) Output: ? 13 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 22:25:18 2005 Input: p=13 for(x=1, (p-3)/2, return(valuation(bernfrac(x), p))) Output: ? 13 ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 22:25:35 2005 Input: p=13 for(x=1, (p-3)/2, print(valuation(bernfrac(x), p))) Output: ? 13 ? 0 0 9223372036854775807 0 9223372036854775807 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sat Mar 26 22:26:01 2005 Input: p=13 for(x=1, (p-3)/2, print(valuation(numerator(bernfrac(x)), p))) Output: ? 13 ? 0 0 9223372036854775807 0 9223372036854775807 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 01:11:21 2005 Input: bernfrac(4) Output: ? -1/30 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 01:17:15 2005 Input: valuation(bernfrac(4), 5) Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 01:17:21 2005 Input: valuation(bernfrac(4), 5)>0 Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 01:17:46 2005 Input: if(valuation(bernfrac(4), 5)>0, return{duck}, return{cow}) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...n(bernfrac(4),5)>0,return *** {duck},return{cow}) ^------------------- Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 01:18:21 2005 Input: if(valuation(bernfrac(4), 5)>0, print{duck}, print{cow}) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...on(bernfrac(4),5)>0,print *** {duck},print{cow}) ^------------------ Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 01:19:02 2005 Input: if(valuation(bernfrac(4), 5)>0, {print{duck}}, {print{cow}}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...luation(bernfrac(4),5)>0,{print{duck}},{print ^-------------------- Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 01:19:10 2005 Input: if(valuation(bernfrac(4), 5)>0, {print{duck}}, {print{cow}}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...luation(bernfrac(4),5)>0,{print{duck}},{print ^-------------------- Timing: real 0m0.013s user 0m0.005s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 01:21:18 2005 Input: if(valuation(bernfrac(4), 5)>0, {print(duck)}, {print(cow)}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...luation(bernfrac(4),5)>0,{print(duck)},{print ^-------------------- Timing: real 0m0.013s user 0m0.010s sys 0m0.002s '219.65.' ************** PARI ***************** Host 219.65.170.29 (219.65.170.29) Time: Sun Mar 27 01:21:42 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '219.65.' ************** PARI ***************** Host 219.65.170.29 (219.65.170.29) Time: Sun Mar 27 01:21:51 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 01:21:52 2005 Input: if(valuation(bernfrac(4), 5)>0, 5, 7) Output: ? 7 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 01:22:14 2005 Input: if(valuation(bernfrac(4), 5)>0, duck, cow) Output: ? cow ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 01:22:23 2005 Input: if(valuation(bernfrac(4), 5)>0, duck, ) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 01:23:40 2005 Input: p=13 for(x=1, (p-3)/2, if(valuation(bernfrac(2x), p)>0, p, 2x) Output: ? 13 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...2,if(valuation(bernfrac(2 *** x),p)>0,p,2x) ^------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 01:23:53 2005 Input: p=13 for(x=1, (p-3)/2, if(valuation(bernfrac(2x), p)>0, p, 2x)) Output: ? 13 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...2,if(valuation(bernfrac(2 *** x),p)>0,p,2x)) ^-------------- Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 01:24:41 2005 Input: p=13 for(x=1, (p-3)/2, ) if(valuation(bernfrac(2x), p)>0, p, 2x) Output: ? 13 ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: if(valuation(bernfrac(2 *** x),p)>0,p,2x) ^------------- Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 01:25:42 2005 Input: p=13 for(x=1, (p-3)/2, x) if(valuation(bernfrac(2), p)>0, p, 2) Output: ? 13 ? ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 01:26:10 2005 Input: p=13 for(x=1, (p-3)/2, {if(valuation(bernfrac(2), p)>0, p, 2)}) Output: ? 13 ? ? Errors (if any) and Timing Info: *** unexpected character: for(x=1,(p-3)/2,{if(valuation(bernfr ^-------------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:22:56 2005 Input: isprime(1091225) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.005s sys 0m0.007s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:24:25 2005 Input: isprime(19) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:26:57 2005 Input: factor(1091225) Output: ? [5 2] [43649 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:28:15 2005 Input: factor(24) Output: ? [2 3] [3 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:32:32 2005 Input: factor(180) Output: ? [2 2] [3 2] [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:32:55 2005 Input: factor(1091225) Output: ? [5 2] [43649 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:33:27 2005 Input: factor(20484) Output: ? [2 2] [3 2] [569 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:34:52 2005 Input: factor(20) Output: ? [2 2] [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:35:14 2005 Input: factor(83447680) Output: ? [2 7] [5 1] [23 1] [5669 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:35:49 2005 Input: factor(38) Output: ? [2 1] [19 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:38:10 2005 Input: factor(5082) Output: ? [2 1] [3 1] [7 1] [11 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:39:13 2005 Input: nextprime(1091225) Output: ? 1091239 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:39:48 2005 Input: nextprime(1091000) Output: ? 1091003 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:39:59 2005 Input: nextprime(1091003) Output: ? 1091003 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:40:05 2005 Input: nextprime(1091003) Output: ? 1091003 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:40:26 2005 Input: nextprime(1091004) Output: ? 1091017 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:40:36 2005 Input: nextprime(1091018) Output: ? 1091021 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:40:56 2005 Input: nextprime(1091022) Output: ? 1091023 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:41:33 2005 Input: nextprime(83447680) Output: ? 83447681 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:41:51 2005 Input: nextprime(83447670) Output: ? 83447671 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:41:59 2005 Input: nextprime(83447672) Output: ? 83447681 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:42:44 2005 Input: gcd(1091225, 20484) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:43:59 2005 Input: gcd(20, 20484) Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:44:22 2005 Input: gcd(20, 20484, 1091225) Output: ? ? Errors (if any) and Timing Info: *** invalid flag in gcd. Timing: real 0m0.013s user 0m0.006s sys 0m0.005s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:45:00 2005 Input: lcm(20,38) Output: ? 380 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.008s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:45:25 2005 Input: lcm(5082,38) Output: ? 96558 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:45:53 2005 Input: lcm(5082,380) Output: ? 965580 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:47:05 2005 Input: Mod(1091225,20) Output: ? Mod(5, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:49:41 2005 Input: Mod(16,5) Output: ? Mod(1, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:52:07 2005 Input: Mod(83447680,20) Output: ? Mod(0, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:54:04 2005 Input: fibonacci(20) Output: ? 6765 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:55:57 2005 Input: fibonacci(20) Output: ? 6765 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:56:06 2005 Input: fibonacci(5) Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:56:32 2005 Input: fibonacci(7) Output: ? 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:56:42 2005 Input: fibonacci(8) Output: ? 21 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:57:04 2005 Input: fibonacci(15) Output: ? 610 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:58:22 2005 Input: fibonacci(19) Output: ? 4181 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:58:41 2005 Input: fibonacci(20) Output: ? 6765 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:59:00 2005 Input: fibonacci(30) Output: ? 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:59:13 2005 Input: fibonacci(35) Output: ? 9227465 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 02:59:49 2005 Input: fibonacci(32) Output: ? 2178309 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 03:00:00 2005 Input: fibonacci(31) Output: ? 1346269 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 03:00:10 2005 Input: fibonacci(30) Output: ? 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 03:00:32 2005 Input: fibonacci(5082) Output: ? 531744183704017632226844924726385488424863640988751065750144861500407248078054049079391095058417403385966229119979523369254452190633784155233348859743638745379445066036314201819506271463500365780882462136606626346918502903479450195939996828818238484376383940422946184238099710007969534155933187975077775488723327273308561557440503457483194198540695320186211799877618178513307841492565973356868881781371428764632856293020050784981964645311141724890521689568131131748952874988759741654549651135051885087287502653262012659239865372237192142654781075370392791597417229851717371309881250331580127944925332948471746526627712723176550416534055972858828079806033727156358006249074264846452821903872654178028291055361729367189518182924617811683738494287235869395515783887836860941574631318997351850307265061145750034905575122826796625595364148647274612943288106879268125424109579051669025878506792511475045406777139578068531722001416711122706961324893154048610031957474657376123995746024833509034651888343889476709221926469505093935528136241819755095296570027391623492216 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 03:01:58 2005 Input: prime(5082) Output: ? 49459 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 03:02:42 2005 Input: binomial(5082, 20) Output: ? 52277027457656332953444022766058979719802664521841084670 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.003s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 03:03:21 2005 Input: pi(32) Output: ? ? ? ? Errors (if any) and Timing Info: *** obsolete function: pi(32) ^------ For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: pi ===> Pi Pi=Pi(): the constant pi, with current precision. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 03:03:47 2005 Input: Pi(3) Output: ? ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: Pi(3) ^-- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 03:04:07 2005 Input: Pi=Pi(3) Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: Pi=Pi(3) ^------ Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 03:04:19 2005 Input: pi(3) Output: ? ? ? ? Errors (if any) and Timing Info: *** obsolete function: pi(3) ^----- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: pi ===> Pi Pi=Pi(): the constant pi, with current precision. Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 03:04:39 2005 Input: Pi=Pi() Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: Pi=Pi() ^----- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '210.84.' ************** PARI ***************** Host 210.84.233.204 (210.84.233.204) Time: Sun Mar 27 03:04:51 2005 Input: Pi Output: ? 3.1415926535897932384626433832795028841 ? ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.004s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 09:47:32 2005 Input: p=13 for(x=1, (p-1)/3, bernfrac(2x)) Output: ? 13 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...or(x=1,(p-1)/3,bernfrac(2x)) ^--- Timing: real 0m0.330s user 0m0.008s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 09:48:46 2005 Input: p=13 for(x=1, (p-3)/2, bernfrac(2x)) Output: ? 13 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...or(x=1,(p-3)/2,bernfrac(2x)) ^--- Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 09:56:24 2005 Input: p=37 for(i=1, (p-3)/2, bernfrac(2i)) Output: ? 37 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...or(i=1,(p-3)/2,bernfrac(2i)) ^--- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 09:58:18 2005 Input: p=37 for(i=1, (p-3)/2, print(bernfrac(2i))) Output: ? 37 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...,(p-3)/2,print(bernfrac(2i))) ^---- Timing: real 0m0.023s user 0m0.008s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 09:58:40 2005 Input: p=37 for(i=1, (p-3)/2, print(bernfrac(2*i))) Output: ? 37 ? 1/6 -1/30 1/42 -1/30 5/66 -691/2730 7/6 -3617/510 43867/798 -174611/330 854513/138 -236364091/2730 8553103/6 -23749461029/870 8615841276005/14322 -7709321041217/510 2577687858367/6 ? Errors (if any) and Timing Info: Timing: real 0m0.045s user 0m0.005s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 09:59:46 2005 Input: p=37 for(i=1, (p-3)/2, print(bernfrac(2i)) ) Output: ? 37 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...,(p-3)/2,print(bernfrac(2i))) ^---- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 10:00:06 2005 Input: p=37 for(i=1, (p-3)/2, print(bernfrac(2*i)) ) Output: ? 37 ? 1/6 -1/30 1/42 -1/30 5/66 -691/2730 7/6 -3617/510 43867/798 -174611/330 854513/138 -236364091/2730 8553103/6 -23749461029/870 8615841276005/14322 -7709321041217/510 2577687858367/6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 10:01:08 2005 Input: p=37 for(i=1, (p-3)/2, if(valuation(bernfrac(2*i), p)>0, print(2*i), print 0) ) Output: ? 37 ? 32 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '68.252.' ************** PARI ***************** Host 68.252.36.153 (68.252.36.153) Time: Sun Mar 27 10:01:13 2005 Input: for(i=1,(p-3)/2,print(bernfrac(2i))) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...,(p-3)/2,print(bernfrac(2i))) ^---- Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 10:01:22 2005 Input: p=37 for(i=1, (p-3)/2, if(valuation(bernfrac(2*i), p)>0, print(2*i), ) ) Output: ? 37 ? 32 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Sun Mar 27 10:01:45 2005 Input: p=59 for(i=1, (p-3)/2, if(valuation(bernfrac(2*i), p)>0, print(2*i), ) ) Output: ? 59 ? 44 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:12:08 2005 Input: Mod(2,9991)^256 Output: ? Mod(2680, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:12:31 2005 Input: Mod(2,9991)^512 Output: ? Mod(8862, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:12:45 2005 Input: Mod(2,1024)^512 Output: ? Mod(0, 1024) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:13:53 2005 Input: Mod(2,9991)^1024 Output: ? Mod(5784, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:14:11 2005 Input: Mod(2,9991)^8192 Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:15:35 2005 Input: Mod(36109512,9991) Output: ? Mod(2038, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:16:10 2005 Input: Mod(18060756,9991) Output: ? Mod(7019, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.001s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:16:41 2005 Input: Mod(18810920,9991) Output: ? Mod(7858, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:17:09 2005 Input: Mod(125728,9991) Output: ? Mod(5836, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:17:30 2005 Input: Mod(23344,9991) Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.007s sys 0m0.007s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:18:01 2005 Input: Mod(2,9991)^9990 Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:19:53 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.042s user 0m0.007s sys 0m0.005s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:20:29 2005 Input: Mod(113,462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:23:23 2005 Input: Mod(347,463)^256 Output: ? Mod(61, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:23:34 2005 Input: Mod(347,463)^64 Output: ? Mod(409, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:23:44 2005 Input: Mod(347,463)^2 Output: ? Mod(29, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:24:18 2005 Input: Mod(347,463)^323 Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:25:58 2005 Input: factor(588) Output: ? [2 2] [3 1] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:27:08 2005 Input: Mod(275,168)^(-1) Output: ? Mod(11, 168) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '155.41.' ************** PARI ***************** Host 155.41.134.97 (155.41.134.97) Time: Sun Mar 27 12:27:56 2005 Input: Mod(139,588)^11 Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:07:21 2005 Input: (2,9991)^(16) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (2,9991)^(16) ^----------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:08:05 2005 Input: Mod(2,9991)^(16) Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:13:18 2005 Input: Mod(2,9991)^(32) Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:13:32 2005 Input: Mod(2,9991)^(64) Output: ? Mod(158, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:13:47 2005 Input: Mod(2,9991)^(128) Output: ? Mod(4982, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:14:08 2005 Input: Mod(2,9991)^(256) Output: ? Mod(2680, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:14:21 2005 Input: Mod(2,9991)^(512) Output: ? Mod(8862, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:14:36 2005 Input: Mod(2,9991)^(1024) Output: ? Mod(5784, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:14:50 2005 Input: Mod(2,9991)^(2048) Output: ? Mod(4788, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:15:08 2005 Input: Mod(2,9991)^(4096) Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:15:25 2005 Input: Mod(2,9991)^(8192) Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:16:17 2005 Input: Mod(2,9991)^(9990) Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:17:38 2005 Input: factor(9991) Output: ? [97 1] [103 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:19:03 2005 Input: factor(643) Output: ? [643 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:19:22 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:20:47 2005 Input: Mod(113,462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:21:52 2005 Input: Mod(347,463)^(323) Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:22:47 2005 Input: factor(588) Output: ? [2 2] [3 1] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:24:12 2005 Input: Mod(275,252)^(-1) Output: ? Mod(11, 252) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:24:59 2005 Input: Mod(139,588)^(11) Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Sun Mar 27 18:25:56 2005 Input: Mod(559,588)^(275) Output: ? Mod(139, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Sun Mar 27 20:34:07 2005 Input: 16^2 Output: ? 256 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Sun Mar 27 20:34:51 2005 Input: Mod(256^2,9991) Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Sun Mar 27 20:35:11 2005 Input: Mod(5590^2,9991) Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '66.119.' ************** PARI ***************** Host 66.119.34.58 (66.119.34.58) Time: Sun Mar 27 20:35:29 2005 Input: Mod(6243^2,9991) Output: ? Mod(158, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '170.224' ************** PARI ***************** Host 170.224.224.154 (170.224.224.154) Time: Sun Mar 27 20:35:49 2005 Input: Mod(158^2,9991) Output: ? Mod(4982, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '170.224' ************** PARI ***************** Host 170.224.224.154 (170.224.224.154) Time: Sun Mar 27 20:36:29 2005 Input: Mod(4982^2,9991) Output: ? Mod(2680, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Sun Mar 27 20:36:56 2005 Input: Mod(2680^2,9991) Output: ? Mod(8862, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Sun Mar 27 20:37:42 2005 Input: Mod(8862^2,9991) Output: ? Mod(5784, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.003s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Sun Mar 27 20:38:01 2005 Input: Mod(5784^2,9991) Output: ? Mod(4788, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Sun Mar 27 20:38:21 2005 Input: Mod(4788^2,9991) Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Sun Mar 27 20:38:52 2005 Input: Mod(5590^2,9991) Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.006s sys 0m0.004s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Sun Mar 27 20:40:46 2005 Input: Mod(6243*5784,9991) Output: ? Mod(2038, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Sun Mar 27 20:41:03 2005 Input: Mod(8862*2680,9991) Output: ? Mod(1553, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Sun Mar 27 20:41:29 2005 Input: Mod(2038*1553,9991) Output: ? Mod(7858, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Sun Mar 27 20:41:49 2005 Input: Mod(7858*64,9991) Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Sun Mar 27 20:42:09 2005 Input: Mod(2^9990,9991) Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '170.224' ************** PARI ***************** Host 170.224.224.154 (170.224.224.154) Time: Sun Mar 27 20:47:35 2005 Input: Mod(347^43,463) Output: ? Mod(198, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '170.224' ************** PARI ***************** Host 170.224.224.154 (170.224.224.154) Time: Sun Mar 27 20:48:11 2005 Input: Mod(198^113,463) Output: ? Mod(183, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '170.224' ************** PARI ***************** Host 170.224.224.122 (170.224.224.122) Time: Sun Mar 27 20:49:01 2005 Input: eulerphi(347) Output: ? 346 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.007s sys 0m0.007s '170.224' ************** PARI ***************** Host 170.224.224.90 (170.224.224.90) Time: Sun Mar 27 20:49:28 2005 Input: eulerphi(463) Output: ? 462 ? Errors (if any) and Timing Info: Timing: real 0m0.038s user 0m0.006s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Mar 27 20:52:51 2005 Input: (((11^31) * ((11^31)-1))/4 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (((11^31)*((11^31)-1))/4 ^ Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Mar 27 20:53:16 2005 Input: ((11^31) * ((11^31)-1))/4 Output: ? 18421139192255795024254182369296769893949345236294982288207183955/2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Mar 27 20:54:08 2005 Input: ((11^31) * ((11^31)-1))/4 ((11^31) * ((11^31)-1))/4 Output: ? 18421139192255795024254182369296769893949345236294982288207183955/2 ? 18421139192255795024254182369296769893949345236294982288207183955/2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Mar 27 20:54:18 2005 Input: ((11^31) * ((11^31)-1))/4 ((13^31) * ((13^31)-1))/4 Output: ? 18421139192255795024254182369296769893949345236294982288207183955/2 ? 290019935548463126228786627845511848621705400747317617801064298680533 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Sun Mar 27 20:58:51 2005 Input: eulerphi(588) Output: ? 168 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Sun Mar 27 20:59:22 2005 Input: Mod(347^(-139),463) Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '66.119.' ************** PARI ***************** Host 66.119.33.186 (66.119.33.186) Time: Sun Mar 27 20:59:31 2005 Input: Mod(37^(113),463) Output: ? Mod(347, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.006s sys 0m0.005s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Sun Mar 27 21:04:10 2005 Input: Mod(139^(-18),588) Output: ? Mod(169, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '216.148' ************** PARI ***************** Host 216.148.246.154 (216.148.246.154) Time: Sun Mar 27 21:04:31 2005 Input: Mod(169^(275),588) Output: ? Mod(337, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '170.224' ************** PARI ***************** Host 170.224.224.154 (170.224.224.154) Time: Sun Mar 27 21:05:24 2005 Input: Mod(139^(11),588) Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '170.224' ************** PARI ***************** Host 170.224.224.154 (170.224.224.154) Time: Sun Mar 27 21:05:43 2005 Input: Mod(559^(275),588) Output: ? Mod(139, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Mar 28 02:22:05 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=472772146107435302536223071973048224632914695302097116459852171130520711256363590397527; c=212345662943758545067169301096268515484624529363308726156734078284873783382724426446282196329271699502779022902918350368480252788809324100652720924774005376313909883241824712025892282168604960987928377282832388754925910899; gcd(a,c) gcd(b,c) Output: ? ? ? ? 1 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Mar 28 02:22:23 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=472772146107435302536223071973048224632914695302097116459852171130520711256363590397527; c=60945478760874683200169345358853307939864868097713506528314916458543499768626982290442322010195019240444873039043924635006434202497283315503491047520025102011126267427114871891725804351900753860451217776109918391255866850; gcd(a,c) gcd(b,c) Output: ? ? ? ? 1 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.007s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Mar 28 02:22:45 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=472772146107435302536223071973048224632914695302097116459852171130520711256363590397527; c=151400184182883861866999955737415207544759661265595219628419161826330283614097444155839874319076680262334149863874425733473818586312040785149229877253980274302783615814709840134166477816704207127477159506722470363670044050; gcd(a,c) gcd(b,c) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.216s user 0m0.011s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Mar 28 02:23:03 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=472772146107435302536223071973048224632914695302097116459852171130520711256363590397527; c=151400184182883861866999955737415207544759661265595219628419161826330283614097444155839874319076680262334149863874425733473818586312040785149229877253980274302783615814709840134166477816704207127477159506722470363670044050; gcd(a,c) c/a gcd(b,c) Output: ? ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? 190312349650240737471527206434482581085847482569182851927561244374625989300063650797550 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Mar 28 02:24:50 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=(2^(2*1485))-1; gcd(a,b); Output: ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Mar 28 02:25:00 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=(2^(2*1485))-1; gcd(a,b) Output: ? ? ? 795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Mar 28 02:25:15 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=(2^(2*1485))-1; mod(a,b) Output: ? ? ? ? Errors (if any) and Timing Info: *** obsolete function: mod(a,b) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.024s user 0m0.004s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Mar 28 02:25:43 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=(2^(2*1485))-1; lcm(a,b) Output: ? ? ? 1145742761121240609261727717962816836909124530606748271515702855922336504435793448961675230263353753446070150708827939730615247209461626432449633704559270601007118216115837001626401506468058253566384993716847971469568534116906742577825757448755847641074374931688106564641458437267436185203225273643943246368899664537497721010760230110712927209541895219035298077281239535959818681686640124584483486118249511125948371602167122704099905126601210566490155265174599964124603838205077733436571837198685346938461818233300649656992276955567624946611691448648164628264970933564082302162712486699038734053863145412070439638775507932234009641728158168271029252653340096757044174401128814295520457980690869733699066980914065706180707160772748483961678416209409095825295600954136215345154193854556540899907240802888456267653707413716247144694720137169095585692906878117368719446547246809594705490276383719423 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Mar 28 02:26:03 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=(2^(2*1485))-1; b/a lcm(a,b) Output: ? ? ? 1440216193530818249802280565999746172651883604876736962348995813438040216009565339423513525669459410985082212851332545157936839526843410065057392743173231355008473573486517212888597315405346791121384577009608549396802605204496069170582986972342043757303568455572568077716357777626531743069658453666912418165800767312879629887353644481536400875516161453488680300395516487313128054577970163689764308020739197769619771403504156140770872975316385329091250895254097968775407724948115817636001705350037224962404272860406323892419016905255085802615182873860741094323520653522486563064264876354960525441667783792886443935956442880653636098270382950024743232142194639939908858111686435231031959462755200524589411309274466390517573372156159260528175108107097367913831233 ? 1145742761121240609261727717962816836909124530606748271515702855922336504435793448961675230263353753446070150708827939730615247209461626432449633704559270601007118216115837001626401506468058253566384993716847971469568534116906742577825757448755847641074374931688106564641458437267436185203225273643943246368899664537497721010760230110712927209541895219035298077281239535959818681686640124584483486118249511125948371602167122704099905126601210566490155265174599964124603838205077733436571837198685346938461818233300649656992276955567624946611691448648164628264970933564082302162712486699038734053863145412070439638775507932234009641728158168271029252653340096757044174401128814295520457980690869733699066980914065706180707160772748483961678416209409095825295600954136215345154193854556540899907240802888456267653707413716247144694720137169095585692906878117368719446547246809594705490276383719423 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Mon Mar 28 02:31:52 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=(2^(2*1485))-1; b/a lcm(a,5972542421912159) Output: ? ? ? 1440216193530818249802280565999746172651883604876736962348995813438040216009565339423513525669459410985082212851332545157936839526843410065057392743173231355008473573486517212888597315405346791121384577009608549396802605204496069170582986972342043757303568455572568077716357777626531743069658453666912418165800767312879629887353644481536400875516161453488680300395516487313128054577970163689764308020739197769619771403504156140770872975316385329091250895254097968775407724948115817636001705350037224962404272860406323892419016905255085802615182873860741094323520653522486563064264876354960525441667783792886443935956442880653636098270382950024743232142194639939908858111686435231031959462755200524589411309274466390517573372156159260528175108107097367913831233 ? 4751368076635190108294542905007443033970439194680147310583115390993411997872502522006253181492807104856008747283853744244685031635167849920810939474529 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:43:50 2005 Input: isprime(1169) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:44:01 2005 Input: isprime(7) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.080s user 0m0.006s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:44:10 2005 Input: isprime(12) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:44:56 2005 Input: factor(24) Output: ? [2 3] [3 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:45:17 2005 Input: factor(8) Output: ? [2 3] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:45:24 2005 Input: factor(24) Output: ? [2 3] [3 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:45:38 2005 Input: factor(1000) Output: ? [2 3] [5 3] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:46:23 2005 Input: prime(2) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:46:30 2005 Input: prime(1) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:46:38 2005 Input: prime(5083) Output: ? 49463 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:47:57 2005 Input: prime(5083) Output: ? 49463 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:49:46 2005 Input: binomial(5,2) Output: ? 10 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.004s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:50:19 2005 Input: binomial(5083,22) Output: ? 2911462227124472434451787680948098252817233007220760383890610 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:51:37 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:52:48 2005 Input: pi*10 Output: ? 10*pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:55:40 2005 Input: pi= Output: ? ? Errors (if any) and Timing Info: *** unexpected character: pi= ^ Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:57:52 2005 Input: GP-PARI Output: ? GP - PARI ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.002s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:58:29 2005 Input: GP-PARI Output: ? GP - PARI ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:59:01 2005 Input: GP-PARI isprime(1169) Output: ? GP - PARI ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.038s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:59:12 2005 Input: GP-PARI isprime(19) Output: ? GP - PARI ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:59:29 2005 Input: GP-PARI isprime(15) Output: ? GP - PARI ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 03:59:44 2005 Input: GP-PARI isprime(15) nextprime(100) Output: ? GP - PARI ? 0 ? 101 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:00:12 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(1067960) Output: ? GP - PARI ? 0 ? 101 ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:00:23 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(151281) Output: ? GP - PARI ? 0 ? 101 ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:00:35 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(151281) Output: ? GP - PARI ? 0 ? 101 ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.159s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:00:57 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(151281) isprime(23) Output: ? GP - PARI ? 0 ? 101 ? 0 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:01:10 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(151281) isprime(82805278) Output: ? GP - PARI ? 0 ? 101 ? 0 ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:01:22 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(151281) isprime(17) Output: ? GP - PARI ? 0 ? 101 ? 0 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:01:31 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(151281) isprime(5108) Output: ? GP - PARI ? 0 ? 101 ? 0 ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:02:06 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(151281) isprime(5108) factor(24) Output: ? GP - PARI ? 0 ? 101 ? 0 ? 0 ? [2 3] [3 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:02:53 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(151281) isprime(5108) factor(1067960) Output: ? GP - PARI ? 0 ? 101 ? 0 ? 0 ? [2 3] [5 1] [26699 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:03:23 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(151281) isprime(5108) factor(1067960) factor(151281) Output: ? GP - PARI ? 0 ? 101 ? 0 ? 0 ? [2 3] [5 1] [26699 1] ? [3 3] [13 1] [431 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:03:40 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(151281) isprime(5108) factor(1067960) factor(23) Output: ? GP - PARI ? 0 ? 101 ? 0 ? 0 ? [2 3] [5 1] [26699 1] ? [23 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:03:43 2005 Input: p Output: ? p ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:03:55 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(151281) isprime(5108) factor(1067960) factor(82805278) Output: ? GP - PARI ? 0 ? 101 ? 0 ? 0 ? [2 3] [5 1] [26699 1] ? [2 1] [31 1] [571 1] [2339 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:04:07 2005 Input: sigma(10) Output: ? 18 ? Errors (if any) and Timing Info: Timing: real 0m0.111s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:04:16 2005 Input: pi(10) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: pi(10) ^------ For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: pi ===> Pi Pi=Pi(): the constant pi, with current precision. Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:04:27 2005 Input: Pi Output: ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:04:37 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(151281) isprime(5108) factor(1067960) factor(17) Output: ? GP - PARI ? 0 ? 101 ? 0 ? 0 ? [2 3] [5 1] [26699 1] ? [17 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:04:52 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(151281) isprime(5108) factor(82805278) Output: ? GP - PARI ? 0 ? 101 ? 0 ? 0 ? [2 1] [31 1] [571 1] [2339 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:05:12 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(151281) isprime(5108) factor(17) Output: ? GP - PARI ? 0 ? 101 ? 0 ? 0 ? [17 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:05:20 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(151281) isprime(5108) factor(5108) Output: ? GP - PARI ? 0 ? 101 ? 0 ? 0 ? [2 2] [1277 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:05:56 2005 Input: fibonacci(10) Output: ? 55 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:06:31 2005 Input: GP-PARI isprime(15) nextprime(100) isprime(151281) isprime(5108) factor(5108) nextprime(1067960) Output: ? GP - PARI ? 0 ? 101 ? 0 ? 0 ? [2 2] [1277 1] ? 1067987 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:06:43 2005 Input: GP-PARI Output: ? GP - PARI ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:06:49 2005 Input: nextprime(10) Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:06:56 2005 Input: prevprime(10) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: prevprime(10) ^------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:07:01 2005 Input: GP-PARI nextprime(1067960) Output: ? GP - PARI ? 1067987 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:07:09 2005 Input: prevprime(1097012) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: prevprime(1097012) ^------------------ Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:07:16 2005 Input: nextprime(1097012) Output: ? 1097017 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:07:45 2005 Input: GP-PARI nextprime(82805278) Output: ? GP - PARI ? 82805323 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:08:17 2005 Input: GP-PARI prevprime(82805278) Output: ? GP - PARI ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: prevprime(82805278) ^------------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:09:13 2005 Input: GP-PARI nextprime(82805270) Output: ? GP - PARI ? 82805273 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:09:30 2005 Input: GP-PARI nextprime(82805273) Output: ? GP - PARI ? 82805273 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:09:34 2005 Input: GP-PARI nextprime(82805273) Output: ? GP - PARI ? 82805273 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:09:47 2005 Input: GP-PARI nextprime(82805273) Output: ? GP - PARI ? 82805273 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:09:53 2005 Input: GP-PARI nextprime(82805272) Output: ? GP - PARI ? 82805273 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:09:59 2005 Input: GP-PARI nextprime(82805274) Output: ? GP - PARI ? 82805323 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:10:12 2005 Input: GP-PARI nextprime(82805270) Output: ? GP - PARI ? 82805273 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:10:27 2005 Input: GP-PARI nextprime(82805273) Output: ? GP - PARI ? 82805273 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:10:36 2005 Input: GP-PARI nextprime(82805274) Output: ? GP - PARI ? 82805323 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:10:47 2005 Input: GP-PARI nextprime(82805270) Output: ? GP - PARI ? 82805273 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:11:12 2005 Input: GP-PARI nextprime(1067950) Output: ? GP - PARI ? 1067951 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:11:19 2005 Input: GP-PARI nextprime(1067952) Output: ? GP - PARI ? 1067987 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:11:33 2005 Input: GP-PARI nextprime(1067950) Output: ? GP - PARI ? 1067951 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:11:53 2005 Input: GP-PARI isprime(1067950) Output: ? GP - PARI ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:11:59 2005 Input: GP-PARI isprime(1067951) Output: ? GP - PARI ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:12:05 2005 Input: GP-PARI isprime(1067953) Output: ? GP - PARI ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:12:10 2005 Input: GP-PARI isprime(1067957) Output: ? GP - PARI ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:12:15 2005 Input: GP-PARI isprime(1067959) Output: ? GP - PARI ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:12:21 2005 Input: GP-PARI isprime(1067960) Output: ? GP - PARI ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:12:32 2005 Input: GP-PARI isprime(1067987) Output: ? GP - PARI ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:12:42 2005 Input: GP-PARI isprime(82805273) Output: ? GP - PARI ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:12:47 2005 Input: GP-PARI isprime(82805275) Output: ? GP - PARI ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:12:51 2005 Input: GP-PARI isprime(82805277) Output: ? GP - PARI ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.000s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:12:56 2005 Input: GP-PARI isprime(82805279) Output: ? GP - PARI ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:13:19 2005 Input: GP-PARI gcd(1067960,151281) Output: ? GP - PARI ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:13:29 2005 Input: GP-PARI gcd(23,151281) Output: ? GP - PARI ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:13:41 2005 Input: GP-PARI gcd(23,151281,1067960) Output: ? GP - PARI ? ? Errors (if any) and Timing Info: *** invalid flag in gcd. Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:13:48 2005 Input: GP-PARI gcd(23,1067960) Output: ? GP - PARI ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:14:15 2005 Input: GP-PARI lcm(23,17) Output: ? GP - PARI ? 391 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:14:31 2005 Input: GP-PARI lcm(17,5108) Output: ? GP - PARI ? 86836 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:14:57 2005 Input: GP-PARI lcm(23,5108) Output: ? GP - PARI ? 117484 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:15:11 2005 Input: GP-PARI lcm(23,5108,17) Output: ? GP - PARI ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: lcm(23,5108,17) ^---- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:15:18 2005 Input: GP-PARI lcm(23,5108) Output: ? GP - PARI ? 117484 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:16:06 2005 Input: GP-PARI lcm(86836,117484) Output: ? GP - PARI ? 1997228 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:16:25 2005 Input: GP-PARI lcm(86836,391) Output: ? GP - PARI ? 1997228 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:16:29 2005 Input: GP-PARI lcm(86836,391) Output: ? GP - PARI ? 1997228 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:16:40 2005 Input: GP-PARI lcm(86836,117484) Output: ? GP - PARI ? 1997228 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:18:01 2005 Input: GP-PARI MOd(23,1067960) Output: ? GP - PARI ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: MOd(23,1067960) ^--------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:18:09 2005 Input: GP-PARI Mod(23,1067960) Output: ? GP - PARI ? Mod(23, 1067960) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:18:36 2005 Input: GP-PARI Mod(16,5) Output: ? GP - PARI ? Mod(1, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:19:37 2005 Input: GP-PARI Mod(1067960,23) Output: ? GP - PARI ? Mod(1, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:20:12 2005 Input: GP-PARI Mod(82805278,23) Output: ? GP - PARI ? Mod(11, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:21:14 2005 Input: GP-PARI fibonacci(10) Output: ? GP - PARI ? 55 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:22:03 2005 Input: GP-PARI fibonacci(1067960) Output: ? GP - PARI ? 1232526782380185540488657035703562981561225360630401203902629673351996712525475653983444628703284552363850046660083633002718893980122143265842353817053199780793479037045174950560181007256928943795832219172762749586699453162350169897516739296097062815606720479629621546831243018984133935711322337276707493278598878703568937983922773015420361001698969310592724473230131301193654745248381285696289814697458673488174817574696064076776698648498953869120811983767563298837963090324293869390149591825801166485123645125318609984658759067158843906540980489058383836780246484802030195551452978107371817582411639275123827994764665458334111824269905254552767404467916294418216935478066070934284357482699339457861635316094300013342135250521653525257950444275120087562949734864268665475243740363193358815803658651885347721423002896223736184864050396895425684956362621642185183846434302470936604798235913802484131489169128568647011557922024483380486159051328591511140684292284870753220859874924041103769664623520805298638370699606811000171194742157109917893283142364481986850555434704717980745326094645129714283751668198758220846181206112784507760699643808353063096076614602441618499494267847042355650701201280258500350978859064836833076876335685641270898352336499693147534213887630455180430196527967666719007754162105085251603486899531737690189082865358593728166810192755047916394304736186363690804843499508659423426458029665683903704630600931997342504090389331201781529932870447255763200640587775159433406242712501192945821664810264896770956998416438537569088814713011554034847197645902553125025425499090992262944732458007673676055856443777331303362674467501083804156517160157277190717723262557823705273444196866794958967623873419785049644078951952849837597107431880562846638693537385511282953674340900833949488053960204823435658843807268281452849607903097644701538410309794149498396196060992334455002834629239352224697580358625212710990041005181508295109328774527921915930554257873860418939917518645828392479669330895962983012811949361543035671237479393202125649790538534188056288754349013070943483115374319907241144252307483971441093147470471818604008922618980939361279186208835445996043855167634466095967492887090353174879108429151305575181579797523348606189811234691465901685149977234689071676590443949595790174834047383847776202376265017434236960714472321401365600361691117557234898788844331871864458326376517802022393390474709770620983482703229428673493746267022131698314895427728890618145556633982741613740729753927155609197307567391020657551183544431911779911611596784399787495307259436501082567212795794338143276901534701967048391574043651116502683769306646610528811346877100246872982502656985015619402944682384257794029680372173698298566517763584898678824146085548875666464517154666477440502222703878596635359026500397773313868930911513075006224947469701293244414740311875435571725540638457258742238783658093413703787265826886191686267487579481693199298083575919926394393513803696523648465864791463359718014358658508810568556914041071793519940846600640560091489564311227304193262538113915957252948676647790885512212762595947966186727610789760651537926412402133512561518017602917133157135663922[+++] ? Errors (if any) and Timing Info: Timing: real 0m11.001s user 0m10.973s sys 0m0.016s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:22:18 2005 Input: GP-PARI fibonacci(23) Output: ? GP - PARI ? 28657 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:22:39 2005 Input: GP-PARI fibonacci(11) Output: ? GP - PARI ? 89 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:22:47 2005 Input: GP-PARI fibonacci(2) Output: ? GP - PARI ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:22:53 2005 Input: GP-PARI fibonacci(5) Output: ? GP - PARI ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:22:58 2005 Input: GP-PARI fibonacci(6) Output: ? GP - PARI ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:23:06 2005 Input: GP-PARI fibonacci(8) Output: ? GP - PARI ? 21 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:23:12 2005 Input: GP-PARI fibonacci(9) Output: ? GP - PARI ? 34 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:23:57 2005 Input: GP-PARI fibonacci(8) Output: ? GP - PARI ? 21 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:24:02 2005 Input: GP-PARI fibonacci(10) Output: ? GP - PARI ? 55 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:24:13 2005 Input: GP-PARI fibonacci(15) Output: ? GP - PARI ? 610 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:24:23 2005 Input: GP-PARI fibonacci(20) Output: ? GP - PARI ? 6765 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:24:29 2005 Input: GP-PARI fibonacci(16) Output: ? GP - PARI ? 987 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:24:35 2005 Input: GP-PARI fibonacci(18) Output: ? GP - PARI ? 2584 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:24:41 2005 Input: GP-PARI fibonacci(19) Output: ? GP - PARI ? 4181 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:24:51 2005 Input: GP-PARI fibonacci(20) Output: ? GP - PARI ? 6765 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:24:57 2005 Input: GP-PARI fibonacci(30) Output: ? GP - PARI ? 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:25:04 2005 Input: GP-PARI fibonacci(40) Output: ? GP - PARI ? 102334155 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:25:13 2005 Input: GP-PARI fibonacci(32) Output: ? GP - PARI ? 2178309 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:25:21 2005 Input: GP-PARI fibonacci(31) Output: ? GP - PARI ? 1346269 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:25:30 2005 Input: GP-PARI fibonacci(30) Output: ? GP - PARI ? 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:25:56 2005 Input: GP-PARI fibonacci(5108) Output: ? GP - PARI ? 144338236455210704759453179434128591958670239037883988352929702937711436856749868595539899345466060509829993908736571858173304797777463084113621139824427045790789166985541862459722477151141447112534974208891626249188704587645260183346464484722991723973108390267950591740365738655194351993920241208351895367101244916813533433327682481612836030579421793910045709873137049006524460267539473423065415405890257812466181189403609326630961946795367291123199883739719754843406420520073412155907135321820689179014723880198559111948811580605745139148117797465182644719922822227733796914065830064638961455560254995179867592006077676285745224634224245374897111468344460733908354379197219075449095447513780138548411073744388849256095369129981851828354890863055328388825703156943489498766064672124279358861642690003973705595778425222555150367357508830267921554777903415537834239595912324749557514283549654695776597750596196502240665622643906501623479737883749969244451060391091794681043349261418907608778358754777452067324468194496188909600376762060698069917550989635577281863250221 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:27:28 2005 Input: GP-PARI prime(5) Output: ? GP - PARI ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:27:43 2005 Input: GP-PARI prime(6) Output: ? GP - PARI ? 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:27:49 2005 Input: GP-PARI prime(5108) Output: ? GP - PARI ? 49741 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:28:31 2005 Input: GP-PARI isprime(49741) Output: ? GP - PARI ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:29:02 2005 Input: GP-PARI binomial(5108,23) Output: ? GP - PARI ? 717354266004445006387974261521400269301297251537179819479564960 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:29:48 2005 Input: GP-PARI pi Output: ? GP - PARI ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:29:57 2005 Input: GP-PARI pi Output: ? GP - PARI ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:30:29 2005 Input: GP-PARI pi Output: ? GP - PARI ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.010s sys 0m0.001s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:31:32 2005 Input: GP-PARI pi pi Output: ? GP - PARI ? pi ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:31:58 2005 Input: GP-PARI pi pi; Output: ? GP - PARI ? pi ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:32:46 2005 Input: GP-PARI precision=100 pi Output: ? GP - PARI ? ? pi ? Errors (if any) and Timing Info: *** expected character: '(' instead of: precision=100 ^---- Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:32:52 2005 Input: GP-PARI precision=100 Output: ? GP - PARI ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: precision=100 ^---- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:33:17 2005 Input: GP-PARI precison=100 Output: ? GP - PARI ? 100 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:33:22 2005 Input: GP-PARI precison=100 pi Output: ? GP - PARI ? 100 ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.009s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:33:28 2005 Input: GP-PARI precison=100 pi Output: ? GP - PARI ? 100 ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:33:42 2005 Input: GP-PARI precison=40 pi Output: ? GP - PARI ? 40 ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:33:46 2005 Input: GP-PARI precison=40 pi Output: ? GP - PARI ? 40 ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:33:58 2005 Input: GP-PARI precison=10 pi Output: ? GP - PARI ? 10 ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:34:03 2005 Input: GP-PARI precison=10 pi Output: ? GP - PARI ? 10 ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:41:44 2005 Input: GP-PARI pi Output: ? GP - PARI ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:42:06 2005 Input: GP-PARI binomial(5108,23) Output: ? GP - PARI ? 717354266004445006387974261521400269301297251537179819479564960 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:44:16 2005 Input: GP-PARI Output: ? GP - PARI ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:44:31 2005 Input: GP-PARI precison=40 Output: ? GP - PARI ? 40 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:44:37 2005 Input: GP-PARI precison=40 pi Output: ? GP - PARI ? 40 ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:44:44 2005 Input: GP-PARI precison=40 =pi Output: ? GP - PARI ? 40 ? ? Errors (if any) and Timing Info: *** unexpected character: =pi ^--- Timing: real 0m0.713s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:44:55 2005 Input: GP-PARI precison=40 (pi) Output: ? GP - PARI ? 40 ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:45:31 2005 Input: GP-PARI precison=40 f(pi) Output: ? GP - PARI ? 40 ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: f(pi) ^ Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Mar 28 04:45:37 2005 Input: GP-PARI precison=40 pi Output: ? GP - PARI ? 40 ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.251.56 (128.197.251.56) Time: Mon Mar 28 11:38:08 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.329s user 0m0.005s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.150.196 (128.197.150.196) Time: Mon Mar 28 12:33:08 2005 Input: Mod(105,8) Output: ? Mod(1, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.150.196 (128.197.150.196) Time: Mon Mar 28 12:33:45 2005 Input: Mod(2240,9) Output: ? Mod(8, 9) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.196 (128.197.150.196) Time: Mon Mar 28 12:34:57 2005 Input: Mod(189,10) Output: ? Mod(9, 10) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.196 (128.197.150.196) Time: Mon Mar 28 12:36:22 2005 Input: Mod(385,12) Output: ? Mod(1, 12) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.196 (128.197.150.196) Time: Mon Mar 28 12:38:40 2005 Input: Mod(19305,14) Output: ? Mod(13, 14) ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.005s sys 0m0.008s '155.207' ************** PARI ***************** Host 155.207.120.6 (155.207.120.6) Time: Mon Mar 28 12:39:55 2005 Input: > R := PolynomialRing(Integers()); > K := NumberField(x^4 - 10*x^2 +1); > UnitEquation(a, a, a); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: >R:=PolynomialRin ^-------------------- *** unexpected character: >K:=NumberField(x ^-------------------- *** unexpected character: >UnitEquation(a,a,a) ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.196 (128.197.150.196) Time: Mon Mar 28 12:40:34 2005 Input: Mod(896896,15) Output: ? Mod(1, 15) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Mon Mar 28 12:46:31 2005 Input: forprime(x=1, 200, for(i=1,(p-3)/2,if(valuation(bernfrac(2*i),p)>0,print(2*i),))) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.031s user 0m0.007s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Mon Mar 28 12:46:49 2005 Input: forprime(p=1, 200, for(i=1,(p-3)/2,if(valuation(bernfrac(2*i),p)>0,print(2*i),))) Output: ? 32 44 58 68 24 22 130 62 110 ? Errors (if any) and Timing Info: Timing: real 0m0.444s user 0m0.417s sys 0m0.010s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Mon Mar 28 12:46:58 2005 Input: forprime(p=1, 200, for(i=1,(p-3)/2,if(valuation(bernfrac(2*i),p)>0,print(p, 2*i),))) Output: ? 3732 5944 6758 10168 10324 13122 149130 15762 157110 ? Errors (if any) and Timing Info: Timing: real 0m0.423s user 0m0.415s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Mon Mar 28 12:47:21 2005 Input: forprime(p=1, 200, for(i=1,(p-3)/2,if(valuation(bernfrac(2*i),p)>0,printp(p, 2*i),))) Output: ? 3732 5944 6758 10168 10324 13122 149130 15762 157110 ? Errors (if any) and Timing Info: Timing: real 0m0.428s user 0m0.418s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Mon Mar 28 12:47:41 2005 Input: forprime(p=1, 200, for(i=1,(p-3)/2,if(valuation(bernfrac(2*i),p)>0,printp(p;2*i),))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...rnfrac(2*i),p)>0,printp(p;2*i),))) ^--------- Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Mon Mar 28 12:48:14 2005 Input: forprime(p=1, 200, for(i=1,(p-3)/2,if(valuation(bernfrac(2*i),p)>0,print(p} print(2*i) print(),))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...ernfrac(2*i),p)>0,print(p}print(2*i)print(),) ^-------------------- Timing: real 0m0.023s user 0m0.007s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Mon Mar 28 12:48:55 2005 Input: forprime(p=1, 200, for(i=1,(p-3)/2,if(valuation(bernfrac(2*i),p)>0,print(p_2*i),))) Output: ? 16*p_2 22*p_2 29*p_2 34*p_2 12*p_2 11*p_2 65*p_2 31*p_2 55*p_2 ? Errors (if any) and Timing Info: Timing: real 0m0.428s user 0m0.420s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Mon Mar 28 12:50:31 2005 Input: forprime(p=1, 200, for(i=1,(p-3)/2,if(valuation(bernfrac(2*i),p)>0,print(p 2*i),))) Output: ? ? 2*i ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...ernfrac(2*i),p)>0,print(p ^ *** Warning: unused characters: ),))). Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Mon Mar 28 12:51:00 2005 Input: forprime(p=1, 200, for(i=1,(p-3)/2,if(valuation(bernfrac(2*i),p)>0,print(p) && print(2*i),))) Output: ? 37 59 67 101 103 131 149 157 157 ? Errors (if any) and Timing Info: Timing: real 0m0.428s user 0m0.417s sys 0m0.010s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Mon Mar 28 12:51:13 2005 Input: forprime(p=1, 200, for(i=1,(p-3)/2,if(valuation(bernfrac(2*i),p)>0,print(p & 2*i),))) Output: ? 1 1 1 1 1 1 1 1 1 ? Errors (if any) and Timing Info: Timing: real 0m0.423s user 0m0.416s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Mon Mar 28 12:51:24 2005 Input: forprime(p=1, 200, for(i=1,(p-3)/2,if(valuation(bernfrac(2*i),p)>0,print(p ; 2*i),))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...ernfrac(2*i),p)>0,print(p;2*i),))) ^--------- Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Mon Mar 28 12:51:32 2005 Input: forprime(p=1, 200, for(i=1,(p-3)/2,if(valuation(bernfrac(2*i),p)>0,print(p tab 2*i),))) Output: ? 16*ptab2 22*ptab2 29*ptab2 34*ptab2 12*ptab2 11*ptab2 65*ptab2 31*ptab2 55*ptab2 ? Errors (if any) and Timing Info: Timing: real 0m0.426s user 0m0.422s sys 0m0.004s '155.207' ************** PARI ***************** Host 155.207.120.6 (155.207.120.6) Time: Mon Mar 28 12:55:16 2005 Input: > R := PolynomialRing(Integers()); > K := NumberField(x^4-10*x^2+1); > O := MaximalOrder(K); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: >R:=PolynomialRin ^-------------------- *** unexpected character: >K:=NumberField(x ^-------------------- *** unexpected character: >O:=MaximalOrder(K); ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '134.7.2' ************** PARI ***************** Host 134.7.248.137 (134.7.248.137) Time: Mon Mar 28 13:16:32 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.005s sys 0m0.007s '128.194' ************** PARI ***************** Host 128.194.177.108 (128.194.177.108) Time: Mon Mar 28 17:59:08 2005 Input: 1<<34 Output: ? 17179869184 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.004s '128.194' ************** PARI ***************** Host 128.194.177.108 (128.194.177.108) Time: Mon Mar 28 18:01:04 2005 Input: 2<<34 Output: ? 34359738368 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.194' ************** PARI ***************** Host 128.194.177.108 (128.194.177.108) Time: Mon Mar 28 18:02:56 2005 Input: 2<<3 Output: ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:28:33 2005 Input: Mod(2, 9991)^32 Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:28:50 2005 Input: Mod(2, 9991)^64 Output: ? Mod(158, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:29:15 2005 Input: Mod(2, 9991)^128 Output: ? Mod(4982, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.003s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:29:30 2005 Input: Mod(2, 9991)^256 Output: ? Mod(2680, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:29:44 2005 Input: Mod(2, 9991)^512 Output: ? Mod(8862, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:29:55 2005 Input: Mod(2, 9991)^1024 Output: ? Mod(5784, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:30:09 2005 Input: Mod(2, 9991)^2048 Output: ? Mod(4788, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:30:21 2005 Input: Mod(2, 9991)^4196 Output: ? Mod(1655, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:30:37 2005 Input: Mod(2, 9991)^8392 Output: ? Mod(1491, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:32:26 2005 Input: Mod(1491*5784*8862*6243*5590*256*16*4, 9991) Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:32:41 2005 Input: factor(9991) Output: ? [97 1] [103 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:44:28 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:45:14 2005 Input: Mod(113, 460)^(-1) Output: ? Mod(57, 460) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:46:17 2005 Input: Mod(347, 463)^(113*57) Output: ? Mod(106, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:47:24 2005 Input: factor(588) Output: ? [2 2] [3 1] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:50:06 2005 Input: Mod(275, 168)^(-1) Output: ? Mod(11, 168) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 19:51:13 2005 Input: Mod(139, 588)^(11*275) Output: ? Mod(139, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '24.218.' ************** PARI ***************** Host 24.218.25.123 (24.218.25.123) Time: Mon Mar 28 20:26:07 2005 Input: Mod(2, 5986)^(-1) Output: ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(2, 5986). Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.239.26 (168.122.239.26) Time: Mon Mar 28 20:54:18 2005 Input: Mod(5^2,19) Output: ? Mod(6, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.239.26 (168.122.239.26) Time: Mon Mar 28 20:54:24 2005 Input: Mod(6^2,19) Output: ? Mod(17, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.239.26 (168.122.239.26) Time: Mon Mar 28 20:54:27 2005 Input: Mod(7^2,19) Output: ? Mod(11, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.239.26 (168.122.239.26) Time: Mon Mar 28 20:54:45 2005 Input: Mod(8^2,19) Output: ? Mod(7, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.239.26 (168.122.239.26) Time: Mon Mar 28 20:54:50 2005 Input: Mod(9^2,19) Output: ? Mod(5, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.239.26 (168.122.239.26) Time: Mon Mar 28 20:54:59 2005 Input: Mod(10^2,19) Output: ? Mod(5, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.239.26 (168.122.239.26) Time: Mon Mar 28 20:56:14 2005 Input: QR(19) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: QR(19) ^------ Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:42:52 2005 Input: nextprime(100) Output: ? 101 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.005s sys 0m0.009s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:43:23 2005 Input: isprime(11) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:43:34 2005 Input: isprime(10) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:44:29 2005 Input: isprime(1062771) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:44:55 2005 Input: isprime(1062773) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:45:02 2005 Input: isprime(1062775) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:45:09 2005 Input: isprime(1062777) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:45:15 2005 Input: isprime(1062779) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:45:33 2005 Input: isprime(1062761) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:45:42 2005 Input: isprime(1062759) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:45:47 2005 Input: isprime(1062757) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:45:52 2005 Input: isprime(1062755) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:45:59 2005 Input: isprime(1062753) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.230' ************** PARI ***************** Host 165.230.10.124 (165.230.10.124) Time: Mon Mar 28 21:46:04 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:46:07 2005 Input: isprime(1062751) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:46:13 2005 Input: isprime(1062749) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:46:19 2005 Input: isprime(1062747) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:46:24 2005 Input: isprime(1062745) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:46:30 2005 Input: isprime(1062743) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:46:37 2005 Input: isprime(1062741) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:46:48 2005 Input: isprime(1062739) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:46:52 2005 Input: isprime(1062737) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.230' ************** PARI ***************** Host 165.230.10.124 (165.230.10.124) Time: Mon Mar 28 21:47:11 2005 Input: 1/7 Output: ? 1/7 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '165.230' ************** PARI ***************** Host 165.230.10.124 (165.230.10.124) Time: Mon Mar 28 21:47:36 2005 Input: 1./7 Output: ? 0.14285714285714285714285714285714285714 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.230' ************** PARI ***************** Host 165.230.10.124 (165.230.10.124) Time: Mon Mar 28 21:47:41 2005 Input: 1/7. Output: ? 0.14285714285714285714285714285714285714 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.230' ************** PARI ***************** Host 165.230.10.124 (165.230.10.124) Time: Mon Mar 28 21:48:40 2005 Input: Pi Output: ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:51:31 2005 Input: for i from 1:8 stat=maple('isprime',2^(2*i+1)-1); fprintf('i=%d : result is %n',i,stat) end Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:51:56 2005 Input: isprime(1062737) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:52:03 2005 Input: isprime(1062739) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:52:08 2005 Input: isprime(1062735) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '212.114' ************** PARI ***************** Host 212.114.232.134 (212.114.232.134) Time: Mon Mar 28 21:52:08 2005 Input: a(n)=if(n<0,0,if(n%2,0,n!)) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:52:40 2005 Input: isprime(1062733) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:52:45 2005 Input: isprime(1062731) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.006s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:53:09 2005 Input: isprime(83534309) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:53:24 2005 Input: isprime(83534307) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:53:29 2005 Input: isprime(83534305) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:53:35 2005 Input: isprime(83534303) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:53:40 2005 Input: isprime(83534301) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:53:46 2005 Input: isprime(83534303) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:57:01 2005 Input: gcd(1062763,311281) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:57:17 2005 Input: gcd(1062763,311281) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 21:57:49 2005 Input: gcd(70,245) Output: ? 35 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:17:47 2005 Input: lcm(5044,649) Output: ? 3273556 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:18:17 2005 Input: lcm(70,245) Output: ? 490 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 22:18:39 2005 Input: factor(9991) Output: ? [97 1] [103 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:18:42 2005 Input: lcm(245) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: lcm(245) ^- Timing: real 0m0.012s user 0m0.003s sys 0m0.008s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:18:58 2005 Input: lcm(245,70) Output: ? 490 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 22:19:42 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.010s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 22:20:30 2005 Input: Mod(113,462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:20:33 2005 Input: lcm[245,70] Output: ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: lcm[245,70] ^-------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 22:20:35 2005 Input: Mod(113,462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:22:59 2005 Input: fibonacci(10) Output: ? 55 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:23:35 2005 Input: fibonacci(15) Output: ? 610 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:23:50 2005 Input: fibonacci(16) Output: ? 987 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:23:59 2005 Input: fibonacci(14) Output: ? 377 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 22:24:08 2005 Input: factor(588) Output: ? [2 2] [3 1] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:24:12 2005 Input: fibonacci(4) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:24:18 2005 Input: fibonacci(6) Output: ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:24:23 2005 Input: fibonacci(8) Output: ? 21 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:24:35 2005 Input: fibonacci(15) Output: ? 610 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:24:41 2005 Input: fibonacci(19) Output: ? 4181 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:24:47 2005 Input: fibonacci(20) Output: ? 6765 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:24:55 2005 Input: fibonacci(50) Output: ? 12586269025 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:25:03 2005 Input: fibonacci(40) Output: ? 102334155 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:25:11 2005 Input: fibonacci(35) Output: ? 9227465 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:25:19 2005 Input: fibonacci(34) Output: ? 5702887 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 22:25:24 2005 Input: 3*2*42 Output: ? 252 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:25:24 2005 Input: fibonacci(32) Output: ? 2178309 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:25:29 2005 Input: fibonacci(31) Output: ? 1346269 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:25:35 2005 Input: fibonacci(30) Output: ? 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:25:41 2005 Input: fibonacci(25) Output: ? 75025 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:25:47 2005 Input: fibonacci(26) Output: ? 121393 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:25:54 2005 Input: fibonacci(27) Output: ? 196418 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:26:00 2005 Input: fibonacci(28) Output: ? 317811 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 22:26:09 2005 Input: Mod(275,252)^(-1) Output: ? Mod(11, 252) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 22:26:58 2005 Input: Mod(139,463)^323 Output: ? Mod(274, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 22:27:24 2005 Input: Mod(347,463)^323 Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 22:27:46 2005 Input: Mod(139,588)^11 Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:28:18 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:28:37 2005 Input: pi(precision = 32) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: pi(precision=32) ^---- Timing: real 0m0.023s user 0m0.007s sys 0m0.003s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:28:47 2005 Input: pi(precision=32) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: pi(precision=32) ^---- Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:29:11 2005 Input: =pi Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: =pi ^--- Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 22:30:26 2005 Input: Mod(2,9991)^9990 Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:30:40 2005 Input: mod(1062763,23) Output: ? ? ? Errors (if any) and Timing Info: *** obsolete function: mod(1062763,23) ^--------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:31:02 2005 Input: Mod(1062763,23) Output: ? Mod(2, 23) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:31:42 2005 Input: Mod(83534308,23) Output: ? Mod(10, 23) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:32:55 2005 Input: binomial(5044,23) Output: ? 536433998944409898148985537034344098854957252386820347783146080 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '203.217' ************** PARI ***************** Host 203.217.1.164 (203.217.1.164) Time: Mon Mar 28 22:33:44 2005 Input: gcd(311281,22) Output: ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 22:59:39 2005 Input: Mod(5,101)^50 Output: ? Mod(1, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:00:11 2005 Input: Mod(2,9991)^2 Output: ? Mod(4, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:00:16 2005 Input: Mod(2,9991)^8 Output: ? Mod(256, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:00:23 2005 Input: Mod(2,9991)^16 Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:00:39 2005 Input: Mod(2,9991)^32 Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:00:50 2005 Input: Mod(2,9991)^64 Output: ? Mod(158, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:00:58 2005 Input: Mod(2,9991)^128 Output: ? Mod(4982, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:01:21 2005 Input: Mod(2,9991)^256 Output: ? Mod(2680, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:01:29 2005 Input: Mod(2,5986)^(-1) Output: ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(2, 5986). Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:01:30 2005 Input: Mod(2,9991)^512 Output: ? Mod(8862, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:01:44 2005 Input: Mod(2,9991)^1024 Output: ? Mod(5784, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:01:54 2005 Input: Mod(2,9991)^2048 Output: ? Mod(4788, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:02:03 2005 Input: Mod(2,9991)^4096 Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:02:05 2005 Input: Mod(2,6780)^(-1) Output: ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(2, 6780). Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:02:16 2005 Input: Mod(2,9991)^8192 Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:02:48 2005 Input: Mod(2,9991)^9990 Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:02:49 2005 Input: 14*14 Output: ? 196 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:03:42 2005 Input: 4*35 Output: ? 140 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:04:13 2005 Input: 196+140 Output: ? 336 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:04:48 2005 Input: 336^(.5) Output: ? 18.330302779823360026352188774912033955 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:08:18 2005 Input: 5986/2 Output: ? 2993 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:08:48 2005 Input: (-1)^2993 Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:09:05 2005 Input: 6780/2 Output: ? 3390 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:10:29 2005 Input: Mod(6780,6781)^3390 Output: ? Mod(1, 6781) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:11:56 2005 Input: 336/2 Output: ? 168 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:12:53 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:13:11 2005 Input: factor(588) Output: ? [2 2] [3 1] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:13:35 2005 Input: Mod(((-14 + (336^.5))/2),337)^168 Output: ? ? Errors (if any) and Timing Info: *** forbidden division t_REAL % t_INT. Timing: real 0m0.012s user 0m0.002s sys 0m0.011s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:14:12 2005 Input: 64^2 Output: ? 4096 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:14:31 2005 Input: 943*4 Output: ? 3772 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:14:33 2005 Input: 943*4 Output: ? 3772 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:14:57 2005 Input: 4096-3772 Output: ? 324 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:15:46 2005 Input: Mod(113,462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:16:08 2005 Input: Mod(275,168)^(-1) Output: ? Mod(11, 168) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Mon Mar 28 23:16:25 2005 Input: Mod((64+(324^.5))*.5,3011)^1506 Output: ? ? Errors (if any) and Timing Info: *** forbidden division t_REAL % t_INT. Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:17:29 2005 Input: Mod(347,463)^323 Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Mon Mar 28 23:17:51 2005 Input: Mod(139,588)^11 Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Mon Mar 28 23:30:27 2005 Input: forprime(p=1,200,for(i=1,(p-3)/2, if(valuation(bernfrac(2*i),p)>0,print(p,'' ''2*i),))) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: ...nfrac(2*i),p)>0,print(p,''''2*i),))) ^----------- Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Mon Mar 28 23:30:47 2005 Input: forprime(p=1,200,for(i=1,(p-3)/2, if(valuation(bernfrac(2*i),p)>0,print(p," "2*i),))) Output: ? 37 32 59 44 67 58 101 68 103 24 131 22 149 130 157 62 157 110 ? Errors (if any) and Timing Info: Timing: real 0m0.425s user 0m0.416s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Mon Mar 28 23:30:56 2005 Input: forprime(p=1,200,for(i=1,(p-3)/2, if(valuation(bernfrac(2*i),p)>0,print(p," "2*i),))) Output: ? 37 32 59 44 67 58 101 68 103 24 131 22 149 130 157 62 157 110 ? Errors (if any) and Timing Info: Timing: real 0m0.536s user 0m0.417s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:35:14 2005 Input: isprime(1068753) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:35:39 2005 Input: isprime(150382) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:35:48 2005 Input: isprime(23) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:36:15 2005 Input: isprime(83534539) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:36:51 2005 Input: factor(1068753) Output: ? [3 1] [7 1] [50893 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:37:28 2005 Input: factor(23) Output: ? [23 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:37:47 2005 Input: factor(150382) Output: ? [2 1] [17 1] [4423 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:38:22 2005 Input: factor(83534539) Output: ? [11 1] [7594049 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:39:02 2005 Input: factor(10) Output: ? [2 1] [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:39:15 2005 Input: factor(5024) Output: ? [2 5] [157 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:40:09 2005 Input: nextprime(1068753) Output: ? 1068757 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:40:50 2005 Input: nextprime(83534539) Output: ? 83534543 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:41:39 2005 Input: prime(4567) Output: ? 43889 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:41:44 2005 Input: prime(456734) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:41:50 2005 Input: prime(45673) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:41:57 2005 Input: prime(9999) Output: ? 104723 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:42:37 2005 Input: nextprime(1068750) Output: ? 1068751 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:42:56 2005 Input: isprime(1068751) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:43:17 2005 Input: nextprime(83534530) Output: ? 83534533 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:43:26 2005 Input: nextprime(83534533) Output: ? 83534533 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:43:34 2005 Input: nextprime(83534533) Output: ? 83534533 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:43:41 2005 Input: nextprime(83534534) Output: ? 83534543 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:44:02 2005 Input: nextprime(8353452) Output: ? 8353459 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:44:20 2005 Input: nextprime(83534532) Output: ? 83534533 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:44:25 2005 Input: nextprime(83534534) Output: ? 83534543 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:45:00 2005 Input: gcd(1068753,150382) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:45:13 2005 Input: gcd(1068753,150382) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:45:32 2005 Input: gcd(23,150382) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:45:45 2005 Input: gcd(23,150382,1068753) Output: ? ? Errors (if any) and Timing Info: *** invalid flag in gcd. Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:45:58 2005 Input: gcd(23,gcd(150382,1068753)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:46:19 2005 Input: lcm(23,10) Output: ? 230 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:46:35 2005 Input: lcm(10,5024) Output: ? 25120 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:47:10 2005 Input: lcm(10,lcm(23,5024)) Output: ? 577760 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:48:49 2005 Input: Mod(1068753,23) Mod(83534539,23) Output: ? Mod(12, 23) ? Mod(11, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:49:49 2005 Input: Mod(24,23) Output: ? Mod(1, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 01:50:19 2005 Input: search(p) = for(i=1,(p-3)/2, if(valuation(bernfrac(2*i),p)>0,print(p," ", 2*i),)) forprime(p=1, 200, search(p) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...orprime(p=1,200,search(p) ^ Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:50:20 2005 Input: fibonacci(1068753) Output: ? 6576503920554175462540472979410719401561565006332650989201582904727241663183173456565685787400503604560252269625353254024243819966811549406824729249877867052297341865500379360688111783070144301350762140191054004936545707587706906863508713796643570692783418674697992183951923768693787553489622821663098937737624454265404041052833583151262829551900419860954661010556650118355809647834962464273259009289093073854490771007401242031381849882239588699727981405835375871485241793953309260896528836217962238034313888278536697782073533967046983706463354003772292314089282134676594026030920585631777763272371489588111136751374545780055899260399959700932625292289808805223119899218733755001618715610136008708139833527639666736951174116061404733036755259003169406376072157255340592136467833791866963858024473160198955483329562751515063294322314427379631454737271992793213629348914083449951951982272978356524368738516843668889880586295402583685072421543033602957899153692473529462373621810006840207198310823525254043547373036465231225807989353070080689591239071340861308066857737272231871436715610586784927105798209383116506618845246248504949959917341751819451543644467293252704844274887589261636206285615949153645886838801560360321352832718182715210725605670374764074956624656711338587860892589074874722401559215418184570643597315689293522666470487941655250590726090367721615478449881887238544580170184469069751158845986503445282456623350188749691632334128809294615523949628396319019344941167620624875128516781220526414460708409881606754085055226761506432989536231969647587947123406455403764566224255337977667029335256026663078411058165543143206658207263311395305115193222251835188798314782001920794423679286671850957016064357461175744376251325475188179952870640718370127806020361378177554292180916889960617351551871489622002020981497777098412492478201791479940660491764639280308831200694071670050171122569679950521036835171704163774415161681382415507948340210368155512352637336235007568737417032862410073954907482161573755034254806504996318910778095125737441797535194975213892979147587670659982950272961665731589501962753317190966175604622473221783811852875493164835331188286338909196519850650286606508040234168676953631791069079650758649032199375484563221957055350524353125514451958611129161630916540339246533275506868184342984359612640446568693168291773935112306531738283232976816135204343673572749223195063053886191215609673880983921914685199709414672579942884236626327153519111714933985028232890741969378232210693753732229441110412935199077746813117323097841698508280241939790385646967751235741679045806379045138751113813483424902806368733907907087390271427497345656648495746901425789366910496530830785585289859883984251928908218021578043541103800595719595867246903523588482649941989494248270308587764907752426608892039976300087198817408728151745215067886846861686884194860170174728257721336270895597232401424632303591790659283588713190735125214521757625988810884098724012754244211629385055622082533270153456399377160255864656585962834001246509475366763117875753034557135611925575477673960255751389827187637250225419263617878982145337413695098569799028215384318567921383921419834214615724987502066[+++] ? Errors (if any) and Timing Info: Timing: real 0m11.029s user 0m10.981s sys 0m0.014s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 01:50:32 2005 Input: search(p) = for(i=1,(p-3)/2, if(valuation(bernfrac(2*i),p)>0,print(p," ", 2*i),)) forprime(p=1, 200, search(p)) Output: ? ? 37 32 59 44 67 58 101 68 103 24 131 22 149 130 157 62 157 110 ? Errors (if any) and Timing Info: Timing: real 0m0.426s user 0m0.422s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:50:52 2005 Input: fibonacci(1068753) Output: ? 6576503920554175462540472979410719401561565006332650989201582904727241663183173456565685787400503604560252269625353254024243819966811549406824729249877867052297341865500379360688111783070144301350762140191054004936545707587706906863508713796643570692783418674697992183951923768693787553489622821663098937737624454265404041052833583151262829551900419860954661010556650118355809647834962464273259009289093073854490771007401242031381849882239588699727981405835375871485241793953309260896528836217962238034313888278536697782073533967046983706463354003772292314089282134676594026030920585631777763272371489588111136751374545780055899260399959700932625292289808805223119899218733755001618715610136008708139833527639666736951174116061404733036755259003169406376072157255340592136467833791866963858024473160198955483329562751515063294322314427379631454737271992793213629348914083449951951982272978356524368738516843668889880586295402583685072421543033602957899153692473529462373621810006840207198310823525254043547373036465231225807989353070080689591239071340861308066857737272231871436715610586784927105798209383116506618845246248504949959917341751819451543644467293252704844274887589261636206285615949153645886838801560360321352832718182715210725605670374764074956624656711338587860892589074874722401559215418184570643597315689293522666470487941655250590726090367721615478449881887238544580170184469069751158845986503445282456623350188749691632334128809294615523949628396319019344941167620624875128516781220526414460708409881606754085055226761506432989536231969647587947123406455403764566224255337977667029335256026663078411058165543143206658207263311395305115193222251835188798314782001920794423679286671850957016064357461175744376251325475188179952870640718370127806020361378177554292180916889960617351551871489622002020981497777098412492478201791479940660491764639280308831200694071670050171122569679950521036835171704163774415161681382415507948340210368155512352637336235007568737417032862410073954907482161573755034254806504996318910778095125737441797535194975213892979147587670659982950272961665731589501962753317190966175604622473221783811852875493164835331188286338909196519850650286606508040234168676953631791069079650758649032199375484563221957055350524353125514451958611129161630916540339246533275506868184342984359612640446568693168291773935112306531738283232976816135204343673572749223195063053886191215609673880983921914685199709414672579942884236626327153519111714933985028232890741969378232210693753732229441110412935199077746813117323097841698508280241939790385646967751235741679045806379045138751113813483424902806368733907907087390271427497345656648495746901425789366910496530830785585289859883984251928908218021578043541103800595719595867246903523588482649941989494248270308587764907752426608892039976300087198817408728151745215067886846861686884194860170174728257721336270895597232401424632303591790659283588713190735125214521757625988810884098724012754244211629385055622082533270153456399377160255864656585962834001246509475366763117875753034557135611925575477673960255751389827187637250225419263617878982145337413695098569799028215384318567921383921419834214615724987502066[+++] ? Errors (if any) and Timing Info: Timing: real 0m10.914s user 0m10.897s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 01:51:14 2005 Input: s(p) = for(i=1,(p-3)/2, if(valuation(bernfrac(2*i),p)>0,print(p," ", 2*i),)) forprime(p=1, 200, s(p)) Output: ? ? 37 32 59 44 67 58 101 68 103 24 131 22 149 130 157 62 157 110 ? Errors (if any) and Timing Info: Timing: real 0m0.425s user 0m0.417s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:51:23 2005 Input: fibonacci(213) Output: ? 146178119651438213260386312206974243796773058 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:51:31 2005 Input: fibonacci(55) Output: ? 139583862445 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:51:37 2005 Input: fibonacci(40) Output: ? 102334155 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:51:43 2005 Input: fibonacci(37) Output: ? 24157817 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:51:55 2005 Input: fibonacci(35) Output: ? 9227465 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:52:02 2005 Input: fibonacci(34) Output: ? 5702887 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:52:07 2005 Input: fibonacci(33) Output: ? 3524578 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:52:13 2005 Input: fibonacci(32) Output: ? 2178309 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:52:21 2005 Input: fibonacci(31) Output: ? 1346269 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:52:37 2005 Input: fibonacci(30) Output: ? 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:52:49 2005 Input: fibonacci(4) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:52:53 2005 Input: fibonacci(6) Output: ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:52:58 2005 Input: fibonacci(7) Output: ? 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:53:02 2005 Input: fibonacci(8) Output: ? 21 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:53:07 2005 Input: fibonacci(9) Output: ? 34 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:53:15 2005 Input: fibonacci(23) Output: ? 28657 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:53:22 2005 Input: fibonacci(10) Output: ? 55 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:53:26 2005 Input: fibonacci(11) Output: ? 89 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:53:30 2005 Input: fibonacci(12) Output: ? 144 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:53:34 2005 Input: fibonacci(13) Output: ? 233 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:53:39 2005 Input: fibonacci(14) Output: ? 377 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:53:44 2005 Input: fibonacci(15) Output: ? 610 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:53:48 2005 Input: fibonacci(17) Output: ? 1597 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:53:55 2005 Input: fibonacci(18) Output: ? 2584 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:54:20 2005 Input: fibonacci(19) Output: ? 4181 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:54:26 2005 Input: fibonacci(20) Output: ? 6765 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:54:45 2005 Input: prime(5024) Output: ? 48857 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:55:45 2005 Input: binomial(5024,23) Output: ? 489490235791339498426388018839758456633468556238308987406805024 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:56:12 2005 Input: binomial(23,5024) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:56:25 2005 Input: binomial(5023,23) Output: ? 487249337020797936232158933562426759877383807672727556931017501 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:56:32 2005 Input: binomial(5024,23) Output: ? 489490235791339498426388018839758456633468556238308987406805024 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:56:45 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:56:58 2005 Input: pi(32) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: pi(32) ^------ For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: pi ===> Pi Pi=Pi(): the constant pi, with current precision. Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:57:25 2005 Input: Pi(32) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: Pi(32) ^--- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 01:57:40 2005 Input: Pi Output: ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 02:58:28 2005 Input: isprime(1106071) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 02:59:06 2005 Input: print(isprime(1106071)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 02:59:50 2005 Input: print(isprime(1106071)); Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 03:03:49 2005 Input: 2+2; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 03:04:20 2005 Input: print(2+2); Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 03:05:16 2005 Input: print(2+2); print(isprime(1)); print(isprime(2)); print(isprime(4)); print(isprime(9)); Output: ? 4 ? 0 ? 1 ? 0 ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 03:06:00 2005 Input: print(2+2); print(isprime(1)); print(isprime(2)); print(isprime(4)); print(isprime(9)); print("Hi"); Output: ? 4 ? 0 ? 1 ? 0 ? 0 ? Hi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 03:06:27 2005 Input: print(2+2); print(isprime(1)); print(isprime(2)); print(isprime(4)); print(isprime(9)); a = 4; print(a); Output: ? 4 ? 0 ? 1 ? 0 ? 0 ? ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 03:08:36 2005 Input: print(2+2); print(isprime(1)); print(isprime(2)); print(isprime(4)); print(isprime(9)); a = 4; print(a + isprime(a)); Output: ? 4 ? 0 ? 1 ? 0 ? 0 ? ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 03:09:20 2005 Input: a = 4; print(a + isprime(a)); print(a isprime(a)); print("done"); Output: ? ? 4 ? ? done ? Errors (if any) and Timing Info: *** expected character: '=' instead of: print(aisprime(a)); ^-- Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 03:09:56 2005 Input: a = 4; print(a + isprime(a)); print(a " " isprime(a)); print("done"); Output: ? ? 4 ? 4 0 ? done ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:05:54 2005 Input: print(fibonacci(10)); Output: ? 55 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:06:02 2005 Input: print(fibonacci(100)); Output: ? 354224848179261915075 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:06:11 2005 Input: print(fibonacci(20)); Output: ? 6765 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:06:20 2005 Input: print(fibonacci(19)); Output: ? 4181 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:07:40 2005 Input: print(fibonacci(19)); print(fibonacci(19)); print(fibonacci(19)); print(fibonacci(19)); print(fibonacci(19)); print(fibonacci(19)); print(fibonacci(19)); print(fibonacci(19)); print(fibonacci(19)); print(fibonacci(19)); print(fibonacci(19)); print(fibonacci(19)); print(fibonacci(19)); print(fibonacci(19)); print(fibonacci(19)); Output: ? 4181 ? 4181 ? 4181 ? 4181 ? 4181 ? 4181 ? 4181 ? 4181 ? 4181 ? 4181 ? 4181 ? 4181 ? 4181 ? 4181 ? 4181 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:08:10 2005 Input: print(fibonacci(25) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: print(fibonacci(25) ^ Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:08:18 2005 Input: print(fibonacci(25); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: print(fibonacci(25); ^- Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:08:36 2005 Input: print(fibonacci(25)); Output: ? 75025 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:08:46 2005 Input: print(fibonacci(26)); Output: ? 121393 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:08:56 2005 Input: print(fibonacci(27)); Output: ? 196418 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:09:06 2005 Input: print(fibonacci(30)); Output: ? 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:09:17 2005 Input: print(fibonacci(35)); Output: ? 9227465 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:09:32 2005 Input: print(fibonacci(30)); Output: ? 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:09:39 2005 Input: print(fibonacci(32)); Output: ? 2178309 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:11:24 2005 Input: print("1: " fibonacci(1) " 11: " fibonacci(11) " 22: " fibonacci(22)); Output: ? 1: 1 11: 89 22: 17711 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:20:31 2005 Input: print("Setting variables..."); a = 1106071; b = 140384; c = 21; d = 0428242561; e = 237; f = 5006; print("-"); print("Testing for primes:"); print(a " : " isprime(a)); print(b " : " isprime(b)); print(c " : " isprime(c)); print(d " : " isprime(d)); print(e " : " isprime(e)); print(f " : " isprime(f)); print("-"); print("Prime decomposition:"); print(a " : " factor(a)); print(b " : " factor(b)); print(c " : " factor(c)); print(d " : " factor(d)); print(e " : " factor(e)); print(f " : " factor(f)); print("-"); print("Before / afters:"); print(" < " a " < " nextprime(a)); print(" < " d " < " nextprime(d)); print("-"); print("GCD"); print("(a,b) = " gcd(a,b)); print("(b,c) = " gcd(b,c)); print("(a,b,c) = " gcd(a,b,c)); print("-"); print("LCM"); print("[c,e] = " lcm(c,e)); print("[e,f] = " lcm(e,f)); print("[c,e,f] = " lcm(c,e,f)); print("-"); print("Least positive residue:"); print("a mod c : " Mod(a,c)); print("d mod c : " Mod(d,c)); print("a =- d (mod c)? : (manuel)"); print("-"); print("Fibonacci numbers:"); print(a " or " c " or " f); print(" 1: " fibonacci(1) " 12: " fibonacci(12) " 23: " fibonacci(23)); print(" 2: " fibonacci(2) " 13: " fibonacci(13) " 24: " fibonacci(24)); print(" 3: " fibonacci(3) " 14: " fibonacci(14) " 25: " fibonacci(25)); print(" 4: " fibonacci(4) " 15: " fibonacci(15) " 26: " fibonacci(26)); print(" 5: " fibonacci(5) " 16: " fibonacci(16) " 27: " fibonacci(27)); print(" 6: " fibonacci(6) " 17: " fibonacci(17) " 28: " fibonacci(28)); print(" 7: " fibonacci(7) " 18: " fibonacci(18) " 29: " fibonacci(29)); print(" 8: " fibonacci(8) " 19: " fibonacci(19) " 30: " fibonacci(30)); print(" 9: " fibonacci(9) " 20: " fibonacci(20) " 31: " fibonacci(31)); print("10: " fibonacci(10) " 21: " fibonacci(21) " 32: " fibonacci(32)); print("11: " fibonacci(11) " 22: " fibonacci(22)); print("-"); print(f "th prime:"); print(prime(f)); print("-"); print("Last four digits of binomial coefficient (f..c):"); print(binomial(f,c)); print("-"); print("32nd digit after decimal in Pi:"); precision=33; print(pi); print(0.12345678901234567890123456789012); Output: ? Setting variables... ? ? ? ? ? ? ? - ? Testing for primes: ? 1106071 : 0 ? 140384 : 0 ? 21 : 0 ? 428242561 : 0 ? 237 : 0 ? 5006 : 0 ? - ? Prime decomposition: ? 1106071 : [17, 1; 65063, 1] ? 140384 : [2, 5; 41, 1; 107, 1] ? 21 : [3, 1; 7, 1] ? 428242561 : [181, 1; 2365981, 1] ? 237 : [3, 1; 79, 1] ? 5006 : [2, 1; 2503, 1] ? - ? Before / afters: ? < 1106071 < 1106087 ? < 428242561 < 428242621 ? - ? GCD ? (a,b) = 1 ? (b,c) = 1 ? ? - ? LCM ? [c,e] = 1659 ? [e,f] = 1186422 ? ? - ? Least positive residue: ? a mod c : Mod(1, 21) ? d mod c : Mod(19, 21) ? a =- d (mod c)? : (manuel) ? - ? Fibonacci numbers: ? 1106071 or 21 or 5006 ? 1: 1 12: 144 23: 28657 ? 2: 1 13: 233 24: 46368 ? 3: 2 14: 377 25: 75025 ? 4: 3 15: 610 26: 121393 ? 5: 5 16: 987 27: 196418 ? 6: 8 17: 1597 28: 317811 ? 7: 13 18: 2584 29: 514229 ? 8: 21 19: 4181 30: 832040 ? 9: 34 20: 6765 31: 1346269 ? 10: 55 21: 10946 32: 2178309 ? 11: 89 22: 17711 ? - ? 5006th prime: ? 48673 ? - ? Last four digits of binomial coefficient (f..c): ? 9177415897211302590765294797044615525260065482298035878000 ? - ? 32nd digit after decimal in Pi: ? ? pi ? 0.12345678901234567890123456789011999999 ? Errors (if any) and Timing Info: *** invalid flag in gcd. *** expected character: ')' instead of: print("[c,e,f] = "lcm(c,e,f)); ^----- *** expected character: '(' instead of: precision=33; ^---- Timing: real 0m0.015s user 0m0.009s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:22:21 2005 Input: print("Setting variables..."); a = 1106071; b = 140384; c = 21; d = 0428242561; e = 237; f = 5006; print("-"); print("Testing for primes:"); print(a " : " isprime(a)); print(b " : " isprime(b)); print(c " : " isprime(c)); print(d " : " isprime(d)); print(e " : " isprime(e)); print(f " : " isprime(f)); print("-"); print("Prime decomposition:"); print(a " : " factor(a)); print(b " : " factor(b)); print(c " : " factor(c)); print(d " : " factor(d)); print(e " : " factor(e)); print(f " : " factor(f)); print("-"); print("Before / afters:"); print(" < " a " < " nextprime(a)); print(" < " d " < " nextprime(d)); print("-"); print("GCD"); print("(a,b) = " gcd(a,b)); print("(b,c) = " gcd(b,c)); print("(a,b,c) = " gcd(a,b,c)); print("-"); print("LCM"); print("[c,e] = " lcm(c,e)); print("[e,f] = " lcm(e,f)); print("[c,e,f] = " lcm(c,(lcm(e,f)); print("-"); print("Least positive residue:"); print("a mod c : " Mod(a,c)); print("d mod c : " Mod(d,c)); print("a =- d (mod c)? : (manuel)"); print("-"); print("Fibonacci numbers:"); print(a " or " c " or " f); print(" 1: " fibonacci(1) " 12: " fibonacci(12) " 23: " fibonacci(23)); print(" 2: " fibonacci(2) " 13: " fibonacci(13) " 24: " fibonacci(24)); print(" 3: " fibonacci(3) " 14: " fibonacci(14) " 25: " fibonacci(25)); print(" 4: " fibonacci(4) " 15: " fibonacci(15) " 26: " fibonacci(26)); print(" 5: " fibonacci(5) " 16: " fibonacci(16) " 27: " fibonacci(27)); print(" 6: " fibonacci(6) " 17: " fibonacci(17) " 28: " fibonacci(28)); print(" 7: " fibonacci(7) " 18: " fibonacci(18) " 29: " fibonacci(29)); print(" 8: " fibonacci(8) " 19: " fibonacci(19) " 30: " fibonacci(30)); print(" 9: " fibonacci(9) " 20: " fibonacci(20) " 31: " fibonacci(31)); print("10: " fibonacci(10) " 21: " fibonacci(21) " 32: " fibonacci(32)); print("11: " fibonacci(11) " 22: " fibonacci(22)); print("-"); print(f "th prime:"); print(prime(f)); print("-"); print("Last four digits of binomial coefficient (f..c):"); print(binomial(f,c)); print("-"); print("32nd digit after decimal in Pi:"); precision=33; print(pi); print(0.12345678901234567890123456789012); Output: ? Setting variables... ? ? ? ? ? ? ? - ? Testing for primes: ? 1106071 : 0 ? 140384 : 0 ? 21 : 0 ? 428242561 : 0 ? 237 : 0 ? 5006 : 0 ? - ? Prime decomposition: ? 1106071 : [17, 1; 65063, 1] ? 140384 : [2, 5; 41, 1; 107, 1] ? 21 : [3, 1; 7, 1] ? 428242561 : [181, 1; 2365981, 1] ? 237 : [3, 1; 79, 1] ? 5006 : [2, 1; 2503, 1] ? - ? Before / afters: ? < 1106071 < 1106087 ? < 428242561 < 428242621 ? - ? GCD ? (a,b) = 1 ? (b,c) = 1 ? ? - ? LCM ? [c,e] = 1659 ? [e,f] = 1186422 ? ? - ? Least positive residue: ? a mod c : Mod(1, 21) ? d mod c : Mod(19, 21) ? a =- d (mod c)? : (manuel) ? - ? Fibonacci numbers: ? 1106071 or 21 or 5006 ? 1: 1 12: 144 23: 28657 ? 2: 1 13: 233 24: 46368 ? 3: 2 14: 377 25: 75025 ? 4: 3 15: 610 26: 121393 ? 5: 5 16: 987 27: 196418 ? 6: 8 17: 1597 28: 317811 ? 7: 13 18: 2584 29: 514229 ? 8: 21 19: 4181 30: 832040 ? 9: 34 20: 6765 31: 1346269 ? 10: 55 21: 10946 32: 2178309 ? 11: 89 22: 17711 ? - ? 5006th prime: ? 48673 ? - ? Last four digits of binomial coefficient (f..c): ? 9177415897211302590765294797044615525260065482298035878000 ? - ? 32nd digit after decimal in Pi: ? ? pi ? 0.12345678901234567890123456789011999999 ? Errors (if any) and Timing Info: *** invalid flag in gcd. *** expected character: ')' instead of: ...,e,f] = "lcm(c,(lcm(e,f)); ^- *** expected character: '(' instead of: precision=33; ^---- Timing: real 0m0.016s user 0m0.008s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:22:47 2005 Input: print("Setting variables..."); a = 1106071; b = 140384; c = 21; d = 0428242561; e = 237; f = 5006; print("-"); print("Testing for primes:"); print(a " : " isprime(a)); print(b " : " isprime(b)); print(c " : " isprime(c)); print(d " : " isprime(d)); print(e " : " isprime(e)); print(f " : " isprime(f)); print("-"); print("Prime decomposition:"); print(a " : " factor(a)); print(b " : " factor(b)); print(c " : " factor(c)); print(d " : " factor(d)); print(e " : " factor(e)); print(f " : " factor(f)); print("-"); print("Before / afters:"); print(" < " a " < " nextprime(a)); print(" < " d " < " nextprime(d)); print("-"); print("GCD"); print("(a,b) = " gcd(a,b)); print("(b,c) = " gcd(b,c)); print("(a,b,c) = " gcd(a,(gcd(b,c)); print("-"); print("LCM"); print("[c,e] = " lcm(c,e)); print("[e,f] = " lcm(e,f)); print("[c,e,f] = " lcm(c,(lcm(e,f)); print("-"); print("Least positive residue:"); print("a mod c : " Mod(a,c)); print("d mod c : " Mod(d,c)); print("a =- d (mod c)? : (manuel)"); print("-"); print("Fibonacci numbers:"); print(a " or " c " or " f); print(" 1: " fibonacci(1) " 12: " fibonacci(12) " 23: " fibonacci(23)); print(" 2: " fibonacci(2) " 13: " fibonacci(13) " 24: " fibonacci(24)); print(" 3: " fibonacci(3) " 14: " fibonacci(14) " 25: " fibonacci(25)); print(" 4: " fibonacci(4) " 15: " fibonacci(15) " 26: " fibonacci(26)); print(" 5: " fibonacci(5) " 16: " fibonacci(16) " 27: " fibonacci(27)); print(" 6: " fibonacci(6) " 17: " fibonacci(17) " 28: " fibonacci(28)); print(" 7: " fibonacci(7) " 18: " fibonacci(18) " 29: " fibonacci(29)); print(" 8: " fibonacci(8) " 19: " fibonacci(19) " 30: " fibonacci(30)); print(" 9: " fibonacci(9) " 20: " fibonacci(20) " 31: " fibonacci(31)); print("10: " fibonacci(10) " 21: " fibonacci(21) " 32: " fibonacci(32)); print("11: " fibonacci(11) " 22: " fibonacci(22)); print("-"); print(f "th prime:"); print(prime(f)); print("-"); print("Last four digits of binomial coefficient (f..c):"); print(binomial(f,c)); print("-"); print("32nd digit after decimal in Pi:"); precision=33; print(pi); print(0.12345678901234567890123456789012); Output: ? Setting variables... ? ? ? ? ? ? ? - ? Testing for primes: ? 1106071 : 0 ? 140384 : 0 ? 21 : 0 ? 428242561 : 0 ? 237 : 0 ? 5006 : 0 ? - ? Prime decomposition: ? 1106071 : [17, 1; 65063, 1] ? 140384 : [2, 5; 41, 1; 107, 1] ? 21 : [3, 1; 7, 1] ? 428242561 : [181, 1; 2365981, 1] ? 237 : [3, 1; 79, 1] ? 5006 : [2, 1; 2503, 1] ? - ? Before / afters: ? < 1106071 < 1106087 ? < 428242561 < 428242621 ? - ? GCD ? (a,b) = 1 ? (b,c) = 1 ? ? - ? LCM ? [c,e] = 1659 ? [e,f] = 1186422 ? ? - ? Least positive residue: ? a mod c : Mod(1, 21) ? d mod c : Mod(19, 21) ? a =- d (mod c)? : (manuel) ? - ? Fibonacci numbers: ? 1106071 or 21 or 5006 ? 1: 1 12: 144 23: 28657 ? 2: 1 13: 233 24: 46368 ? 3: 2 14: 377 25: 75025 ? 4: 3 15: 610 26: 121393 ? 5: 5 16: 987 27: 196418 ? 6: 8 17: 1597 28: 317811 ? 7: 13 18: 2584 29: 514229 ? 8: 21 19: 4181 30: 832040 ? 9: 34 20: 6765 31: 1346269 ? 10: 55 21: 10946 32: 2178309 ? 11: 89 22: 17711 ? - ? 5006th prime: ? 48673 ? - ? Last four digits of binomial coefficient (f..c): ? 9177415897211302590765294797044615525260065482298035878000 ? - ? 32nd digit after decimal in Pi: ? ? pi ? 0.12345678901234567890123456789011999999 ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...,b,c) = "gcd(a,(gcd(b,c)); ^- *** expected character: ')' instead of: ...,e,f] = "lcm(c,(lcm(e,f)); ^- *** expected character: '(' instead of: precision=33; ^---- Timing: real 0m0.016s user 0m0.005s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:23:14 2005 Input: print("Setting variables..."); a = 1106071; b = 140384; c = 21; d = 0428242561; e = 237; f = 5006; print("-"); print("Testing for primes:"); print(a " : " isprime(a)); print(b " : " isprime(b)); print(c " : " isprime(c)); print(d " : " isprime(d)); print(e " : " isprime(e)); print(f " : " isprime(f)); print("-"); print("Prime decomposition:"); print(a " : " factor(a)); print(b " : " factor(b)); print(c " : " factor(c)); print(d " : " factor(d)); print(e " : " factor(e)); print(f " : " factor(f)); print("-"); print("Before / afters:"); print(" < " a " < " nextprime(a)); print(" < " d " < " nextprime(d)); print("-"); print("GCD"); print("(a,b) = " gcd(a,b)); print("(b,c) = " gcd(b,c)); print("(a,b,c) = " gcd(a,(gcd(b,c))); print("-"); print("LCM"); print("[c,e] = " lcm(c,e)); print("[e,f] = " lcm(e,f)); print("[c,e,f] = " lcm(c,(lcm(e,f))); print("-"); print("Least positive residue:"); print("a mod c : " Mod(a,c)); print("d mod c : " Mod(d,c)); print("a =- d (mod c)? : (manuel)"); print("-"); print("Fibonacci numbers:"); print(a " or " c " or " f); print(" 1: " fibonacci(1) " 12: " fibonacci(12) " 23: " fibonacci(23)); print(" 2: " fibonacci(2) " 13: " fibonacci(13) " 24: " fibonacci(24)); print(" 3: " fibonacci(3) " 14: " fibonacci(14) " 25: " fibonacci(25)); print(" 4: " fibonacci(4) " 15: " fibonacci(15) " 26: " fibonacci(26)); print(" 5: " fibonacci(5) " 16: " fibonacci(16) " 27: " fibonacci(27)); print(" 6: " fibonacci(6) " 17: " fibonacci(17) " 28: " fibonacci(28)); print(" 7: " fibonacci(7) " 18: " fibonacci(18) " 29: " fibonacci(29)); print(" 8: " fibonacci(8) " 19: " fibonacci(19) " 30: " fibonacci(30)); print(" 9: " fibonacci(9) " 20: " fibonacci(20) " 31: " fibonacci(31)); print("10: " fibonacci(10) " 21: " fibonacci(21) " 32: " fibonacci(32)); print("11: " fibonacci(11) " 22: " fibonacci(22)); print("-"); print(f "th prime:"); print(prime(f)); print("-"); print("Last four digits of binomial coefficient (f..c):"); print(binomial(f,c)); print("-"); print("32nd digit after decimal in Pi:"); precision=33; print(pi); print(0.12345678901234567890123456789012); Output: ? Setting variables... ? ? ? ? ? ? ? - ? Testing for primes: ? 1106071 : 0 ? 140384 : 0 ? 21 : 0 ? 428242561 : 0 ? 237 : 0 ? 5006 : 0 ? - ? Prime decomposition: ? 1106071 : [17, 1; 65063, 1] ? 140384 : [2, 5; 41, 1; 107, 1] ? 21 : [3, 1; 7, 1] ? 428242561 : [181, 1; 2365981, 1] ? 237 : [3, 1; 79, 1] ? 5006 : [2, 1; 2503, 1] ? - ? Before / afters: ? < 1106071 < 1106087 ? < 428242561 < 428242621 ? - ? GCD ? (a,b) = 1 ? (b,c) = 1 ? ? - ? LCM ? [c,e] = 1659 ? [e,f] = 1186422 ? ? - ? Least positive residue: ? a mod c : Mod(1, 21) ? d mod c : Mod(19, 21) ? a =- d (mod c)? : (manuel) ? - ? Fibonacci numbers: ? 1106071 or 21 or 5006 ? 1: 1 12: 144 23: 28657 ? 2: 1 13: 233 24: 46368 ? 3: 2 14: 377 25: 75025 ? 4: 3 15: 610 26: 121393 ? 5: 5 16: 987 27: 196418 ? 6: 8 17: 1597 28: 317811 ? 7: 13 18: 2584 29: 514229 ? 8: 21 19: 4181 30: 832040 ? 9: 34 20: 6765 31: 1346269 ? 10: 55 21: 10946 32: 2178309 ? 11: 89 22: 17711 ? - ? 5006th prime: ? 48673 ? - ? Last four digits of binomial coefficient (f..c): ? 9177415897211302590765294797044615525260065482298035878000 ? - ? 32nd digit after decimal in Pi: ? ? pi ? 0.12345678901234567890123456789011999999 ? Errors (if any) and Timing Info: *** unexpected character: ...b,c) = "gcd(a,(gcd(b,c))); ^- *** unexpected character: ...e,f] = "lcm(c,(lcm(e,f))); ^- *** expected character: '(' instead of: precision=33; ^---- Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:24:18 2005 Input: print("Setting variables..."); a = 1106071; b = 140384; c = 21; d = 0428242561; e = 237; f = 5006; print("-"); print("Testing for primes:"); print(a " : " isprime(a)); print(b " : " isprime(b)); print(c " : " isprime(c)); print(d " : " isprime(d)); print(e " : " isprime(e)); print(f " : " isprime(f)); print("-"); print("Prime decomposition:"); print(a " : " factor(a)); print(b " : " factor(b)); print(c " : " factor(c)); print(d " : " factor(d)); print(e " : " factor(e)); print(f " : " factor(f)); print("-"); print("Before / afters:"); print(" < " a " < " nextprime(a)); print(" < " d " < " nextprime(d)); print("-"); print("GCD"); print("(a,b) = " gcd(a,b)); print("(b,c) = " gcd(b,c)); print("(a,b,c) = " gcd(a,(gcd(b,c)))); print("-"); print("LCM"); print("[c,e] = " lcm(c,e)); print("[e,f] = " lcm(e,f)); print("[c,e,f] = " lcm(c,(lcm(e,f)))); print("-"); print("Least positive residue:"); print("a mod c : " Mod(a,c)); print("d mod c : " Mod(d,c)); print("a =- d (mod c)? : (manuel)"); print("-"); print("Fibonacci numbers:"); print(a " or " c " or " f); print(" 1: " fibonacci(1) " 12: " fibonacci(12) " 23: " fibonacci(23)); print(" 2: " fibonacci(2) " 13: " fibonacci(13) " 24: " fibonacci(24)); print(" 3: " fibonacci(3) " 14: " fibonacci(14) " 25: " fibonacci(25)); print(" 4: " fibonacci(4) " 15: " fibonacci(15) " 26: " fibonacci(26)); print(" 5: " fibonacci(5) " 16: " fibonacci(16) " 27: " fibonacci(27)); print(" 6: " fibonacci(6) " 17: " fibonacci(17) " 28: " fibonacci(28)); print(" 7: " fibonacci(7) " 18: " fibonacci(18) " 29: " fibonacci(29)); print(" 8: " fibonacci(8) " 19: " fibonacci(19) " 30: " fibonacci(30)); print(" 9: " fibonacci(9) " 20: " fibonacci(20) " 31: " fibonacci(31)); print("10: " fibonacci(10) " 21: " fibonacci(21) " 32: " fibonacci(32)); print("11: " fibonacci(11) " 22: " fibonacci(22)); print("-"); print(f "th prime:"); print(prime(f)); print("-"); print("Last four digits of binomial coefficient (f..c):"); print(binomial(f,c)); print("-"); print("32nd digit after decimal in Pi:"); precision=33; print(pi); print(0.12345678901234567890123456789012); Output: ? Setting variables... ? ? ? ? ? ? ? - ? Testing for primes: ? 1106071 : 0 ? 140384 : 0 ? 21 : 0 ? 428242561 : 0 ? 237 : 0 ? 5006 : 0 ? - ? Prime decomposition: ? 1106071 : [17, 1; 65063, 1] ? 140384 : [2, 5; 41, 1; 107, 1] ? 21 : [3, 1; 7, 1] ? 428242561 : [181, 1; 2365981, 1] ? 237 : [3, 1; 79, 1] ? 5006 : [2, 1; 2503, 1] ? - ? Before / afters: ? < 1106071 < 1106087 ? < 428242561 < 428242621 ? - ? GCD ? (a,b) = 1 ? (b,c) = 1 ? (a,b,c) = 1 ? - ? LCM ? [c,e] = 1659 ? [e,f] = 1186422 ? [c,e,f] = 8304954 ? - ? Least positive residue: ? a mod c : Mod(1, 21) ? d mod c : Mod(19, 21) ? a =- d (mod c)? : (manuel) ? - ? Fibonacci numbers: ? 1106071 or 21 or 5006 ? 1: 1 12: 144 23: 28657 ? 2: 1 13: 233 24: 46368 ? 3: 2 14: 377 25: 75025 ? 4: 3 15: 610 26: 121393 ? 5: 5 16: 987 27: 196418 ? 6: 8 17: 1597 28: 317811 ? 7: 13 18: 2584 29: 514229 ? 8: 21 19: 4181 30: 832040 ? 9: 34 20: 6765 31: 1346269 ? 10: 55 21: 10946 32: 2178309 ? 11: 89 22: 17711 ? - ? 5006th prime: ? 48673 ? - ? Last four digits of binomial coefficient (f..c): ? 9177415897211302590765294797044615525260065482298035878000 ? - ? 32nd digit after decimal in Pi: ? ? pi ? 0.12345678901234567890123456789011999999 ? Errors (if any) and Timing Info: *** expected character: '(' instead of: precision=33; ^---- Timing: real 0m0.016s user 0m0.006s sys 0m0.011s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:25:00 2005 Input: print("Setting variables..."); a = 1106071; b = 140384; c = 21; d = 0428242561; e = 237; f = 5006; print("-"); print("Testing for primes:"); print(a " : " isprime(a)); print(b " : " isprime(b)); print(c " : " isprime(c)); print(d " : " isprime(d)); print(e " : " isprime(e)); print(f " : " isprime(f)); print("-"); print("Prime decomposition:"); print(a " : " factor(a)); print(b " : " factor(b)); print(c " : " factor(c)); print(d " : " factor(d)); print(e " : " factor(e)); print(f " : " factor(f)); print("-"); print("Before / afters:"); print(" < " a " < " nextprime(a)); print(" < " d " < " nextprime(d)); print("-"); print("GCD"); print("(a,b) = " gcd(a,b)); print("(b,c) = " gcd(b,c)); print("(a,b,c) = " gcd(a,(gcd(b,c)))); print("-"); print("LCM"); print("[c,e] = " lcm(c,e)); print("[e,f] = " lcm(e,f)); print("[c,e,f] = " lcm(c,(lcm(e,f)))); print("-"); print("Least positive residue:"); print("a mod c : " Mod(a,c)); print("d mod c : " Mod(d,c)); print("a =- d (mod c)? : (manuel)"); print("-"); print("Fibonacci numbers:"); print(a " or " c " or " f); print(" 1: " fibonacci(1) " 12: " fibonacci(12) " 23: " fibonacci(23)); print(" 2: " fibonacci(2) " 13: " fibonacci(13) " 24: " fibonacci(24)); print(" 3: " fibonacci(3) " 14: " fibonacci(14) " 25: " fibonacci(25)); print(" 4: " fibonacci(4) " 15: " fibonacci(15) " 26: " fibonacci(26)); print(" 5: " fibonacci(5) " 16: " fibonacci(16) " 27: " fibonacci(27)); print(" 6: " fibonacci(6) " 17: " fibonacci(17) " 28: " fibonacci(28)); print(" 7: " fibonacci(7) " 18: " fibonacci(18) " 29: " fibonacci(29)); print(" 8: " fibonacci(8) " 19: " fibonacci(19) " 30: " fibonacci(30)); print(" 9: " fibonacci(9) " 20: " fibonacci(20) " 31: " fibonacci(31)); print("10: " fibonacci(10) " 21: " fibonacci(21) " 32: " fibonacci(32)); print("11: " fibonacci(11) " 22: " fibonacci(22)); print("-"); print(f "th prime:"); print(prime(f)); print("-"); print("Last four digits of binomial coefficient (f..c):"); print(binomial(f,c)); print("-"); print("32nd digit after decimal in Pi:"); precision(33); print(pi); print(0.12345678901234567890123456789012); Output: ? Setting variables... ? ? ? ? ? ? ? - ? Testing for primes: ? 1106071 : 0 ? 140384 : 0 ? 21 : 0 ? 428242561 : 0 ? 237 : 0 ? 5006 : 0 ? - ? Prime decomposition: ? 1106071 : [17, 1; 65063, 1] ? 140384 : [2, 5; 41, 1; 107, 1] ? 21 : [3, 1; 7, 1] ? 428242561 : [181, 1; 2365981, 1] ? 237 : [3, 1; 79, 1] ? 5006 : [2, 1; 2503, 1] ? - ? Before / afters: ? < 1106071 < 1106087 ? < 428242561 < 428242621 ? - ? GCD ? (a,b) = 1 ? (b,c) = 1 ? (a,b,c) = 1 ? - ? LCM ? [c,e] = 1659 ? [e,f] = 1186422 ? [c,e,f] = 8304954 ? - ? Least positive residue: ? a mod c : Mod(1, 21) ? d mod c : Mod(19, 21) ? a =- d (mod c)? : (manuel) ? - ? Fibonacci numbers: ? 1106071 or 21 or 5006 ? 1: 1 12: 144 23: 28657 ? 2: 1 13: 233 24: 46368 ? 3: 2 14: 377 25: 75025 ? 4: 3 15: 610 26: 121393 ? 5: 5 16: 987 27: 196418 ? 6: 8 17: 1597 28: 317811 ? 7: 13 18: 2584 29: 514229 ? 8: 21 19: 4181 30: 832040 ? 9: 34 20: 6765 31: 1346269 ? 10: 55 21: 10946 32: 2178309 ? 11: 89 22: 17711 ? - ? 5006th prime: ? 48673 ? - ? Last four digits of binomial coefficient (f..c): ? 9177415897211302590765294797044615525260065482298035878000 ? - ? 32nd digit after decimal in Pi: ? ? pi ? 0.12345678901234567890123456789011999999 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:25:36 2005 Input: print(Pi); Output: ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:25:57 2005 Input: print("Setting variables..."); a = 1106071; b = 140384; c = 21; d = 0428242561; e = 237; f = 5006; print("-"); print("Testing for primes:"); print(a " : " isprime(a)); print(b " : " isprime(b)); print(c " : " isprime(c)); print(d " : " isprime(d)); print(e " : " isprime(e)); print(f " : " isprime(f)); print("-"); print("Prime decomposition:"); print(a " : " factor(a)); print(b " : " factor(b)); print(c " : " factor(c)); print(d " : " factor(d)); print(e " : " factor(e)); print(f " : " factor(f)); print("-"); print("Before / afters:"); print(" < " a " < " nextprime(a)); print(" < " d " < " nextprime(d)); print("-"); print("GCD"); print("(a,b) = " gcd(a,b)); print("(b,c) = " gcd(b,c)); print("(a,b,c) = " gcd(a,(gcd(b,c)))); print("-"); print("LCM"); print("[c,e] = " lcm(c,e)); print("[e,f] = " lcm(e,f)); print("[c,e,f] = " lcm(c,(lcm(e,f)))); print("-"); print("Least positive residue:"); print("a mod c : " Mod(a,c)); print("d mod c : " Mod(d,c)); print("a =- d (mod c)? : (manuel)"); print("-"); print("Fibonacci numbers:"); print(a " or " c " or " f); print(" 1: " fibonacci(1) " 12: " fibonacci(12) " 23: " fibonacci(23)); print(" 2: " fibonacci(2) " 13: " fibonacci(13) " 24: " fibonacci(24)); print(" 3: " fibonacci(3) " 14: " fibonacci(14) " 25: " fibonacci(25)); print(" 4: " fibonacci(4) " 15: " fibonacci(15) " 26: " fibonacci(26)); print(" 5: " fibonacci(5) " 16: " fibonacci(16) " 27: " fibonacci(27)); print(" 6: " fibonacci(6) " 17: " fibonacci(17) " 28: " fibonacci(28)); print(" 7: " fibonacci(7) " 18: " fibonacci(18) " 29: " fibonacci(29)); print(" 8: " fibonacci(8) " 19: " fibonacci(19) " 30: " fibonacci(30)); print(" 9: " fibonacci(9) " 20: " fibonacci(20) " 31: " fibonacci(31)); print("10: " fibonacci(10) " 21: " fibonacci(21) " 32: " fibonacci(32)); print("11: " fibonacci(11) " 22: " fibonacci(22)); print("-"); print(f "th prime:"); print(prime(f)); print("-"); print("Last four digits of binomial coefficient (f..c):"); print(binomial(f,c)); print("-"); print("32nd digit after decimal in Pi:"); precision(33); print(Pi); print(0.12345678901234567890123456789012); Output: ? Setting variables... ? ? ? ? ? ? ? - ? Testing for primes: ? 1106071 : 0 ? 140384 : 0 ? 21 : 0 ? 428242561 : 0 ? 237 : 0 ? 5006 : 0 ? - ? Prime decomposition: ? 1106071 : [17, 1; 65063, 1] ? 140384 : [2, 5; 41, 1; 107, 1] ? 21 : [3, 1; 7, 1] ? 428242561 : [181, 1; 2365981, 1] ? 237 : [3, 1; 79, 1] ? 5006 : [2, 1; 2503, 1] ? - ? Before / afters: ? < 1106071 < 1106087 ? < 428242561 < 428242621 ? - ? GCD ? (a,b) = 1 ? (b,c) = 1 ? (a,b,c) = 1 ? - ? LCM ? [c,e] = 1659 ? [e,f] = 1186422 ? [c,e,f] = 8304954 ? - ? Least positive residue: ? a mod c : Mod(1, 21) ? d mod c : Mod(19, 21) ? a =- d (mod c)? : (manuel) ? - ? Fibonacci numbers: ? 1106071 or 21 or 5006 ? 1: 1 12: 144 23: 28657 ? 2: 1 13: 233 24: 46368 ? 3: 2 14: 377 25: 75025 ? 4: 3 15: 610 26: 121393 ? 5: 5 16: 987 27: 196418 ? 6: 8 17: 1597 28: 317811 ? 7: 13 18: 2584 29: 514229 ? 8: 21 19: 4181 30: 832040 ? 9: 34 20: 6765 31: 1346269 ? 10: 55 21: 10946 32: 2178309 ? 11: 89 22: 17711 ? - ? 5006th prime: ? 48673 ? - ? Last four digits of binomial coefficient (f..c): ? 9177415897211302590765294797044615525260065482298035878000 ? - ? 32nd digit after decimal in Pi: ? ? 3.1415926535897932384626433832795028841 ? 0.12345678901234567890123456789011999999 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:28:40 2005 Input: print("Setting variables..."); a = 1106071; b = 140384; c = 21; d = 0428242561; e = 237; f = 5006; print("-"); print("Testing for primes:"); print(a " : " isprime(a)); print(b " : " isprime(b)); print(c " : " isprime(c)); print(d " : " isprime(d)); print(e " : " isprime(e)); print(f " : " isprime(f)); print("-"); print("Prime decomposition:"); print(a " : " factor(a)); print(b " : " factor(b)); print(c " : " factor(c)); print(d " : " factor(d)); print(e " : " factor(e)); print(f " : " factor(f)); print("-"); print("Before / afters:"); print(" < " a " < " nextprime(a)); print(" < " d " < " nextprime(d)); print("-"); print("GCD"); print("(a,b) = " gcd(a,b)); print("(b,c) = " gcd(b,c)); print("(a,b,c) = " gcd(a,(gcd(b,c)))); print("-"); print("LCM"); print("[c,e] = " lcm(c,e)); print("[e,f] = " lcm(e,f)); print("[c,e,f] = " lcm(c,(lcm(e,f)))); print("-"); print("Least positive residue:"); print("a mod c : " Mod(a,c)); print("d mod c : " Mod(d,c)); print("a =- d (mod c)? : (manuel)"); print("-"); print("Fibonacci numbers:"); print(a " or " c " or " f); print(" 1: " fibonacci(1) " 12: " fibonacci(12) " 23: " fibonacci(23)); print(" 2: " fibonacci(2) " 13: " fibonacci(13) " 24: " fibonacci(24)); print(" 3: " fibonacci(3) " 14: " fibonacci(14) " 25: " fibonacci(25)); print(" 4: " fibonacci(4) " 15: " fibonacci(15) " 26: " fibonacci(26)); print(" 5: " fibonacci(5) " 16: " fibonacci(16) " 27: " fibonacci(27)); print(" 6: " fibonacci(6) " 17: " fibonacci(17) " 28: " fibonacci(28)); print(" 7: " fibonacci(7) " 18: " fibonacci(18) " 29: " fibonacci(29)); print(" 8: " fibonacci(8) " 19: " fibonacci(19) " 30: " fibonacci(30)); print(" 9: " fibonacci(9) " 20: " fibonacci(20) " 31: " fibonacci(31)); print("10: " fibonacci(10) " 21: " fibonacci(21) " 32: " fibonacci(32)); print("11: " fibonacci(11) " 22: " fibonacci(22)); print("-"); print(f "th prime:"); print(prime(f)); print("-"); print("Last four digits of binomial coefficient (f..c):"); print(binomial(f,c)); print("-"); print("32nd digit after decimal in Pi:"); precision(33); print(Pi); print(" " 0.12345678901234567890123456789012); Output: ? Setting variables... ? ? ? ? ? ? ? - ? Testing for primes: ? 1106071 : 0 ? 140384 : 0 ? 21 : 0 ? 428242561 : 0 ? 237 : 0 ? 5006 : 0 ? - ? Prime decomposition: ? 1106071 : [17, 1; 65063, 1] ? 140384 : [2, 5; 41, 1; 107, 1] ? 21 : [3, 1; 7, 1] ? 428242561 : [181, 1; 2365981, 1] ? 237 : [3, 1; 79, 1] ? 5006 : [2, 1; 2503, 1] ? - ? Before / afters: ? < 1106071 < 1106087 ? < 428242561 < 428242621 ? - ? GCD ? (a,b) = 1 ? (b,c) = 1 ? (a,b,c) = 1 ? - ? LCM ? [c,e] = 1659 ? [e,f] = 1186422 ? [c,e,f] = 8304954 ? - ? Least positive residue: ? a mod c : Mod(1, 21) ? d mod c : Mod(19, 21) ? a =- d (mod c)? : (manuel) ? - ? Fibonacci numbers: ? 1106071 or 21 or 5006 ? 1: 1 12: 144 23: 28657 ? 2: 1 13: 233 24: 46368 ? 3: 2 14: 377 25: 75025 ? 4: 3 15: 610 26: 121393 ? 5: 5 16: 987 27: 196418 ? 6: 8 17: 1597 28: 317811 ? 7: 13 18: 2584 29: 514229 ? 8: 21 19: 4181 30: 832040 ? 9: 34 20: 6765 31: 1346269 ? 10: 55 21: 10946 32: 2178309 ? 11: 89 22: 17711 ? - ? 5006th prime: ? 48673 ? - ? Last four digits of binomial coefficient (f..c): ? 9177415897211302590765294797044615525260065482298035878000 ? - ? 32nd digit after decimal in Pi: ? ? 3.1415926535897932384626433832795028841 ? 0.12345678901234567890123456789011999999 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:29:14 2005 Input: print("Setting variables..."); a = 1106071; b = 140384; c = 21; d = 0428242561; e = 237; f = 5006; print("-"); print("Testing for primes:"); print(a " : " isprime(a)); print(b " : " isprime(b)); print(c " : " isprime(c)); print(d " : " isprime(d)); print(e " : " isprime(e)); print(f " : " isprime(f)); print("-"); print("Prime decomposition:"); print(a " : " factor(a)); print(b " : " factor(b)); print(c " : " factor(c)); print(d " : " factor(d)); print(e " : " factor(e)); print(f " : " factor(f)); print("-"); print("Before / afters:"); print(" < " a " < " nextprime(a)); print(" < " d " < " nextprime(d)); print("-"); print("GCD"); print("(a,b) = " gcd(a,b)); print("(b,c) = " gcd(b,c)); print("(a,b,c) = " gcd(a,(gcd(b,c)))); print("-"); print("LCM"); print("[c,e] = " lcm(c,e)); print("[e,f] = " lcm(e,f)); print("[c,e,f] = " lcm(c,(lcm(e,f)))); print("-"); print("Least positive residue:"); print("a mod c : " Mod(a,c)); print("d mod c : " Mod(d,c)); print("a =- d (mod c)? : (manuel)"); print("-"); print("Fibonacci numbers:"); print(a " or " c " or " f); print(" 1: " fibonacci(1) " 12: " fibonacci(12) " 23: " fibonacci(23)); print(" 2: " fibonacci(2) " 13: " fibonacci(13) " 24: " fibonacci(24)); print(" 3: " fibonacci(3) " 14: " fibonacci(14) " 25: " fibonacci(25)); print(" 4: " fibonacci(4) " 15: " fibonacci(15) " 26: " fibonacci(26)); print(" 5: " fibonacci(5) " 16: " fibonacci(16) " 27: " fibonacci(27)); print(" 6: " fibonacci(6) " 17: " fibonacci(17) " 28: " fibonacci(28)); print(" 7: " fibonacci(7) " 18: " fibonacci(18) " 29: " fibonacci(29)); print(" 8: " fibonacci(8) " 19: " fibonacci(19) " 30: " fibonacci(30)); print(" 9: " fibonacci(9) " 20: " fibonacci(20) " 31: " fibonacci(31)); print("10: " fibonacci(10) " 21: " fibonacci(21) " 32: " fibonacci(32)); print("11: " fibonacci(11) " 22: " fibonacci(22)); print("-"); print(f "th prime:"); print(prime(f)); print("-"); print("Last four digits of binomial coefficient (f..c):"); print(binomial(f,c)); print("-"); print("32nd digit after decimal in Pi:"); precision(33); print(Pi); print(" 0.12345678901234567890123456789012"); Output: ? Setting variables... ? ? ? ? ? ? ? - ? Testing for primes: ? 1106071 : 0 ? 140384 : 0 ? 21 : 0 ? 428242561 : 0 ? 237 : 0 ? 5006 : 0 ? - ? Prime decomposition: ? 1106071 : [17, 1; 65063, 1] ? 140384 : [2, 5; 41, 1; 107, 1] ? 21 : [3, 1; 7, 1] ? 428242561 : [181, 1; 2365981, 1] ? 237 : [3, 1; 79, 1] ? 5006 : [2, 1; 2503, 1] ? - ? Before / afters: ? < 1106071 < 1106087 ? < 428242561 < 428242621 ? - ? GCD ? (a,b) = 1 ? (b,c) = 1 ? (a,b,c) = 1 ? - ? LCM ? [c,e] = 1659 ? [e,f] = 1186422 ? [c,e,f] = 8304954 ? - ? Least positive residue: ? a mod c : Mod(1, 21) ? d mod c : Mod(19, 21) ? a =- d (mod c)? : (manuel) ? - ? Fibonacci numbers: ? 1106071 or 21 or 5006 ? 1: 1 12: 144 23: 28657 ? 2: 1 13: 233 24: 46368 ? 3: 2 14: 377 25: 75025 ? 4: 3 15: 610 26: 121393 ? 5: 5 16: 987 27: 196418 ? 6: 8 17: 1597 28: 317811 ? 7: 13 18: 2584 29: 514229 ? 8: 21 19: 4181 30: 832040 ? 9: 34 20: 6765 31: 1346269 ? 10: 55 21: 10946 32: 2178309 ? 11: 89 22: 17711 ? - ? 5006th prime: ? 48673 ? - ? Last four digits of binomial coefficient (f..c): ? 9177415897211302590765294797044615525260065482298035878000 ? - ? 32nd digit after decimal in Pi: ? ? 3.1415926535897932384626433832795028841 ? 0.12345678901234567890123456789012 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.011s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:30:36 2005 Input: print("Setting variables..."); a = 1106071; b = 140384; c = 21; d = 0428242561; e = 237; f = 5006; print("-"); print("Testing for primes:"); print(a " : " isprime(a)); print(b " : " isprime(b)); print(c " : " isprime(c)); print(d " : " isprime(d)); print(e " : " isprime(e)); print(f " : " isprime(f)); print("-"); print("Prime decomposition:"); print(a " : " factor(a)); print(b " : " factor(b)); print(c " : " factor(c)); print(d " : " factor(d)); print(e " : " factor(e)); print(f " : " factor(f)); print("-"); print("Before / afters:"); print(" < " a " < " nextprime(a)); print(" < " d " < " nextprime(d)); print("-"); print("GCD"); print("(a,b) = " gcd(a,b)); print("(b,c) = " gcd(b,c)); print("(a,b,c) = " gcd(a,(gcd(b,c)))); print("-"); print("LCM"); print("[c,e] = " lcm(c,e)); print("[e,f] = " lcm(e,f)); print("[c,e,f] = " lcm(c,(lcm(e,f)))); print("-"); print("Least positive residue:"); print("a mod c : " Mod(a,c)); print("d mod c : " Mod(d,c)); print("a =- d (mod c)? : (manuel)"); print("-"); print("Fibonacci numbers:"); print(a " or " c " or " f); print(" 1: " fibonacci(1) " 12: " fibonacci(12) " 23: " fibonacci(23)); print(" 2: " fibonacci(2) " 13: " fibonacci(13) " 24: " fibonacci(24)); print(" 3: " fibonacci(3) " 14: " fibonacci(14) " 25: " fibonacci(25)); print(" 4: " fibonacci(4) " 15: " fibonacci(15) " 26: " fibonacci(26)); print(" 5: " fibonacci(5) " 16: " fibonacci(16) " 27: " fibonacci(27)); print(" 6: " fibonacci(6) " 17: " fibonacci(17) " 28: " fibonacci(28)); print(" 7: " fibonacci(7) " 18: " fibonacci(18) " 29: " fibonacci(29)); print(" 8: " fibonacci(8) " 19: " fibonacci(19) " 30: " fibonacci(30)); print(" 9: " fibonacci(9) " 20: " fibonacci(20) " 31: " fibonacci(31)); print("10: " fibonacci(10) " 21: " fibonacci(21) " 32: " fibonacci(32)); print("11: " fibonacci(11) " 22: " fibonacci(22)); print("-"); print(f "th prime:"); print(prime(f)); print("-"); print("Last four digits of binomial coefficient (f..c):"); print(binomial(f,c)); print("-"); print("32nd digit after decimal in Pi:"); precision(33); print(Pi); print(" 0.12345678901234567890123456789012"); Output: ? Setting variables... ? ? ? ? ? ? ? - ? Testing for primes: ? 1106071 : 0 ? 140384 : 0 ? 21 : 0 ? 428242561 : 0 ? 237 : 0 ? 5006 : 0 ? - ? Prime decomposition: ? 1106071 : [17, 1; 65063, 1] ? 140384 : [2, 5; 41, 1; 107, 1] ? 21 : [3, 1; 7, 1] ? 428242561 : [181, 1; 2365981, 1] ? 237 : [3, 1; 79, 1] ? 5006 : [2, 1; 2503, 1] ? - ? Before / afters: ? < 1106071 < 1106087 ? < 428242561 < 428242621 ? - ? GCD ? (a,b) = 1 ? (b,c) = 1 ? (a,b,c) = 1 ? - ? LCM ? [c,e] = 1659 ? [e,f] = 1186422 ? [c,e,f] = 8304954 ? - ? Least positive residue: ? a mod c : Mod(1, 21) ? d mod c : Mod(19, 21) ? a =- d (mod c)? : (manuel) ? - ? Fibonacci numbers: ? 1106071 or 21 or 5006 ? 1: 1 12: 144 23: 28657 ? 2: 1 13: 233 24: 46368 ? 3: 2 14: 377 25: 75025 ? 4: 3 15: 610 26: 121393 ? 5: 5 16: 987 27: 196418 ? 6: 8 17: 1597 28: 317811 ? 7: 13 18: 2584 29: 514229 ? 8: 21 19: 4181 30: 832040 ? 9: 34 20: 6765 31: 1346269 ? 10: 55 21: 10946 32: 2178309 ? 11: 89 22: 17711 ? - ? 5006th prime: ? 48673 ? - ? Last four digits of binomial coefficient (f..c): ? 9177415897211302590765294797044615525260065482298035878000 ? - ? 32nd digit after decimal in Pi: ? ? 3.1415926535897932384626433832795028841 ? 0.12345678901234567890123456789012 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:31:00 2005 Input: print("Setting variables..."); a = 1106071; b = 140384; c = 21; d = 0428242561; e = 237; f = 5006; print("-"); print("Testing for primes:"); print(a " : " isprime(a)); print(b " : " isprime(b)); print(c " : " isprime(c)); print(d " : " isprime(d)); print(e " : " isprime(e)); print(f " : " isprime(f)); print("-"); print("Prime decomposition:"); print(a " : " factor(a)); print(b " : " factor(b)); print(c " : " factor(c)); print(d " : " factor(d)); print(e " : " factor(e)); print(f " : " factor(f)); print("-"); print("Before / afters:"); print(" < " a " < " nextprime(a)); print(" < " d " < " nextprime(d)); print("-"); print("GCD"); print("(a,b) = " gcd(a,b)); print("(b,c) = " gcd(b,c)); print("(a,b,c) = " gcd(a,(gcd(b,c)))); print("-"); print("LCM"); print("[c,e] = " lcm(c,e)); print("[e,f] = " lcm(e,f)); print("[c,e,f] = " lcm(c,(lcm(e,f)))); print("-"); print("Least positive residue:"); print("a mod c : " Mod(a,c)); print("d mod c : " Mod(d,c)); print("a =- d (mod c)? : (manuel)"); print("-"); print("Fibonacci numbers:"); print(a " or " c " or " f); print(" 1: " fibonacci(1) " 12: " fibonacci(12) " 23: " fibonacci(23)); print(" 2: " fibonacci(2) " 13: " fibonacci(13) " 24: " fibonacci(24)); print(" 3: " fibonacci(3) " 14: " fibonacci(14) " 25: " fibonacci(25)); print(" 4: " fibonacci(4) " 15: " fibonacci(15) " 26: " fibonacci(26)); print(" 5: " fibonacci(5) " 16: " fibonacci(16) " 27: " fibonacci(27)); print(" 6: " fibonacci(6) " 17: " fibonacci(17) " 28: " fibonacci(28)); print(" 7: " fibonacci(7) " 18: " fibonacci(18) " 29: " fibonacci(29)); print(" 8: " fibonacci(8) " 19: " fibonacci(19) " 30: " fibonacci(30)); print(" 9: " fibonacci(9) " 20: " fibonacci(20) " 31: " fibonacci(31)); print("10: " fibonacci(10) " 21: " fibonacci(21) " 32: " fibonacci(32)); print("11: " fibonacci(11) " 22: " fibonacci(22)); print("-"); print(f "th prime:"); print(prime(f)); print("-"); print("Last four digits of binomial coefficient (f..c):"); print(binomial(f,c)); print("-"); print("32nd digit after decimal in Pi:"); precision(33); print(Pi); print(" 0.12345678901234567890123456789012"); Output: ? Setting variables... ? ? ? ? ? ? ? - ? Testing for primes: ? 1106071 : 0 ? 140384 : 0 ? 21 : 0 ? 428242561 : 0 ? 237 : 0 ? 5006 : 0 ? - ? Prime decomposition: ? 1106071 : [17, 1; 65063, 1] ? 140384 : [2, 5; 41, 1; 107, 1] ? 21 : [3, 1; 7, 1] ? 428242561 : [181, 1; 2365981, 1] ? 237 : [3, 1; 79, 1] ? 5006 : [2, 1; 2503, 1] ? - ? Before / afters: ? < 1106071 < 1106087 ? < 428242561 < 428242621 ? - ? GCD ? (a,b) = 1 ? (b,c) = 1 ? (a,b,c) = 1 ? - ? LCM ? [c,e] = 1659 ? [e,f] = 1186422 ? [c,e,f] = 8304954 ? - ? Least positive residue: ? a mod c : Mod(1, 21) ? d mod c : Mod(19, 21) ? a =- d (mod c)? : (manuel) ? - ? Fibonacci numbers: ? 1106071 or 21 or 5006 ? 1: 1 12: 144 23: 28657 ? 2: 1 13: 233 24: 46368 ? 3: 2 14: 377 25: 75025 ? 4: 3 15: 610 26: 121393 ? 5: 5 16: 987 27: 196418 ? 6: 8 17: 1597 28: 317811 ? 7: 13 18: 2584 29: 514229 ? 8: 21 19: 4181 30: 832040 ? 9: 34 20: 6765 31: 1346269 ? 10: 55 21: 10946 32: 2178309 ? 11: 89 22: 17711 ? - ? 5006th prime: ? 48673 ? - ? Last four digits of binomial coefficient (f..c): ? 9177415897211302590765294797044615525260065482298035878000 ? - ? 32nd digit after decimal in Pi: ? ? 3.1415926535897932384626433832795028841 ? 0.12345678901234567890123456789012 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.009s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 04:31:15 2005 Input: print("Setting variables..."); a = 1106071; b = 140384; c = 21; d = 0428242561; e = 237; f = 5006; print("-"); print("Testing for primes:"); print(a " : " isprime(a)); print(b " : " isprime(b)); print(c " : " isprime(c)); print(d " : " isprime(d)); print(e " : " isprime(e)); print(f " : " isprime(f)); print("-"); print("Prime decomposition:"); print(a " : " factor(a)); print(b " : " factor(b)); print(c " : " factor(c)); print(d " : " factor(d)); print(e " : " factor(e)); print(f " : " factor(f)); print("-"); print("Before / afters:"); print(" < " a " < " nextprime(a)); print(" < " d " < " nextprime(d)); print("-"); print("GCD"); print("(a,b) = " gcd(a,b)); print("(b,c) = " gcd(b,c)); print("(a,b,c) = " gcd(a,(gcd(b,c)))); print("-"); print("LCM"); print("[c,e] = " lcm(c,e)); print("[e,f] = " lcm(e,f)); print("[c,e,f] = " lcm(c,(lcm(e,f)))); print("-"); print("Least positive residue:"); print("a mod c : " Mod(a,c)); print("d mod c : " Mod(d,c)); print("a =- d (mod c)? : (manuel)"); print("-"); print("Fibonacci numbers:"); print(a " or " c " or " f); print(" 1: " fibonacci(1) " 12: " fibonacci(12) " 23: " fibonacci(23)); print(" 2: " fibonacci(2) " 13: " fibonacci(13) " 24: " fibonacci(24)); print(" 3: " fibonacci(3) " 14: " fibonacci(14) " 25: " fibonacci(25)); print(" 4: " fibonacci(4) " 15: " fibonacci(15) " 26: " fibonacci(26)); print(" 5: " fibonacci(5) " 16: " fibonacci(16) " 27: " fibonacci(27)); print(" 6: " fibonacci(6) " 17: " fibonacci(17) " 28: " fibonacci(28)); print(" 7: " fibonacci(7) " 18: " fibonacci(18) " 29: " fibonacci(29)); print(" 8: " fibonacci(8) " 19: " fibonacci(19) " 30: " fibonacci(30)); print(" 9: " fibonacci(9) " 20: " fibonacci(20) " 31: " fibonacci(31)); print("10: " fibonacci(10) " 21: " fibonacci(21) " 32: " fibonacci(32)); print("11: " fibonacci(11) " 22: " fibonacci(22)); print("-"); print(f "th prime:"); print(prime(f)); print("-"); print("Last four digits of binomial coefficient (f..c):"); print(binomial(f,c)); print("-"); print("32nd digit after decimal in Pi:"); precision(33); print(Pi); print(" 0.12345678901234567890123456789012"); Output: ? Setting variables... ? ? ? ? ? ? ? - ? Testing for primes: ? 1106071 : 0 ? 140384 : 0 ? 21 : 0 ? 428242561 : 0 ? 237 : 0 ? 5006 : 0 ? - ? Prime decomposition: ? 1106071 : [17, 1; 65063, 1] ? 140384 : [2, 5; 41, 1; 107, 1] ? 21 : [3, 1; 7, 1] ? 428242561 : [181, 1; 2365981, 1] ? 237 : [3, 1; 79, 1] ? 5006 : [2, 1; 2503, 1] ? - ? Before / afters: ? < 1106071 < 1106087 ? < 428242561 < 428242621 ? - ? GCD ? (a,b) = 1 ? (b,c) = 1 ? (a,b,c) = 1 ? - ? LCM ? [c,e] = 1659 ? [e,f] = 1186422 ? [c,e,f] = 8304954 ? - ? Least positive residue: ? a mod c : Mod(1, 21) ? d mod c : Mod(19, 21) ? a =- d (mod c)? : (manuel) ? - ? Fibonacci numbers: ? 1106071 or 21 or 5006 ? 1: 1 12: 144 23: 28657 ? 2: 1 13: 233 24: 46368 ? 3: 2 14: 377 25: 75025 ? 4: 3 15: 610 26: 121393 ? 5: 5 16: 987 27: 196418 ? 6: 8 17: 1597 28: 317811 ? 7: 13 18: 2584 29: 514229 ? 8: 21 19: 4181 30: 832040 ? 9: 34 20: 6765 31: 1346269 ? 10: 55 21: 10946 32: 2178309 ? 11: 89 22: 17711 ? - ? 5006th prime: ? 48673 ? - ? Last four digits of binomial coefficient (f..c): ? 9177415897211302590765294797044615525260065482298035878000 ? - ? 32nd digit after decimal in Pi: ? ? 3.1415926535897932384626433832795028841 ? 0.12345678901234567890123456789012 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.005s sys 0m0.011s '217.148' ************** PARI ***************** Host 217.148.68.113 (217.148.68.113) Time: Tue Mar 29 06:14:01 2005 Input: kf:=GF(2); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: kf:=GF(2); ^------- Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 06:48:55 2005 Input: print("Setting variables..."); a = 1106071; b = 140384; c = 21; d = 0428242561; e = 237; f = 5006; print("Done :D"); print("-"); print("Testing for primes:"); print(a " : " isprime(a)); print(b " : " isprime(b)); print(c " : " isprime(c)); print(d " : " isprime(d)); print(e " : " isprime(e)); print(f " : " isprime(f)); print("-"); print("Prime decomposition:"); print(a " : " factor(a)); print(b " : " factor(b)); print(c " : " factor(c)); print(d " : " factor(d)); print(e " : " factor(e)); print(f " : " factor(f)); print("-"); print("Before / afters:"); print(" < " a " < " nextprime(a)); print(" < " d " < " nextprime(d)); print("-"); print("GCD"); print("(a,b) = " gcd(a,b)); print("(b,c) = " gcd(b,c)); print("(a,b,c) = " gcd(a,(gcd(b,c)))); print("-"); print("LCM"); print("[c,e] = " lcm(c,e)); print("[e,f] = " lcm(e,f)); print("[c,e,f] = " lcm(c,(lcm(e,f)))); print("-"); print("Least positive residue:"); print("a mod c : " Mod(a,c)); print("d mod c : " Mod(d,c)); print("a =- d (mod c)? : (manuel)"); print("-"); print("Fibonacci numbers:"); print(a " or " c " or " f); print(" 1: " fibonacci(1) " 12: " fibonacci(12) " 23: " fibonacci(23)); print(" 2: " fibonacci(2) " 13: " fibonacci(13) " 24: " fibonacci(24)); print(" 3: " fibonacci(3) " 14: " fibonacci(14) " 25: " fibonacci(25)); print(" 4: " fibonacci(4) " 15: " fibonacci(15) " 26: " fibonacci(26)); print(" 5: " fibonacci(5) " 16: " fibonacci(16) " 27: " fibonacci(27)); print(" 6: " fibonacci(6) " 17: " fibonacci(17) " 28: " fibonacci(28)); print(" 7: " fibonacci(7) " 18: " fibonacci(18) " 29: " fibonacci(29)); print(" 8: " fibonacci(8) " 19: " fibonacci(19) " 30: " fibonacci(30)); print(" 9: " fibonacci(9) " 20: " fibonacci(20) " 31: " fibonacci(31)); print("10: " fibonacci(10) " 21: " fibonacci(21) " 32: " fibonacci(32)); print("11: " fibonacci(11) " 22: " fibonacci(22)); print("-"); print(f "th prime:"); print(prime(f)); print("-"); print("Last four digits of binomial coefficient (f..c):"); print(binomial(f,c)); print("-"); print("32nd digit after decimal in Pi:"); precision(33); print(Pi); print(" 0.12345678901234567890123456789012"); Output: ? Setting variables... ? ? ? ? ? ? ? Done :D ? - ? Testing for primes: ? 1106071 : 0 ? 140384 : 0 ? 21 : 0 ? 428242561 : 0 ? 237 : 0 ? 5006 : 0 ? - ? Prime decomposition: ? 1106071 : [17, 1; 65063, 1] ? 140384 : [2, 5; 41, 1; 107, 1] ? 21 : [3, 1; 7, 1] ? 428242561 : [181, 1; 2365981, 1] ? 237 : [3, 1; 79, 1] ? 5006 : [2, 1; 2503, 1] ? - ? Before / afters: ? < 1106071 < 1106087 ? < 428242561 < 428242621 ? - ? GCD ? (a,b) = 1 ? (b,c) = 1 ? (a,b,c) = 1 ? - ? LCM ? [c,e] = 1659 ? [e,f] = 1186422 ? [c,e,f] = 8304954 ? - ? Least positive residue: ? a mod c : Mod(1, 21) ? d mod c : Mod(19, 21) ? a =- d (mod c)? : (manuel) ? - ? Fibonacci numbers: ? 1106071 or 21 or 5006 ? 1: 1 12: 144 23: 28657 ? 2: 1 13: 233 24: 46368 ? 3: 2 14: 377 25: 75025 ? 4: 3 15: 610 26: 121393 ? 5: 5 16: 987 27: 196418 ? 6: 8 17: 1597 28: 317811 ? 7: 13 18: 2584 29: 514229 ? 8: 21 19: 4181 30: 832040 ? 9: 34 20: 6765 31: 1346269 ? 10: 55 21: 10946 32: 2178309 ? 11: 89 22: 17711 ? - ? 5006th prime: ? 48673 ? - ? Last four digits of binomial coefficient (f..c): ? 9177415897211302590765294797044615525260065482298035878000 ? - ? 32nd digit after decimal in Pi: ? ? 3.1415926535897932384626433832795028841 ? 0.12345678901234567890123456789012 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.011s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 07:02:32 2005 Input: a = 1106071; d = 0428242561; a = a - 20; print(nextprime(a)); b = b - 20; print(nextprime(b)); Output: ? ? ? ? ? 1106069 ? ? ? ? Errors (if any) and Timing Info: *** not an integer argument in an arithmetic function Timing: real 0m0.029s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 07:03:17 2005 Input: a = 1106071; d = 0428242561; print("OMGWTFBBQ"); a = a - 20; print(nextprime(a)); b = b - 20; print(nextprime(b)); Output: ? ? ? ? OMGWTFBBQ ? ? ? 1106069 ? ? ? ? Errors (if any) and Timing Info: *** not an integer argument in an arithmetic function Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 07:04:07 2005 Input: a = 1106071; d = 0428242561; a = a - 20; print(nextprime(a)); d = d - 20; print(nextprime(d)); Output: ? ? ? ? ? 1106069 ? ? ? 428242553 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 07:04:18 2005 Input: a = 1106071; d = 0428242561; a = a - 20; print(nextprime(a)); d = d - 50; print(nextprime(d)); Output: ? ? ? ? ? 1106069 ? ? ? 428242511 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 07:04:43 2005 Input: a = 1106071; d = 0428242561; a = a - 20; print(nextprime(a)); d = d - 20; print(nextprime(d)); Output: ? ? ? ? ? 1106069 ? ? ? 428242553 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 07:05:29 2005 Input: a = 1106071; d = 0428242561; a = a - 20; print(nextprime(a)); d = d - 10; print(nextprime(d)); Output: ? ? ? ? ? 1106069 ? ? ? 428242553 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 07:05:35 2005 Input: a = 1106071; d = 0428242561; a = a - 20; print(nextprime(a)); d = d - 5; print(nextprime(d)); Output: ? ? ? ? ? 1106069 ? ? ? 428242559 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 07:07:12 2005 Input: print("Setting variables..."); a = 1106071; b = 140384; c = 21; d = 0428242561; e = 237; f = 5006; print("Done :D"); print("-"); print("Testing for primes:"); print(a " : " isprime(a)); print(b " : " isprime(b)); print(c " : " isprime(c)); print(d " : " isprime(d)); print(e " : " isprime(e)); print(f " : " isprime(f)); print("-"); print("Prime decomposition:"); print(a " : " factor(a)); print(b " : " factor(b)); print(c " : " factor(c)); print(d " : " factor(d)); print(e " : " factor(e)); print(f " : " factor(f)); print("-"); print("Before / afters:"); print(" < " a " < " nextprime(a)); print(" < " d " < " nextprime(d)); print("-"); print("GCD"); print("(a,b) = " gcd(a,b)); print("(b,c) = " gcd(b,c)); print("(a,b,c) = " gcd(a,(gcd(b,c)))); print("-"); print("LCM"); print("[c,e] = " lcm(c,e)); print("[e,f] = " lcm(e,f)); print("[c,e,f] = " lcm(c,(lcm(e,f)))); print("-"); print("Least positive residue:"); print("a mod c : " Mod(a,c)); print("d mod c : " Mod(d,c)); print("a =- d (mod c)? : (manuel)"); print("-"); print("Fibonacci numbers:"); print(a " or " c " or " f); print(" 1: " fibonacci(1) " 12: " fibonacci(12) " 23: " fibonacci(23)); print(" 2: " fibonacci(2) " 13: " fibonacci(13) " 24: " fibonacci(24)); print(" 3: " fibonacci(3) " 14: " fibonacci(14) " 25: " fibonacci(25)); print(" 4: " fibonacci(4) " 15: " fibonacci(15) " 26: " fibonacci(26)); print(" 5: " fibonacci(5) " 16: " fibonacci(16) " 27: " fibonacci(27)); print(" 6: " fibonacci(6) " 17: " fibonacci(17) " 28: " fibonacci(28)); print(" 7: " fibonacci(7) " 18: " fibonacci(18) " 29: " fibonacci(29)); print(" 8: " fibonacci(8) " 19: " fibonacci(19) " 30: " fibonacci(30)); print(" 9: " fibonacci(9) " 20: " fibonacci(20) " 31: " fibonacci(31)); print("10: " fibonacci(10) " 21: " fibonacci(21) " 32: " fibonacci(32)); print("11: " fibonacci(11) " 22: " fibonacci(22)); print("-"); print(f "th prime:"); print(prime(f)); print("-"); print("Last four digits of binomial coefficient (f..c):"); print(binomial(f,c)); print("-"); print("32nd digit after decimal in Pi:"); precision(33); print(Pi); print(" 0.12345678901234567890123456789012"); Output: ? Setting variables... ? ? ? ? ? ? ? Done :D ? - ? Testing for primes: ? 1106071 : 0 ? 140384 : 0 ? 21 : 0 ? 428242561 : 0 ? 237 : 0 ? 5006 : 0 ? - ? Prime decomposition: ? 1106071 : [17, 1; 65063, 1] ? 140384 : [2, 5; 41, 1; 107, 1] ? 21 : [3, 1; 7, 1] ? 428242561 : [181, 1; 2365981, 1] ? 237 : [3, 1; 79, 1] ? 5006 : [2, 1; 2503, 1] ? - ? Before / afters: ? < 1106071 < 1106087 ? < 428242561 < 428242621 ? - ? GCD ? (a,b) = 1 ? (b,c) = 1 ? (a,b,c) = 1 ? - ? LCM ? [c,e] = 1659 ? [e,f] = 1186422 ? [c,e,f] = 8304954 ? - ? Least positive residue: ? a mod c : Mod(1, 21) ? d mod c : Mod(19, 21) ? a =- d (mod c)? : (manuel) ? - ? Fibonacci numbers: ? 1106071 or 21 or 5006 ? 1: 1 12: 144 23: 28657 ? 2: 1 13: 233 24: 46368 ? 3: 2 14: 377 25: 75025 ? 4: 3 15: 610 26: 121393 ? 5: 5 16: 987 27: 196418 ? 6: 8 17: 1597 28: 317811 ? 7: 13 18: 2584 29: 514229 ? 8: 21 19: 4181 30: 832040 ? 9: 34 20: 6765 31: 1346269 ? 10: 55 21: 10946 32: 2178309 ? 11: 89 22: 17711 ? - ? 5006th prime: ? 48673 ? - ? Last four digits of binomial coefficient (f..c): ? 9177415897211302590765294797044615525260065482298035878000 ? - ? 32nd digit after decimal in Pi: ? ? 3.1415926535897932384626433832795028841 ? 0.12345678901234567890123456789012 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.009s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 09:44:26 2005 Input: t(i) = if(valuation(bernfrac(2*i),p)>0,print(p," ",2*i),) s(p) = for(i=1,(p-3)/2,t(i)) forprime(p=1, 200, s(p)) Output: ? ? ? 37 32 59 44 67 58 101 68 103 24 131 22 149 130 157 62 157 110 ? Errors (if any) and Timing Info: Timing: real 0m0.664s user 0m0.421s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 09:45:08 2005 Input: t(i) = if(valuation(bernfrac(2*i),p)>0,print(p," ",2*i),) forprime(p=1, 200, for(i=1,(p-3)/2,t(i))) Output: ? ? 37 32 59 44 67 58 101 68 103 24 131 22 149 130 157 62 157 110 ? Errors (if any) and Timing Info: Timing: real 0m0.426s user 0m0.421s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 11:35:32 2005 Input: p=37 eta(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, eta(a)^(lift(Mod(a^k, p)))) Output: ? 37 ? ? ? Errors (if any) and Timing Info: *** unexpected character: eta(a)=Mod(x^a+1/x^a,sum(n ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 11:36:18 2005 Input: p=37 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, b(a)^(lift(Mod(a^k, p)))) Output: ? 37 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 11:36:32 2005 Input: p=37 eta(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, b(a)^(lift(Mod(a^k, p)))) Output: ? 37 ? ? ? Errors (if any) and Timing Info: *** unexpected character: eta(n)=Mod(x^n+1/x^n,sum(n ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 11:36:39 2005 Input: p=37 e(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, b(a)^(lift(Mod(a^k, p)))) Output: ? 37 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 11:36:45 2005 Input: p=37 et(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, b(a)^(lift(Mod(a^k, p)))) Output: ? 37 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 11:36:49 2005 Input: p=37 eta(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, b(a)^(lift(Mod(a^k, p)))) Output: ? 37 ? ? ? Errors (if any) and Timing Info: *** unexpected character: eta(n)=Mod(x^n+1/x^n,sum(n ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 11:36:56 2005 Input: p=37 et(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, b(a)^(lift(Mod(a^k, p)))) Output: ? 37 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 11:37:16 2005 Input: p=37 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, b(a)^(lift(Mod(a^k, p)))) Output: ? 37 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 11:37:27 2005 Input: p=37 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, b(a)^(lift(Mod(a^k, p)))) c(4) Output: ? 37 ? ? ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: b(a)^(lift(Mod(a^k,p)))) ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 11:37:44 2005 Input: p=37 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) Output: ? 37 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.057s user 0m0.035s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 11:38:18 2005 Input: p=37 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j) Output: ? 37 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 37 ? 32 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.068s user 0m0.061s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 12:03:53 2005 Input: p=37 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^{n})) d=lift(q)*Mod(1, p) (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) truncate(a^{p}) Output: ? 37 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? Mod(1, 37)*q ? 0 ? 0 ? q + O(37^2) ? ? Errors (if any) and Timing Info: *** forbidden division t_SER % t_INT. *** unexpected character: w=Mod(1-x,sum(n=0,p-1,x^{n})) ^----- *** unexpected character: truncate(a^{p}) ^---- Timing: real 0m0.051s user 0m0.035s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 12:05:39 2005 Input: p=37 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^{n})) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) truncate(a^p) Output: ? 37 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? Mod(1, 37)*q ? q ? 0 ? 0 ? q + O(37^2) ? q^37 + O(37^2)*q^36 + O(37^4)*q^35 + O(37^6)*q^34 + O(37^8)*q^33 + O(37^10)*q^32 + O(37^12)*q^31 + O(37^14)*q^30 + O(37^16)*q^29 + O(37^18)*q^28 + O(37^20)*q^27 + O(37^22)*q^26 + O(37^24)*q^25 + O(37^26)*q^24 + O(37^28)*q^23 + O(37^30)*q^22 + O(37^32)*q^21 + O(37^34)*q^20 + O(37^36)*q^19 + O(37^38)*q^18 + O(37^40)*q^17 + O(37^42)*q^16 + O(37^44)*q^15 + O(37^46)*q^14 + O(37^48)*q^13 + O(37^50)*q^12 + O(37^52)*q^11 + O(37^54)*q^10 + O(37^56)*q^9 + O(37^58)*q^8 + O(37^60)*q^7 + O(37^62)*q^6 + O(37^64)*q^5 + O(37^66)*q^4 + O(37^68)*q^3 + O(37^70)*q^2 + O(37^72)*q + O(37^74) ? Errors (if any) and Timing Info: *** forbidden division t_SER % t_INT. *** unexpected character: w=Mod(1-x,sum(n=0,p-1,x^{n})) ^----- Timing: real 0m0.041s user 0m0.032s sys 0m0.010s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 12:06:18 2005 Input: p=37 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) truncate(a^p) Output: ? 37 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(1, 37)*q ? q ? 0 ? 0 ? q + O(37^2) ? q^37 + O(37^2)*q^36 + O(37^4)*q^35 + O(37^6)*q^34 + O(37^8)*q^33 + O(37^10)*q^32 + O(37^12)*q^31 + O(37^14)*q^30 + O(37^16)*q^29 + O(37^18)*q^28 + O(37^20)*q^27 + O(37^22)*q^26 + O(37^24)*q^25 + O(37^26)*q^24 + O(37^28)*q^23 + O(37^30)*q^22 + O(37^32)*q^21 + O(37^34)*q^20 + O(37^36)*q^19 + O(37^38)*q^18 + O(37^40)*q^17 + O(37^42)*q^16 + O(37^44)*q^15 + O(37^46)*q^14 + O(37^48)*q^13 + O(37^50)*q^12 + O(37^52)*q^11 + O(37^54)*q^10 + O(37^56)*q^9 + O(37^58)*q^8 + O(37^60)*q^7 + O(37^62)*q^6 + O(37^64)*q^5 + O(37^66)*q^4 + O(37^68)*q^3 + O(37^70)*q^2 + O(37^72)*q + O(37^74) ? Errors (if any) and Timing Info: *** forbidden division t_SER % t_INT. Timing: real 0m0.050s user 0m0.040s sys 0m0.011s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:07:16 2005 Input: Mod(2,9991)^9990 Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:07:22 2005 Input: Mod(2,9991)^9990 Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 12:07:32 2005 Input: p=37 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) truncate(a^p) Output: ? 37 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(1, 37)*q ? q ? 0 ? 0 ? q + O(37^2) ? q^37 + O(37^2)*q^36 + O(37^4)*q^35 + O(37^6)*q^34 + O(37^8)*q^33 + O(37^10)*q^32 + O(37^12)*q^31 + O(37^14)*q^30 + O(37^16)*q^29 + O(37^18)*q^28 + O(37^20)*q^27 + O(37^22)*q^26 + O(37^24)*q^25 + O(37^26)*q^24 + O(37^28)*q^23 + O(37^30)*q^22 + O(37^32)*q^21 + O(37^34)*q^20 + O(37^36)*q^19 + O(37^38)*q^18 + O(37^40)*q^17 + O(37^42)*q^16 + O(37^44)*q^15 + O(37^46)*q^14 + O(37^48)*q^13 + O(37^50)*q^12 + O(37^52)*q^11 + O(37^54)*q^10 + O(37^56)*q^9 + O(37^58)*q^8 + O(37^60)*q^7 + O(37^62)*q^6 + O(37^64)*q^5 + O(37^66)*q^4 + O(37^68)*q^3 + O(37^70)*q^2 + O(37^72)*q + O(37^74) ? Errors (if any) and Timing Info: *** forbidden division t_SER % t_INT. Timing: real 0m0.049s user 0m0.041s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 12:08:04 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) A=a^p*Mod(1, w^37) Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 + O(37^2) ? ? Errors (if any) and Timing Info: *** forbidden division t_INT % t_POLMOD. Timing: real 0m0.052s user 0m0.046s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:08:06 2005 Input: Mod(2,9991)^4 Output: ? Mod(16, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 12:08:29 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) truncate(a^p) Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Errors (if any) and Timing Info: Timing: real 0m0.052s user 0m0.048s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 12:08:54 2005 Input: p=37 j=32 b(n)=Mod(x^n+1/x^n, sum(n=0, p-1, x^n)); c(k)=prod(n=1, p-1, b(n)^(lift(Mod(n^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); (q-d)/w^(p-1) (q-d)/w^p a=lift(d)+O(p^2) k=truncate(a^p) k Output: ? 37 ? 32 ? ? ? ? ? ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/37*x^8 + 22129235589291529919288621839239489607695107424268971676734461112204547244160/37*x^7 + 20588710814232861874358507278146722076845838122042806799065764346102424674700/37*x^6 + 18553971763967974912908774197022536466016855535240551812818412645562206277110/37*x^5 + 16083554176334345621736444047303676656961979371067245873825611691930812039021/37*x^4 + 13248527467450008112859773860712560063504278525093409015049928319517355743049/37*x^3 + 10130450194007621893569959087657510538331435576346057879997892491292036887201/37*x^2 + 6819023762091920892943823171810392268997304410336865850686547057877635219062/37*x + 3409511881045960446471911585905196134498652205168432925343273528938817609531/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^3[+++] ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Errors (if any) and Timing Info: Timing: real 0m0.052s user 0m0.047s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 12:10:50 2005 Input: p=37 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) truncate(a^p) Output: ? 37 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(1, 37)*q ? q ? 0 ? 0 ? q + O(37^2) ? q^37 + O(37^2)*q^36 + O(37^4)*q^35 + O(37^6)*q^34 + O(37^8)*q^33 + O(37^10)*q^32 + O(37^12)*q^31 + O(37^14)*q^30 + O(37^16)*q^29 + O(37^18)*q^28 + O(37^20)*q^27 + O(37^22)*q^26 + O(37^24)*q^25 + O(37^26)*q^24 + O(37^28)*q^23 + O(37^30)*q^22 + O(37^32)*q^21 + O(37^34)*q^20 + O(37^36)*q^19 + O(37^38)*q^18 + O(37^40)*q^17 + O(37^42)*q^16 + O(37^44)*q^15 + O(37^46)*q^14 + O(37^48)*q^13 + O(37^50)*q^12 + O(37^52)*q^11 + O(37^54)*q^10 + O(37^56)*q^9 + O(37^58)*q^8 + O(37^60)*q^7 + O(37^62)*q^6 + O(37^64)*q^5 + O(37^66)*q^4 + O(37^68)*q^3 + O(37^70)*q^2 + O(37^72)*q + O(37^74) ? Errors (if any) and Timing Info: *** forbidden division t_SER % t_INT. Timing: real 0m0.050s user 0m0.045s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 12:11:18 2005 Input: p=37 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) d D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) truncate(a^p) Output: ? 37 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(1, 37)*q ? Mod(1, 37)*q ? q ? 0 ? 0 ? q + O(37^2) ? q^37 + O(37^2)*q^36 + O(37^4)*q^35 + O(37^6)*q^34 + O(37^8)*q^33 + O(37^10)*q^32 + O(37^12)*q^31 + O(37^14)*q^30 + O(37^16)*q^29 + O(37^18)*q^28 + O(37^20)*q^27 + O(37^22)*q^26 + O(37^24)*q^25 + O(37^26)*q^24 + O(37^28)*q^23 + O(37^30)*q^22 + O(37^32)*q^21 + O(37^34)*q^20 + O(37^36)*q^19 + O(37^38)*q^18 + O(37^40)*q^17 + O(37^42)*q^16 + O(37^44)*q^15 + O(37^46)*q^14 + O(37^48)*q^13 + O(37^50)*q^12 + O(37^52)*q^11 + O(37^54)*q^10 + O(37^56)*q^9 + O(37^58)*q^8 + O(37^60)*q^7 + O(37^62)*q^6 + O(37^64)*q^5 + O(37^66)*q^4 + O(37^68)*q^3 + O(37^70)*q^2 + O(37^72)*q + O(37^74) ? Errors (if any) and Timing Info: *** forbidden division t_SER % t_INT. Timing: real 0m0.050s user 0m0.044s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 12:11:39 2005 Input: p=37 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) d (q-d)/w^(p-1) (q-d)/w^p a=D+O(p^2) truncate(a^p) Output: ? 37 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(1, 37)*q ? Mod(1, 37)*q ? 0 ? 0 ? D + O(37^2) ? D^37 + O(37^2)*D^36 + O(37^4)*D^35 + O(37^6)*D^34 + O(37^8)*D^33 + O(37^10)*D^32 + O(37^12)*D^31 + O(37^14)*D^30 + O(37^16)*D^29 + O(37^18)*D^28 + O(37^20)*D^27 + O(37^22)*D^26 + O(37^24)*D^25 + O(37^26)*D^24 + O(37^28)*D^23 + O(37^30)*D^22 + O(37^32)*D^21 + O(37^34)*D^20 + O(37^36)*D^19 + O(37^38)*D^18 + O(37^40)*D^17 + O(37^42)*D^16 + O(37^44)*D^15 + O(37^46)*D^14 + O(37^48)*D^13 + O(37^50)*D^12 + O(37^52)*D^11 + O(37^54)*D^10 + O(37^56)*D^9 + O(37^58)*D^8 + O(37^60)*D^7 + O(37^62)*D^6 + O(37^64)*D^5 + O(37^66)*D^4 + O(37^68)*D^3 + O(37^70)*D^2 + O(37^72)*D + O(37^74) ? Errors (if any) and Timing Info: *** forbidden division t_SER % t_INT. Timing: real 0m0.050s user 0m0.042s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:13:13 2005 Input: Mod(2,9991)^8 Output: ? Mod(256, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:13:40 2005 Input: Mod(2,9991)^256 Output: ? Mod(2680, 9991) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:13:53 2005 Input: Mod(2,9991)^512 Output: ? Mod(8862, 9991) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:14:03 2005 Input: Mod(2,9991)^1024 Output: ? Mod(5784, 9991) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:14:19 2005 Input: Mod(2,9991)^8192 Output: ? Mod(6243, 9991) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:16:32 2005 Input: Mod(4*256*2680*8862*5784*6243,9991) Output: ? Mod(3837, 9991) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:17:32 2005 Input: Mod(2,9991)^2 Output: ? Mod(4, 9991) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:17:40 2005 Input: Mod(2,9991)^256 Output: ? Mod(2680, 9991) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:18:00 2005 Input: Mod(2,9991)^4 Output: ? Mod(16, 9991) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:18:50 2005 Input: Mod(4*16*2680*8862*5784*6243,9991) Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:19:34 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:21:04 2005 Input: Mod(347,463)^(-1) Output: ? Mod(459, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:21:32 2005 Input: Mod(347,463)^(-113) Output: ? Mod(217, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:21:55 2005 Input: Mod(217,463)^(113) Output: ? Mod(403, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:22:16 2005 Input: Mod(347,463)^(-113) Output: ? Mod(217, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:22:29 2005 Input: Mod(217,463)^(113) Output: ? Mod(403, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:23:44 2005 Input: Mod(347,463)^(113) Output: ? Mod(431, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:24:01 2005 Input: Mod(413,463)^(113) Output: ? Mod(333, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:25:25 2005 Input: Mod(347,463)^(-113) Output: ? Mod(217, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:25:39 2005 Input: Mod(217,463)^(-113) Output: ? Mod(54, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:25:47 2005 Input: Mod(217,463)^(113) Output: ? Mod(403, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:25:59 2005 Input: Mod(403,463)^(113) Output: ? Mod(372, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:26:04 2005 Input: Mod(403,463)^(-113) Output: ? Mod(290, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.161 (128.197.150.161) Time: Tue Mar 29 12:26:36 2005 Input: factor(588) Output: ? [2 2] [3 1] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 12:33:15 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) d (q-d)/w^(p-1) (q-d)/w^p a=D+O(p^2) truncate(a^p) Output: ? 37 ? 32 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9, 37) ? Mod(9, 37) ? Mod(-5225652931711210306387057913299155247602384250320024169170529869975211143*x^35 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^34 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^33 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^32 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^31 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^30 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^29 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^28 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^27 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^26 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^25 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^24 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^23 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^22 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^21 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^20 - 181980149395188105603517631499471397225694853671869845805311433103269578995*x^19 - 180649878034896796681606806427647745760011008171586509351908762574351001445*x^18 - 176697333439046964680229345710945853785066342082845881417537411954343094592*x^17 - 170236223119302971805863754891874478570848576970175855934667895304621532112*x^16 - 161452421455883142414476179038255574160852253809833538954287003283001362641*x^15 - 150598622430057716819638080224577269169803825245027205763400672776743539200*x^14 - 137987070078381786449734294881521883727927995718146863490183317895809375070*x^13 - 123980575800259836374230801840121413021538147778160688042894281625228341994*x^12 - 108982080934549093737489512045435954665966155231594297577286379026328414462*x^11 - 93423064870869987385904695792059377968009167501997573824038092785801638186*x^10 - 77751132173156482776577618916670691974213371372473340757127493246445412921*x^9 - 62417135811302005370254237334563614543428259774284054104868650476538763237*x^8 - 47862206942081971775568144723090560499590861183325058152504018035467002667*x^7 - 34505064368940919977740617154673855635274285924511811974702533320923872177*x^6 - 22729968764380316471724480165628607034574459509078002441041742696838038650*x^5 - 12875668190036851128363938628540585834498116757712301906369244891917442491*x^4 - 5225652931711210306387057913299155247602384250320024169170529869975211143*x^3 + 2650958084601606644480423515083185544987055112411916108971029608767998416*x + 2650958084601606644480423515083185544987055112411916108971029608767998416, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-3311426431915701000626135915847118269334131166009192029311345433414401668139/37*x^35 - 6429503705358087219915950688902167794506974114756543164363381261639720523987/37*x^34 - 9264530414242424728792620875493284387964674960730380023139064634053176819959/37*x^33 - 11734948001876054019964951025212144197019551124903685962131865587684571058048/37*x^32 - 13769687052140940981414684106336329807848533711705940948379217288224789455638/37*x^31 - 15310211827199609026344798667429097338697803013932105826047914054326912025098/37*x^30 - 16312204234097135828271527801897361869925088568292787853479119420109379453468/37*x^29 - 16746838775606046966164291817827664536213324993520466274776747603405300843530/37*x^28 - 16601611807299558433511953989368585820731116961955748072598683603745041898787/37*x^27 - 15880701244636942965850977959534573767424500384395951091550433013185292231832/37*x^26 - 14604846371943030020630574207297199754961720082613197663274690026466245246193/37*x^25 - 12810751210958604922616541212528008326362515407050955743449252697735700036742/37*x^24 - 10550028612962170400916068160065767636413905038994141159514773238410590754481/37*x^23 - 7887715451010195132206585451497429661796502814039492247517499550353942004903/37*x^22 - 4900401627511686176015762436345192224009236632152177607246132857497346984898/37*x^21 - 1674026722182649483473412560887313903295913141096072024108594048601054153133/37*x^20 + 1698592333192830993119903361088534420490362995243436792600684733235531232193/37*x^19 + 5120431428899089899823919810721857848506941415093429058085862324642103986869/37*x^18 + 8493050484274570376417235732697706172293217551432937874795141106478689372195/37*x^17 + 11719425389603607068959585608155584493006541042489043457932679915374982203960/37*x^16 + 14706739213102116025150408623307821930793807224376358098204046608231577223965/37*x^15 + 17369052375054091293859891331876159905411209449331007010201320296288225973543/37*x^14 + 19629774973050525815560364384338400595359819817387821594135799755613335255804/37*x^13 + 21423870134034950913574397379107592023959024492950063513961237084343880465255/37*x^12 + 22699725006728863858794801131344966036421804794732816942236980071062927450894/37*x^11 + 23420635569391479326455777161178978089728421372292613923285230661622677117849/37*x^10 + 23565862537697967859108114989638056805210629403857332125463294661282936062592/37*x^9 + 23131227996189056721215350973707754138922392978629653704165666477987014672530/3 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.081s user 0m0.076s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:39:55 2005 Input: 36*x*y+6*y-6*x-217 Output: ? (36*y - 6)*x + (6*y - 217) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:40:36 2005 Input: 36*x*y+6*y-6*x-217 Output: ? (36*y - 6)*x + (6*y - 217) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:43:07 2005 Input: x=3 y=4 x+y Output: ? 3 ? 4 ? 7 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:43:37 2005 Input: x=10 y=11 x(36y-6)+(6y-217) Output: ? 10 ? 11 ? 10 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: (36y-6)+(6y-217). Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:43:49 2005 Input: x=10 y=11 x*(36*y-6)+(6*y-217) Output: ? 10 ? 11 ? 3749 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:43:58 2005 Input: x=10 y=11 x*(36*y-6)+(6*y-217) Output: ? 10 ? 11 ? 3749 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:44:30 2005 Input: x=10 y=11 x*(36*y-6)+(6*y-217) 36*x*y+6*y-6*x-217 Output: ? 10 ? 11 ? 3749 ? 3749 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:44:42 2005 Input: x=10 y=11 x*(36*y-6)+(6*y-217) 36*x*y+6*y-6*x-1 Output: ? 10 ? 11 ? 3749 ? 3965 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:45:49 2005 Input: x=10 y=11 36*x*y+6*y-6*y-229 x*(36*y-6)+(6*y-217) 36*x*y+6*y-6*x-1 Output: ? 10 ? 11 ? 3731 ? 3749 ? 3965 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:46:00 2005 Input: x=10 y=11 36*x*y+6*y-6*y-227 x*(36*y-6)+(6*y-217) 36*x*y+6*y-6*x-1 Output: ? 10 ? 11 ? 3733 ? 3749 ? 3965 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:46:05 2005 Input: x=10 y=11 36*x*y+6*y-6*y-224 x*(36*y-6)+(6*y-217) 36*x*y+6*y-6*x-1 Output: ? 10 ? 11 ? 3736 ? 3749 ? 3965 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:46:09 2005 Input: x=10 y=11 36*x*y+6*y-6*y-223 x*(36*y-6)+(6*y-217) 36*x*y+6*y-6*x-1 Output: ? 10 ? 11 ? 3737 ? 3749 ? 3965 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:46:40 2005 Input: 36*x*y+6*y-6*y-223 x*(36*y-6)+(6*y-217) 36*x*y+6*y-6*x-1 Output: ? ? 36*y*x - 223 ? (36*y - 6)*x + (6*y - 217) ? (36*y - 6)*x + (6*y - 1) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:46:55 2005 Input: 36*x*y+6*y-6*y-229 x*(36*y-6)+(6*y-217) 36*x*y+6*y-6*x-1 Output: ? 36*y*x - 229 ? (36*y - 6)*x + (6*y - 217) ? (36*y - 6)*x + (6*y - 1) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:47:07 2005 Input: 36*x*y+6*x-6*y-223 x*(36*y-6)+(6*y-217) 36*x*y+6*y-6*x-1 Output: ? (36*y + 6)*x + (-6*y - 223) ? (36*y - 6)*x + (6*y - 217) ? (36*y - 6)*x + (6*y - 1) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:47:30 2005 Input: x=1 y=10 36*x*y+6*x-6*y-223 (36*y + 6)*x + (-6*y - 223) x*(36*y-6)+(6*y-217) 36*x*y+6*y-6*x-1 Output: ? 1 ? 10 ? 83 ? 83 ? 197 ? 413 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:47:38 2005 Input: x=11 y=10 36*x*y+6*x-6*y-223 (36*y + 6)*x + (-6*y - 223) x*(36*y-6)+(6*y-217) 36*x*y+6*y-6*x-1 Output: ? 11 ? 10 ? 3743 ? 3743 ? 3737 ? 3953 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:48:09 2005 Input: x=11 y=10 36*x*y+6*x-6*y-223 (36*y + 6)*x + (-6*y - 223) 36*x*y+6*y-6*x-1 x*(36*y-6)+(6*y-217) Output: ? 11 ? 10 ? 3743 ? 3743 ? ? 3953 ? ? 3737 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:49:12 2005 Input: x=11 y=10 36*x*y+6*x-6*y-223 (36*y + 6)*x + (-6*y - 223) 36*x*y+6*y-6*x-1 x*(36*y-6)+(6*y-217) 6*y-217 Output: ? 11 ? 10 ? 3743 ? 3743 ? ? 3953 ? ? 3737 ? -157 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:51:40 2005 Input: x=11 y=10 36*x*y+6*x-6*y-223 (36*y + 6)*x + (-6*y - 223) 36*x*y+6*y-6*x-1 x*(36*y-6)+(6*y-217) 6*y-217 6*y*x+y-x-36 Output: ? 11 ? 10 ? 3743 ? 3743 ? ? 3953 ? ? 3737 ? -157 ? ? 623 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:51:47 2005 Input: 36*x*y+6*x-6*y-223 (36*y + 6)*x + (-6*y - 223) 36*x*y+6*y-6*x-1 x*(36*y-6)+(6*y-217) 6*y-217 6*y*x+y-x-36 Output: ? ? (36*y + 6)*x + (-6*y - 223) ? (36*y + 6)*x + (-6*y - 223) ? ? (36*y - 6)*x + (6*y - 1) ? ? (36*y - 6)*x + (6*y - 217) ? 6*y - 217 ? ? (6*y - 1)*x + (y - 36) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:52:41 2005 Input: x=11 y=10 36*x*y+6*x-6*y-223 (36*y + 6)*x + (-6*y - 223) 36*x*y+6*y-6*x-1 x*(36*y-6)+(6*y-217) 6*y-217 6*y*x+y-x-36 Output: ? 11 ? 10 ? 3743 ? 3743 ? ? 3953 ? ? 3737 ? -157 ? ? 623 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:53:02 2005 Input: x=11 y=10 36*x*y+6*x-6*y-223 (36*y + 6)*x + (-6*y - 223) 36*x*y+6*y-6*x-1 x*(36*y-6)+(6*y-217) 6*y-217 6*y*x+y-x-36 36*y-6 Output: ? 11 ? 10 ? 3743 ? 3743 ? ? 3953 ? ? 3737 ? -157 ? ? 623 ? ? 354 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:53:16 2005 Input: x=11 y=10 36*x*y+6*x-6*y-223 (36*y + 6)*x + (-6*y - 223) 36*x*y+6*y-6*x-1 x*(36*y-6)+(6*y-217) 6*y-217 6*y*x+y-x-36 x*(36*y-6) Output: ? 11 ? 10 ? 3743 ? 3743 ? ? 3953 ? ? 3737 ? -157 ? ? 623 ? ? 3894 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:53:46 2005 Input: x=11 y=10 36*x*y+6*x-6*y-223 (36*y + 6)*x + (-6*y - 223) 36*x*y+6*y-6*x-1 x*(36*y-6)+(6*y-217) 6*y-217 6*y*x+y-x-36 x*(36*y-6)+(6y-217) Output: ? 11 ? 10 ? 3743 ? 3743 ? ? 3953 ? ? 3737 ? -157 ? ? 623 ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: x*(36*y-6)+(6y-217) ^------ Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:54:12 2005 Input: x=11 y=10 36*x*y+6*x-6*y-223 (36*y + 6)*x + (-6*y - 223) x*(36*y-6)+(6*y-217) 6*y*x+y-x-36 x*(36*y-6)+(6*y-217) Output: ? 11 ? 10 ? 3743 ? 3743 ? ? 3737 ? ? 623 ? ? 3737 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:54:28 2005 Input: x=11 y=10 36*x*y+6*x-6*y-223 (36*y + 6)*x + (-6*y - 223) x*(36*y-6)+(6*y-217) 6*y*x+y-x-36 x*(36*y-6) x*(36*y-6)+(6*y-217) Output: ? 11 ? 10 ? 3743 ? 3743 ? ? 3737 ? ? 623 ? ? ? 3894 ? ? 3737 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:55:29 2005 Input: x=11 y=10 x*(36*y-6)+(6*y-217) x*(36*y-6) (6*y-217) Output: ? 11 ? 10 ? ? 3737 ? ? 3894 ? -157 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:55:56 2005 Input: x=11 y=10 x*(36*y-6)+(6*y-217) (36*y-6) (6*y-217) Output: ? 11 ? 10 ? ? 3737 ? ? 354 ? -157 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:56:09 2005 Input: x=11 y=10 x*(36*y-6)+(6*y-217) (36*y-6) (6*y-217) factor(36) Output: ? 11 ? 10 ? ? 3737 ? ? 354 ? -157 ? ? [2 2] [3 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:56:21 2005 Input: x=11 y=10 x*(36*y-6)+(6*y-217) (36*y-6) (6*y-217) factor(354) Output: ? 11 ? 10 ? ? 3737 ? ? 354 ? -157 ? ? [2 1] [3 1] [59 1] ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.004s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:56:34 2005 Input: x=11 y=10 x*(36*y-6)+(6*y-217) (36*y-6) (6*y-217) factor(157) Output: ? 11 ? 10 ? ? 3737 ? ? 354 ? -157 ? ? [157 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:56:44 2005 Input: x=11 y=10 x*(36*y-6)+(6*y-217) (36*y-6)*x (6*y-217) factor(157) Output: ? 11 ? 10 ? ? 3737 ? ? 3894 ? -157 ? ? [157 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 12:56:52 2005 Input: x=11 y=10 x*(36*y-6)+(6*y-217) (36*y-6)*x (6*y-217) factor(3894) Output: ? 11 ? 10 ? ? 3737 ? ? 3894 ? -157 ? ? [2 1] [3 1] [11 1] [59 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 13:01:09 2005 Input: x=47 y=23 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-217) (36*y-6)*x (6*y-217) factor(3894) Output: ? 47 ? 23 ? 38771 ? 38555 ? ? 38634 ? -79 ? ? [2 1] [3 1] [11 1] [59 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 13:03:38 2005 Input: x=16 y=67 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-217) (36*y-6)*x (6*y-217) factor(3894) Output: ? 16 ? 67 ? 38897 ? ? 38681 ? ? 38496 ? 185 ? ? [2 1] [3 1] [11 1] [59 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 13:05:06 2005 Input: x=16 y=67 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-117) 36*x*y+6*y-6*x-127 (36*y-6)*x (6*y-217) factor(3894) Output: ? 16 ? 67 ? 38897 ? ? 38781 ? ? 38771 ? ? 38496 ? 185 ? ? [2 1] [3 1] [11 1] [59 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 13:05:26 2005 Input: (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-117) 36*x*y+6*y-6*x-127 (36*y-6)*x (6*y-217) factor(3894) Output: ? ? (36*y - 6)*x + (6*y - 1) ? ? (36*y - 6)*x + (6*y - 117) ? ? (36*y - 6)*x + (6*y - 127) ? ? (36*y - 6)*x ? 6*y - 217 ? ? [2 1] [3 1] [11 1] [59 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 13:05:38 2005 Input: x=16 y=67 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-117) 36*x*y+6*y-6*x-127 (36*y-6)*x (6*y-217) factor((36*y-6)*x) Output: ? 16 ? 67 ? 38897 ? ? 38781 ? ? 38771 ? ? 38496 ? 185 ? ? [2 5] [3 1] [401 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 13:06:13 2005 Input: x=16 y=67 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-117) 36*x*y+6*y-6*x-127 (36*y-6)*x (6*y-217) factor((36*y-6)*x+(6*y-217)) Output: ? 16 ? 67 ? 38897 ? ? 38781 ? ? 38771 ? ? 38496 ? 185 ? ? [47 1] [823 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 13:07:55 2005 Input: x=16 y=67 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-117) 36*x*y+6*y-6*x-127 (36*y-6)*x (6*y-217) Output: ? 16 ? 67 ? 38897 ? ? 38781 ? ? 38771 ? ? 38496 ? 185 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 13:08:03 2005 Input: x=16 y=67 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-117) 36*x*y+6*y-6*x-127 (36*y-6)*x (6*y-217) factor((36*y-6)*x+(6*y-217)) Output: ? 16 ? 67 ? 38897 ? ? 38781 ? ? 38771 ? ? 38496 ? 185 ? ? ? [47 1] [823 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 13:08:25 2005 Input: x=16 y=67 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-117) 36*x*y+6*y-6*x-127 (36*y-6)*x (6*y-117) factor((36*y-6)*x+(6*y-217)) Output: ? 16 ? 67 ? 38897 ? ? 38781 ? ? 38771 ? ? 38496 ? 285 ? ? ? [47 1] [823 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 13:08:44 2005 Input: x=16 y=67 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-117) 36*x*y+6*y-6*x-127 (36*y-6)*x (6*y-117) factor((6*y-117)) Output: ? 16 ? 67 ? 38897 ? ? 38781 ? ? 38771 ? ? 38496 ? 285 ? ? ? [3 1] [5 1] [19 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 13:09:08 2005 Input: x=16 y=67 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-127) 36*x*y+6*y-6*x-127 (36*y-6)*x (6*y-117) factor((6*y-127)) Output: ? 16 ? 67 ? 38897 ? ? 38771 ? ? 38771 ? ? 38496 ? 285 ? ? ? [5 2] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 13:09:22 2005 Input: x=16 y=67 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-127) 36*x*y+6*y-6*x-127 (36*y-6)*x (6*y-117) factor((36*y-6)*x) Output: ? 16 ? 67 ? 38897 ? ? 38771 ? ? 38771 ? ? 38496 ? 285 ? ? ? [2 5] [3 1] [401 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 13:16:20 2005 Input: x=158 y=38 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-127) 36*x*y+6*y-6*x-127 (36*y-6)*x (6*y-117) factor((36*y-6)*x) Output: ? 158 ? 38 ? 215423 ? ? 215297 ? ? 215297 ? ? 215196 ? 111 ? ? ? [2 2] [3 1] [79 1] [227 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 13:22:14 2005 Input: x=55 y=56 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-127) 36*x*y+6*y-6*x-127 (36*y-6)*x (6*y-117) factor((36*y-6)*x) Output: ? 55 ? 56 ? 110885 ? ? 110759 ? ? 110759 ? ? 110550 ? 219 ? ? ? [2 1] [3 1] [5 2] [11 1] [67 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 13:22:49 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) truncate(a^p) Output: ? 37 ? 32 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9, 37) ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Errors (if any) and Timing Info: Timing: real 0m0.080s user 0m0.075s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 13:23:41 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) A=truncate(a^p) (q-A)/w^p Output: ? 37 ? 32 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9, 37) ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Mod((8 + O(37))*x^35 + (17 + O(37))*x^34 + (10 + O(37))*x^33 + (22 + O(37))*x^32 + (24 + O(37))*x^31 + (12 + O(37))*x^30 + (18 + O(37))*x^29 + (17 + O(37))*x^28 + (1 + O(37))*x^27 + (21 + O(37))*x^26 + (35 + O(37))*x^25 + (10 + O(37))*x^24 + (27 + O(37))*x^23 + (17 + O(37))*x^22 + (15 + O(37))*x^21 + (15 + O(37))*x^20 + (15 + O(37))*x^19 + (5 + O(37))*x^18 + (5 + O(37))*x^17 + (5 + O(37))*x^16 + (3 + O(37))*x^15 + (30 + O(37))*x^14 + (10 + O(37))*x^13 + (22 + O(37))*x^12 + (36 + O(37))*x^11 + (19 + O(37))*x^10 + (3 + O(37))*x^9 + (2 + O(37))*x^8 + (8 + O(37))*x^7 + (33 + O(37))*x^6 + (35 + O(37))*x^5 + (10 + O(37))*x^4 + (3 + O(37))*x^3 + (12 + O(37))*x^2 + (20 + O(37))*x + (10 + O(37)), x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.087s user 0m0.080s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 13:24:41 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) A=truncate(a^p) (q-lift(A))/w^p Output: ? 37 ? 32 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9, 37) ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? ? Errors (if any) and Timing Info: *** incorrect type in lift. Timing: real 0m0.080s user 0m0.072s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 13:25:15 2005 Input: x=9225 y=9225 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-127) 36*x*y+6*y-6*x-127 (36*y-6)*x (6*y-117) factor((36*y-6)*x) Output: ? 9225 ? 9225 ? 3063622499 ? ? 3063622373 ? ? 3063622373 ? ? 3063567150 ? 55233 ? ? ? [2 1] [3 3] [5 2] [7 1] [41 1] [7907 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 13:25:34 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) A=truncate(a^p) A (q-lift(A))/w^p Output: ? 37 ? 32 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9, 37) ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? 9 + 28*37 + 34*37^2 + O(37^3) ? ? Errors (if any) and Timing Info: *** incorrect type in lift. Timing: real 0m0.080s user 0m0.074s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 13:26:09 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) A=truncate(a^p) A (q-A)/w^p Output: ? 37 ? 32 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9, 37) ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Mod((8 + O(37))*x^35 + (17 + O(37))*x^34 + (10 + O(37))*x^33 + (22 + O(37))*x^32 + (24 + O(37))*x^31 + (12 + O(37))*x^30 + (18 + O(37))*x^29 + (17 + O(37))*x^28 + (1 + O(37))*x^27 + (21 + O(37))*x^26 + (35 + O(37))*x^25 + (10 + O(37))*x^24 + (27 + O(37))*x^23 + (17 + O(37))*x^22 + (15 + O(37))*x^21 + (15 + O(37))*x^20 + (15 + O(37))*x^19 + (5 + O(37))*x^18 + (5 + O(37))*x^17 + (5 + O(37))*x^16 + (3 + O(37))*x^15 + (30 + O(37))*x^14 + (10 + O(37))*x^13 + (22 + O(37))*x^12 + (36 + O(37))*x^11 + (19 + O(37))*x^10 + (3 + O(37))*x^9 + (2 + O(37))*x^8 + (8 + O(37))*x^7 + (33 + O(37))*x^6 + (35 + O(37))*x^5 + (10 + O(37))*x^4 + (3 + O(37))*x^3 + (12 + O(37))*x^2 + (20 + O(37))*x + (10 + O(37)), x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.088s user 0m0.075s sys 0m0.013s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 13:26:39 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) A=truncate(a^p)/O(p^3) A (q-A)/w^p Output: ? 37 ? 32 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9, 37) ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? ? A ? Mod((-393155596797403749679491227282/1369*A + 21266509997286420210125736280651244772079420741484557/1369)*x^35 + (-763355435599641803241005836019/1369*A + 29892129270221218879569389149892958898742544337300631/1369)*x^34 + (-1099949541065903806780931428784/1369*A + 23686193933310303015176875894632423569778670455519917/1369)*x^33 + (-1393254713617485147128344162637/1369*A + 4224836516542082922634833748113153008159894968349674/1369)*x^32 + (-1634833097459484677175624360202/1369*A - 23549307490829760186592638207944807108234633594710906/1369)*x^31 + (-1817734922329255857131213256733/1369*A - 52582389605082411745645835512526377155783029859401576/1369)*x^30 + (-1936698435733467480060578554934/1369*A - 75500826460795424252005667858099801703165259443492416/1369)*x^29 + (-1988301273987327253110294800394/1369*A - 86483981868 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.087s user 0m0.081s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 13:28:02 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) A=truncate(a^p) (q-A)/w^p Output: ? 37 ? 32 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9, 37) ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Mod((8 + O(37))*x^35 + (17 + O(37))*x^34 + (10 + O(37))*x^33 + (22 + O(37))*x^32 + (24 + O(37))*x^31 + (12 + O(37))*x^30 + (18 + O(37))*x^29 + (17 + O(37))*x^28 + (1 + O(37))*x^27 + (21 + O(37))*x^26 + (35 + O(37))*x^25 + (10 + O(37))*x^24 + (27 + O(37))*x^23 + (17 + O(37))*x^22 + (15 + O(37))*x^21 + (15 + O(37))*x^20 + (15 + O(37))*x^19 + (5 + O(37))*x^18 + (5 + O(37))*x^17 + (5 + O(37))*x^16 + (3 + O(37))*x^15 + (30 + O(37))*x^14 + (10 + O(37))*x^13 + (22 + O(37))*x^12 + (36 + O(37))*x^11 + (19 + O(37))*x^10 + (3 + O(37))*x^9 + (2 + O(37))*x^8 + (8 + O(37))*x^7 + (33 + O(37))*x^6 + (35 + O(37))*x^5 + (10 + O(37))*x^4 + (3 + O(37))*x^3 + (12 + O(37))*x^2 + (20 + O(37))*x + (10 + O(37)), x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.087s user 0m0.078s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:02:45 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-127) 36*x*y+6*y-6*x-127 (36*y-6)*x (6*y-117) factor((36*y-6)*x) Output: ? 11 ? 252 ? 101237 ? ? 101111 ? ? 101111 ? ? 99726 ? 1395 ? ? ? [2 1] [3 1] [11 1] [1511 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:03:08 2005 Input: x=252 y=11 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-127) 36*x*y+6*y-6*x-127 (36*y-6)*x (6*y-117) factor((36*y-6)*x) Output: ? 252 ? 11 ? 98345 ? ? 98219 ? ? 98219 ? ? 98280 ? -51 ? ? ? [2 3] [3 3] [5 1] [7 1] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.007s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:03:17 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-127) 36*x*y+6*y-6*x-127 (36*y-6)*x (6*y-117) factor((36*y-6)*x) Output: ? 11 ? 252 ? 101237 ? ? 101111 ? ? 101111 ? ? 99726 ? 1395 ? ? ? [2 1] [3 1] [11 1] [1511 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Tue Mar 29 15:05:26 2005 Input: factor(302) Output: ? [2 1] [151 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Tue Mar 29 15:05:37 2005 Input: factor(302) Output: ? [2 1] [151 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:05:52 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-675) 36*x*y+6*y-6*x-675 (36*y-6)*x (6*y-117) factor((36*y-6)*x) Output: ? 11 ? 252 ? 101237 ? ? 100563 ? ? 100563 ? ? 99726 ? 1395 ? ? ? [2 1] [3 1] [11 1] [1511 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:06:01 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y-675) 36*x*y+6*y-6*x+674 (36*y-6)*x (6*y-117) factor((36*y-6)*x) Output: ? 11 ? 252 ? 101237 ? ? 100563 ? ? 101912 ? ? 99726 ? 1395 ? ? ? [2 1] [3 1] [11 1] [1511 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:06:13 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+674) 36*x*y+6*y-6*x+674 (36*y-6)*x (6*y-117) factor((36*y-6)*x) Output: ? 11 ? 252 ? 101237 ? ? 101912 ? ? 101912 ? ? 99726 ? 1395 ? ? ? [2 1] [3 1] [11 1] [1511 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:06:51 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+674) 36*x*y+6*y-6*x+674 (36*y-6)*x factor((36*y-6)*x) Output: ? 11 ? 252 ? 101237 ? ? 101912 ? ? 101912 ? ? 99726 ? ? [2 1] [3 1] [11 1] [1511 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:07:18 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+674) 36*x*y+6*y-6*x+674 (36*y-6)*x factor((36*y-6)*x+674) Output: ? 11 ? 252 ? 101237 ? ? 101912 ? ? 101912 ? ? 99726 ? ? [2 4] [5 2] [251 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:07:38 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+674) 36*x*y+6*y-6*x+674 (36*y-6)*x factor((36*y-6)*x-1) Output: ? 11 ? 252 ? 101237 ? ? 101912 ? ? 101912 ? ? 99726 ? ? [5 2] [3989 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Tue Mar 29 15:08:47 2005 Input: factor(151) Output: ? [151 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Tue Mar 29 15:08:55 2005 Input: factor(35) Output: ? [5 1] [7 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:09:09 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+673) 36*x*y+6*y-6*x+673 (36*y-6)*x factor((36*y-6)*x-1) Output: ? 11 ? 252 ? 101237 ? ? 101911 ? ? 101911 ? ? 99726 ? ? [5 2] [3989 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:09:22 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+673) 36*x*y+6*y-6*x+673 (36*y-6)*x factor((36*y-6)*x+673) Output: ? 11 ? 252 ? 101237 ? ? 101911 ? ? 101911 ? ? 99726 ? ? [13 1] [7723 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:09:29 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+673) 36*x*y+6*y-6*x+673 (36*y-6)*x factor((36*y-6)*x-673) Output: ? 11 ? 252 ? 101237 ? ? 101911 ? ? 101911 ? ? 99726 ? ? [99053 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:09:42 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+673) 36*x*y+6*y-6*x+673 (36*y-6)*x factor((36*y-6)*x+(6*y)) Output: ? 11 ? 252 ? 101237 ? ? 101911 ? ? 101911 ? ? 99726 ? ? [2 1] [3 1] [47 1] [359 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:10:16 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+673) 36*x*y+6*y-6*x+673 (36*y-6)*x factor((6*y-1)*x/6) Output: ? 11 ? 252 ? 101237 ? ? 101911 ? ? 101911 ? ? 99726 ? ? [2 -1] [3 -1] [11 1] [1511 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:10:43 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+673) 36*x*y+6*y-6*x+673 (36*y-6)*x factor(6*y+673) Output: ? 11 ? 252 ? 101237 ? ? 101911 ? ? 101911 ? ? 99726 ? ? [5 1] [19 1] [23 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:11:00 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+673) 36*x*y+6*y-6*x+673 (36*y-6)*x factor((36*y-6)*x) Output: ? 11 ? 252 ? 101237 ? ? 101911 ? ? 101911 ? ? 99726 ? ? [2 1] [3 1] [11 1] [1511 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:17:29 2005 Input: (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+673) 36*x*y+6*y-6*x+673 (36*y-6)*x factor((36*y-6)*x) Output: ? ? (36*y - 6)*x + (6*y - 1) ? ? (36*y - 6)*x + (6*y + 673) ? ? (36*y - 6)*x + (6*y + 673) ? ? (36*y - 6)*x ? ? ? Errors (if any) and Timing Info: *** sorry, factor for general polynomials is not yet implemented. Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:35:55 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+673) 36*x*y+6*y-6*x+673 (36*y-6)*x factor((36*y-6)*x) (673/(6*.000000001+1)+1)/6 Output: ? 11 ? 252 ? 101237 ? ? 101911 ? ? 101911 ? ? 99726 ? ? [2 1] [3 1] [11 1] [1511 1] ? ? 112.33333266033333737133330910533347870 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:36:47 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+673) 36*x*y+6*y-6*x+673 (36*y-6)*x factor((36*y-6)*x) (673/(6*12+1)+1)/6 Output: ? 11 ? 252 ? 101237 ? ? 101911 ? ? 101911 ? ? 99726 ? ? [2 1] [3 1] [11 1] [1511 1] ? ? 373/219 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:37:02 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+673) 36*x*y+6*y-6*x+673 (36*y-6)*x factor((36*y-6)*x) (673/(6*1+1)+1)/6 Output: ? 11 ? 252 ? 101237 ? ? 101911 ? ? 101911 ? ? 99726 ? ? [2 1] [3 1] [11 1] [1511 1] ? ? 340/21 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:37:12 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+673) 36*x*y+6*y-6*x+673 (36*y-6)*x factor((36*y-6)*x) (673/(6*3+1)+1)/6 Output: ? 11 ? 252 ? 101237 ? ? 101911 ? ? 101911 ? ? 99726 ? ? [2 1] [3 1] [11 1] [1511 1] ? ? 346/57 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:37:39 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+673) 36*x*y+6*y-6*x+673 (36*y-6)*x factor((36*y-6)*x) (673/(6*2+1)+1)/6 Output: ? 11 ? 252 ? 101237 ? ? 101911 ? ? 101911 ? ? 99726 ? ? [2 1] [3 1] [11 1] [1511 1] ? ? 343/39 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Mar 29 15:38:12 2005 Input: x=11 y=252 (6*x+1)*(6*y-1) x*(36*y-6)+(6*y+673) 36*x*y+6*y-6*x+673 (36*y-6)*x factor((36*y-6)*x) (673/(6*2+1)+1)/6 (6*2+1)*(6*343/39-1) Output: ? 11 ? 252 ? 101237 ? ? 101911 ? ? 101911 ? ? 99726 ? ? [2 1] [3 1] [11 1] [1511 1] ? ? 343/39 ? ? 673 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Tue Mar 29 16:34:13 2005 Input: Mod(113,462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Tue Mar 29 16:34:44 2005 Input: Mod(323*113,462) Output: ? Mod(1, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Tue Mar 29 16:35:27 2005 Input: Mod(347,463)^323 Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Tue Mar 29 16:35:51 2005 Input: Mod(37,463)^113 Output: ? Mod(347, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Tue Mar 29 16:37:46 2005 Input: Mod(275,168)^(-1) Output: ? Mod(11, 168) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Tue Mar 29 16:38:04 2005 Input: Mod(275*11,168) Output: ? Mod(1, 168) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Tue Mar 29 16:40:51 2005 Input: Mod(139,588)^11 Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.51.56 (128.197.51.56) Time: Tue Mar 29 16:41:06 2005 Input: Mod(559,588)^275 Output: ? Mod(139, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:18:59 2005 Input: Mod(452,463)^139 Output: ? Mod(110, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.007s sys 0m0.005s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:20:39 2005 Input: factor(1) Output: ? [;] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:20:51 2005 Input: factor(2) Output: ? [2 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:21:00 2005 Input: factor(13) Output: ? [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:21:07 2005 Input: factor(2752727678) Output: ? [2 1] [47 2] [623071 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:23:10 2005 Input: factor(1357924052968432077) Output: ? [3 1] [452641350989477359 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:23:41 2005 Input: factor(135792405296843203837837377) Output: ? [3 3] [7 1] [103 1] [107227 1] [105709427 1] [615401539 1] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.009s sys 0m0.005s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:23:53 2005 Input: factor(1357924052968432038378373077) Output: ? [3 2] [7 2] [77563 1] [39699249176462946919 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:24:05 2005 Input: factor(13579240529684320383783730227272077) Output: ? [61 1] [75277 1] [2957218014621042323855201941 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:24:38 2005 Input: factor(1357924052968432038378373022727204254205442077) Output: ? [3 3] [23 1] [47 1] [131 1] [601 1] [19973 1] [1463113 1] [2739977 1] [935957251 1] [7885262467 1] ? Errors (if any) and Timing Info: Timing: real 0m0.095s user 0m0.048s sys 0m0.012s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:25:24 2005 Input: Mod(452,463)^139 Output: ? Mod(110, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:25:42 2005 Input: Mod(110,463)^113 Output: ? Mod(42, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:26:14 2005 Input: Mod(347,463)^139 Output: ? Mod(438, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.009s sys 0m0.007s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:26:25 2005 Input: Mod(438,463)^113 Output: ? Mod(459, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:28:10 2005 Input: Mod(347,463)^-139 Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.430s user 0m0.006s sys 0m0.006s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:28:42 2005 Input: Mod(37,463)^(115) Output: ? Mod(5, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.111s user 0m0.006s sys 0m0.006s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:28:48 2005 Input: Mod(37,463)^(113) Output: ? Mod(347, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:30:22 2005 Input: Mod(347,463)^(139) Output: ? Mod(438, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:39:51 2005 Input: Mod(37,463)^(113) Output: ? Mod(347, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:40:50 2005 Input: Mod(138,588)^(11) Output: ? Mod(444, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:42:00 2005 Input: Mod(444,588)^(275) Output: ? Mod(432, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:42:21 2005 Input: Mod(139,588)^(11) Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:42:33 2005 Input: Mod(559,588)^(275) Output: ? Mod(139, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:44:36 2005 Input: Mod(138,588)^(8) Output: ? Mod(564, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:44:48 2005 Input: Mod(138,588)^(2) Output: ? Mod(228, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:45:23 2005 Input: Mod(138*228*564,588)^(2) Output: ? Mod(156, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:46:45 2005 Input: Mod(138,588)^(2) Output: ? Mod(228, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:46:54 2005 Input: Mod(138,588)^(8) Output: ? Mod(564, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:47:22 2005 Input: Mod(138*228*564,588)^(8) Output: ? Mod(240, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:47:31 2005 Input: Mod(138*228*564,588)^(8) Output: ? Mod(240, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:48:19 2005 Input: Mod(559,588)^(275) Output: ? Mod(139, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.038s user 0m0.005s sys 0m0.005s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:48:41 2005 Input: Mod(138,588)^(11) Output: ? Mod(444, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:48:58 2005 Input: Mod(139,588)^(11) Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:49:07 2005 Input: Mod(139,588)^(8) Output: ? Mod(253, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:49:40 2005 Input: Mod(139,588)^(2) Output: ? Mod(505, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:50:11 2005 Input: Mod(139*505*253,588)^(2) Output: ? Mod(253, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 19:50:33 2005 Input: Mod(139*505*253,588) Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '12.221.' ************** PARI ***************** Host 12.221.98.177 (12.221.98.177) Time: Tue Mar 29 20:01:46 2005 Input: K := NumberField((x^2-2)*(x62-5)); G, phi := UnitGroup(K); G; Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: K:=NumberField((x^2-2 ^-------------------- *** Warning: unused characters: ,phi:=UnitGroup(K);. Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '12.221.' ************** PARI ***************** Host 12.221.98.177 (12.221.98.177) Time: Tue Mar 29 20:01:57 2005 Input: K := NumberField((x^2-2)*(x^2-5)); G, phi := UnitGroup(K); G; Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: K:=NumberField((x^2-2 ^-------------------- *** Warning: unused characters: ,phi:=UnitGroup(K);. Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '4.156.2' ************** PARI ***************** Host 4.156.252.209 (4.156.252.209) Time: Tue Mar 29 20:25:32 2005 Input: factor(6781) Output: ? [6781 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Tue Mar 29 21:00:15 2005 Input: Mod(6780,6781)^3390 Output: ? Mod(1, 6781) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 21:08:12 2005 Input: precision = 32 Output: ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: precision=32 ^--- Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Tue Mar 29 21:10:04 2005 Input: Mod((133-2*sqrt(21)),337)^168 Output: ? ? Errors (if any) and Timing Info: *** forbidden division t_REAL % t_INT. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Tue Mar 29 21:10:21 2005 Input: sqrt(9) Output: ? 3.0000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Tue Mar 29 21:11:00 2005 Input: Mod(133-sqrt(336),337)^168 Output: ? ? Errors (if any) and Timing Info: *** forbidden division t_REAL % t_INT. Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Tue Mar 29 21:13:44 2005 Input: (133-7*sqrt(336))^168 Output: ? 5.2973429614558570722462585600269113000 E112 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Tue Mar 29 21:14:29 2005 Input: Mod(5.2973429614558570722462585600269113000*10^112,337) Output: ? ? Errors (if any) and Timing Info: *** forbidden division t_REAL % t_INT. Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Tue Mar 29 21:20:10 2005 Input: Mod(5,101)^50 Output: ? Mod(1, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 21:29:46 2005 Input: factor(70785) Output: ? [3 2] [5 1] [11 2] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 21:30:44 2005 Input: factor(83550368) Output: ? [2 5] [11 1] [97 1] [2447 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 21:31:18 2005 Input: factor(5022) Output: ? [2 1] [3 4] [31 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 21:32:31 2005 Input: lcm(19,5022) Output: ? 95418 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Tue Mar 29 21:37:44 2005 Input: Mod(2,7)^(-1) Output: ? Mod(4, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Tue Mar 29 22:14:11 2005 Input: Mod(5,101)^50 Output: ? Mod(1, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:16:00 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:16:58 2005 Input: factor(1078866) Output: ? [2 1] [3 3] [19979 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:17:33 2005 Input: factor(1067960) Output: ? [2 3] [5 1] [26699 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:17:52 2005 Input: factor(1078866) Output: ? [2 1] [3 3] [19979 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.237.190 (168.122.237.190) Time: Tue Mar 29 22:17:59 2005 Input: factor (463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.237.190 (168.122.237.190) Time: Tue Mar 29 22:18:00 2005 Input: factor (463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.237.190 (168.122.237.190) Time: Tue Mar 29 22:18:03 2005 Input: factor (463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:18:21 2005 Input: factor(10680) Output: ? [2 3] [3 1] [5 1] [89 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:18:46 2005 Input: factor(25) Output: ? [5 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:19:01 2005 Input: factor(83453564) Output: ? [2 2] [20863391 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.237.190 (168.122.237.190) Time: Tue Mar 29 22:19:05 2005 Input: factor(347) factor(113) Output: ? [347 1] ? [113 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:19:26 2005 Input: factor(16) Output: ? [2 4] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:19:33 2005 Input: factor(5012) Output: ? [2 2] [7 1] [179 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:20:03 2005 Input: nextprime(1078866) Output: ? 1078873 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.237.190 (168.122.237.190) Time: Tue Mar 29 22:20:12 2005 Input: Mod(113,462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:20:51 2005 Input: privprime(1078866) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: privprime(1078866) ^------------------ Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.237.190 (168.122.237.190) Time: Tue Mar 29 22:20:58 2005 Input: Mod(347, 463)^323 Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:21:00 2005 Input: prevprime(1078866) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: prevprime(1078866) ^------------------ Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:21:13 2005 Input: prevprime(1078866) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: prevprime(1078866) ^------------------ Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:21:31 2005 Input: prevprime(1078866) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: prevprime(1078866) ^------------------ Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.237.190 (168.122.237.190) Time: Tue Mar 29 22:21:43 2005 Input: factor(588) Output: ? [2 2] [3 1] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:21:56 2005 Input: nextprime(83453564) Output: ? 83453593 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.237.190 (168.122.237.190) Time: Tue Mar 29 22:22:10 2005 Input: factor(139) Output: ? [139 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.237.190 (168.122.237.190) Time: Tue Mar 29 22:22:16 2005 Input: factor(275) Output: ? [5 2] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:22:21 2005 Input: prevprime(83453564) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: prevprime(83453564) ^------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:22:46 2005 Input: prevprime(83453564); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: prevprime(83453564); ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:23:36 2005 Input: fibonacci(5012) Output: ? 1249015795710970801788546999043360076764217499797565685668011872771326927355798811718490494025140849631174912700418526720693391610754768973890455190979026580165019495000324605559387676221160242083826954841812494003084469873090862909566668139266297959797229211247393945184824656460575401424398051163045315024586095864888473786702990105923236894601897112621320864524294266824605506226931075987574264877595220783270237354077742541267287854258657272487414898609756409818916856579476369555300590018086640540593663765633274878713662762943851934067852433541688447758933936945846363092341900729622285466973800015059547870560541062057306331589954150411564861786468940148924567339518840583110273602114779687440318596759152362042989460904177712189204728969995446965252381830868457650729271257330914714009980272774171490957963151436467302613849560206072449489700542858513031052718372255741753968554290051897893937341345297050232006277844822366129295596089869677026465155935145320723686773495827581351068255136283173731488390874338503904406606311521989406588269 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:23:58 2005 Input: fibonacci(5108) Output: ? 144338236455210704759453179434128591958670239037883988352929702937711436856749868595539899345466060509829993908736571858173304797777463084113621139824427045790789166985541862459722477151141447112534974208891626249188704587645260183346464484722991723973108390267950591740365738655194351993920241208351895367101244916813533433327682481612836030579421793910045709873137049006524460267539473423065415405890257812466181189403609326630961946795367291123199883739719754843406420520073412155907135321820689179014723880198559111948811580605745139148117797465182644719922822227733796914065830064638961455560254995179867592006077676285745224634224245374897111468344460733908354379197219075449095447513780138548411073744388849256095369129981851828354890863055328388825703156943489498766064672124279358861642690003973705595778425222555150367357508830267921554777903415537834239595912324749557514283549654695776597750596196502240665622643906501623479737883749969244451060391091794681043349261418907608778358754777452067324468194496188909600376762060698069917550989635577281863250221 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.237.190 (168.122.237.190) Time: Tue Mar 29 22:24:02 2005 Input: Mod(275, 28)^(-1) Output: ? Mod(11, 28) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:24:34 2005 Input: prime(5108) Output: ? 49741 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:24:42 2005 Input: prime(5012) Output: ? 48757 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.237.190 (168.122.237.190) Time: Tue Mar 29 22:25:11 2005 Input: Mod(139, 588)^(11) Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:25:16 2005 Input: binomial(5012,25) Output: ? 19212909536191885006277130841460721259099721528452783061011546699200 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 22:26:31 2005 Input: prevprime(1078866) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: prevprime(1078866) ^------------------ Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '141.149' ************** PARI ***************** Host 141.149.179.186 (141.149.179.186) Time: Tue Mar 29 22:48:51 2005 Input: Mod(6780,6781)^3390 Output: ? Mod(1, 6781) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '141.149' ************** PARI ***************** Host 141.149.179.186 (141.149.179.186) Time: Tue Mar 29 22:59:53 2005 Input: Mod(1681,3011)^1505 Output: ? Mod(1, 3011) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '141.149' ************** PARI ***************** Host 141.149.179.186 (141.149.179.186) Time: Tue Mar 29 23:00:28 2005 Input: Mod(529,3011)^1505 Output: ? Mod(1, 3011) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.006s sys 0m0.007s '141.149' ************** PARI ***************** Host 141.149.179.186 (141.149.179.186) Time: Tue Mar 29 23:00:31 2005 Input: Mod(529,3011)^1505 Output: ? Mod(1, 3011) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '141.149' ************** PARI ***************** Host 141.149.179.186 (141.149.179.186) Time: Tue Mar 29 23:00:59 2005 Input: Mod(529,3011)^1505 Output: ? Mod(1, 3011) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:04:19 2005 Input: isprime(1094296) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:04:36 2005 Input: isprime(50184) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:04:49 2005 Input: isprime(83328883) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:05:01 2005 Input: isprime(5069) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:06:44 2005 Input: nextprime(1094296) Output: ? 1094299 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:07:08 2005 Input: nextprime(1094100) Output: ? 1094101 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:07:16 2005 Input: nextprime(1094101) Output: ? 1094101 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:07:24 2005 Input: nextprime(1094102) Output: ? 1094123 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:07:31 2005 Input: nextprime(1094124) Output: ? 1094129 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:07:38 2005 Input: nextprime(1094130) Output: ? 1094131 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:07:44 2005 Input: nextprime(1094200) Output: ? 1094209 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:07:50 2005 Input: nextprime(1094210) Output: ? 1094237 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:07:56 2005 Input: nextprime(1094240) Output: ? 1094263 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:08:02 2005 Input: nextprime(1094265) Output: ? 1094293 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:08:10 2005 Input: nextprime(1094294) Output: ? 1094299 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:08:15 2005 Input: nextprime(1094293) Output: ? 1094293 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:08:36 2005 Input: nextprime(83328883) Output: ? 83328887 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:08:56 2005 Input: nextprime(83328880) Output: ? 83328881 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:09:59 2005 Input: gcd(1094296,50184) Output: ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:10:20 2005 Input: gcd(50184,21) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:10:36 2005 Input: gcd(1094296,50184,21) Output: ? ? Errors (if any) and Timing Info: *** invalid flag in gcd. Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:13:24 2005 Input: lcm(21,51) Output: ? 357 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:13:46 2005 Input: lcm(51,5069) Output: ? 258519 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:16:16 2005 Input: binomial(5069,21) Output: ? 11940096118774349994637993011293607472104455360252471927460 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:17:05 2005 Input: fibonacci(10) Output: ? 55 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:17:10 2005 Input: fibonacci(9) Output: ? 34 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:17:21 2005 Input: fibonacci(15) Output: ? 610 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:17:34 2005 Input: fibonacci(5) Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:17:39 2005 Input: fibonacci(7) Output: ? 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:17:46 2005 Input: fibonacci(9) Output: ? 34 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:17:50 2005 Input: fibonacci(8) Output: ? 21 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:18:18 2005 Input: fibonacci(30) Output: ? 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:18:25 2005 Input: fibonacci(25) Output: ? 75025 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:18:32 2005 Input: fibonacci(18) Output: ? 2584 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:18:39 2005 Input: fibonacci(22) Output: ? 17711 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:18:44 2005 Input: fibonacci(19) Output: ? 4181 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:18:50 2005 Input: fibonacci(20) Output: ? 6765 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:19:01 2005 Input: fibonacci(40) Output: ? 102334155 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:19:16 2005 Input: fibonacci(35) Output: ? 9227465 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:19:34 2005 Input: fibonacci(33) Output: ? 3524578 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:19:42 2005 Input: fibonacci(32) Output: ? 2178309 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:19:49 2005 Input: fibonacci(31) Output: ? 1346269 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:19:58 2005 Input: fibonacci(30) Output: ? 832040 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:20:17 2005 Input: fibonacci(8) Output: ? 21 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:23:26 2005 Input: mod(1094296,21) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(1094296,21) ^--------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:23:45 2005 Input: Mod(1094296,21) Output: ? Mod(7, 21) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:24:34 2005 Input: Mod(83328883,21) Output: ? Mod(1, 21) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:25:45 2005 Input: isprime(136787) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Mar 29 23:26:06 2005 Input: isprime(19541) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:36:32 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) truncate(a^p) Output: ? ? ? ? 37 ? 32 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9, 37) ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Errors (if any) and Timing Info: Timing: real 0m0.080s user 0m0.075s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:36:47 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) c(4) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) truncate(truncate(a^p)) Output: ? 37 ? 32 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9, 37) ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Errors (if any) and Timing Info: Timing: real 0m0.080s user 0m0.073s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:41:11 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)) type(et(a)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) truncate(truncate(a^p)) Output: ? 37 ? 32 ? ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9, 37) ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m0.053s user 0m0.045s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:41:37 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); type(et(1)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))) q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) truncate(truncate(a^p)) Output: ? 37 ? 32 ? ? "t_POLMOD" ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9, 37) ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.047s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:42:05 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); type(et(1)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); type(q=c((p-1)-j)) w=Mod(1-x, sum(n=0, p-1, x^n)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) truncate(truncate(a^p)) Output: ? 37 ? 32 ? ? "t_POLMOD" ? ? "t_POLMOD" ? Mod(-x + 1, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(9, 37) ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Errors (if any) and Timing Info: Timing: real 0m0.052s user 0m0.046s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:43:01 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); type(et(1)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); type(q=c((p-1)-j)) w=Mod(1-x, sum(n=0, p-1, x^n)); type(w) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) truncate(truncate(a^p)) Output: ? 37 ? 32 ? ? "t_POLMOD" ? ? "t_POLMOD" ? ? "t_POLMOD" ? Mod(9, 37) ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Errors (if any) and Timing Info: Timing: real 0m0.052s user 0m0.045s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:45:01 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); type(et(1)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); type(q=c((p-1)-j)) w=Mod(1-x, sum(n=0, p-1, x^n)); type(lift(q)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) if truncate(truncate(a^p)) Output: ? 37 ? 32 ? ? "t_POLMOD" ? ? "t_POLMOD" ? ? "t_POL" ? Mod(9, 37) ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? ? 9 + 28*37 + 34*37^2 + O(37^3) ? Errors (if any) and Timing Info: *** expected character: '(' instead of: if ^ Timing: real 0m0.053s user 0m0.046s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:49:08 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); type(et(1)) c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); type(q=c((p-1)-j)) w=Mod(1-x, sum(n=0, p-1, x^n)); type(lift(q)) d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) if (poldegree(D)=0, E=polcoeff(D, 0), print(D bad)) (q-E)/w^(p+1) Output: ? 37 ? 32 ? ? "t_POLMOD" ? ? "t_POLMOD" ? ? "t_POL" ? Mod(9, 37) ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? ? Mod((404800984089803737832893160661/1369*E - 28506307347594978819411688516411944813567784214777203/1369)*x^35 + (1202757564977011225345277548604/1369*E - 78279124692476377848949113313475134399214989171038963/1369)*x^34 + (2370913984666456766419176545284/1369*E - 136677561310292575547930190979780038111525317723116797/1369)*x^33 + (3875664509822164311033001134729/1369*E - 188870062591197857382518755390824406494871772393413917/1369)*x^32 + (5673720207529453195994238458027/1369*E - 221601206455334919124565277655349504316599451576540794/1369)*x^31 + (7713354289078741611002755978890/1369*E - 226558206312100137757384327963816642021932602196607091/1369)*x^30 + (9935890195497801205966862396284/1369*E - 202482124054612704831150180967702209679717356551982718/1369)*x^29 + (12277389615321072423860334111879/1369*E - 155487604941412259398556201626014352790119881323267505/1369)*x^28 + (14670491873398203414803522072934/1369*E - 97509930420121840606247494860571205555517358388240998/1369)*x^27 + (17046351774874773015949677531525/1369*E - 43273793359076128888741811986913679705613526831843582/1369)*x^26 + (19336620156102105204331927909221/1369*E - 6553641600476361490256386694205775686653535763602751/1369)*x^25 + (21475410165632481509913501724419/1369*E + 3324642798733194360712977513797617393890479052916737/1369)*x^24 + (23401192708975512325031637829382/1369*E - 16147745659550632186193635587485389619027514032933712/1369)*x^23 + (25058566528621041445595275281049/1369*E - 60025369933310750300898571142935848836871108519278218/1369)*x^22 + (26399851997349083600226406960459/1369*E - 117164551874580330225453601585654852398013877225122660/1369)*x^21 + (27386462774295058992720244847054/1369*E - 173053552128659278071577419597408100558679979091094537/1369)*x^20 + (27990015863722673770731976748214/1369*E - 213498142250936660439161374381022420005443796149941969/1369)*x^19 + (28193148142134608951349163864578/1369*E - 228226537902893210232829344500287396950488944041321863/1369)*x^18 + (27990015863722673770731976748214/1369*E - 213498142250936660439161374381022420005443796149941969/1369)*x^17 + (27386462774295058992720244847054/1369*E - 173053552128659278071577419597408100558679979091094537/1369)*x^16 + (26399851997349083600226406960459/1369*E - 117164551874580330225453601585654852398013877225122660/1369)*x^15 + (25058566528621041445595275281049/1369*E - 60025369933310750300898571142935848836871108519278218/1369)*x^14 + (23401192708975512325031637829382/1369*E - 16147745659550632186193635587485389619027514032933712/1369)*x^13 + (21475410165632481509913501724419/1369*E + 3324642798733194360712977513797617393890479052916737/1369)*x^12 + (19336620156102105204331927909221/1369*E - 6553641600476361490256386694205775686653535763602751/1369)*x^11 + (17046351774874773015949677531525/1369*E - 43273793359076128888741811986913679705613526831843582/1369)*x^10 + (14670491873398203414803522072934/1369*E - 97509930420121840606247494860571205555517358388240998/1369)*x^9 + (12277389615321072423860334111879/1369*E - 155487604941412259398556201626014352790119881323267505/1369)*x^8 + (9935890195497801205966862396284/1369*E - 202482124054612704831150180967702209679717356551982718/1369)*x^[+++] ? Errors (if any) and Timing Info: *** unexpected character: if(poldegree(D)=0,E=polcoeff(D,0),p ^-------------------- Timing: real 0m0.061s user 0m0.057s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:51:11 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j) w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p) D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) if (poldegree(D)=0, E=polcoeff(D, 0), print("D bad")) (q-E)/w^(p+1) Output: ? 37 ? 32 ? ? ? Mod(-8348142943996432295022298130665420931108350905*x^35 + 205920727010599473812858531312861612904610154329*x^34 + 79369841126443550406882669545909921560311503396*x^33 + 112928095186692909965206243053957361684548554499*x^32 + 112928095186692909965206243053957361684548554499*x^30 + 258031600833836166467110824752796217137104012221*x^29 - 97437619911159925968855315210911434924770953465*x^28 + 83880928627165860750038438283286685398444866890*x^27 + 258031600833836166467110824752796217137104012221*x^26 - 8348142943996432295022298130665420931108350905*x^25 + 79369841126443550406882669545909921560311503396*x^24 + 83880928627165860750038438283286685398444866890*x^23 + 146758194936647407470940547838713493124827756232*x^22 + 146758194936647407470940547838713493124827756232*x^21 - 97437619911159925968855315210911434924770953465*x^20 + 205920727010599473812858531312861612904610154329*x^19 + 205920727010599473812858531312861612904610154329*x^18 - 97437619911159925968855315210911434924770953465*x^17 + 146758194936647407470940547838713493124827756232*x^16 + 146758194936647407470940547838713493124827756232*x^15 + 83880928627165860750038438283286685398444866890*x^14 + 79369841126443550406882669545909921560311503396*x^13 - 8348142943996432295022298130665420931108350905*x^12 + 258031600833836166467110824752796217137104012221*x^11 + 83880928627165860750038438283286685398444866890*x^10 - 97437619911159925968855315210911434924770953465*x^9 + 258031600833836166467110824752796217137104012221*x^8 + 112928095186692909965206243053957361684548554499*x^7 + 112928095186692909965206243053957361684548554499*x^5 + 79369841126443550406882669545909921560311503396*x^4 + 205920727010599473812858531312861612904610154329*x^3 - 8348142943996432295022298130665420931108350905*x^2 + 311639409381263146092026634548079830617045688850, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? Mod(9, 37) ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? ? Mod((404800984089803737832893160661/1369*E - 28506307347594978819411688516411944813567784214777203/1369)*x^35 + (1202757564977011225345277548604/1369*E - 78279124692476377848949113313475134399214989171038963/1369)*x^34 + (2370913984666456766419176545284/1369*E - 136677561310292575547930190979780038111525317723116797/1369)*x^33 + (3875664509822164311033001134729/1369*E - 188870062591197857382518755390824406494871772393413917/1369)*x^32 + (5673720207529453195994238458027/1369*E - 221601206455334919124565277655349504316599451576540794/1369)*x^31 + (7713354289078741611002755978890/1369*E - 226558206312100137757384327963816642021932602196607091/1369)*x^30 + (9935890195497801205966862396284/1369*E - 202482124054612704831150180967702209679717356551982718/1369)*x^29 + (12277389615321072423860334111879/1369*E - 155487604941412259398556201626014352790119881323267505/1369)*x^28 + (14670491873398203414803522072934/1369*E - 97509930420121840606247494860571205555517358388240998/1369)*x^27 + (17046351774874773015949677531525/1369*E - 43273793359076128888741811986913679705613526831843582/1369)*x^26 + (19336620156102105204331927909221/1369*E - 6553641600476361490256386694205775686653535763602751/1369)*x^25 + (21475410165632481509913501724419/1369*E + 3324642798733194360712977513797617393890479052916737/1369)*x^24 + (23401192708975512325031637829382/1369*E - 16147745659550632186193635587485389619027514032933712/1369)*x^23 + (25058566528621041445595275281049/1369*E - 60025369933310750300898571142935848836871108519278218/1369)*x^22 + (26399851997349083600226406960459/1369*E - 117164551874580330225453601585654852398013877225122660/1369)*x^21 + (27386462774295058992720244847054/1369*E - 173053552128659278071577419597408100558679979091094537/1369)*x^20 + (27990015863722673770731976748214/1369*E - 213498142250936660439161374381022420005443796149941969/1369)*x^19 + (28193148142134608951349163864578/1369*E - 228226537902893210232829344500287396950488944041321863/1369)*x^18 + (27990015863722673770731976748214/1369*E - 213498142250936660439161374381022420005443796149941969/1369)*x^17 + (27386462774295058992720244847054/1369*E - 173053552128659278071577419597408100558679979091094537/1369)*x^16 + (26399851997349083600226406960459/1369*E - 117164551874580330225453601585654852398013877225122660/1369)*x^15 + (25058566528621041445595275281049/1369*E - 60025369933310750300898571142935848836871108519278218/1369)*x^14 + (23401192708975512325031637829382/1369*E - 16147745659550632186193635587485389619027514032933712/1369)*x^13 + (21475410165632481509913501724419/1369*E + 3324642798733194360712977513797617393890479052916737/1369)*x^12 + (19336620156102105204331927909221/1369*E - 6553641600476361490256386694205775686653535763602751/1369)*x^11 + (17046351774874773015949677531525/1369*E - 43273793359076128888741811986913679705613526831843582/1369)*x^10 + (14670491873398203414803522072934/1369*E - 97509930420121840606247494860571205555517358388240998/1369)*x^9 + (12277389615321072423860334111879/1369*E - 155487604941412259398556201626014352790119881323267505/1369)*x^8 + (9935890195497801205966862396284/1369*E - 2024821240546127048311501 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** unexpected character: if(poldegree(D)=0,E=polcoeff(D,0),p ^-------------------- Timing: real 0m0.062s user 0m0.054s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:52:20 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) if (poldegree(D)==0, E=polcoeff(D, 0), print("D bad")) (q-E)/w^(p+1) Output: ? 37 ? 32 ? ? ? ? ? ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 ? Mod(-770440739124188616740757981285273961619656437198142/37*x^35 - 2115652018715577779701034824199738954005050856029771/37*x^34 - 3693988143521420960754293317673460540557501219843493/37*x^33 - 5104596286248590740067131740817189378812769604951388/37*x^32 - 5989221796090132949311194977661668628049608200822123/37*x^31 - 6123194765191895615062565075005809009390096686291813/37*x^30 - 5472489839313856887325966431241695391050369048389626/37*x^29 - 4202367701119250254012046084310174679413652386925962/37*x^28 - 2635403524868157854219336768478665452021192613232016/37*x^27 - 1169561982677733213205091751917292074282972425244861/37*x^26 - 177125448661523283515739381427050182157149957092426/37*x^25 + 89855210776572820565033951494278641283235150498284/37*x^24 - 436425558366233302323865536570394865083844034931602/37*x^23 - 1622307295494885143261433622815628634158398676804021/37*x^22 - 3166609510123792708789621700477802990421941609796717/37*x^21 - 4677123030504304812738674092768633649398526942904623/37*x^20 - 5770220060836125957808363898331051782202897523221839/37*x^19 - 6168284808186302979258800166675896904592616258555153/37*x^18 - 5770220060836125957808363898331051782202897523221839/37*x^17 - 4677123030504304812738674092768633649398526942904623/37*x^16 - 3166609510123792708789621700477802990421941609796717/37*x^15 - 1622307295494885143261433622815628634158398676804021/37*x^14 - 436425558366233302323865536570394865083844034931602/37*x^13 + 89855210776572820565033951494278641283235150498284/37*x^12 - 177125448661523283515739381427050182157149957092426/37*x^11 - 1169561982677733213205091751917292074282972425244861/37*x^10 - 2635403524868157854219336768478665452021192613232016/37*x^9 - 4202367701119250254012046084310174679413652386925962/37*x^8 - 5472489839313856887325966431241695391050369048389626/37*x^7 - 6123194765191895615062565075005809009390096686291813/37*x^6 - 5989221796090132949311194977661668628049608200822123/37*x^5 - 5104596286248590740067131740817189378812769604951388/37*x^4 - 3693988143521420960754293317673460540557501219843493/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 770440739124188616740757981285273961619656437198142/37*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.056s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:52:47 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) if (poldegree(D)==0, E=polcoeff(D, 0), print("D bad")) (q-E)/w^(p) Output: ? 37 ? 32 ? ? ? ? ? ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.052s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:53:02 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) if (poldegree(D)==0, E=polcoeff(D, 0), print("D bad")) E (q-E)/w^(p) Output: ? 37 ? 32 ? ? ? ? ? ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 ? 9 ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.052s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:53:47 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")) E (q-E)/w^(p) Output: ? 37 ? 32 ? ? ? ? ? ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? 9 + 28*37 + 34*37^2 + O(37^3) ? Mod((8 + O(37))*x^35 + (17 + O(37))*x^34 + (10 + O(37))*x^33 + (22 + O(37))*x^32 + (24 + O(37))*x^31 + (12 + O(37))*x^30 + (18 + O(37))*x^29 + (17 + O(37))*x^28 + (1 + O(37))*x^27 + (21 + O(37))*x^26 + (35 + O(37))*x^25 + (10 + O(37))*x^24 + (27 + O(37))*x^23 + (17 + O(37))*x^22 + (15 + O(37))*x^21 + (15 + O(37))*x^20 + (15 + O(37))*x^19 + (5 + O(37))*x^18 + (5 + O(37))*x^17 + (5 + O(37))*x^16 + (3 + O(37))*x^15 + (30 + O(37))*x^14 + (10 + O(37))*x^13 + (22 + O(37))*x^12 + (36 + O(37))*x^11 + (19 + O(37))*x^10 + (3 + O(37))*x^9 + (2 + O(37))*x^8 + (8 + O(37))*x^7 + (33 + O(37))*x^6 + (35 + O(37))*x^5 + (10 + O(37))*x^4 + (3 + O(37))*x^3 + (12 + O(37))*x^2 + (20 + O(37))*x + (10 + O(37)), x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.053s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:54:15 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")) truncate(E) (q-E)/w^(p) Output: ? 37 ? 32 ? ? ? ? ? ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? 47591 ? Mod((8 + O(37))*x^35 + (17 + O(37))*x^34 + (10 + O(37))*x^33 + (22 + O(37))*x^32 + (24 + O(37))*x^31 + (12 + O(37))*x^30 + (18 + O(37))*x^29 + (17 + O(37))*x^28 + (1 + O(37))*x^27 + (21 + O(37))*x^26 + (35 + O(37))*x^25 + (10 + O(37))*x^24 + (27 + O(37))*x^23 + (17 + O(37))*x^22 + (15 + O(37))*x^21 + (15 + O(37))*x^20 + (15 + O(37))*x^19 + (5 + O(37))*x^18 + (5 + O(37))*x^17 + (5 + O(37))*x^16 + (3 + O(37))*x^15 + (30 + O(37))*x^14 + (10 + O(37))*x^13 + (22 + O(37))*x^12 + (36 + O(37))*x^11 + (19 + O(37))*x^10 + (3 + O(37))*x^9 + (2 + O(37))*x^8 + (8 + O(37))*x^7 + (33 + O(37))*x^6 + (35 + O(37))*x^5 + (10 + O(37))*x^4 + (3 + O(37))*x^3 + (12 + O(37))*x^2 + (20 + O(37))*x + (10 + O(37)), x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.070s user 0m0.051s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:55:19 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d) (q-D)/w^(p-1) (q-D)/w^p a=D+O(p^2) if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")) e=truncate(E+O(p^2)) (q-e)/w^(p) Output: ? 37 ? 32 ? ? ? ? ? ? 9 ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(574770540467200546219518861629191030765737981633487/37*x^35 + 807895385681654564312500512188447624932793926615580/37*x^34 + 640167403602981162572080441858454876635611947909753/37*x^33 + 114184770717353592503305255559205287617182158672593/37*x^32 - 636467770022425950989387883941133580279167951728452/37*x^31 - 1421145665002227344477356625049387579959384075100329/37*x^30 - 2040562877318795250054678328216794673256373098661806/37*x^29 - 2337404915375281016533467297116783189012116210892088/37*x^28 - 2236282281314613257755002997846647339357876625185297/37*x^27 - 1762877273140398546430110351775515853745478905350577/37*x^26 - 1037421398562284720821531314206602785060041544788852/37*x^25 - 244159969981382493851858493220600455252577251768256/37*x^24 + 415440998004463224196810104959959807454898204674277/37*x^23 + 773861475504718948787430096376900394643886495794554/37*x^22 + 740072781256323487208294411005556697356928895909764/37*x^21 + 322656291207632528328931824277144171184714143119074/37*x^20 - 372375991774011595290321712940428839229937701864828/37*x^19 - 1168505486474365638191194249630119084009375172531456/37*x^18 - 1863537769456009761810447786847692094424027017515358/37*x^17 - 2280954259504700720689810373576104620596241770306048/37*x^16 - 2314742953753096182268946058947448317883199370190838/37*x^15 - 1956322476252840457678326067530507730694211079070561/37*x^14 - 1296721508266994739629657469349947467986735622628028/37*x^13 - 503460079686092512659984648363945138179271329607432/37*x^12 + 221995794892021312948594389204967930506166030954293/37*x^11 + 695400803066236024273487035276099416118563750789013/37*x^10 + 796523437126903783051951334546235265772803336495804/37*x^9 + 499681399070418016573162365646246750017060224265522/37*x^8 - 119735813246149889004159337521160343279928799295955/37*x^7 - 904413708225951282492128078629414342960144922667832/37*x^6 - 1655066248965730825984821218129753210856495033068877/37*x^5 - 2181048881851358396053596404429002799874924822306037/37*x^4 - 2348776863930031797794016474758995548172106801011864/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 1540881478248377233481515962570547923239312874396284/37*x - 770440739124188616740757981285273961619656437198142/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? 9 + O(37^2) ? 9 + 28*37 + 34*37^2 + O(37^3) ? 1045 ? Mod(15534338931545960708338121754563884480397627764043*x^35 + 21835010423828501737598015134909666336271507113704*x^34 + 17301821718999490879494104181313772163398536970373*x^33 + 3086074884252799796332273610213937932367257354561*x^32 - 17201831622227728406355762450540517601083390103084*x^31 - 38409342297357495798060897374989371458352920169969*x^30 - 55150348035643114867808267146414371964812683735134*x^29 - 63173105820953540988895668453741306813492012575760*x^28 - 60440061657151709670545747230634507662990485662901*x^27 - 47645331706497258013051444294469368928671916416961*x^26 - 28038416177359046510002243430241589647486610895024*x^25 - 6598918107604932267417458834586238200447677140776*x^24 + 11228135081201708761128055826064851263201009852057*x^23 + 20915175013641052669221852183973776188473941007286*x^22 + 20001967060981715870054155048799564622335741718476*x^21 + 8720440302908987251982885549396904379992071848246*x^20 - 10064215993892205277964188896795905935889133314176*x^19 - 31581229364172044274977624818380280926831700669588*x^18 - 50365885660973236804924699264573091242712905832010*x^17 - 61647412419045965422995968763975751485056575702240*x^16 - 62560620371705302222163665899149963051194774991050*x^15 - 52873580439265958314069869541241038125921843835821*x^14 - 35046527250459317285524354880589948662273156842988*x^13 - 13607029180705203042939570284934597215234223088740*x^12 + 5999886348433008460109630579293182065951082433197*x^11 + 18794616299087460117603933515458320800269651679137*x^10 + 21527660462889291435953854738565119950771178591996*x^9 + 13504902677578865314866453431238185102091849751370*x^8 - 3236103060706753754880916340186815404367913813795*x^7 - 24443613735836521146586051264635669261637443880680*x^6 - 44731520242317049349274087325390124795088091338325*x^5 - 58947267077063740432435917896489959026119370954137*x^4 - 63480455781892751290539828850085853198992341097468*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 41645445358064249552941813715176186862720833983764*x - 20822722679032124776470906857588093431360416991882, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.053s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:56:58 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d); (q-D)/w^(p-1); (q-D)/w^p; a=D+O(p^2); if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1); Output: ? 37 ? 32 ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.051s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:57:05 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d); (q-D)/w^(p-1); (q-D)/w^p; a=D+O(p^2); if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1) Output: ? 37 ? 32 ? ? ? ? ? ? ? ? ? ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.056s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:57:13 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d); (q-D)/w^(p-1); (q-D)/w^p; a=D+O(p^2); if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+2) Output: ? 37 ? 32 ? ? ? ? ? ? ? ? ? ? ? ? Mod(-81988334396163986472772292910744513076889070886303*x^35 - 143153946113295848169073678963900932722417724780724*x^34 - 167962496219849624380566036404905374456188333919220*x^33 - 150113313223542774077989471853412056422327018952130*x^32 - 94139585829204308119447896263016872793706750022785*x^31 - 14257060871580917588103140204819657801358806746997*x^30 + 69246355142846869313356760260425133021266163417589*x^29 + 135163151538949285193226670208268645816898630404088*x^28 + 166752322578440710981759219867285880079078830647335*x^27 + 155991110476010720557867007930149900959127435306704*x^26 + 105612559395461145239899955619967507607545971295054*x^25 + 28411399287446436685352365872903838758653007858325*x^24 - 56005454318895193602726560446813326306366149481546*x^23 - 126198503353809631381752038743528636140472566970311*x^22 - 164340694628490235623178554356591001280017557615137*x^21 - 160744988210497662418912310928091496799728190260795*x^20 - 116324592052491248568121005593204334265742664196095*x^19 - 42361032912543722688875907851332173920404649291267*x^18 + 42361032912543722688875907851332173920404649291267*x^17 + 116324592052491248568121005593204334265742664196095*x^16 + 160744988210497662418912310928091496799728190260795*x^15 + 164340694628490235623178554356591001280017557615137*x^14 + 126198503353809631381752038743528636140472566970311*x^13 + 56005454318895193602726560446813326306366149481546*x^12 - 28411399287446436685352365872903838758653007858325*x^11 - 105612559395461145239899955619967507607545971295054*x^10 - 155991110476010720557867007930149900959127435306704*x^9 - 166752322578440710981759219867285880079078830647335*x^8 - 135163151538949285193226670208268645816898630404088*x^7 - 69246355142846869313356760260425133021266163417589*x^6 + 14257060871580917588103140204819657801358806746997*x^5 + 94139585829204308119447896263016872793706750022785*x^4 + 150113313223542774077989471853412056422327018952130*x^3 + 167962496219849624380566036404905374456188333919220*x^2 + 143153946113295848169073678963900932722417724780724*x + 81988334396163986472772292910744513076889070886303, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.050s sys 0m0.011s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:57:22 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d); (q-D)/w^(p-1); (q-D)/w^p; a=D+O(p^2); if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+3) Output: ? 37 ? 32 ? ? ? ? ? ? ? ? ? ? ? ? Mod(81988334396163986472772292910744513076889070886303*x^34 + 225142280509459834641845971874645445799306795667027*x^33 + 393104776729309459022412008279550820255495129586247*x^32 + 543218089952852233100401480132962876677822148538377*x^31 + 637357675782056541219849376395979749471528898561162*x^30 + 651614736653637458807952516600799407272887705308159*x^29 + 582368381510790589494595756340374274251621541890570*x^28 + 447205229971841304301369086132105628434722911486482*x^27 + 280452907393400593319609866264819748355644080839147*x^26 + 124461796917389872761742858334669847396516645532443*x^25 + 18849237521928727521842902714702339788970674237389*x^24 - 9562161765517709163509463158201498969682333620936*x^23 + 46443292553377484439217097288611827336683815860610*x^22 + 172641795907187115820969136032140463477156382830921*x^21 + 336982490535677351444147690388731464757173940446058*x^20 + 497727478746175013863060001316822961556902130706853*x^19 + 614052070798666262431181006910027295822644794902948*x^18 + 656413103711209985120056914761359469743049444194215*x^17 + 614052070798666262431181006910027295822644794902948*x^16 + 497727478746175013863060001316822961556902130706853*x^15 + 336982490535677351444147690388731464757173940446058*x^14 + 172641795907187115820969136032140463477156382830921*x^13 + 46443292553377484439217097288611827336683815860610*x^12 - 9562161765517709163509463158201498969682333620936*x^11 + 18849237521928727521842902714702339788970674237389*x^10 + 124461796917389872761742858334669847396516645532443*x^9 + 280452907393400593319609866264819748355644080839147*x^8 + 447205229971841304301369086132105628434722911486482*x^7 + 582368381510790589494595756340374274251621541890570*x^6 + 651614736653637458807952516600799407272887705308159*x^5 + 637357675782056541219849376395979749471528898561162*x^4 + 543218089952852233100401480132962876677822148538377*x^3 + 393104776729309459022412008279550820255495129586247*x^2 + 225142280509459834641845971874645445799306795667027*x + 81988334396163986472772292910744513076889070886303, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.056s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:57:28 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d); (q-D)/w^(p-1); (q-D)/w^p; a=D+O(p^2); if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+4) Output: ? 37 ? 32 ? ? ? ? ? ? ? ? ? ? ? ? Mod(11944509931940002224118976084280333799267618111513735/37*x^35 + 23889019863880004448237952168560667598535236223027470/37*x^34 + 32799961423161939172864353415143454413957958711747994/37*x^33 + 36414206976251927515235028540061906718651225383581730/37*x^32 + 33813840169207479755524760317998860168465523700404326/37*x^31 + 25659280772891949354928881637359567530653722315998112/37*x^30 + 14021556700895859553913430794988650599474771180748853/37*x^29 + 1856321376651275802138163765039406329645544195860705/37*x^28 - 7746798807307973785042903135274108018396834742576650/37*x^27 - 12348882384326099820074583237881682471213964356062749/37*x^26 - 10781130025941919548781172205399679361105177235597453/37*x^25 - 3441706579945342616846681879502129915508675008784109/37*x^24 + 7805381563683296688964106804334217311567028155946233/37*x^23 + 20103691480947454152132933025468006572712892611434600/37*x^22 + 30329799588412489452000876510069702760523209536105765/37*x^21 + 35886563071786568390743994561160839411136041482875423/37*x^20 + 35362720853906508611429506101058109014388223797885012/37*x^19 + 28891314072238035322615262136615993236050463073245186/37*x^18 + 18115897384627385836780540965225317089880223773349845/37*x^17 + 5773122479252618611457411203335350508655012449677625/37*x^16 - 5002294208358030874377309968055325637515226850217716/37*x^15 - 11473700990026504163191553932497441415852987574857542/37*x^14 - 11997543207906563942506042392600171812600805259847953/37*x^13 - 6440779724532485003762924341509035161987973313078295/37*x^12 + 3785328382932550296105019143092661025822343611592870/37*x^11 + 16083638300196707759273845364226450286968208067081237/37*x^10 + 27330726443825347065084634048062797514043911231811579/37*x^9 + 34670149889821923997019124373960346959640413458624923/37*x^8 + 36237902248206104268312535406442350069749200579090219/37*x^7 + 31635818671187978233280855303834775616932070965604120/37*x^6 + 22032698487228728646099788403521261268889692027166765/37*x^5 + 9867463162984144894324521373572016999060465042278617/37*x^4 - 1770260909011944906690929468798899932118486092970642/37*x^3 - 9924820305327475307286808149438192569930287477376856/37*x^2 - 12525187112371923066997076371501239120115989160554260/37*x - 8910941559281934724626401246582786815422722488720524/37, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.061s user 0m0.057s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:58:10 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d); type(D) (q-D)/w^(p-1); (q-D)/w^p; a=D+O(p^2); if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1) Output: ? 37 ? 32 ? ? ? ? ? ? ? "t_POL" ? ? ? ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.053s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:58:47 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j); type(q) w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d); (q-D)/w^(p-1); (q-D)/w^p; a=D+O(p^2); if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1) Output: ? 37 ? 32 ? ? ? ? "t_POLMOD" ? ? ? ? ? ? ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.053s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Tue Mar 29 23:59:52 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=lift(d); type(q-D) (q-D)/w^(p-1); (q-D)/w^p; a=D+O(p^2); if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1) Output: ? 37 ? 32 ? ? ? ? ? ? ? "t_POLMOD" ? ? ? ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.054s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:02:07 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=Mod(lift(d), sum(n=0, p-1, x^n)); type(q-D) (q-D)/w^(p-1); (q-D)/w^p; a=D+O(p^2); if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1) Output: ? 37 ? 32 ? ? ? ? ? ? ? "t_POLMOD" ? ? ? ? ? ? Mod((404800984089803737832893160661/1369*e - 28506307347594978819411688516411944813567784214777203/1369)*x^35 + (1202757564977011225345277548604/1369*e - 78279124692476377848949113313475134399214989171038963/1369)*x^34 + (2370913984666456766419176545284/1369*e - 136677561310292575547930190979780038111525317723116797/1369)*x^33 + (3875664509822164311033001134729/1369*e - 188870062591197857382518755390824406494871772393413917/1369)*x^32 + (5673720207529453195994238458027/1369*e - 221601206455334919124565277655349504316599451576540794/1369)*x^31 + (7713354289078741611002755978890/1369*e - 226558206312100137757384327963816642021932602196607091/1369)*x^30 + (9935890195497801205966862396284/1369*e - 202482124054612704831150180967702209679717356551982718/1369)*x^29 + (12277389615321072423860334111879/1369*e - 155487604941412259398556201626014352790119881323267505/1369)*x^28 + (14670491873398203414803522072934/1369*e - 97509930420121840606247494860571205555517358388240998/1369)*x^27 + (17046351774874773015949677531525/1369*e - 43273793359076128888741811986913679705613526831843582/1369)*x^26 + (19336620156102105204331927909221/1369*e - 6553641600476361490256386694205775686653535763602751/1369)*x^25 + (21475410165632481509913501724419/1369*e + 3324642798733194360712977513797617393890479052916737/1369)*x^24 + (23401192708975512325031637829382/1369*e - 16147745659550632186193635587485389619027514032933712/1369)*x^23 + (25058566528621041445595275281049/1369*e - 60025369933310750300898571142935848836871108519278218/1369)*x^22 + (26399851997349083600226406960459/1369*e - 117164551874580330225453601585654852398013877225122660/1369)*x^21 + (27386462774295058992720244847054/1369*e - 173053552128659278071577419597408100558679979091094537/1369)*x^20 + (27990015863722673770731976748214/1369*e - 213498142250936660439161374381022420005443796149941969/1369)*x^19 + (28193148142134608951349163864578/1369*e - 228226537902893210232829344500287396950488944041321863/1369)*x^18 + (27990015863722673770731976748214/1369*e - 213498142250936660439161374381022420005443796149941969/1369)*x^17 + (27386462774295058992720244847054/1369*e - 173053552128659278071577419597408100558679979091094537/1369)*x^16 + (26399851997349083600226406960459/1369*e - 117164551874580330225453601585654852398013877225122660/1369)*x^15 + (25058566528621041445595275281049/1369*e - 60025369933310750300898571142935848836871108519278218/1369)*x^14 + (23401192708975512325031637829382/1369*e - 16147745659550632186193635587485389619027514032933712/1369)*x^13 + (21475410165632481509913501724419/1369*e + 3324642798733194360712977513797617393890479052916737/1369)*x^12 + (19336620156102105204331927909221/1369*e - 6553641600476361490256386694205775686653535763602751/1369)*x^11 + (17046351774874773015949677531525/1369*e - 43273793359076128888741811986913679705613526831843582/1369)*x^10 + (14670491873398203414803522072934/1369*e - 97509930420121840606247494860571205555517358388240998/1369)*x^9 + (12277389615321072423860334111879/1369*e - 155487604941412259398556201626014352790119881323267505/1369)*x^8 + (9935890195497801205966862396284/1369*e - 202482124054612704831150180967702209679717356551982718/1369)*x^[+++] ? Errors (if any) and Timing Info: *** incorrect type in gtrunc. Timing: real 0m0.060s user 0m0.053s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:03:10 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); q=c((p-1)-j); w=Mod(1-x, sum(n=0, p-1, x^n)); d=lift(q)*Mod(1, p); D=Mod(lift(d), sum(n=0, p-1, x^n)); type(q-D) (q-D)/w^(p-1) (q-D)/w^p; a=lift(D)+O(p^2); if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1) Output: ? 37 ? 32 ? ? ? ? ? ? ? "t_POLMOD" ? Mod(9233667439263419679095600299187417205369784774362*x^35 + 20067527636374971566484835998896858893592431360522*x^34 + 29750085766292651791575514808876773507680210023531*x^33 + 35822245438026488911140864895392699963840218703636*x^32 + 36741849606675728100202367641552568390431192027172*x^31 + 32275344669831579778292988237745895244938567707972*x^30 + 23557096716856386829683995419707555311391380915237*x^29 + 12801294767744129390298771955650140030040497187208*x^28 + 2739608980891509051206113934001609328468655724291*x^27 - 4072576597592250794298923674046541565397280511574*x^26 - 5905159138208153533787944847481386460587197605057*x^25 - 2292714257260680319706749636523492755182093913758*x^24 + 5847298999106616800781050546277039015587829473330*x^23 + 16447546884205297508071744513527965623045826527521*x^22 + 26815865689618689326996795901556852890214938768221*x^21 + 34318995228347153238885740509372001112983508827497*x^20 + 37051352301825799705956524278888683122842579791895*x^19 + 34318995228347153238885740509372001112983508827497*x^18 + 26815865689618689326996795901556852890214938768221*x^17 + 16447546884205297508071744513527965623045826527521*x^16 + 5847298999106616800781050546277039015587829473330*x^15 - 2292714257260680319706749636523492755182093913758*x^14 - 5905159138208153533787944847481386460587197605057*x^13 - 4072576597592250794298923674046541565397280511574*x^12 + 2739608980891509051206113934001609328468655724291*x^11 + 12801294767744129390298771955650140030040497187208*x^10 + 23557096716856386829683995419707555311391380915237*x^9 + 32275344669831579778292988237745895244938567707972*x^8 + 36741849606675728100202367641552568390431192027172*x^7 + 35822245438026488911140864895392699963840218703636*x^6 + 29750085766292651791575514808876773507680210023531*x^5 + 20067527636374971566484835998896858893592431360522*x^4 + 9233667439263419679095600299187417205369784774362*x^3 - 5288383747486164068141597828542781914970769069315*x - 5288383747486164068141597828542781914970769069315, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.054s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:11:47 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); D=Mod(lift(d), sum(n=0, p-1, x^n)); (q-D)/w^(p+1) a=lift(D)+O(p^2); if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1) Output: ? 37 ? 32 ? ? ? ? ? ? ? Mod(-770440739124188616740757981285273961619656437198142/37*x^35 - 2115652018715577779701034824199738954005050856029771/37*x^34 - 3693988143521420960754293317673460540557501219843493/37*x^33 - 5104596286248590740067131740817189378812769604951388/37*x^32 - 5989221796090132949311194977661668628049608200822123/37*x^31 - 6123194765191895615062565075005809009390096686291813/37*x^30 - 5472489839313856887325966431241695391050369048389626/37*x^29 - 4202367701119250254012046084310174679413652386925962/37*x^28 - 2635403524868157854219336768478665452021192613232016/37*x^27 - 1169561982677733213205091751917292074282972425244861/37*x^26 - 177125448661523283515739381427050182157149957092426/37*x^25 + 89855210776572820565033951494278641283235150498284/37*x^24 - 436425558366233302323865536570394865083844034931602/37*x^23 - 1622307295494885143261433622815628634158398676804021/37*x^22 - 3166609510123792708789621700477802990421941609796717/37*x^21 - 4677123030504304812738674092768633649398526942904623/37*x^20 - 5770220060836125957808363898331051782202897523221839/37*x^19 - 6168284808186302979258800166675896904592616258555153/37*x^18 - 5770220060836125957808363898331051782202897523221839/37*x^17 - 4677123030504304812738674092768633649398526942904623/37*x^16 - 3166609510123792708789621700477802990421941609796717/37*x^15 - 1622307295494885143261433622815628634158398676804021/37*x^14 - 436425558366233302323865536570394865083844034931602/37*x^13 + 89855210776572820565033951494278641283235150498284/37*x^12 - 177125448661523283515739381427050182157149957092426/37*x^11 - 1169561982677733213205091751917292074282972425244861/37*x^10 - 2635403524868157854219336768478665452021192613232016/37*x^9 - 4202367701119250254012046084310174679413652386925962/37*x^8 - 5472489839313856887325966431241695391050369048389626/37*x^7 - 6123194765191895615062565075005809009390096686291813/37*x^6 - 5989221796090132949311194977661668628049608200822123/37*x^5 - 5104596286248590740067131740817189378812769604951388/37*x^4 - 3693988143521420960754293317673460540557501219843493/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 770440739124188616740757981285273961619656437198142/37*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.050s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:15:57 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(lift(d))==0, D=Mod(lift(d), sum(n=0, p-1, x^n)), print("bad")) (q-D)/w^(p+1) a=lift(D)+O(p^2); if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1) Output: ? 37 ? 32 ? ? ? ? ? ? Mod(9, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-770440739124188616740757981285273961619656437198142/37*x^35 - 2115652018715577779701034824199738954005050856029771/37*x^34 - 3693988143521420960754293317673460540557501219843493/37*x^33 - 5104596286248590740067131740817189378812769604951388/37*x^32 - 5989221796090132949311194977661668628049608200822123/37*x^31 - 6123194765191895615062565075005809009390096686291813/37*x^30 - 5472489839313856887325966431241695391050369048389626/37*x^29 - 4202367701119250254012046084310174679413652386925962/37*x^28 - 2635403524868157854219336768478665452021192613232016/37*x^27 - 1169561982677733213205091751917292074282972425244861/37*x^26 - 177125448661523283515739381427050182157149957092426/37*x^25 + 89855210776572820565033951494278641283235150498284/37*x^24 - 436425558366233302323865536570394865083844034931602/37*x^23 - 1622307295494885143261433622815628634158398676804021/37*x^22 - 3166609510123792708789621700477802990421941609796717/37*x^21 - 4677123030504304812738674092768633649398526942904623/37*x^20 - 5770220060836125957808363898331051782202897523221839/37*x^19 - 6168284808186302979258800166675896904592616258555153/37*x^18 - 5770220060836125957808363898331051782202897523221839/37*x^17 - 4677123030504304812738674092768633649398526942904623/37*x^16 - 3166609510123792708789621700477802990421941609796717/37*x^15 - 1622307295494885143261433622815628634158398676804021/37*x^14 - 436425558366233302323865536570394865083844034931602/37*x^13 + 89855210776572820565033951494278641283235150498284/37*x^12 - 177125448661523283515739381427050182157149957092426/37*x^11 - 1169561982677733213205091751917292074282972425244861/37*x^10 - 2635403524868157854219336768478665452021192613232016/37*x^9 - 4202367701119250254012046084310174679413652386925962/37*x^8 - 5472489839313856887325966431241695391050369048389626/37*x^7 - 6123194765191895615062565075005809009390096686291813/37*x^6 - 5989221796090132949311194977661668628049608200822123/37*x^5 - 5104596286248590740067131740817189378812769604951388/37*x^4 - 3693988143521420960754293317673460540557501219843493/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 770440739124188616740757981285273961619656437198142/37*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.056s user 0m0.047s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:16:20 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(lift(d))==0, D=Mod(lift(d), sum(n=0, p-1, x^n)), print("bad")) (q-D)/w^(p+1); a=lift(D)+O(p^2); if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1); Output: ? 37 ? 32 ? ? ? ? ? ? Mod(9, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.051s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:17:27 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(lift(d))==0, D=Mod(lift(d), sum(n=0, p-1, x^n)), print("bad")) (q-D)/w^(p+1) a=lift(D)+O(p^2); if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1); Output: ? 37 ? 32 ? ? ? ? ? ? Mod(9, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Mod(-770440739124188616740757981285273961619656437198142/37*x^35 - 2115652018715577779701034824199738954005050856029771/37*x^34 - 3693988143521420960754293317673460540557501219843493/37*x^33 - 5104596286248590740067131740817189378812769604951388/37*x^32 - 5989221796090132949311194977661668628049608200822123/37*x^31 - 6123194765191895615062565075005809009390096686291813/37*x^30 - 5472489839313856887325966431241695391050369048389626/37*x^29 - 4202367701119250254012046084310174679413652386925962/37*x^28 - 2635403524868157854219336768478665452021192613232016/37*x^27 - 1169561982677733213205091751917292074282972425244861/37*x^26 - 177125448661523283515739381427050182157149957092426/37*x^25 + 89855210776572820565033951494278641283235150498284/37*x^24 - 436425558366233302323865536570394865083844034931602/37*x^23 - 1622307295494885143261433622815628634158398676804021/37*x^22 - 3166609510123792708789621700477802990421941609796717/37*x^21 - 4677123030504304812738674092768633649398526942904623/37*x^20 - 5770220060836125957808363898331051782202897523221839/37*x^19 - 6168284808186302979258800166675896904592616258555153/37*x^18 - 5770220060836125957808363898331051782202897523221839/37*x^17 - 4677123030504304812738674092768633649398526942904623/37*x^16 - 3166609510123792708789621700477802990421941609796717/37*x^15 - 1622307295494885143261433622815628634158398676804021/37*x^14 - 436425558366233302323865536570394865083844034931602/37*x^13 + 89855210776572820565033951494278641283235150498284/37*x^12 - 177125448661523283515739381427050182157149957092426/37*x^11 - 1169561982677733213205091751917292074282972425244861/37*x^10 - 2635403524868157854219336768478665452021192613232016/37*x^9 - 4202367701119250254012046084310174679413652386925962/37*x^8 - 5472489839313856887325966431241695391050369048389626/37*x^7 - 6123194765191895615062565075005809009390096686291813/37*x^6 - 5989221796090132949311194977661668628049608200822123/37*x^5 - 5104596286248590740067131740817189378812769604951388/37*x^4 - 3693988143521420960754293317673460540557501219843493/37*x^3 - 2115652018715577779701034824199738954005050856029771/37*x^2 - 770440739124188616740757981285273961619656437198142/37*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.052s sys 0m0.002s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:17:40 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(lift(d))==0, D=Mod(lift(d), sum(n=0, p-1, x^n)), print("bad")) (q-D)/w^(p+1); a=lift(D)+O(p^2) if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1); Output: ? 37 ? 32 ? ? ? ? ? ? Mod(9, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? 9 + O(37^2) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.050s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:17:57 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=Mod(lift(d), sum(n=0, p-1, x^n)), print("bad")) (q-D)/w^(p+1); a=lift(D)+O(p^2) if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1); Output: ? 37 ? 32 ? ? ? ? ? ? Mod(9, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? 9 + O(37^2) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.047s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:18:06 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=Mod(lift(d), sum(n=0, p-1, x^n)), print("bad")) (q-D)/w^(p+1); a=lift(D)+O(p^2) if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1) Output: ? 37 ? 32 ? ? ? ? ? ? Mod(9, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? 9 + O(37^2) ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.045s sys 0m0.011s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:19:46 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("bad")); (q-D)/w^(p+1); a=lift(D)+O(p^2) if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1) Output: ? 37 ? 32 ? ? ? ? ? ? ? ? 9 + O(37^2) ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.050s sys 0m0.004s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:21:10 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")); (q-D)/w^(p+1); D^p a=lift(D)+O(p^2) if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1) Output: ? 37 ? 32 ? ? ? ? ? ? ? ? 202755595904452569706561330872953769 ? 9 + O(37^2) ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.047s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:22:22 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")); (q-D)/w^(p+1); (D*Mod(1, p^2))^p a=lift(D)+O(p^2) if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1) Output: ? 37 ? 32 ? ? ? ? ? ? ? ? Mod(1045, 1369) ? 9 + O(37^2) ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.048s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:23:16 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")); (q-D)/w^(p+1); Mod(D, p^2)^p a=lift(D)+O(p^2) if (poldegree(a^p)==0, E=polcoeff(a^p, 0), print("bad")); e=truncate(E+O(p^2)); (q-e)/w^(p+1) Output: ? 37 ? 32 ? ? ? ? ? ? ? ? Mod(1045, 1369) ? 9 + O(37^2) ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.048s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:24:10 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")); (q-D)/w^(p+1); e=Mod(D, p^2)^p E=lift(e) (q-E)/w^(p+1) Output: ? 37 ? 32 ? ? ? ? ? ? ? ? Mod(1045, 1369) ? 1045 ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.050s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:24:39 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")); (q-D)/w^(p+1); e=Mod(D, p^2)^p E=lift(e) type((q-E)/w^(p+1)) Output: ? 37 ? 32 ? ? ? ? ? ? ? ? Mod(1045, 1369) ? 1045 ? "t_POLMOD" ? Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.049s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:26:27 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")); (q-D)/w^(p+1); e=Mod(D, p^2)^p E=lift(e) (q-E)/w^(p+1) for Output: ? 37 ? 32 ? ? ? ? ? ? ? ? Mod(1045, 1369) ? 1045 ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: for ^ Timing: real 0m0.056s user 0m0.050s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:27:13 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")); (q-D)/w^(p+1); e=Mod(D, p^2)^p E=lift(e) l=(q-E)/w^(p+1) for(i=0, 35, isinteger(l)) Output: ? 37 ? 32 ? ? ? ? ? ? ? ? Mod(1045, 1369) ? 1045 ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: isinteger(l)) ^- Timing: real 0m0.055s user 0m0.048s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:27:34 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")); (q-D)/w^(p+1); e=Mod(D, p^2)^p E=lift(e) l=(q-E)/w^(p+1) for(i=0, 35, isinteger(l)) isinteger(7) Output: ? 37 ? 32 ? ? ? ? ? ? ? ? Mod(1045, 1369) ? 1045 ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: isinteger(l)) ^- *** unknown function or error in formal parameters: isinteger(7) ^------------ Timing: real 0m0.055s user 0m0.047s sys 0m0.008s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:27:45 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")); (q-D)/w^(p+1); e=Mod(D, p^2)^p E=lift(e) l=(q-E)/w^(p+1) for(i=0, 35, isinteger(l)) isint(7) Output: ? 37 ? 32 ? ? ? ? ? ? ? ? Mod(1045, 1369) ? 1045 ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: isinteger(l)) ^- *** unknown function or error in formal parameters: isint(7) ^-------- Timing: real 0m0.055s user 0m0.050s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:30:56 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")); (q-D)/w^(p+1); e=Mod(D, p^2)^p E=lift(e) l=(q-E)/w^(p+1) isint(k)=if(valuation(lift(polcoeff(l, i)), p)<0, print("failure"), ) for(i=0, p-2, valuation(polcoeff(l, i)) Output: ? 37 ? 32 ? ? ? ? ? ? ? ? Mod(1045, 1369) ? 1045 ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...2,valuation(polcoeff(l,i)) ^- Timing: real 0m0.055s user 0m0.046s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:32:01 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")); (q-D)/w^(p+1); e=Mod(D, p^2)^p E=lift(e) l=(q-E)/w^(p+1) L=lift(l) isint(k)=if(valuation(polcoeff(L, i)), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) Output: ? 37 ? 32 ? ? ? ? ? ? ? ? Mod(1045, 1369) ? 1045 ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? -20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...f(valuation(polcoeff(L,i) *** ),p)<0,print("failur ^-------------------- *** expected character: '=' instead of: isint(k)) ^- Timing: real 0m0.055s user 0m0.048s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:32:28 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")); (q-D)/w^(p+1); e=Mod(D, p^2)^p E=lift(e) l=(q-E)/w^(p+1) L=lift(l) isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) Output: ? 37 ? 32 ? ? ? ? ? ? ? ? Mod(1045, 1369) ? 1045 ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? -20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.056s user 0m0.051s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:33:59 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")); (q-D)/w^(p+1); e=Mod(D, p^2)^p E=lift(e) l=(q-E)/w^(p+1) L=lift(l) isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l Output: ? 37 ? 32 ? ? ? ? ? ? ? ? Mod(1045, 1369) ? 1045 ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? -20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.050s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:34:13 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")) (q-D)/w^(p+1); e=Mod(D, p^2)^p E=lift(e) l=(q-E)/w^(p+1) L=lift(l) isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l Output: ? 37 ? 32 ? ? ? ? ? ? 9 ? ? Mod(1045, 1369) ? 1045 ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? -20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.050s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:34:29 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0);, print("failure")) (q-D)/w^(p+1); e=Mod(D, p^2)^p E=lift(e) l=(q-E)/w^(p+1) L=lift(l) isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l Output: ? 37 ? 32 ? ? ? ? ? ? 9 ? ? Mod(1045, 1369) ? 1045 ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? -20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.056s user 0m0.048s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:35:03 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0);, print("failure")) (q-D)/w^(p+1); e=Mod(D, p^2)^p; E=lift(e); l=(q-E)/w^(p+1); L=lift(l); isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l Output: ? 37 ? 32 ? ? ? ? ? ? 9 ? ? ? ? ? ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.056s user 0m0.049s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:35:17 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")) (q-D)/w^(p+1); e=Mod(D, p^2)^p; E=lift(e); l=(q-E)/w^(p+1); L=lift(l); isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l Output: ? 37 ? 32 ? ? ? ? ? ? 9 ? ? ? ? ? ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.056s user 0m0.047s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:36:35 2005 Input: p=59 j=44 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")) (q-D)/w^(p+1); e=Mod(D, p^2)^p; E=lift(e); l=(q-E)/w^(p+1); L=lift(l); isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l Output: ? 59 ? 44 ? ? ? ? ? ? 22 ? ? ? ? ? ? ? ? Mod(85781915262452698720103588253621231921569281951750557315954535793137983267727574379854365522727879926655187988784225*x^57 + 76147771096851066296460320994232659909434441983446954710267774333391809229127861042081035712700550765360216627907195*x^56 - 18130695405506498880525806575703833083046093510219551752435947145946647837228165057796620828765285025696548291765432*x^55 - 14692328837227519940209541235931054999872171402783867288104171581238012738700488823680514647959089504208300265895988*x^54 + 67840595445364276388295641204593976239385629977279468942448011127021988768150187368667094541748243815860111595848176*x^53 + 49954279903618935763517288708238968234385086522349400350724033886314470551293898016045101106224323101460870951074095*x^52 - 38350269877162764072977479253561330622241254402759664254194915111478240816428514583325492995676113685820668878755813*x^51 - 17730060487442116344790631906887907411266109619613905805051010056032085258890686887121860126454997301205067866891432*x^50 + 72722591674465285115091710902747728909382410110562397697602001947971744629679051305402234134339557780650286991571800*x^49 + 55002025859294555833594546573937002629515708365030551442613479051456221679103890552081381709711390275226730036538723*x^48 - 23901252436459992500848780960442363628216310795313867476915251680853949295471809455829688804532957667526308662094923*x^47 + 9669331877793260031801016357927911766946975147529398654425919319808366085788901376094930686450630932486929276492753*x^46 + 97623506203111358765565940011580638490210893501610823759284822857031012716496462025396776505464435297500266636696827*x^45 + 67543634100695628421918363492717615984179764928239914902549125664549690637397530276993706888573261514347620740404390*x^44 - 14941030376828498414094641614463041367526808153420789068429276396671023801636189195630732641828887367764347180075418*x^43 + 18214521806740696727232474241851588206296826974398238494673775411971914510821256857616766881690290473899531181983589*x^42 + 92741155326331745759988624958397752433847905288630735481464284287928913960979947511560117073535426080618186219405069*x^41 + 45883459938104043169810804381189218514926074203566303508634555083488966239345960989464564097180005465577442703732482*x^40 - 37624186858486282764106205928146337651206312396316367631961607158265796210022887306177249665927289548468354520419474*x^39 + 2319493772048487911214239760639868246116746772521212242402506579517292738054239152650842803043157039873089363986580*x^38 + 74314459685031344141918511157044787517130369861436353923036644434313757243919086729217498702598784303998802276513256*x^37 + 24897726684534409205939736643623002097311145537504873847793766164313313859055534979012131508851007223641154449740861*x^36 - 45125450719227816601669049386835046500073300800532357079700775498215698796330451014063722930003867772974848313143989*x^35 + 12495129136913424933928324518468680462409946721467365841979565188951870974454026212010354766649557103286590532836325*x^34 + 88055617347704850336225733834548671106142032927481188642794017201800351936896264434450548036498138278255483500380139*x^33 + 374534565030757138404764810222967627976793599735643167280110357006626232924133072476483[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.274s user 0m0.260s sys 0m0.014s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:36:55 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")) (q-D)/w^(p+1); e=Mod(D, p^2)^p; E=lift(e); l=(q-E)/w^(p+1); L=lift(l); isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l Output: ? 37 ? 32 ? ? ? ? ? ? 9 ? ? ? ? ? ? ? ? Mod(-20822722679032124776470906857588093431360416991882*x^35 - 57179784289610210261279935469740071343118461747807*x^34 - 99837517392470836775348857462237831110750385853393*x^33 - 137962061790502452431313868501139696705509339815648*x^32 - 161870859353787377004117048968941728069237014162091*x^31 - 165491750410591773374232193375989303899514041050889*x^30 - 147905130792266402352642202858588025872521537872802*x^29 - 113577505435655412261304842569761747339069271129550*x^28 - 71227122293733996048880080973608533956937675545672*x^27 - 31609783315614411154805240600562119725307606874653*x^26 - 4787174288149277918224703163680844227996107449574*x^25 + 2428519210177643815306633408972651988130086453568*x^24 - 11795285361249548693746814614029203242782653397538*x^23 - 43846143121483382231345777297682147937344080241477*x^22 - 85584040814156559677038536339244017557178438240645*x^21 - 126408730554170400323563598245631675610874596951003*x^20 - 155951893536111512352017390652616673422227085791131*x^19 - 166710400221251431850524108613408860917698369468837*x^18 - 155951893536111512352017390652616673422227085791131*x^17 - 126408730554170400323563598245631675610874596951003*x^16 - 85584040814156559677038536339244017557178438240645*x^15 - 43846143121483382231345777297682147937344080241477*x^14 - 11795285361249548693746814614029203242782653397538*x^13 + 2428519210177643815306633408972651988130086453568*x^12 - 4787174288149277918224703163680844227996107449574*x^11 - 31609783315614411154805240600562119725307606874653*x^10 - 71227122293733996048880080973608533956937675545672*x^9 - 113577505435655412261304842569761747339069271129550*x^8 - 147905130792266402352642202858588025872521537872802*x^7 - 165491750410591773374232193375989303899514041050889*x^6 - 161870859353787377004117048968941728069237014162091*x^5 - 137962061790502452431313868501139696705509339815648*x^4 - 99837517392470836775348857462237831110750385853393*x^3 - 57179784289610210261279935469740071343118461747807*x^2 - 20822722679032124776470906857588093431360416991882*x, x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.056s user 0m0.049s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:49:57 2005 Input: p=59 j=44 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")) (q-D)/w^(p+1); e=Mod(D, p^2)^p; E=lift(e); l=(q-E)/w^(p+1); L=lift(l); isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l; Output: ? 59 ? 44 ? ? ? ? ? ? 22 ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.272s user 0m0.263s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:50:15 2005 Input: p=59 j=44 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")) (q-D)/w^(p+1); e=Mod(D, p^2)^p; E=lift(e); E l=(q-E)/w^(p+1); L=lift(l); isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l; Output: ? 59 ? 44 ? ? ? ? ? ? 22 ? ? ? ? 612 ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.273s user 0m0.259s sys 0m0.013s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:50:25 2005 Input: p=37 j=32 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")) (q-D)/w^(p+1); e=Mod(D, p^2)^p; E=lift(e); E l=(q-E)/w^(p+1); L=lift(l); isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l; Output: ? 37 ? 32 ? ? ? ? ? ? 9 ? ? ? ? 1045 ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.050s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:50:43 2005 Input: p=59 j=44 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")) (q-D)/w^(p+1); e=Mod(D, p^2)^p; E=lift(e); E l=(q-E)/w^(p+1); L=lift(l); isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l; Output: ? 59 ? 44 ? ? ? ? ? ? 22 ? ? ? ? 612 ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.272s user 0m0.262s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:50:57 2005 Input: p=67 j=58 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")) (q-D)/w^(p+1); e=Mod(D, p^2)^p; E=lift(e); E l=(q-E)/w^(p+1); L=lift(l); isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l; Output: ? 67 ? 58 ? ? ? ? ? ? 33 ? ? ? ? 2579 ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.463s user 0m0.449s sys 0m0.015s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:51:11 2005 Input: p=101 j=68 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")) (q-D)/w^(p+1); e=Mod(D, p^2)^p; E=lift(e); E l=(q-E)/w^(p+1); L=lift(l); isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l; Output: ** WARNING: Computation used more memory than allowed. ** ? 101 ? 68 ? ? ? ? ? ? 37 ? ? ? ? 2158 ? ? ? ? ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m1.642s user 0m1.623s sys 0m0.018s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:51:45 2005 Input: p=37 j=34 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")) (q-D)/w^(p+1); e=Mod(D, p^2)^p; E=lift(e); E l=(q-E)/w^(p+1); L=lift(l); isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l; Output: ? 37 ? 34 ? ? ? ? ? ? failure ? ? ? ? e ? ? ? ? failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure failure ? ? Errors (if any) and Timing Info: *** forbidden division t_POL % t_INT. Timing: real 0m0.059s user 0m0.051s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:52:41 2005 Input: p=101 j=68 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")) (q-D)/w^(p+1); e=Mod(D, p^2)^p; E=lift(e); E l=(q-E)/w^(p+1); L=lift(l); isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l; Output: ** WARNING: Computation used more memory than allowed. ** ? 101 ? 68 ? ? ? ? ? ? 37 ? ? ? ? 2158 ? ? ? ? ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m1.643s user 0m1.622s sys 0m0.023s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 00:53:54 2005 Input: allocatemem(20) p=101 j=68 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")) (q-D)/w^(p+1); e=Mod(D, p^2)^p; E=lift(e); E l=(q-E)/w^(p+1); L=lift(l); isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l; Output: WARNING: PARI command contains unsafe command 'allocatemem', so it will not be executed. '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Mar 30 01:32:18 2005 Input: t(i) = if(valuation(bernfrac(2*i),p)>0,print(p," ",2*i),) forprime(p=1, 200, for(i=1,(p-3)/2,t(i))) p=101 j=68 et(a)=Mod(x^a+1/x^a, sum(n=0, p-1, x^n)); c(k)=prod(a=1, p-1, et(a)^(lift(Mod(a^k, p)))); w=Mod(1-x, sum(n=0, p-1, x^n)); q=c((p-1)-j); d=lift(q)*Mod(1, p); if(poldegree(d)==0, D=polcoeff(lift(d), 0), print("failure")) (q-D)/w^(p+1); e=Mod(D, p^2)^p; E=lift(e); E l=(q-E)/w^(p+1); L=lift(l); isint(k)=if(valuation(polcoeff(L, i), p)<0, print("failure"), ) for(i=0, p-2, isint(k)) l; Output: ** WARNING: Computation used more memory than allowed. ** ? ? 37 32 59 44 67 58 101 68 103 24 131 22 149 130 157 62 157 110 ? 101 ? 68 ? ? ? ? ? ? 37 ? ? ? ? 2158 ? ? ? ? ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m2.045s user 0m2.031s sys 0m0.014s '145.89.' ************** PARI ***************** Host 145.89.51.113 (145.89.51.113) Time: Wed Mar 30 03:33:18 2005 Input: 4^45 Output: ? 1237940039285380274899124224 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '145.89.' ************** PARI ***************** Host 145.89.51.113 (145.89.51.113) Time: Wed Mar 30 03:33:46 2005 Input: x^2+2x+6 Output: ? x^2 + 2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+6. Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '145.89.' ************** PARI ***************** Host 145.89.51.113 (145.89.51.113) Time: Wed Mar 30 03:34:00 2005 Input: x^2+2*x+6 Output: ? x^2 + 2*x + 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '145.89.' ************** PARI ***************** Host 145.89.51.113 (145.89.51.113) Time: Wed Mar 30 03:35:33 2005 Input: x:=4 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: x:=4 ^-- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '145.89.' ************** PARI ***************** Host 145.89.51.113 (145.89.51.113) Time: Wed Mar 30 03:35:44 2005 Input: x:4 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '145.89.' ************** PARI ***************** Host 145.89.51.113 (145.89.51.113) Time: Wed Mar 30 03:35:56 2005 Input: x:4 2*x+4 Output: ? 4 ? 2*x + 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '158.109' ************** PARI ***************** Host 158.109.66.114 (158.109.66.114) Time: Wed Mar 30 04:28:44 2005 Input: GF3 := FG(3); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: GF3:=FG(3); ^------- Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '58.8.0.' ************** PARI ***************** Host 58.8.0.252 (58.8.0.252) Time: Wed Mar 30 04:34:37 2005 Input: polgalois(x^4-x^3-x-1) Output: ? ? Errors (if any) and Timing Info: *** sorry, galois of reducible polynomial is not yet implemented. Timing: real 0m0.031s user 0m0.003s sys 0m0.010s '158.109' ************** PARI ***************** Host 158.109.66.116 (158.109.66.116) Time: Wed Mar 30 04:47:59 2005 Input: (2+3+2+4+2+2+0+2+2+4+0+2+2+2+0+1+2+2+0+2+0+1+2+1+0+1+1)/27; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '61.199.' ************** PARI ***************** Host 61.199.185.203 (61.199.185.203) Time: Wed Mar 30 08:39:23 2005 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.463s user 0m0.007s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 09:44:43 2005 Input: Mod(6780,5987)^3390 Output: ? Mod(4869, 5987) ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.009s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 09:44:55 2005 Input: Mod(4869,5987)^2 Output: ? Mod(4628, 5987) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 09:45:30 2005 Input: Mod(6780,6781)^3390 Output: ? Mod(1, 6781) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 09:46:48 2005 Input: Mod(6780,6781)^1695 Output: ? Mod(6780, 6781) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 09:47:15 2005 Input: Mod(6780,6781)^2 Output: ? Mod(1, 6781) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 09:54:03 2005 Input: Mod(-1,6781)^(1/2994) Output: ? Mod(995, 6781) ? Errors (if any) and Timing Info: Timing: real 0m0.050s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 09:54:37 2005 Input: Mod(995,6781)^(2994) Output: ? Mod(6780, 6781) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 09:55:32 2005 Input: Mod(995,6781)^(1497) Output: ? Mod(995, 6781) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 09:55:51 2005 Input: Mod(995,6781)^(2) Output: ? Mod(6780, 6781) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 10:40:10 2005 Input: Mod(10,101)^(1/2) Output: ? ? Errors (if any) and Timing Info: *** n-root does not exists in gpow. Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 10:40:25 2005 Input: Mod(5,101)^(1/2) Output: ? Mod(56, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 10:47:43 2005 Input: Mod(56,101)^(2) Output: ? Mod(5, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 11:05:40 2005 Input: Mod((1/2),101) Output: ? Mod(51, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 11:17:13 2005 Input: Mod(-8,11)^(1/2) Output: ? Mod(5, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 11:20:33 2005 Input: Mod(5,11)^(2) Output: ? Mod(3, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 11:24:02 2005 Input: Mod(4/5,11)^(2) Output: ? Mod(9, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 11:24:29 2005 Input: Mod(3/4,11) Output: ? Mod(9, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 11:25:57 2005 Input: Mod(1/4,11) Output: ? Mod(3, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '194.27.' ************** PARI ***************** Host 194.27.200.8 (194.27.200.8) Time: Wed Mar 30 11:28:39 2005 Input: for i in [20..300] do p:=NextPrime(i); count:=0; for x in [1..(p-1)] do for y in [1..(p-1)] do delta:=4*x^3+27*y^2; deltam:= delta mod p; if deltam eq 0 then count:=count+1; end if; end for; end for; print p, count; end for; Output: ? ? ? ? ? ? ? ? ifdeltameq0then ? ? ? ? ? (count) ? ? Errors (if any) and Timing Info: *** Warning: unused characters: do. *** unexpected character: foriin[20..300]do ^----------- *** unexpected character: p:=NextPrime(i); ^-------------- *** unexpected character: count:=0; ^--- *** expected character: ']' instead of: forxin[1..(p-1)]do ^-------- *** expected character: ']' instead of: foryin[1..(p-1)]do ^-------- *** unexpected character: delta:=4*x^3+27*y^2; ^-------------- *** unexpected character: deltam:=deltamodp; ^----------- *** unexpected character: count:=count+1; ^--------- *** Warning: unused characters: ,count;. Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 11:30:05 2005 Input: Mod(9/4,11) Output: ? Mod(5, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 11:32:34 2005 Input: Mod(1/2,11) Output: ? Mod(6, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 11:34:14 2005 Input: Mod(1/5,11) Output: ? Mod(9, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 11:34:19 2005 Input: Mod(1/5,11) Output: ? Mod(9, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 11:52:36 2005 Input: Mod(5,11)^(1/2) Output: ? Mod(4, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 11:54:36 2005 Input: Mod(-8,11)^(1/2) Output: ? Mod(5, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 11:54:52 2005 Input: Mod(-8,11)^(1/2) Output: ? Mod(5, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 11:54:58 2005 Input: Mod(-8,11) Output: ? Mod(3, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.150.169 (128.197.150.169) Time: Wed Mar 30 11:59:17 2005 Input: Mod(-8,11)^(1/2) Output: ? Mod(5, 11) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '66.185.' ************** PARI ***************** Host 66.185.84.74 (66.185.84.74) Time: Wed Mar 30 18:14:10 2005 Input: 4333 Output: ? 4333 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 19:44:45 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.006s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:04:38 2005 Input: Mod(347,463)^323 Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:06:31 2005 Input: Mod(347,463)^2 Output: ? Mod(29, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:07:17 2005 Input: Mod(347,463)^4 Output: ? Mod(378, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:08:03 2005 Input: Mod(347,463)^8 Output: ? Mod(280, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:08:22 2005 Input: Mod(347,463)^16 Output: ? Mod(153, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:08:31 2005 Input: Mod(347,463)^32 Output: ? Mod(259, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:08:40 2005 Input: Mod(347,463)^64 Output: ? Mod(409, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:08:54 2005 Input: Mod(347,463)^128 Output: ? Mod(138, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:09:08 2005 Input: Mod(347,463)^256 Output: ? Mod(61, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:13:09 2005 Input: Factor(588) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(588) ^----------- Timing: real 0m0.023s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:13:12 2005 Input: Factor(588) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(588) ^----------- Timing: real 0m0.012s user 0m0.002s sys 0m0.010s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:13:19 2005 Input: factor(588) Output: ? [2 2] [3 1] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:28:50 2005 Input: Mod(139,588)^11 Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:33:45 2005 Input: Mod(2,9991)^16 Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:34:00 2005 Input: Mod(2,9991)^32 Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:34:13 2005 Input: Mod(2,9991)^64 Output: ? Mod(158, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:34:23 2005 Input: Mod(2,9991)^128 Output: ? Mod(4982, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:34:42 2005 Input: Mod(2,9991)^256 Output: ? Mod(2680, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:34:53 2005 Input: Mod(2,9991)^512 Output: ? Mod(8862, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:35:04 2005 Input: Mod(2,9991)^1024 Output: ? Mod(5784, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:35:18 2005 Input: Mod(2,9991)^2048 Output: ? Mod(4788, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:35:33 2005 Input: Mod(2,9991)^4096 Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.003s sys 0m0.011s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:36:46 2005 Input: Mod(2,9991)^8192 Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.88.46 (128.197.88.46) Time: Wed Mar 30 20:40:22 2005 Input: factor(9991) Output: ? [97 1] [103 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Wed Mar 30 22:10:09 2005 Input: factor(943) Output: ? [23 1] [41 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.172.245 (168.122.172.245) Time: Wed Mar 30 23:59:13 2005 Input: Mod(324,3011)^1505 Output: ? Mod(1, 3011) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '137.226' ************** PARI ***************** Host 137.226.37.186 (137.226.37.186) Time: Thu Mar 31 04:21:31 2005 Input: IntegralQuarticPoints([1,0,-8,8,1]); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: IntegralQuarticPoint ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Mar 31 06:37:29 2005 Input: (2^341)^2-2 Output: ? 20065826040452474621738395244141115820123061381619162977212070095324448220432589806036630768881181530864650607514107580997541169167266097500334986765487216377087492641938951866881041556870737904629872328702 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '130.156' ************** PARI ***************** Host 130.156.70.48 (130.156.70.48) Time: Thu Mar 31 09:42:22 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.288s user 0m0.027s sys 0m0.009s '130.156' ************** PARI ***************** Host 130.156.70.48 (130.156.70.48) Time: Thu Mar 31 09:42:55 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.027s sys 0m0.005s '130.156' ************** PARI ***************** Host 130.156.70.48 (130.156.70.48) Time: Thu Mar 31 09:43:23 2005 Input: for(b=1,1000, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 89,233 233,610 ? Errors (if any) and Timing Info: Timing: real 0m2.014s user 0m2.006s sys 0m0.007s '130.156' ************** PARI ***************** Host 130.156.70.48 (130.156.70.48) Time: Thu Mar 31 09:45:02 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.025s sys 0m0.005s '130.156' ************** PARI ***************** Host 130.156.70.48 (130.156.70.48) Time: Thu Mar 31 09:45:27 2005 Input: for(b=1,1000, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 89,233 233,610 ? Errors (if any) and Timing Info: Timing: real 0m2.053s user 0m2.035s sys 0m0.011s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Thu Mar 31 10:30:55 2005 Input: decimalcycle(p0,q0)= { local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans } decimalcycle(7,17) Output: ? ? [4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9] ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.004s sys 0m0.008s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Thu Mar 31 10:31:33 2005 Input: decimalcycle(p0,q0)= { local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans } for(j=1,8,print(decimalcycle(j,17))) Output: ? ? [0, 5, 8, 8, 2, 3, 5, 2, 9, 4, 1, 1, 7, 6, 4, 7] [1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9, 4] [1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9, 4, 1] [2, 3, 5, 2, 9, 4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8] [2, 9, 4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5] [3, 5, 2, 9, 4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2] [4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9] [4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9, 4, 1, 1, 7, 6] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Thu Mar 31 10:33:25 2005 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.006s sys 0m0.006s '68.89.2' ************** PARI ***************** Host 68.89.249.77 (68.89.249.77) Time: Thu Mar 31 10:33:36 2005 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: ? 366,378,582,594,846,1026,1374,1386, ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.007s sys 0m0.003s '161.116' ************** PARI ***************** Host 161.116.84.21 (161.116.84.21) Time: Thu Mar 31 11:38:19 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '161.116' ************** PARI ***************** Host 161.116.84.21 (161.116.84.21) Time: Thu Mar 31 11:38:58 2005 Input: Galois[x^4+1) Output: ? ? Errors (if any) and Timing Info: *** expected character: ']' instead of: Galois[x^4+1) ^- Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '161.116' ************** PARI ***************** Host 161.116.84.21 (161.116.84.21) Time: Thu Mar 31 11:39:01 2005 Input: Galois[x^4+1) Output: ? ? Errors (if any) and Timing Info: *** expected character: ']' instead of: Galois[x^4+1) ^- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '161.116' ************** PARI ***************** Host 161.116.84.21 (161.116.84.21) Time: Thu Mar 31 11:39:11 2005 Input: Galois[x^4+1); Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ']' instead of: Galois[x^4+1); ^-- Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '161.116' ************** PARI ***************** Host 161.116.84.21 (161.116.84.21) Time: Thu Mar 31 11:39:25 2005 Input: Galois[x^4+1]; Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: Galois[x^4+1]; ^-------- Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 31 12:26:21 2005 Input: Mod(7,337)^168 Output: ? Mod(1, 337) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 31 12:26:32 2005 Input: Mod(3,337)^168 Output: ? Mod(1, 337) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 31 12:26:35 2005 Input: Mod(3,337)^168 Output: ? Mod(1, 337) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '141.217' ************** PARI ***************** Host 141.217.18.139 (141.217.18.139) Time: Thu Mar 31 15:53:52 2005 Input: 2^10 Output: ? 1024 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '141.217' ************** PARI ***************** Host 141.217.18.139 (141.217.18.139) Time: Thu Mar 31 15:54:23 2005 Input: 2^10 20! Output: ? 1024 ? 2432902008176640000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Mar 31 19:19:46 2005 Input: 36*x*(42*x-7)+6*(42*x-7)=1962 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 36*x*(42*x-7)+6*(42*x-7)=1962 ^----- Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Mar 31 19:20:32 2005 Input: 36*x*(42*x-7)+6*(42*x-7)=1962 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 36*x*(42*x-7)+6*(42*x-7)=1962 ^----- Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Mar 31 19:21:05 2005 Input: 36x=6 Output: ? 36 ? Errors (if any) and Timing Info: *** Warning: unused characters: x=6. Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Mar 31 19:21:20 2005 Input: x*3=18 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: x*3=18 ^--- Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Mar 31 19:21:37 2005 Input: solve(6x=36) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: solve(6x=36) ^------ Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Mar 31 19:21:44 2005 Input: solve(6x=36, x) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: solve(6x=36,x) ^-------- Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Mar 31 19:33:05 2005 Input: eval(6x=36) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Mar 31 19:33:20 2005 Input: 6x=36 x=? Output: ? 6 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: x=36. *** unexpected character: x=? ^- Timing: real 0m0.016s user 0m0.008s sys 0m0.003s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Mar 31 19:36:34 2005 Input: 36x(42x-7)+6(42x-7)=1962 Output: ? 36 ? Errors (if any) and Timing Info: *** Warning: unused characters: x(42x-7)+6(42x-7)=1962. Timing: real 0m0.018s user 0m0.007s sys 0m0.003s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Mar 31 19:37:16 2005 Input: 36x(42x-7)+6(42x-7)=1962 Output: ? 36 ? Errors (if any) and Timing Info: *** Warning: unused characters: x(42x-7)+6(42x-7)=1962. Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Mar 31 19:37:22 2005 Input: 36x(42x-7)+6(42x-7)=1963 Output: ? 36 ? Errors (if any) and Timing Info: *** Warning: unused characters: x(42x-7)+6(42x-7)=1963. Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Mar 31 19:37:25 2005 Input: 36x(42x-7)+6(42x-7)=1962 Output: ? 36 ? Errors (if any) and Timing Info: *** Warning: unused characters: x(42x-7)+6(42x-7)=1962. Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Mar 31 19:37:40 2005 Input: 36x(42x-7)+6(42x-7)-1962 Output: ? 36 ? Errors (if any) and Timing Info: *** Warning: unused characters: x(42x-7)+6(42x-7)-1962. Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Mar 31 19:37:51 2005 Input: factor(36x(42x-7)+6(42x-7)-1962) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: factor(36x(42x-7)+6(42x-7)-19 ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Mar 31 19:38:19 2005 Input: factor(36*x*(42*x-7)+6*(42*x-7)-1962) Output: ? [126*x^2 - 167 1] ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.009s sys 0m0.004s '199.46.' ************** PARI ***************** Host 199.46.200.230 (199.46.200.230) Time: Thu Mar 31 20:55:00 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.237.190 (168.122.237.190) Time: Thu Mar 31 21:23:20 2005 Input: Mod(2, 6780)^(-1) Output: ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(2, 6780). Timing: real 0m0.019s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.237.190 (168.122.237.190) Time: Thu Mar 31 21:23:23 2005 Input: Mod(2, 6780)^(-1) Output: ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(2, 6780). Timing: real 0m0.014s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.237.190 (168.122.237.190) Time: Thu Mar 31 21:24:55 2005 Input: factor(35) Mod(2, 6780)^(-1) Output: ? [5 1] [7 1] ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(2, 6780). Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 31 21:32:05 2005 Input: factor(436) Output: ? [2 2] [109 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.237.190 (168.122.237.190) Time: Thu Mar 31 21:32:28 2005 Input: Mod(2, 3010)^(-1) Output: ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(2, 3010). Timing: real 0m0.017s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 31 21:33:35 2005 Input: mob(113,216)^(-1) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: mob(113,216)^(-1) ^----------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 31 21:34:02 2005 Input: Mod(113,216)^(-1) Output: ? Mod(65, 216) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 31 21:34:34 2005 Input: Mod(347,463)^(65) Output: ? Mod(245, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 31 21:34:54 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 31 21:36:42 2005 Input: Mod(113,463)^(-1) Output: ? Mod(168, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 31 21:37:01 2005 Input: Mod(113,462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.003s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 31 21:37:28 2005 Input: Mod(347,463)^(323) Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 31 21:37:39 2005 Input: factor(588) Output: ? [2 2] [3 1] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 21:38:21 2005 Input: Mod(5590,9991)^2 Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 31 21:38:36 2005 Input: Mod(275,168)^(-1) Output: ? Mod(11, 168) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 21:38:46 2005 Input: Mod(6243,9991)^2 Output: ? Mod(158, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 31 21:39:02 2005 Input: Mod(139,588)^(11) Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 21:39:06 2005 Input: Mod(158,9991)^2 Output: ? Mod(4982, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 21:40:03 2005 Input: Mod(4982,9991)^2 Output: ? Mod(2680, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 21:40:16 2005 Input: Mod(2680,9991)^2 Output: ? Mod(8862, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 21:42:40 2005 Input: Mod(8862,9991)^2 Output: ? Mod(5784, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 21:44:20 2005 Input: Mod(5784,9991)^2 Output: ? Mod(4788, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 21:44:49 2005 Input: Mod(4788,9991)^2 Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 21:45:50 2005 Input: Mod(5590,9991)^2 Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 31 21:50:22 2005 Input: Mod(6780,6781)^(3390) Output: ? Mod(1, 6781) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 31 21:51:20 2005 Input: Mod(2^9990,9991) Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 21:51:21 2005 Input: Mod(5590,9991) Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 31 21:51:34 2005 Input: factor(9991) Output: ? [97 1] [103 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 21:52:03 2005 Input: Mod(6243*5784*8862*2680*16*4,9991) Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 31 21:52:26 2005 Input: Mod(1681,3011)^(1501) Output: ? Mod(243, 3011) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 31 21:52:45 2005 Input: Mod(529,3011)^(1501) Output: ? Mod(1004, 3011) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 31 21:58:34 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 21:59:13 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 21:59:38 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 31 21:59:39 2005 Input: Mod(113, 263)^(-1) Output: ? Mod(135, 263) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 31 22:00:12 2005 Input: Mod(113, 462) Output: ? Mod(113, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 31 22:00:25 2005 Input: Mod(113, 462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 31 22:01:20 2005 Input: Mod(347^323, 463) Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 31 22:01:32 2005 Input: factor(588) Output: ? [2 2] [3 1] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 31 22:02:27 2005 Input: (2^2-2)*2*(7^2-7) Output: ? 168 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 22:02:55 2005 Input: Mod(113,462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 31 22:03:02 2005 Input: Mod(275, 168)^(-1) Output: ? Mod(11, 168) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 31 22:03:32 2005 Input: factor(588) Output: ? [2 2] [3 1] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.001s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 22:03:43 2005 Input: Mod(347,463)^(323) Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.190.240 (168.122.190.240) Time: Thu Mar 31 22:04:04 2005 Input: Mod(139^11,588) Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 22:04:17 2005 Input: Mod(37,463)^(113) Output: ? Mod(347, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 22:05:55 2005 Input: factor(588) Output: ? [2 2] [3 1] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.247.123 (168.122.247.123) Time: Thu Mar 31 22:09:29 2005 Input: Mod(5,101)^(50) Output: ? Mod(1, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 22:15:46 2005 Input: Mod(275,168)^(-1) Output: ? Mod(11, 168) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Thu Mar 31 22:18:25 2005 Input: Mod(139,588)^(11) Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.239.26 (168.122.239.26) Time: Thu Mar 31 22:25:11 2005 Input: Mod(5^4,101) Output: ? Mod(19, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.239.26 (168.122.239.26) Time: Thu Mar 31 22:25:21 2005 Input: Mod(5^8,101) Output: ? Mod(58, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.239.26 (168.122.239.26) Time: Thu Mar 31 22:25:32 2005 Input: Mod(5^16,101) Output: ? Mod(31, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.239.26 (168.122.239.26) Time: Thu Mar 31 22:25:43 2005 Input: Mod(5^32,101) Output: ? Mod(52, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.239.26 (168.122.239.26) Time: Thu Mar 31 22:26:43 2005 Input: Mod(52*31*25,101) Output: ? Mod(1, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.237.190 (168.122.237.190) Time: Thu Mar 31 23:03:19 2005 Input: factor(9991) Output: ? [97 1] [103 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:24:32 2005 Input: Mod(3,19)^3 Output: ? Mod(8, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:24:56 2005 Input: Mod(3,19)^8 Output: ? Mod(6, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:25:14 2005 Input: Mod(3,19)^9 Output: ? Mod(18, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.008s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:26:04 2005 Input: Mod(4,19)^8 Output: ? Mod(5, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:26:43 2005 Input: Mod(5,19)^4 Output: ? Mod(17, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:27:03 2005 Input: Mod(5,19)^8 Output: ? Mod(4, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:27:46 2005 Input: Mod(6,19)^2 Output: ? Mod(17, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:28:19 2005 Input: Mod(6,19)^9 Output: ? Mod(1, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:29:09 2005 Input: Mod(7,19)^2 Output: ? Mod(11, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:29:30 2005 Input: Mod(7,19)^4 Output: ? Mod(7, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.004s sys 0m0.007s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:29:44 2005 Input: Mod(7,19)^8 Output: ? Mod(11, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:30:09 2005 Input: Mod(7,19)^9 Output: ? Mod(1, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:31:49 2005 Input: Mod(8,19)^2 Output: ? Mod(7, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:32:01 2005 Input: Mod(8,19)^4 Output: ? Mod(11, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:32:08 2005 Input: Mod(8,19)^4 Output: ? Mod(11, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:32:25 2005 Input: Mod(8,19)^8 Output: ? Mod(7, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:32:41 2005 Input: Mod(8,19)^9 Output: ? Mod(18, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:33:03 2005 Input: Mod(9,19)^2 Output: ? Mod(5, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.177s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 31 23:33:15 2005 Input: Mod(-1,5987)^2993 Output: ? Mod(5986, 5987) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 31 23:33:17 2005 Input: Mod(-1,5987)^2993 Output: ? Mod(5986, 5987) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 31 23:33:18 2005 Input: Mod(-1,5987)^2993 Output: ? Mod(5986, 5987) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:33:29 2005 Input: Mod(9,19)^4 Output: ? Mod(6, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:33:42 2005 Input: Mod(9,19)^8 Output: ? Mod(17, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:34:03 2005 Input: Mod(9,19)^9 Output: ? Mod(1, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:34:20 2005 Input: Mod(10,19)^2 Output: ? Mod(5, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:34:26 2005 Input: Mod(10,19)^2 Output: ? Mod(5, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.005s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:34:45 2005 Input: Mod(10,19)^8 Output: ? Mod(17, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:35:31 2005 Input: Mod(11,19)^2 Output: ? Mod(7, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:35:40 2005 Input: Mod(11,19)^4 Output: ? Mod(11, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:35:51 2005 Input: Mod(11,19)^8 Output: ? Mod(7, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:36:04 2005 Input: Mod(11,19)^8 Output: ? Mod(7, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:36:31 2005 Input: Mod(11,19)^9 Output: ? Mod(1, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:37:04 2005 Input: Mod(12,19)^4 Output: ? Mod(7, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.003s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:38:09 2005 Input: Mod(12,19)^8 Output: ? Mod(11, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.006s sys 0m0.004s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:38:20 2005 Input: Mod(12,19)^9 Output: ? Mod(18, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:39:11 2005 Input: Mod(13,19)^2 Output: ? Mod(17, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.003s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:39:35 2005 Input: Mod(13,19)^8 Output: ? Mod(16, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.003s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:40:21 2005 Input: Mod(14,19)^4 Output: ? Mod(17, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.009s sys 0m0.001s '130.102' ************** PARI ***************** Host 130.102.128.60 (130.102.128.60) Time: Thu Mar 31 23:40:26 2005 Input: ellint([0,0,0,0,2]) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: ellint([0,0,0,0,2]) ^------------------- Timing: real 0m0.022s user 0m0.006s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:40:33 2005 Input: Mod(14,19)^8 Output: ? Mod(4, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.006s sys 0m0.004s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:40:46 2005 Input: Mod(14,19)^9 Output: ? Mod(18, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:40:50 2005 Input: Mod(14,19)^9 Output: ? Mod(18, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '130.102' ************** PARI ***************** Host 130.102.2.60 (130.102.2.60) Time: Thu Mar 31 23:41:01 2005 Input: ellinit([0,0,0,0,2]) Output: ? [0, 0, 0, 0, 2, 0, 0, 8, 0, 0, -1728, -1728, 0, [-1.2599210498948731647672106072782283505, 0.62996052494743658238360530363911417528 - 1.0911236359717214035600726141898088813*I, 0.62996052494743658238360530363911417528 + 1.0911236359717214035600726141898088813*I]~, 3.7476067207013083074870676650616844153, -1.8738033603506541537435338325308422076 + 1.0818408745068755047361014128486792641*I, -1.4519661475269148920545259593893769622 + 7.542870838913096998 E-39*I, 0.72598307376345744602726297969468848113 - 1.2574395691933322826509718984498162707*I, 4.0543141320313473204231515101938051175] ? Errors (if any) and Timing Info: Timing: real 0m0.125s user 0m0.014s sys 0m0.001s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:41:18 2005 Input: Mod(15,19)^8 Output: ? Mod(5, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:41:35 2005 Input: Mod(15,19)^9 Output: ? Mod(18, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:42:07 2005 Input: Mod(16,19)^9 Output: ? Mod(1, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.004s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:42:10 2005 Input: Mod(17,19)^9 Output: ? Mod(1, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.007s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:42:14 2005 Input: Mod(18,19)^9 Output: ? Mod(18, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:42:23 2005 Input: Mod(15,19)^9 Output: ? Mod(18, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:42:28 2005 Input: Mod(14,19)^9 Output: ? Mod(18, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:42:35 2005 Input: Mod(13,19)^9 Output: ? Mod(18, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:42:39 2005 Input: Mod(12,19)^9 Output: ? Mod(18, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:42:48 2005 Input: Mod(11,19)^9 Output: ? Mod(1, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:44:26 2005 Input: Mod(9,19)^9 Output: ? Mod(1, 19) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 31 23:48:52 2005 Input: factor(2124) Output: ? [2 2] [3 2] [59 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.004s '67.183.' ************** PARI ***************** Host 67.183.111.171 (67.183.111.171) Time: Thu Mar 31 23:49:08 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '67.183.' ************** PARI ***************** Host 67.183.111.171 (67.183.111.171) Time: Thu Mar 31 23:49:57 2005 Input: polroots( x*(x+3)*(x+6)*(x+9)-189) Output: ? [-9.7613379215894300323883022567923354804 + 0.E-38*I, 0.76133792158943003238830225679233548047 + 0.E-38*I, -4.4999999999999999999999999999999999999 + 2.2763296609135908291232398388566388939*I, -4.4999999999999999999999999999999999999 - 2.2763296609135908291232398388566388939*I]~ ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 31 23:50:35 2005 Input: Mod(59,3011)^1505 Output: ? Mod(1, 3011) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:51:01 2005 Input: Mod(5987,4)^1 Output: ? Mod(3, 4) ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 31 23:53:17 2005 Input: Mod(5,101)^2 Output: ? Mod(25, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Thu Mar 31 23:53:36 2005 Input: Mod(6781,4)^1 Output: ? Mod(1, 4) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 31 23:54:26 2005 Input: Mod(5,101)^4 Output: ? Mod(19, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 31 23:54:47 2005 Input: Mod(5,101)^8 Output: ? Mod(58, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 31 23:54:56 2005 Input: Mod(5,101)^16 Output: ? Mod(31, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 31 23:55:06 2005 Input: Mod(5,101)^32 Output: ? Mod(52, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.213.132 (168.122.213.132) Time: Thu Mar 31 23:56:09 2005 Input: Mod(5,101)^50 Output: ? Mod(1, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Apr 1 00:00:28 2005 Input: Mod(6780,6781)^(3390) Output: ? Mod(1, 6781) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:28:44 2005 Input: Mod(5,101)^4 Output: ? Mod(19, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:28:56 2005 Input: Mod(5,101)^4 Output: ? Mod(19, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Apr 1 00:29:02 2005 Input: Mod(25,101)^(2) Output: ? Mod(19, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Apr 1 00:29:13 2005 Input: Mod(19,101)^(2) Output: ? Mod(58, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.004s sys 0m0.008s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:29:14 2005 Input: Mod(5,101)^8 Output: ? Mod(58, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:29:30 2005 Input: Mod(5,101)^16 Output: ? Mod(31, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Apr 1 00:29:34 2005 Input: Mod(58,101)^(2) Output: ? Mod(31, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Apr 1 00:29:46 2005 Input: Mod(31,101)^(2) Output: ? Mod(52, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:29:56 2005 Input: Mod(5,101)^32 Output: ? Mod(52, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:30:15 2005 Input: Mod(5,101)^32 Output: ? Mod(52, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.158.47 (168.122.158.47) Time: Fri Apr 1 00:30:41 2005 Input: Mod(52*31*25,101) Output: ? Mod(1, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.010s sys 0m0.002s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:30:55 2005 Input: Mod(52*31,101)^32 Output: ? Mod(79, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:31:09 2005 Input: Mod(52*31*25,101)^1 Output: ? Mod(1, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.011s sys 0m0.001s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:50:09 2005 Input: Mod(2,9991)^8 Output: ? Mod(256, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.214s user 0m0.005s sys 0m0.008s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:50:27 2005 Input: Mod(2,9991)^16 Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:50:30 2005 Input: Mod(2,9991)^16 Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.006s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:51:15 2005 Input: Mod(256*256,9991)^1 Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:51:40 2005 Input: Mod(2,9991)^32 Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:52:19 2005 Input: Mod(2,9991)^64 Output: ? Mod(158, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.002s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:52:33 2005 Input: Mod(2,9991)^128 Output: ? Mod(4982, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.002s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:52:58 2005 Input: Mod(2,9991)^256 Output: ? Mod(2680, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:53:27 2005 Input: Mod(2,9991)^512 Output: ? Mod(8862, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:54:33 2005 Input: Mod(2,9991)^1024 Output: ? Mod(5784, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:55:01 2005 Input: Mod(2,9991)^2048 Output: ? Mod(4788, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:55:04 2005 Input: Mod(2,9991)^2048 Output: ? Mod(4788, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:55:33 2005 Input: Mod(2,9991)^4096 Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 00:56:17 2005 Input: Mod(2,9991)^8192 Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.007s sys 0m0.003s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 01:02:00 2005 Input: Mod(6243*5784,9991)^1 Output: ? Mod(2038, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 01:02:33 2005 Input: Mod(2680*16*4,9991)^1 Output: ? Mod(1673, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 01:03:41 2005 Input: Mod(2038*1673*8862,9991)^1 Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 01:04:00 2005 Input: Mod(2,9991)^9990 Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 01:04:37 2005 Input: Factor(9991) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(9991) ^------------ Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 01:04:49 2005 Input: factor(9991) Output: ? [97 1] [103 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '216.162' ************** PARI ***************** Host 216.162.216.186 (216.162.216.186) Time: Fri Apr 1 03:51:22 2005 Input: sqrt(2) Output: ? 1.4142135623730950488016887242096980785 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 10:31:26 2005 Input: Mod(7,30)^(-1) Output: ? Mod(13, 30) ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.006s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 10:31:43 2005 Input: Mod(17,30)^(-1) Output: ? Mod(23, 30) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 10:31:52 2005 Input: Mod(19,30)^(-1) Output: ? Mod(19, 30) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 10:32:00 2005 Input: Mod(29,30)^(-1) Output: ? Mod(29, 30) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 10:32:09 2005 Input: Mod(11,30)^(-1) Output: ? Mod(11, 30) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 10:35:00 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.038s user 0m0.007s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 10:36:11 2005 Input: Mod(113,462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 10:36:25 2005 Input: Mod(113*323,462) Output: ? Mod(1, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 10:36:56 2005 Input: Mod(347,462)^323 Output: ? Mod(359, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.005s sys 0m0.007s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 10:37:39 2005 Input: Mod(359,462)^113 Output: ? Mod(431, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 10:37:45 2005 Input: Mod(359,463)^113 Output: ? Mod(410, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.002s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 10:39:43 2005 Input: Mod(113,462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 10:40:28 2005 Input: Mod(347,463)^(323) Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '70.22.2' ************** PARI ***************** Host 70.22.216.121 (70.22.216.121) Time: Fri Apr 1 10:40:50 2005 Input: Mod(37,463)^(113) Output: ? Mod(347, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.150.164 (128.197.150.164) Time: Fri Apr 1 10:47:58 2005 Input: Mod(25,101)^2 Output: ? Mod(19, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.164 (128.197.150.164) Time: Fri Apr 1 10:48:00 2005 Input: Mod(25,101)^2 Output: ? Mod(19, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.164 (128.197.150.164) Time: Fri Apr 1 10:48:00 2005 Input: Mod(25,101)^2 Output: ? Mod(19, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.150.164 (128.197.150.164) Time: Fri Apr 1 10:48:21 2005 Input: Mod(19,101)^2 Output: ? Mod(58, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.164 (128.197.150.164) Time: Fri Apr 1 10:48:31 2005 Input: Mod(58,101)^2 Output: ? Mod(31, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.164 (128.197.150.164) Time: Fri Apr 1 10:48:42 2005 Input: Mod(32,101)^2 Output: ? Mod(14, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.150.164 (128.197.150.164) Time: Fri Apr 1 10:49:37 2005 Input: Mod(5,101)^50 Output: ? Mod(1, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '63.80.1' ************** PARI ***************** Host 63.80.156.139 (63.80.156.139) Time: Fri Apr 1 11:47:48 2005 Input: g Output: ? g ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.108.4 (168.122.108.4) Time: Fri Apr 1 11:58:25 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.108.4 (168.122.108.4) Time: Fri Apr 1 11:58:43 2005 Input: factor(588) Output: ? [2 2] [3 1] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.108.4 (168.122.108.4) Time: Fri Apr 1 11:59:05 2005 Input: factor(14) Output: ? [2 1] [7 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.108.4 (168.122.108.4) Time: Fri Apr 1 11:59:14 2005 Input: factor(21) Output: ? [3 1] [7 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.108.4 (168.122.108.4) Time: Fri Apr 1 11:59:19 2005 Input: factor(24) Output: ? [2 3] [3 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:00:31 2005 Input: Mod(14,337)^168 Output: ? Mod(1, 337) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.108.4 (168.122.108.4) Time: Fri Apr 1 12:01:13 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:01:22 2005 Input: Mod(113,462)^-1 Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:01:58 2005 Input: Mod(347,463)^323 Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:02:26 2005 Input: Mod(275,168)^-1 Output: ? Mod(11, 168) ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:03:40 2005 Input: Mod(139,588)^11 Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:04:04 2005 Input: Mod(2,9991)^16 Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:04:16 2005 Input: Mod(2,9991)^32 Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:04:33 2005 Input: Mod(2,9991)^64 Output: ? Mod(158, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.011s sys 0m0.000s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:04:43 2005 Input: Mod(2,9991)^128 Output: ? Mod(4982, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:05:18 2005 Input: Mod(2,9991)^256 Output: ? Mod(2680, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:05:32 2005 Input: Mod(2,9991)^512 Output: ? Mod(8862, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.006s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:06:49 2005 Input: Mod(2,9991)^1024 Output: ? Mod(5784, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:07:07 2005 Input: Mod(2,9991)^2048 Output: ? Mod(4788, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:07:16 2005 Input: Mod(2,9991)^4096 Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.010s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:07:48 2005 Input: Mod(2,9991)^8192 Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:09:14 2005 Input: Mod(6243*5784*8862*2680*16*4,9991) Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.009s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.244.129 (128.197.244.129) Time: Fri Apr 1 12:10:21 2005 Input: Mod(5,101)^50 Output: ? Mod(1, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:28:04 2005 Input: mod(88817841970012523233890533447265625,101) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(8881784197001252 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:28:28 2005 Input: Mod(88817841970012523233890533447265625,101) Output: ? Mod(1, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:34:08 2005 Input: Mod(2,3) Output: ? Mod(2, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:34:16 2005 Input: Mod(-2,3) Output: ? Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Fri Apr 1 12:35:15 2005 Input: 7! Output: ? 5040 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Fri Apr 1 12:35:24 2005 Input: 5! Output: ? 120 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '24.63.2' ************** PARI ***************** Host 24.63.26.250 (24.63.26.250) Time: Fri Apr 1 12:35:35 2005 Input: 120 * 42 Output: ? 5040 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:36:50 2005 Input: 2^64 Output: ? 18446744073709551616 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:37:22 2005 Input: Mod(18446744073709551616,9991) Output: ? Mod(158, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:37:54 2005 Input: 158^2 Output: ? 24964 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:38:14 2005 Input: Mod(24964,9991) Output: ? Mod(4982, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:39:11 2005 Input: 4982^2 Output: ? 24820324 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:39:27 2005 Input: Mod(24820324,9991) Output: ? Mod(2680, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:39:52 2005 Input: 2680^2 Output: ? 7182400 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:40:09 2005 Input: Mod(7182400,9991) Output: ? Mod(8862, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:40:52 2005 Input: (-1129)^2 Output: ? 1274641 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:41:06 2005 Input: Mod(1274641,9991) Output: ? Mod(5784, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.010s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:42:21 2005 Input: 5784^2 Output: ? 33454656 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:42:36 2005 Input: Mod(33454656,9991) Output: ? Mod(4788, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:42:55 2005 Input: 4788^2 Output: ? 22924944 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:43:13 2005 Input: Mod(22924944,9991) Output: ? Mod(5590, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:43:35 2005 Input: 5590^2 Output: ? 31248100 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:43:50 2005 Input: Mod(31248100,9991) Output: ? Mod(6243, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:44:15 2005 Input: 91 Output: ? 91 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:44:21 2005 Input: 49 Output: ? 49 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:44:27 2005 Input: factor(49) Output: ? [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:45:21 2005 Input: factor(91) Output: ? [7 1] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:45:35 2005 Input: factor(133) Output: ? [7 1] [19 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:45:40 2005 Input: factor(133) Output: ? [7 1] [19 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.003s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:45:48 2005 Input: factor(217) Output: ? [7 1] [31 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:45:55 2005 Input: factor(259) Output: ? [7 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:46:15 2005 Input: factor(91) Output: ? [7 1] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 12:46:27 2005 Input: 2^9990 Output: ? 19483038250788656102380294557456885584213836248888598191914149900907655107638619757734337582066596287011065556077352660421441886083411895622650181574312816365093486373822064967544186085220761616719287194256048155803231062949822367856942455923915649304775869037927743412052376228369747625302220607965734753969946383441283633834726437135727981662957556798529605249638321057457891367902566928800431129085894903768524867089268399375523699044008419362630267613794497704619729631523666962305015560856104940720481718423608990402912140046869334159772830318050549101598928599108644434408656817826807185478126381673751577865808729743257206805780544727370075913744574338927752693199536623758128700459678099416861711944754036368556273628585635326231855131193676405079344586081352741632804941027144775518547715079793301569927668281407488762000484624845032074278844471632311635015932725673579603714173652541925430622652797613291411958829654367231409049820815490156866215025803003817061426342389079938429601031303777589111724616718595958884823473748100043738352447651604051112521467487699680822633555514270540799517616995520700325677397092481018720642046394767364231260725870424222238161645281747907497009693782442968163942272129695672693201198870393335129173493723383578234662489974424669538499270792944153437692972830353482126441306801300057064585898303500127078306060823707665125674336960528205679515587876728635163129229085035028358710551370512669098225789718853430957913821116616738032611716518806108682138879209909493760501440259512475853502293260252285895447222311170529174384276639664621195020863704234196498351358787327132661960287539327113459815434641531004262256424447754981301745910536595633495645346041170710003866327134585103299977679316112039190878402132033282690412277205089247139871338775221501402559157691329509427456726294545805256743156700223271563999593074345802722339703353851112261141773069727387585474768206610008626483851289430950429779742428635990576563162136009607182984772194236949454138175206022186090869881931738522255742361593677688848908615189480764413484813432631520183974314450084220347962281634671263140431062145255739952202523657948729599791472870797443019028447748264033152065198309722136931330933789416774665745880239581651559386016399091290905470018206699969288710801303322556515192888620493404657663010828021744090055671924922189810054968915073963985711267962491949627669775889619405872964296475577732572904704429991852476592892822205048827369904035505881945178363843065562263842781445155504184194579962000937726801134935323845787458022918441463498368938333862913561090273961877560565394112332824571843273968103811787137790692041570856599126481179217674994267296228213037027520815597210945047510325380427198164384946586764759588198639964895819373498128941818128617101123671668946037943039254180569802709505195769891402215410388625213505000078850409718083933747680125291521935068071179714135470287781378510498447004018633299014116995524245068151505191467979185929210626732719524020224 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:46:40 2005 Input: factor(133) Output: ? [7 1] [19 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:46:45 2005 Input: factor(175) Output: ? [5 2] [7 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 12:46:55 2005 Input: Mod(19483038250788656102380294557456885584213836248888598191914149900907655107638619757734337582066596287011065556077352660421441886083411895622650181574312816365093486373822064967544186085220761616719287194256048155803231062949822367856942455923915649304775869037927743412052376228369747625302220607965734753969946383441283633834726437135727981662957556798529605249638321057457891367902566928800431129085894903768524867089268399375523699044008419362630267613794497704619729631523666962305015560856104940720481718423608990402912140046869334159772830318050549101598928599108644434408656817826807185478126381673751577865808729743257206805780544727370075913744574338927752693199536623758128700459678099416861711944754036368556273628585635326231855131193676405079344586081352741632804941027144775518547715079793301569927668281407488762000484624845032074278844471632311635015932725673579603714173652541925430622652797613291411958829654367231409049820815490156866215025803003817061426342389079938429601031303777589111724616718595958884823473748100043738352447651604051112521467487699680822633555514270540799517616995520700325677397092481018720642046394767364231260725870424222238161645281747907497009693782442968163942272129695672693201198870393335129173493723383578234662489974424669538499270792944153437692972830353482126441306801300057064585898303500127078306060823707665125674336960528205679515587876728635163129229085035028358710551370512669098225789718853430957913821116616738032611716518806108682138879209909493760501440259512475853502293260252285895447222311170529174384276639664621195020863704234196498351358787327132661960287539327113459815434641531004262256424447754981301745910536595633495645346041170710003866327134585103299977679316112039190878402132033282690412277205089247139871338775221501402559157691329509427456726294545805256743156700223271563999593074345802722339703353851112261141773069727387585474768206610008626483851289430950429779742428635990576563162136009607182984772194236949454138175206022186090869881931738522255742361593677688848908615189480764413484813432631520183974314450084220347962281634671263140431062145255739952202523657948729599791472870797443019028447748264033152065198309722136931330933789416774665745880239581651559386016399091290905470018206699969288710801303322556515192888620493404657663010828021744090055671924922189810054968915073963985711267962491949627669775889619405872964296475577732572904704429991852476592892822205048827369904035505881945178363843065562263842781445155504184194579962000937726801134935323845787458022918441463498368938333862913561090273961877560565394112332824571843273968103811787137790692041570856599126481179217674994267296228213037027520815597210945047510325380427198164384946586764759588198639964895819373498128941818128617101123671668946037943039254180569802709505195769891402215410388625213505000078850409718083933747680125291521935068071179714135470287781378510498447004018633299014116995524245068151505191467979185929210626732719524020224 ,9991) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...5929210626732719524020224 ^ *** Warning: unused characters: ,9991). Timing: real 0m0.014s user 0m0.009s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:47:01 2005 Input: factor(217) Output: ? [7 1] [31 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 12:47:11 2005 Input: Mod(19483038250788656102380294557456885584213836248888598191914149900907655107638619757734337582066596287011065556077352660421441886083411895622650181574312816365093486373822064967544186085220761616719287194256048155803231062949822367856942455923915649304775869037927743412052376228369747625302220607965734753969946383441283633834726437135727981662957556798529605249638321057457891367902566928800431129085894903768524867089268399375523699044008419362630267613794497704619729631523666962305015560856104940720481718423608990402912140046869334159772830318050549101598928599108644434408656817826807185478126381673751577865808729743257206805780544727370075913744574338927752693199536623758128700459678099416861711944754036368556273628585635326231855131193676405079344586081352741632804941027144775518547715079793301569927668281407488762000484624845032074278844471632311635015932725673579603714173652541925430622652797613291411958829654367231409049820815490156866215025803003817061426342389079938429601031303777589111724616718595958884823473748100043738352447651604051112521467487699680822633555514270540799517616995520700325677397092481018720642046394767364231260725870424222238161645281747907497009693782442968163942272129695672693201198870393335129173493723383578234662489974424669538499270792944153437692972830353482126441306801300057064585898303500127078306060823707665125674336960528205679515587876728635163129229085035028358710551370512669098225789718853430957913821116616738032611716518806108682138879209909493760501440259512475853502293260252285895447222311170529174384276639664621195020863704234196498351358787327132661960287539327113459815434641531004262256424447754981301745910536595633495645346041170710003866327134585103299977679316112039190878402132033282690412277205089247139871338775221501402559157691329509427456726294545805256743156700223271563999593074345802722339703353851112261141773069727387585474768206610008626483851289430950429779742428635990576563162136009607182984772194236949454138175206022186090869881931738522255742361593677688848908615189480764413484813432631520183974314450084220347962281634671263140431062145255739952202523657948729599791472870797443019028447748264033152065198309722136931330933789416774665745880239581651559386016399091290905470018206699969288710801303322556515192888620493404657663010828021744090055671924922189810054968915073963985711267962491949627669775889619405872964296475577732572904704429991852476592892822205048827369904035505881945178363843065562263842781445155504184194579962000937726801134935323845787458022918441463498368938333862913561090273961877560565394112332824571843273968103811787137790692041570856599126481179217674994267296228213037027520815597210945047510325380427198164384946586764759588198639964895819373498128941818128617101123671668946037943039254180569802709505195769891402215410388625213505000078850409718083933747680125291521935068071179714135470287781378510498447004018633299014116995524245068151505191467979185929210626732719524020224,9991) Output: ? Mod(3362, 9991) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:47:27 2005 Input: x=259 factor(x) Output: ? 259 ? [7 1] [37 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.004s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:48:09 2005 Input: x=301 factor(x) Output: ? 301 ? [7 1] [43 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 12:48:10 2005 Input: factor(9991) Output: ? [97 1] [103 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:48:20 2005 Input: x=343 factor(x) Output: ? 343 ? [7 3] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:48:39 2005 Input: x=427 factor(x) Output: ? 427 ? [7 1] [61 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.010s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:48:47 2005 Input: Mod(113,462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:48:50 2005 Input: x=469 factor(x) Output: ? 469 ? [7 1] [67 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:49:05 2005 Input: x=511 factor(x) Output: ? 511 ? [7 1] [73 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:49:15 2005 Input: x=553 factor(x) Output: ? 553 ? [7 1] [79 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 12:49:17 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 12:49:19 2005 Input: factor(463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:49:29 2005 Input: x=595 factor(x) Output: ? 595 ? [5 1] [7 1] [17 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:49:37 2005 Input: x=511 factor(x) Output: ? 511 ? [7 1] [73 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:49:44 2005 Input: x=637 factor(x) Output: ? 637 ? [7 2] [13 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 12:50:04 2005 Input: Mod(113,462)^-1 Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:50:31 2005 Input: Mod(139,463)^(323) Output: ? Mod(274, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 12:51:02 2005 Input: Mod(347,463)^323 Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:51:07 2005 Input: 274^113 Output: ? 292289758677321927721536021868981590018598524114674370782903029923764625905210160221015956407791900142541262819601865655649244765863515143560257065079463173717814872902565178946152637453824377776208869740202765842437333077684466553058882375269400373465618495202223958549069824 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:51:25 2005 Input: Mod(292289758677321927721536021868981590018598524114674370782903029923764625905210160221015956407791900142541262819601865655649244765863515143560257065079463173717814872902565178946152637453824377776208869740202765842437333077684466553058882375269400373465618495202223958549069824,463) Output: ? Mod(139, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.006s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:51:43 2005 Input: x=679 factor(x) Output: ? 679 ? [7 1] [97 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:51:56 2005 Input: x=721 factor(x) Output: ? 721 ? [7 1] [103 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 12:52:00 2005 Input: factor(588) Output: ? [2 2] [3 1] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:52:12 2005 Input: x=763 factor(x) Output: ? 763 ? [7 1] [109 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:52:24 2005 Input: x=847 factor(x) Output: ? 847 ? [7 1] [11 2] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:52:35 2005 Input: Mod(113,462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:52:38 2005 Input: x=889 factor(x) Output: ? 889 ? [7 1] [127 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.007s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:52:46 2005 Input: x=931 factor(x) Output: ? 931 ? [7 2] [19 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:52:52 2005 Input: x=973 factor(x) Output: ? 973 ? [7 1] [139 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:53:12 2005 Input: x=343 factor(x) Output: ? 343 ? [7 3] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:53:17 2005 Input: 347^323 Output: ? 33606273495355907425874514706504407812081556216490323124088628358647329150420902436029909698842449649256516732266588212654817227837870670173668027034775631998737772918525117230875377273552233864746660528129875258425798297134104082739422367749950126407158599688907385439722537017999364970599000371101144209531159377966861390000616972489197505525861864644606420390449588147874955987039012809202933744512000597864929479712088975300837406484082121466663555352610956937119808370301607457203208573004238375359550810945573278649880955358605369667619742797962112899148457456611853032654363583299833262598143377482268760278847762389110976884078158521060230682462247160705714171088928100022258830496818958093465085158669901515484233404810989794564246742578801815435758084706748161127459492240880844313667530744812015071324224009123 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 12:53:29 2005 Input: x=1057 factor(x) Output: ? 1057 ? [7 1] [151 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 12:53:29 2005 Input: Mod(275,168)^-1 Output: ? Mod(11, 168) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:53:40 2005 Input: Mod(33606273495355907425874514706504407812081556216490323124088628358647329150420902436029909698842449649256516732266588212654817227837870670173668027034775631998737772918525117230875377273552233864746660528129875258425798297134104082739422367749950126407158599688907385439722537017999364970599000371101144209531159377966861390000616972489197505525861864644606420390449588147874955987039012809202933744512000597864929479712088975300837406484082121466663555352610956937119808370301607457203208573004238375359550810945573278649880955358605369667619742797962112899148457456611853032654363583299833262598143377482268760278847762389110976884078158521060230682462247160705714171088928100022258830496818958093465085158669901515484233404810989794564246742578801815435758084706748161127459492240880844313667530744812015071324224009123,463) Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 12:54:02 2005 Input: Mod(139,588)^11 Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:54:04 2005 Input: 347^323 Output: ? 33606273495355907425874514706504407812081556216490323124088628358647329150420902436029909698842449649256516732266588212654817227837870670173668027034775631998737772918525117230875377273552233864746660528129875258425798297134104082739422367749950126407158599688907385439722537017999364970599000371101144209531159377966861390000616972489197505525861864644606420390449588147874955987039012809202933744512000597864929479712088975300837406484082121466663555352610956937119808370301607457203208573004238375359550810945573278649880955358605369667619742797962112899148457456611853032654363583299833262598143377482268760278847762389110976884078158521060230682462247160705714171088928100022258830496818958093465085158669901515484233404810989794564246742578801815435758084706748161127459492240880844313667530744812015071324224009123 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:54:26 2005 Input: Mod(33606273495355907425874514706504407812081556216490323124088628358647329150420902436029909698842449649256516732266588212654817227837870670173668027034775631998737772918525117230875377273552233864746660528129875258425798297134104082739422367749950126407158599688907385439722537017999364970599000371101144209531159377966861390000616972489197505525861864644606420390449588147874955987039012809202933744512000597864929479712088975300837406484082121466663555352610956937119808370301607457203208573004238375359550810945573278649880955358605369667619742797962112899148457456611853032654363583299833262598143377482268760278847762389110976884078158521060230682462247160705714171088928100022258830496818958093465085158669901515484233404810989794564246742578801815435758084706748161127459492240880844313667530744812015071324224009123,463) Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:55:04 2005 Input: Mod(113,462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:55:17 2005 Input: 347^323 Output: ? 33606273495355907425874514706504407812081556216490323124088628358647329150420902436029909698842449649256516732266588212654817227837870670173668027034775631998737772918525117230875377273552233864746660528129875258425798297134104082739422367749950126407158599688907385439722537017999364970599000371101144209531159377966861390000616972489197505525861864644606420390449588147874955987039012809202933744512000597864929479712088975300837406484082121466663555352610956937119808370301607457203208573004238375359550810945573278649880955358605369667619742797962112899148457456611853032654363583299833262598143377482268760278847762389110976884078158521060230682462247160705714171088928100022258830496818958093465085158669901515484233404810989794564246742578801815435758084706748161127459492240880844313667530744812015071324224009123 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:55:35 2005 Input: Mod(33606273495355907425874514706504407812081556216490323124088628358647329150420902436029909698842449649256516732266588212654817227837870670173668027034775631998737772918525117230875377273552233864746660528129875258425798297134104082739422367749950126407158599688907385439722537017999364970599000371101144209531159377966861390000616972489197505525861864644606420390449588147874955987039012809202933744512000597864929479712088975300837406484082121466663555352610956937119808370301607457203208573004238375359550810945573278649880955358605369667619742797962112899148457456611853032654363583299833262598143377482268760278847762389110976884078158521060230682462247160705714171088928100022258830496818958093465085158669901515484233404810989794564246742578801815435758084706748161127459492240880844313667530744812015071324224009123,463) Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:56:09 2005 Input: 37^113 Output: ? 1609884872782827331140941603272764854862805248564786075660814055187786610035093796974433010639685409404854358889891201137718944856371618554573039355471188396102219101305090903397 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.009s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:56:28 2005 Input: Mod(1609884872782827331140941603272764854862805248564786075660814055187786610035093796974433010639685409404854358889891201137718944856371618554573039355471188396102219101305090903397,463) Output: ? Mod(347, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 12:56:45 2005 Input: factor(5987) Output: ? [5987 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:56:49 2005 Input: Mod(275,168)^(-1) Output: ? Mod(11, 168) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 12:57:12 2005 Input: Mod(2,5986)^-1 Output: ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(2, 5986). Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:57:13 2005 Input: 139^11 Output: ? 374250856383374715683539 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:57:31 2005 Input: Mod(374250856383374715683539,588) Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:57:51 2005 Input: 559^275 Output: ? 345340225904782112004937124203791641393276606779628505830316861707934058272611325111763274821239295781304063237182523302872747703176762884678377310325176361133238325961482866384143779932759325034371617718237963652247416754812383816311428089754161348483579260602967465422959912691969235292312866349177455212384574013803319770924176027537708116179876122975836790598816358198276961090005132508383381946324173653501587591155001059940931564144237258796930551491695003855760465177192328377582165266406619166438546650107338908614777877282893114887179331279100847469711299137611953588967098246874665303644226105702006278639071412264644308373463004755251468446569233430575922746109584828336141830063376871740251788551489778198985340035233897605617071609732454073999 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 12:58:01 2005 Input: Mod(2,6780)^-1 Output: ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(2, 6780). Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 12:58:02 2005 Input: Mod(2,6780)^-1 Output: ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(2, 6780). Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 12:58:03 2005 Input: Mod(2,6780)^-1 Output: ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(2, 6780). Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 12:58:12 2005 Input: Mod(345340225904782112004937124203791641393276606779628505830316861707934058272611325111763274821239295781304063237182523302872747703176762884678377310325176361133238325961482866384143779932759325034371617718237963652247416754812383816311428089754161348483579260602967465422959912691969235292312866349177455212384574013803319770924176027537708116179876122975836790598816358198276961090005132508383381946324173653501587591155001059940931564144237258796930551491695003855760465177192328377582165266406619166438546650107338908614777877282893114887179331279100847469711299137611953588967098246874665303644226105702006278639071412264644308373463004755251468446569233430575922746109584828336141830063376871740251788551489778198985340035233897605617071609732454073999,588) Output: ? Mod(139, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Apr 1 12:59:18 2005 Input: factor (463) Output: ? [463 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:00:00 2005 Input: Mod(113,462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Apr 1 13:01:58 2005 Input: Mod(113, 462)^(-1) Output: ? Mod(323, 462) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:03:17 2005 Input: Mod(347,463)^(323) Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 13:03:26 2005 Input: 6780^3390 Output: ? 7390302398516513041140840330179774099549778796726726863458939651611420123093024151748339933648319363583889200933785497377702940088689008839157308012034041719382103036847529384205071340712170489173391273451771711926876052149895169283091506086816399400836082211174391340625041050262271786607236463690817049004794231049676366054649760823991817909218066921552647579754004180914332416174057990424049938734357864899196590939017753224085321378724650826424570336685445991999243110606976706073156432312265488395474243386861740222384589178617186270887981455770412113625004771566864347727007634586830382000392194293899607003285008680019418882995198403078283801737201055062823775423256003046115812822567147571850452679739307639056964989245327041433193034021369494835887645267720379408990516480261942433881916348673977295238784903966445340228835496469528420630544535954715805198785344879715532620562841473292756986246293400020236416016390847029005260843680107125113755635306622829086527554027318554288895726666081691693988381372974750832922211077291672457174158792586190835042525376163085657715939821473434568713077909968906409646821296209761540319624431240174018829209290898689704992957461183923146349638843723689222032555585866373751164700619196989921512499177158276820061266710975921279436216691096874951220922055197909538848951507388516875561948473232697858971593595045334394843130324395910084085640274977289427504406046893062698290182285814324262313719761379348262517988089748843200389472594324352094391031301422174327748949273687409432675638098776855967006717582248823117243882337221400851782223032054137061416717080562102826877273933458542572296082297809934814103057936691909683407533604156612651453408620442663688976827159389479033905900064711523702716890139517670229398454603530483451362619429673547960196001055102936748682037695367853558218773309992304302852047324592428229330775938197687256148065533249888063074234153031088903442555650419514500878173061497142972974028602072454168370384236178124977095739103480748300102991385268352051529664629871273185883790570249230905285413693774117241969945946880897934018443610645714175533964767617132982206503032762708707977666402696741294610003098216033888797667913008777646590228364420567388279132402275562478754064598870118465298800127538222707830696168867348964201758621392977129643058906189172833991620837733528384785923931269851930075071307178395457504709697646208617809706906784431353247591830565960287839806241813658814999563028689886231211520724304755426349341408825940090445879066289403524439333591084362751490961488084168586198448126114697665957669059422067897937093476508350924373577267720880304364735868980663974357103684517156131343560167969438527635858560314974572397595387318374227222388891682394147025592436096274172630317642563120715845764469104260483038864622593689286056831287529978195070058038578948505643196704312661324926223743702584039477422513149510856469868886118764735469478942151983716753586109934253065363967700830803654127558264036110804032170581710810748360826273971007699428018615114546867536615395256997769393667073214181691854000550407669810804152003598790108572752787859722948211957433880230172899980116679112948573438[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.054s user 0m0.046s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:03:33 2005 Input: Mod(37,463)^(323) Output: ? Mod(102, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:03:41 2005 Input: Mod(37,463)^(113) Output: ? Mod(347, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 13:04:06 2005 Input: Mod(7390302398516513041140840330179774099549778796726726863458939651611420123093024151748339933648319363583889200933785497377702940088689008839157308012034041719382103036847529384205071340712170489173391273451771711926876052149895169283091506086816399400836082211174391340625041050262271786607236463690817049004794231049676366054649760823991817909218066921552647579754004180914332416174057990424049938734357864899196590939017753224085321378724650826424570336685445991999243110606976706073156432312265488395474243386861740222384589178617186270887981455770412113625004771566864347727007634586830382000392194293899607003285008680019418882995198403078283801737201055062823775423256003046115812822567147571850452679739307639056964989245327041433193034021369494835887645267720379408990516480261942433881916348673977295238784903966445340228835496469528420630544535954715805198785344879715532620562841473292756986246293400020236416016390847029005260843680107125113755635306622829086527554027318554288895726666081691693988381372974750832922211077291672457174158792586190835042525376163085657715939821473434568713077909968906409646821296209761540319624431240174018829209290898689704992957461183923146349638843723689222032555585866373751164700619196989921512499177158276820061266710975921279436216691096874951220922055197909538848951507388516875561948473232697858971593595045334394843130324395910084085640274977289427504406046893062698290182285814324262313719761379348262517988089748843200389472594324352094391031301422174327748949273687409432675638098776855967006717582248823117243882337221400851782223032054137061416717080562102826877273933458542572296082297809934814103057936691909683407533604156612651453408620442663688976827159389479033905900064711523702716890139517670229398454603530483451362619429673547960196001055102936748682037695367853558218773309992304302852047324592428229330775938197687256148065533249888063074234153031088903442555650419514500878173061497142972974028602072454168370384236178124977095739103480748300102991385268352051529664629871273185883790570249230905285413693774117241969945946880897934018443610645714175533964767617132982206503032762708707977666402696741294610003098216033888797667913008777646590228364420567388279132402275562478754064598870118465298800127538222707830696168867348964201758621392977129643058906189172833991620837733528384785923931269851930075071307178395457504709697646208617809706906784431353247591830565960287839806241813658814999563028689886231211520724304755426349341408825940090445879066289403524439333591084362751490961488084168586198448126114697665957669059422067897937093476508350924373577267720880304364735868980663974357103684517156131343560167969438527635858560314974572397595387318374227222388891682394147025592436096274172630317642563120715845764469104260483038864622593689286056831287529978195070058038578948505643196704312661324926223743702584039477422513149510856469868886118764735469478942151983716753586109934253065363967700830803654127558264036110804032170581710810748360826273971007699428018615114546867536615395256997769393667073214181691854000550407669810804152003598790108572752787859722948211957433880230172899980116679112948573438,6781 Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...80116679112948573438,6781 ^ Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:04:18 2005 Input: Mod(347,463)^(323) Output: ? Mod(37, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Apr 1 13:04:26 2005 Input: factor(588) Output: ? [2 2] [3 1] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:04:35 2005 Input: Mod(37,463)^(113) Output: ? Mod(347, 463) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.60.186 (128.197.60.186) Time: Fri Apr 1 13:04:56 2005 Input: Mod(7390302398516513041140840330179774099549778796726726863458939651611420123093024151748339933648319363583889200933785497377702940088689008839157308012034041719382103036847529384205071340712170489173391273451771711926876052149895169283091506086816399400836082211174391340625041050262271786607236463690817049004794231049676366054649760823991817909218066921552647579754004180914332416174057990424049938734357864899196590939017753224085321378724650826424570336685445991999243110606976706073156432312265488395474243386861740222384589178617186270887981455770412113625004771566864347727007634586830382000392194293899607003285008680019418882995198403078283801737201055062823775423256003046115812822567147571850452679739307639056964989245327041433193034021369494835887645267720379408990516480261942433881916348673977295238784903966445340228835496469528420630544535954715805198785344879715532620562841473292756986246293400020236416016390847029005260843680107125113755635306622829086527554027318554288895726666081691693988381372974750832922211077291672457174158792586190835042525376163085657715939821473434568713077909968906409646821296209761540319624431240174018829209290898689704992957461183923146349638843723689222032555585866373751164700619196989921512499177158276820061266710975921279436216691096874951220922055197909538848951507388516875561948473232697858971593595045334394843130324395910084085640274977289427504406046893062698290182285814324262313719761379348262517988089748843200389472594324352094391031301422174327748949273687409432675638098776855967006717582248823117243882337221400851782223032054137061416717080562102826877273933458542572296082297809934814103057936691909683407533604156612651453408620442663688976827159389479033905900064711523702716890139517670229398454603530483451362619429673547960196001055102936748682037695367853558218773309992304302852047324592428229330775938197687256148065533249888063074234153031088903442555650419514500878173061497142972974028602072454168370384236178124977095739103480748300102991385268352051529664629871273185883790570249230905285413693774117241969945946880897934018443610645714175533964767617132982206503032762708707977666402696741294610003098216033888797667913008777646590228364420567388279132402275562478754064598870118465298800127538222707830696168867348964201758621392977129643058906189172833991620837733528384785923931269851930075071307178395457504709697646208617809706906784431353247591830565960287839806241813658814999563028689886231211520724304755426349341408825940090445879066289403524439333591084362751490961488084168586198448126114697665957669059422067897937093476508350924373577267720880304364735868980663974357103684517156131343560167969438527635858560314974572397595387318374227222388891682394147025592436096274172630317642563120715845764469104260483038864622593689286056831287529978195070058038578948505643196704312661324926223743702584039477422513149510856469868886118764735469478942151983716753586109934253065363967700830803654127558264036110804032170581710810748360826273971007699428018615114546867536615395256997769393667073214181691854000550407669810804152003598790108572752787859722948211957433880230172899980116679112948573438,6781) Output: ? Mod(6289, 6781) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.005s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Apr 1 13:05:19 2005 Input: eulerphi(588) Output: ? 168 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.008s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:05:32 2005 Input: factor(588) Output: ? [2 2] [3 1] [7 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Apr 1 13:06:10 2005 Input: eulerphi(8800) Output: ? 3200 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Apr 1 13:06:27 2005 Input: eulerphi(588) Output: ? 168 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:07:38 2005 Input: mod(275,164)^(-1) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(275,164)^(-1) ^----------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:07:46 2005 Input: Mod(275,164)^(-1) Output: ? Mod(99, 164) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.246.186 (168.122.246.186) Time: Fri Apr 1 13:07:55 2005 Input: Mod(275, 168)^(-1) Output: ? Mod(11, 168) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:08:37 2005 Input: Mod(139,588)^(99) Output: ? Mod(139, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:08:56 2005 Input: Mod(139,588)^(275) Output: ? Mod(475, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:08:58 2005 Input: Mod(139,588)^(275) Output: ? Mod(475, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:09:23 2005 Input: Mod(139,588)^(99) Output: ? Mod(139, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:09:28 2005 Input: x=1099 factor(x) Output: ? 1099 ? [7 1] [157 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:09:33 2005 Input: x=1141 factor(x) Output: ? 1141 ? [7 1] [163 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:09:39 2005 Input: x=1183 factor(x) Output: ? 1183 ? [7 1] [13 2] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:10:01 2005 Input: x=1897 factor(x) Output: ? 1897 ? [7 1] [271 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:10:29 2005 Input: Mod(275,168)^(-1) Output: ? Mod(11, 168) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:10:52 2005 Input: Mod(139,588)^(11) Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:11:18 2005 Input: Mod(559,588)^(275) Output: ? Mod(139, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:12:27 2005 Input: Mod(107,168)^(-1) Output: ? Mod(11, 168) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:15:09 2005 Input: x=1897 factor(x) e^((ln 1897/46.745)/1.069) Output: ? 1897 ? [7 1] [271 1] ? ? ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m0.027s user 0m0.005s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:15:20 2005 Input: Mod(139,588)^(11) Output: ? Mod(559, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:15:58 2005 Input: Mod(559,588)^(275) Output: ? Mod(139, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:16:00 2005 Input: Mod(559,588)^(275) Output: ? Mod(139, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:16:01 2005 Input: Mod(559,588)^(275) Output: ? Mod(139, 588) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:19:04 2005 Input: x=1897 factor(x) e^((ln 1897/46.745)/1.069) e(2) Output: ? 1897 ? [7 1] [271 1] ? ? ? e ? Errors (if any) and Timing Info: *** negative exponent in glog. *** Warning: unused characters: (2). Timing: real 0m0.019s user 0m0.006s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:19:08 2005 Input: x=1897 factor(x) e^((ln 1897/46.745)/1.069) e(3) Output: ? 1897 ? [7 1] [271 1] ? ? ? e ? Errors (if any) and Timing Info: *** negative exponent in glog. *** Warning: unused characters: (3). Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:20:37 2005 Input: x=1897 factor(x) e^((ln 1897/46.745)/1.069) exp(3) Output: ? 1897 ? [7 1] [271 1] ? ? ? 20.085536923187667740928529654581717896 ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m0.021s user 0m0.008s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:20:40 2005 Input: x=1897 factor(x) e^((ln 1897/46.745)/1.069) exp(1) Output: ? 1897 ? [7 1] [271 1] ? ? ? 2.7182818284590452353602874713526624977 ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:20:46 2005 Input: x=1897 factor(x) exp((ln 1897/46.745)/1.069) ) Output: ? 1897 ? [7 1] [271 1] ? ? 1 + 0.020011845011062047625989823376456524616*ln1897 + 0.00020023697037338448253511076582685816351*ln1897^2 + 0.0000013357037388655977642173787053013889822*ln1897^3 + 0.0000000066824740507186091658521614208519471787*ln1897^4 + 2.6745726998684958290220627272690494218 E-11*ln1897^5 + 8.9205223900976849164422512594172804943 E-14*ln1897^6 + 2.5502301641191949847807063456337750584 E-16*ln1897^7 + 6.3793513483610823866164041136793244381 E-19*ln1897^8 + 1.4184732272723519243521138192094399426 E-21*ln1897^9 + 2.8386266376515297891864470964552717606 E-24*ln1897^10 + 5.1641960288140546556533122800026640507 E-27*ln1897^11 + 8.6120908779474148342625871586769943307 E-30*ln1897^12 + 1.3257217528512687943474645963987614008 E-32*ln1897^13 + 1.8950098747037925953335559266083329020 E-35*ln1897^14 + 2.5281762604669605210438137354944830538 E-38*ln1897^15 + O(ln1897^16) ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:21:02 2005 Input: x=1897 factor(x) exp((ln(1897/46.745))/1.069) ) Output: ? 1897 ? [7 1] [271 1] ? ? ? ? Errors (if any) and Timing Info: *** obsolete function: exp((ln(1897/46.745))/1.0 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: ln(x) ===> log(x) log(x,{flag=0}): natural logarithm of x. flag is optional, and can be 0: default, or 1: calls logagm, computed using the agm. *** Warning: unused characters: ). Timing: real 0m0.020s user 0m0.006s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:21:24 2005 Input: x=1897 factor(x) exp((log(1897/46.745))/1.069) ) Output: ? 1897 ? [7 1] [271 1] ? ? 31.953634870172268435235242036694683233 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:23:05 2005 Input: Mod(56,337)^(168) Output: ? Mod(1, 337) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:24:00 2005 Input: x=1897 factor(x) exp((log(1393/49.625))/1.0319) ) Output: ? 1897 ? [7 1] [271 1] ? ? 25.320926785479549912092002506485639038 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:26:28 2005 Input: x=1897 factor(x) exp((log(7273/49.625))/1.0319) ) Output: ? 1897 ? [7 1] [271 1] ? ? 125.61840319159984503037467942664526605 ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.013s user 0m0.007s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:27:00 2005 Input: Mod(324,3011)^(1505) Output: ? Mod(1, 3011) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.150.179 (128.197.150.179) Time: Fri Apr 1 13:27:02 2005 Input: Mod(324,3011)^(1505) Output: ? Mod(1, 3011) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:27:29 2005 Input: x=1897 factor(x) exp((log(7273/49.625))/1.0319) ) factor(3y=27) Output: ? 1897 ? [7 1] [271 1] ? ? 125.61840319159984503037467942664526605 ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ). *** expected character: ',' instead of: factor(3y=27) ^----- Timing: real 0m0.019s user 0m0.008s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:27:34 2005 Input: x=1897 factor(x) exp((log(7273/49.625))/1.0319) ) factor(3*y=27) Output: ? 1897 ? [7 1] [271 1] ? ? 125.61840319159984503037467942664526605 ? ? ? [3 4] ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.016s user 0m0.005s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:27:49 2005 Input: x=1897 factor(x) exp((log(7273/49.625))/1.0319) ) factor(3*y=15) Output: ? 1897 ? [7 1] [271 1] ? ? 125.61840319159984503037467942664526605 ? ? ? [3 2] [5 1] ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.019s user 0m0.007s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:28:11 2005 Input: x=1897 factor(x) exp((log(7273/49.625))/1.0319) factor(3*y=15) Output: ? 1897 ? [7 1] [271 1] ? ? 125.61840319159984503037467942664526605 ? ? ? [3 2] [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:29:03 2005 Input: x=1897 factor(x) exp((log(7273/49.625))/1.0319) factor(7021=-0.107*x^2+57.672*x-11.935) Output: ? 1897 ? [7 1] [271 1] ? ? 125.61840319159984503037467942664526605 ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: factor(7021=-0.107*x^2+57.672*x ^-------------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:29:15 2005 Input: x=1897 factor(x) exp((log(7273/49.625))/1.0319) factor(7021=-0.107*y^2+57.672*y-11.935) Output: ? 1897 ? [7 1] [271 1] ? ? 125.61840319159984503037467942664526605 ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: factor(7021=-0.107*y^2+57.672*y ^-------------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Fri Apr 1 13:29:26 2005 Input: x=1897 factor(x) exp((log(7273/49.625))/1.0319) factor(7021=-0.107*y*y+57.672*y-11.935) Output: ? 1897 ? [7 1] [271 1] ? ? 125.61840319159984503037467942664526605 ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: factor(7021=-0.107*y*y+57.672*y ^-------------------- Timing: real 0m0.017s user 0m0.006s sys 0m0.007s '130.156' ************** PARI ***************** Host 130.156.64.187 (130.156.64.187) Time: Fri Apr 1 13:48:10 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.027s sys 0m0.005s '130.156' ************** PARI ***************** Host 130.156.64.187 (130.156.64.187) Time: Fri Apr 1 13:48:18 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.026s sys 0m0.005s '130.156' ************** PARI ***************** Host 130.156.64.187 (130.156.64.187) Time: Fri Apr 1 13:48:31 2005 Input: for(b=1,1000, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 89,233 233,610 ? Errors (if any) and Timing Info: Timing: real 0m2.186s user 0m1.984s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.60.176 (128.197.60.176) Time: Fri Apr 1 14:07:39 2005 Input: Mod(324,3011)^1505 Output: ? Mod(1, 3011) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 14:30:06 2005 Input: Mod(5,101)^50 Output: ? Mod(1, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 14:30:26 2005 Input: 5^50 Output: ? 88817841970012523233890533447265625 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 14:30:43 2005 Input: Mod(88817841970012523233890533447265625,101) Output: ? Mod(1, 101) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.225.100 (168.122.225.100) Time: Fri Apr 1 14:31:05 2005 Input: Mod(324,337)^1505 Output: ? Mod(129, 337) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 20:49:02 2005 Input: m=a=3;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 20:50:45 2005 Input: m=a=3;r=1;n=7;print(m,r);while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 20:52:07 2005 Input: m=a=3;r=1;n=7;print(m,r);if(n=a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 03 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 20:52:25 2005 Input: m=a=3;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)))) Output: ? 31 92 63 44 55 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 20:54:37 2005 Input: m=a=3;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r)));print(m,r)) Output: ? 31 92 63 63 44 44 55 55 16 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.001s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 20:55:40 2005 Input: m=a=3;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r))));print(m,r) Output: ? 31 92 63 44 55 16 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 20:57:03 2005 Input: m=a=3;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r))));print n;print a;print r Output: ? 31 92 63 44 55 16 printr ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 20:57:49 2005 Input: m=a=3;r=1;n=7;print(m,r);if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r))));print(n);print(a);print(r) Output: ? 31 92 63 44 55 16 7 3 6 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 20:58:33 2005 Input: m=a=3;r=1;n=7;if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r))));print(n);print(a);print(r) Output: ? 92 63 44 55 16 7 3 6 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.001s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 20:58:49 2005 Input: m=a=3;r=1;n=7;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r))));print(n);print(a);print(r) Output: ? 7 3 1 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.006s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 21:00:14 2005 Input: m=a=3;r=1;n=7;if(n<>a*m,print(m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r))));print(n);print(a);print(r) Output: ? 92 63 44 55 16 7 3 6 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 21:00:33 2005 Input: m=a=3;r=1;n=7;if(n<>a*m,m=a*m,r=r+1));while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r))));print(n);print(a);print(r) Output: ? 9 ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: );while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r))));print(n);print(a);print(r). Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 21:00:53 2005 Input: m=a=3;r=1;n=7;if(n<>a*m,m=a*m,r=r+1);while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r))));print(n);print(a);print(r) Output: ? 62 43 54 15 7 3 5 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 21:01:37 2005 Input: m=a=3;r=1;n=7;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r))));print(n);print(a);print(r) Output: ? 63 44 55 16 7 3 6 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.008s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 21:02:37 2005 Input: m=a=3;r=1;n=7;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r))));print(n);print(a);print(r) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 20414 Killed /usr/bin/gp -q -emacs Timing: real 0m23.064s user 0m20.992s sys 0m0.009s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 21:03:33 2005 Input: m=a=3;r=1;n=7;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r))));print(n);print(a);print(r) Output: ? 63 44 55 16 7 3 6 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 21:05:00 2005 Input: m=a=3;r=1;n=7;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n);if(m<>a,print(m,r))));print(n);print(a);print(r) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 20428 Killed /usr/bin/gp -q -emacs Timing: real 0m23.074s user 0m20.994s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 21:06:35 2005 Input: m=a=3;r=1;n=7;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n)));print(n);print(a);print(r) Output: ? 7 3 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 21:06:56 2005 Input: m=a=2;r=1;n=7;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n)));print(n);print(a);print(r) Output: ? 7 2 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 21:07:06 2005 Input: m=a=5;r=1;n=7;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n)));print(n);print(a);print(r) Output: ? 7 5 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 21:07:42 2005 Input: m=a=2;r=1;n=7;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n)));print(n);print(a);print(r) Output: ? 7 2 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 21:07:51 2005 Input: m=a=2;r=1;n=9;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n)));print(n);print(a);print(r) Output: ? 83 9 2 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 21:08:05 2005 Input: m=a=2;r=1;n=11;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n)));print(n);print(a);print(r) Output: ? 83 105 69 11 2 10 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.5 (165.95.7.5) Time: Fri Apr 1 21:08:26 2005 Input: m=a=2;r=1;n=13;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n)));print(n);print(a);print(r) Output: ? 83 65 126 1010 13 2 12 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.009s '165.95.' ************** PARI ***************** Host 165.95.7.116 (165.95.7.116) Time: Fri Apr 1 21:08:35 2005 Input: m=a=2;r=1;n=15;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n)));print(n);print(a);print(r) Output: ? 83 15 2 4 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.116 (165.95.7.116) Time: Fri Apr 1 21:11:22 2005 Input: m=a=2;r=1;n=15;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n)));print(n);print(a);print(r) Output: ? 15 2 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '165.95.' ************** PARI ***************** Host 165.95.7.116 (165.95.7.116) Time: Fri Apr 1 21:11:46 2005 Input: m=a=2;r=1;n=13;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n)));print(n);print(a);print(r) Output: ? 13 2 12 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.116 (165.95.7.116) Time: Fri Apr 1 21:11:55 2005 Input: m=a=2;r=1;n=11;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n)));print(n);print(a);print(r) Output: ? 11 2 10 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.116 (165.95.7.116) Time: Fri Apr 1 21:12:04 2005 Input: m=a=2;r=1;n=9;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n)));print(n);print(a);print(r) Output: ? 9 2 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.116 (165.95.7.116) Time: Fri Apr 1 21:12:12 2005 Input: m=a=2;r=1;n=7;if(n<>a*m,m=a*m);r=r+1;while(m>a,r=r+1;if(a*m=n,m=m-n)));print(n);print(a);print(r) Output: ? 7 2 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 21:50:58 2005 Input: zeta(2) Output: ? 1.6449340668482264364724151666460251892 ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.006s sys 0m0.006s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 21:51:14 2005 Input: zeta(-1) Output: ? -0.083333333333333333333333333333333333333 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 21:51:26 2005 Input: zeta(1) Output: ? ? Errors (if any) and Timing Info: *** argument equal to one in zeta. Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 21:51:48 2005 Input: zeta(0.5+5i) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: zeta(0.5+5i) ^-- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 21:53:46 2005 Input: zeta(2+3i) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: zeta(2+3i) ^-- Timing: real 0m0.024s user 0m0.007s sys 0m0.006s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 21:54:10 2005 Input: zeta(2+3i). Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: zeta(2+3i). ^--- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 21:54:21 2005 Input: zeta(3) Output: ? 1.2020569031595942853997381615114499907 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.003s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 21:54:35 2005 Input: zeta(7) Output: ? 1.0083492773819228268397975498497967595 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.004s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 21:54:50 2005 Input: zeta(-2) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 21:55:07 2005 Input: zeta(-3) Output: ? 0.0083333333333333333333333333333333333332 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 21:55:15 2005 Input: zeta(-4) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 21:55:45 2005 Input: zeta(-4+3i) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: zeta(-4+3i) ^-- Timing: real 0m0.020s user 0m0.007s sys 0m0.004s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 21:57:05 2005 Input: zeta(-4+3I) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: zeta(-4+3I) ^-- Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 21:58:52 2005 Input: gp Output: ? gp ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 21:59:47 2005 Input: pi Output: ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 21:59:59 2005 Input: pi*pi Output: ? pi^2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 22:00:13 2005 Input: pi^2 Output: ? pi^2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 22:00:36 2005 Input: zeta(pi^2) Output: ? ? Errors (if any) and Timing Info: *** sorry, zeta of power series is not yet implemented. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 22:01:58 2005 Input: { t1 = 1/2 + 14*I; t2 = 1/2 + 15*I; eps = 10^(-50); z1 = zeta(t1); until (norm(z2) < eps, z2 = zeta(t2); if (norm(z2) < norm(z1), t3 = t1; t1 = t2; t2 = t3; z1 = z2 ); t2 = (t1+t2) / 2.; print(t1 ": " z1) ) } Output: ? 1/2 + 14*I: 0.022241142609993589246213199203968626386 - 0.10325812326645005790236309555257383450*I 1/2 + 14*I: 0.022241142609993589246213199203968626386 - 0.10325812326645005790236309555257383450*I 0.50000000000000000000000000000000000000 + 14.250000000000000000000000000000000000*I: -0.010213208887230807522525955767002816511 + 0.091698089621017640081465962929933653198*I 0.50000000000000000000000000000000000000 + 14.125000000000000000000000000000000000*I: 0.0012417291852137510346673085802853350647 - 0.0076067313356130555106430474935370339114*I 0.50000000000000000000000000000000000000 + 14.125000000000000000000000000000000000*I: 0.0012417291852137510346673085802853350647 - 0.0076067313356130555106430474935370339114*I 0.50000000000000000000000000000000000000 + 14.125000000000000000000000000000000000*I: 0.0012417291852137510346673085802853350647 - 0.0076067313356130555106430474935370339114*I 0.50000000000000000000000000000000000000 + 14.140625000000000000000000000000000000*I: -0.00072500707529812503468942479076164825284 + 0.0046253214673438971249880769138653783886*I 0.50000000000000000000000000000000000000 + 14.132812500000000000000000000000000000*I: 0.00023962954107211412834588625490278397267 - 0.0014977447536980232040348813712444919242*I 0.50000000000000000000000000000000000000 + 14.132812500000000000000000000000000000*I: 0.00023962954107211412834588625490278397267 - 0.0014977447536980232040348813712444919242*I 0.50000000000000000000000000000000000000 + 14.134765625000000000000000000000000000*I: -0.0000050477528112895105346089337394953122802 + 0.000031710588793744007891097264313007623870*I 0.50000000000000000000000000000000000000 + 14.134765625000000000000000000000000000*I: -0.0000050477528112895105346089337394953122802 + 0.000031710588793744007891097264313007623870*I 0.50000000000000000000000000000000000000 + 14.134765625000000000000000000000000000*I: -0.0000050477528112895105346089337394953122802 + 0.000031710588793744007891097264313007623870*I 0.50000000000000000000000000000000000000 + 14.134765625000000000000000000000000000*I: -0.0000050477528112895105346089337394953122802 + 0.000031710588793744007891097264313007623870*I 0.50000000000000000000000000000000000000 + 14.134765625000000000000000000000000000*I: -0.0000050477528112895105346089337394953122802 + 0.000031710588793744007891097264313007623870*I 0.50000000000000000000000000000000000000 + 14.134704589843750000000000000000000000*I: 0.0000025629470585022928664553282786112377754 - 0.000016098175959828936822394045075238461739*I 0.50000000000000000000000000000000000000 + 14.134735107421875000000000000000000000*I: -0.0000012426889847373687918207327003320961140 + 0.0000078060994177939847324764298429698262538*I 0.50000000000000000000000000000000000000 + 14.134719848632812500000000000000000000*I: 0.00000066005751036606240409998196372114534632 - 0.0000041460650216441673191517954226161104709*I 0.50000000000000000000000000000000000000 + 14.134727478027343750000000000000000000*I: -0.00000029133361888594635474828658803415387787 + 0.0000018300105105227104907165816658767034581*I 0.50000000000000000000000000000000000000 + 14.134723663330078125000000000000000000*I: 0.00000018435747532388384677381445113139406869 - 0.0000011580289274618373462866323141851235516*I 0.50000000000000000000000000000000000000 + 14.134725570678710937500000000000000000*I: -0.000000053489189386187190268566160316319835330 + 0.00000033599037355679175816071910681797482240*I 0.50000000000000000000000000000000000000 + 14.134725570678710937500000000000000000*I: -0.000000053489189386187190268566160316319835330 + 0.00000033599037355679175816071910681797482240*I 0.50000000000000000000000000000000000000 + 14.134725093841552734375000000000000000*I: 0.0000000059722672404507364302655529844075510389 - 0.000000037514530068051453459458095959312990640*I 0.50000000000000000000000000000000000000 + 14.134725093841552734375000000000000000*I: 0.0000000059722672404507364302655529844075510389 - 0.000000037514530068051453459458095959312990640*I 0.50000000000000000000000000000000000000 + 14.134725093841552734375000000000000000*I: 0.0000000059722672404507364302655529844075510389 - 0.000000037514530068051453459458095959312990640*I 0.50000000000000000000000000000000000000 + 14.134725153446197509765625000000000000*I: -0.0000000014604224777568119054521443839306049290 + 0.0000000091735800278104917820589383501792529841*I 0.50000000000000000000000000000000000000 + 14.134725153446197509765625000000000000*I: -0.0000000014604224777568119054521443839306049290 + 0.0000000091735800278104917820589383501792529841*I 0.50000000000000000000000000000000000000 + 14.134725138545036315917968750000000000*I: 0.00000000039774974715550643150187096082597754920 - 0.0000000024984475726883239646786773010674587327*I 0.50000000000000000000000000000000000000 + 14.134725138545036315917968750000000000*I: 0.00000000039774974715550643150187096082597754920 - 0.0000000024984475726883239646786773010674587327*I 0.50000000000000000000000000000000000000 + 14.134725142270326614379882812500000000*I: -6.6793321862546307166026951304723319480 E-11 + 0.00000000041955932265304704034555983115678186579*I 0.50000000000000000000000000000000000000 + 14.134725142270326614379882812500000000*I: -6.6793321862546307166026951304723319480 E-11 + 0.00000000041955932265304704034555983115678186579*I 0.50000000000000000000000000000000000000 + 14.134725141339004039764404296875000000*I: 4.9342444592593557032601485722012306636 E-11 - 0.00000000030994240148125402160976350267265024432*I 0.50000000000000000000000000000000000000 + 14.134725141804665327072143554687500000*I: -8.7254387015908184768455363910496821172 E-12 + 5.4808460560983316865054125864368132180 E-11*I 0.50000000000000000000000000000000000000 + 14.134725141804665327072143554687500000*I: -8.7254387015908184768455363910496821172 E-12 + 5.4808460560983316865054125864368132180 E-11*I 0.50000000000000000000000000000000000000 + 14.134725141688250005245208740234375000*I: 5.7915321094650672623809602084198113218 E-12 - 3.6379254954247241349789385537925217794 E-11*I 0.50000000000000000000000000000000000000 + 14.134725141746457666158676147460937500*I: -1.4669532971037262854839971039165662123 E-12 + 9.2146028029787691247290358867524080481 E-12*I 0.50000000000000000000000000000000000000 + 14.134725141746457666158676147460937500*I: -1.4669532971037262854839971039165662123 E-12 + 9.2146028029787691247290358867524080481 E-12*I 0.50000000000000000000000000000000000000 + 14.134725141731905750930309295654296875*I: 3.4766805434331259931251678771524941625 E-13 - 2.1838616364007213625735693475677751302 E-12*I 0.50000000000000000000000000000000000000 + 14.134725141731905750930309295654296875*I: 3.4766805434331259931251678771524941625 E-13 - 2.1838616364007213625735693475677751302 E-12*I 0.50000000000000000000000000000000000000 + 14.134725141735543729737401008605957031*I: -1.0598728353064459077231986885952638167 E-13 + 6.6575447343958951746016672211867868257 E-13*I 0.50000000000000000000000000000000000000 + 14.134725141735543729737401008605957031*I: -1.0598728353064459077231986885952638167 E-13 + 6.6575447343958951746016672211867868257 E-13*I 0.50000000000000000000000000000000000000 + 14.134725141734634235035628080368041992*I: 7.4265509370823649435341016782498442409 E-15 - 4.6649554020773311410264298569578535273 E-14*I 0.50000000000000000000000000000000000000 + 14.134725141734634235035628080368041992*I: 7.4265509370823649435341016782498442409 E-15 - 4.6649554020773311410264298569578535273 E-14*I 0.50000000000000000000000000000000000000 + 14.134725141734634235035628080368041992*I: 7.4265509370823649435341016782498442409 E-15 - 4.6649554020773311410264298569578535273 E-14*I 0.50000000000000000000000000000000000000 + 14.134725141734747921873349696397781372*I: -6.7501783714112982326012331467310164508 E-15 + 4.2400949411761647604612625103600418582 E-14*I 0.50000000000000000000000000000000000000 + 14.134725141734691078454488888382911682*I: 3.3818628283454072290737768056313147286 E-16 - 2.1243023045062031383232281602114210256 E-15*I 0.50000000000000000000000000000000000000 + 14.134725141734691078454488888382911682*I: 3.3818628283454072290737768056313147286 E-16 - 2.1243023045062031383232281602114210256 E-15*I 0.50000000000000000000000000000000000000 + 14.134725141734691078454488888382911682*I: 3.3818628283454072290737768056313147286 E-16 - 2.1243023045062031383232281602114210256 E-15*I 0.50000000000000000000000000000000000000 + 14.134725141734691078454488888382911682*I: 3.3818628283454072290737768056313147286 E-16 - 2.1243023045062031383232281602114210256 E-15*I 0.50000000000000000000000000000000000000 + 14.134725141734694631168167688883841037*I: -1.0483650805588237387591771854263320968 E-16 + 6.5852592776051578103033739073469652253 E-16*I 0.50000000000000000000000000000000000000 + 14.134725141734694631168167688883841037*I: -1.0483650805588237387591771854263320968 E-16 + 6.5852592776051578103033739073469652253 E-16*I 0.50000000000000000000000000000000000000 + 14.134725141734693742989747988758608698*I: 5.9191896667226732941060409606611432805 E-18 - 3.7181130306164220709053062987414167102 E-17*I 0.50000000000000000000000000000000000000 + 14.134725141734693742989747988758608698*I: 5.9191896667226732941060409606611432805 E-18 - 3.7181130306164220709053062987414167102 E-17*I 0.50000000000000000000000000000000000000 + 14.134725141734693742989747988758608698*I: 5.9191896667226732941060409606611432805 E-18 - 3.7181130306164220709053062987414167102 E-17*I 0.50000000000000000000000000000000000000 + 14.134725141734693742989747988758608698*I: 5.9191896667226732941060409606611432805 E-18 - 3.7181130306164220709053062987414167102 E-17*I 0.50000000000000000000000000000000000000 + 14.134725141734693798500899220016435720*I: -1.0030414409401563537431020214488710865 E-18 + 6.3005608230032740890924523626967255390 E-18*I 0.50000000000000000000000000000000000000 + 14.134725141734693798500899220016435720*I: -1.0030414409401563537431020214488710865 E-18 + 6.30056082300327408909245236269 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.176s user 0m0.140s sys 0m0.007s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 22:02:50 2005 Input: zeta(0.5+4*I) Output: ? 0.60678376452243726922252380096327054611 + 0.091112139972515029788916594718089332604*I ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.005s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 22:03:10 2005 Input: zeta(2+4*I) Output: ? 0.80424930564085386506508180349477029412 + 0.0084359128162171094284981092959930819734*I ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.005s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 22:03:50 2005 Input: zeta(2+3*I) Output: ? 0.79802198514627572062229450072481268602 - 0.11374430805293850021591336585731507556*I ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.006s '219.89.' ************** PARI ***************** Host 219.89.2.246 (219.89.2.246) Time: Fri Apr 1 22:04:02 2005 Input: zeta(0.5+3*I) Output: ? 0.53273667097423288392338412168111954147 - 0.078896513425833382656205086905974193242*I ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.007s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Fri Apr 1 22:42:32 2005 Input: pi^2 / 6 Output: ? 1/6*pi^2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Fri Apr 1 22:42:42 2005 Input: pi^2 / 6; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Fri Apr 1 22:42:58 2005 Input: 1+1 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Fri Apr 1 22:43:13 2005 Input: pi^2 Output: ? pi^2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Fri Apr 1 22:43:21 2005 Input: pi^2+1 Output: ? pi^2 + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Fri Apr 1 22:43:27 2005 Input: pi^2+1= Output: ? ? Errors (if any) and Timing Info: *** unexpected character: pi^2+1= ^- Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Fri Apr 1 22:43:46 2005 Input: eval(pi^2+1) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Fri Apr 1 22:43:57 2005 Input: (pi^2+1) Output: ? pi^2 + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Fri Apr 1 23:07:55 2005 Input: zeta(-1) Output: ? -0.083333333333333333333333333333333333333 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Fri Apr 1 23:08:06 2005 Input: zeta(-0.5) Output: ? -0.20788622497735456601730672539704930222 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.007s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Fri Apr 1 23:08:28 2005 Input: zeta(pi) Output: ? ? Errors (if any) and Timing Info: *** sorry, zeta of power series is not yet implemented. Timing: real 0m0.022s user 0m0.006s sys 0m0.005s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Fri Apr 1 23:08:43 2005 Input: zeta(3.14159) Output: ? 1.1762421831331325393666051823318937704 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.010s sys 0m0.005s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Sat Apr 2 00:06:18 2005 Input: zeta(PI) Output: ? ? Errors (if any) and Timing Info: *** sorry, zeta of power series is not yet implemented. Timing: real 0m0.020s user 0m0.005s sys 0m0.009s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Sat Apr 2 00:06:34 2005 Input: zeta(-1) Output: ? -0.083333333333333333333333333333333333333 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Sat Apr 2 00:06:45 2005 Input: zeta(-2) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Sat Apr 2 00:06:55 2005 Input: zeta(-10) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Sat Apr 2 00:07:32 2005 Input: zeta(-9898765) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 21060 Killed /usr/bin/gp -q -emacs Timing: real 0m23.061s user 0m20.985s sys 0m0.015s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Sat Apr 2 00:07:52 2005 Input: zeta(-989) Output: ? -5.3898264601135411209432036791813159571 E1744 ? Errors (if any) and Timing Info: Timing: real 0m0.061s user 0m0.056s sys 0m0.004s '210.55.' ************** PARI ***************** Host 210.55.82.8 (210.55.82.8) Time: Sat Apr 2 00:08:09 2005 Input: zeta(-988) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '209.6.2' ************** PARI ***************** Host 209.6.221.213 (209.6.221.213) Time: Sat Apr 2 02:57:13 2005 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '24.86.2' ************** PARI ***************** Host 24.86.202.121 (24.86.202.121) Time: Sat Apr 2 19:25:17 2005 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) /* Boole's rule. The h conveniently cancel */ for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); /* Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result */ if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, /* dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified */ return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( /* Trapezoidal rule. Could be improved */ sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) /* Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 */ + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each evaluated at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, /* redundancy could be avoided by counting how often each gcd(i,S) value occurs */ n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } /* The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and evaluating nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function */ ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '80.58.5' ************** PARI ***************** Host 80.58.50.235 (80.58.50.235) Time: Sun Apr 3 08:59:55 2005 Input: z25:=integers(25); {x: x in Z25}; Output: ? ? @ Euler I List Mat Mod O Pi Pol Polrev Qfb Ser Set Str Vec abs acos acosh addhelp addprimes agm algdep alias allocatemem arg asin asinh atan atanh bernfrac bernreal bernvec besseljh besselk bestappr bezout bezoutres bigomega binary binomial bitand bitneg bitnegimply bitor bittest bitxor bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark break ceil centerlift changevar charpoly chinese component concat conj conjvec content contfrac contfracpnqn core coredisc cos cosh cotan default denominator deriv dilog dirdiv direuler dirmul dirzetak divisors divrem eint1 elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint erfc error eta eulerphi eval exp extern factor factorback factorcantor factorff factorial factorint factormod factornf factorpadic ffinit fibonacci floor for fordiv forprime forstep forsubgroup forvec frac galoisfixedfield galoisinit galoispermtopol galoissubcyclo gamma gammah gcd getheap getrand getstack gettime global hilbert hyperu idealadd idealaddtoone idealappr idealchinese idealcoprime idealdiv idealfactor idealhnf idealintersect idealinv ideallist ideallistarch ideallog idealmin idealmul idealnorm idealpow idealprimedec idealprincipal idealred idealstar idealtwoelt idealval ideleprincipal if imag incgam incgamc input install intformal intnum isfundamental isprime ispseudoprime issquare issquarefree kill kronecker lcm length lex lift lindep listcreate listinsert listkill listput listsort lngamma log matadjoint matalgtobasis matbasistoalg matcompanion matdet matdetint matdiagonal mateigen mathess mathilbert mathnf mathnfmod mathnfmodid matid matimage matimagecompl matindexrank matintersect matinverseimage matisdiagonal matker matkerint matmuldiagonal matmultodiagonal matpascal matrank matrix matrixqz matsize matsnf matsolve matsolvemod matsupplement mattranspose max min modreverse moebius newtonpoly next nextprime nfalgtobasis nfbasis nfbasistoalg nfdetint nfdisc nfeltdiv nfeltdiveuc nfeltdivmodpr nfeltdivrem nfeltmod nfeltmul nfeltmulmodpr nfeltpow nfeltpowmodpr nfeltreduce nfeltreducemodpr nfeltval nffactor nffactormod nfgaloisapply nfgaloisconj nfhilbert nfhnf nfhnfmod nfinit nfisideal nfisincl nfisisom nfkermodpr nfmodprinit nfnewprec nfroots nfrootsof1 nfsnf nfsolvemodpr nfsubfields norm norml2 numdiv numerator numtoperm omega padicappr padicprec permtonum plot plotbox plotclip plotcolor plotcopy plotcursor plotdraw plotfile ploth plothraw plothsizes plotinit plotkill plotlines plotlinetype plotmove plotpoints plotpointsize plotpointtype plotrbox plotrecth plotrecthraw plotrline plotrmove plotrpoint plotscale plotstring plotterm polcoeff polcompositum polcyclo poldegree poldisc poldiscreduced polgalois polhensellift polinterpolate polisirreducible pollead pollegendre polrecip polred polredabs polredord polresultant polroots polrootsmod polrootspadic polsturm polsubcyclo polsylvestermatrix polsym poltchebi poltschirnhaus polylog polzagier precision precprime prime primes print print1 printp printp1 printtex prod prodeuler prodinf psdraw psi psploth psplothraw qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfgaussred qfjacobi qflll qflllgram qfminim qfperfection qfsign quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit quit random read real removeprimes reorder return rnfalgtobasis rnfbasis rnfbasistoalg rnfcharpoly rnfconductor rnfdedekind rnfdet rnfdisc rnfeltabstorel rnfeltdown rnfeltreltoabs rnfeltup rnfequation rnfhnfbasis rnfidealabstorel rnfidealdown rnfidealhnf rnfidealmul rnfidealnormabs rnfidealnormrel rnfidealreltoabs rnfidealtwoelt rnfidealup rnfinit rnfisfree rnfisnorm rnfkummer rnflllgram rnfnormgroup rnfpolred rnfpolredabs rnfpseudobasis rnfsteinitz round serconvol serlaplace serreverse setintersect setisset setminus setrand setsearch setunion shift shiftmul sigma sign simplify sin sinh sizebyte sizedigit solve sqr sqrt sqrtint sqrtn subgrouplist subst sum sumalt sumdiv suminf sumpos system tan tanh taylor teichmuller theta thetanullk thue thueinit trace trap truncate type until valuation variable vecextract vecmax vecmin vecsort vector vectorv weber whatnow while write write1 writetex x zeta zetak zetakinit znlog znorder znprimroot znstar @E_N_D? Errors (if any) and Timing Info: *** unexpected character: z25:=integers(25); ^-------------- *** unexpected character: _{x:xinZ25}; ^------------ Timing: real 0m0.234s user 0m0.010s sys 0m0.007s '82.50.1' ************** PARI ***************** Host 82.50.103.32 (82.50.103.32) Time: Sun Apr 3 09:24:32 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.009s sys 0m0.005s '82.89.2' ************** PARI ***************** Host 82.89.214.50 (82.89.214.50) Time: Sun Apr 3 12:41:07 2005 Input: mod(33213454^27221447,5) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(33213454^2722144 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '82.89.2' ************** PARI ***************** Host 82.89.214.50 (82.89.214.50) Time: Sun Apr 3 12:41:38 2005 Input: Mod(33213454^27221447,5) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m3.446s user 0m3.085s sys 0m0.014s '82.89.2' ************** PARI ***************** Host 82.89.214.50 (82.89.214.50) Time: Sun Apr 3 12:42:37 2005 Input: Mod(19^19^19,7) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m4.315s user 0m3.888s sys 0m0.014s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:03:18 2005 Input: lucas(p) = { local(u,q); u=4; q=1<

Pi Pi=Pi(): the constant pi, with current precision. Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:05:29 2005 Input: exp(1) Output: ? 2.7182818284590452353602874713526624977 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.009s sys 0m0.001s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:05:38 2005 Input: Pi() Output: ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.008s sys 0m0.004s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:06:59 2005 Input: exp(Pi*sqrt(163)) Output: ? 262537412640768743.99999999999925007253 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:07:17 2005 Input: p 50 Output: ? p50 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:07:38 2005 Input: p 50 exp(Pi*sqrt(163)) Output: ? p50 ? 262537412640768743.99999999999925007253 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.008s sys 0m0.003s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:09:03 2005 Input: p 50 exp(Pi*sqrt(163)) sqr(log(%)/Pi) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:09:12 2005 Input: p 50 exp(Pi*sqrt(163)) Output: ? p50 ? 262537412640768743.99999999999925007253 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.002s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:09:17 2005 Input: p 10 exp(Pi*sqrt(163)) Output: ? p10 ? 262537412640768743.99999999999925007253 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:09:21 2005 Input: p 1 exp(Pi*sqrt(163)) Output: ? p1 ? 262537412640768743.99999999999925007253 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:09:25 2005 Input: p 0 exp(Pi*sqrt(163)) Output: ? p0 ? 262537412640768743.99999999999925007253 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:09:44 2005 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.005s sys 0m0.006s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:11:58 2005 Input: 1/0 Output: ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:13:05 2005 Input: log(x) Output: ? ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m0.032s user 0m0.007s sys 0m0.005s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:13:26 2005 Input: sqrt(-1) Output: ? 1.0000000000000000000000000000000000000*I ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.004s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:13:56 2005 Input: I² Output: ? I ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:14:02 2005 Input: i² Output: ? i ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:14:10 2005 Input: i^2 Output: ? i^2 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.004s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:14:17 2005 Input: I^2 Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:14:51 2005 Input: 6*zeta(2)/Pi^2 Output: ? 0.99999999999999999999999999999999999999 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:16:08 2005 Input: cos(x) Output: ? 1 - 1/2*x^2 + 1/24*x^4 - 1/720*x^6 + 1/40320*x^8 - 1/3628800*x^10 + 1/479001600*x^12 - 1/87178291200*x^14 + 1/20922789888000*x^16 + O(x^17) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.007s sys 0m0.005s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:16:20 2005 Input: cos(x)^2 Output: ? 1 - x^2 + 1/3*x^4 - 2/45*x^6 + 1/315*x^8 - 2/14175*x^10 + 2/467775*x^12 - 4/42567525*x^14 + 1/638512875*x^16 + O(x^17) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:16:47 2005 Input: O(x) Output: ? O(x) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:16:58 2005 Input: (1+x)^3 Output: ? x^3 + 3*x^2 + 3*x + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:17:20 2005 Input: (1+x)^-3 Output: ? 1/(x^3 + 3*x^2 + 3*x + 1) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:18:06 2005 Input: (1+x)^-3+O(x^16) Output: ? 1 - 3*x + 6*x^2 - 10*x^3 + 15*x^4 - 21*x^5 + 28*x^6 - 36*x^7 + 45*x^8 - 55*x^9 + 66*x^10 - 78*x^11 + 91*x^12 - 105*x^13 + 120*x^14 - 136*x^15 + O(x^16) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '129.16.' ************** PARI ***************** Host 129.16.35.82 (129.16.35.82) Time: Sun Apr 3 13:20:54 2005 Input: ploth(X=-2,2,sin(X^7)) Output: WARNING: PARI command contains unsafe command 'plot', so it will not be executed. '24.5.19' ************** PARI ***************** Host 24.5.192.7 (24.5.192.7) Time: Sun Apr 3 20:05:43 2005 Input: ? E = ellinit([0,1,-3,-2]) ? R = ellglobalred(E) Output: ? ? ? Errors (if any) and Timing Info: *** E=ellinit([0,1,-3,-2]): unknown identifier. *** R=ellglobalred(E): unknown identifier. Timing: real 0m0.019s user 0m0.008s sys 0m0.002s '24.5.19' ************** PARI ***************** Host 24.5.192.7 (24.5.192.7) Time: Sun Apr 3 20:06:00 2005 Input: ? E = ellinit([0,0,1,-3,-2]) ? R = ellglobalred(E) Output: ? ? ? Errors (if any) and Timing Info: *** E=ellinit([0,0,1,-3,-2]): unknown identifier. *** R=ellglobalred(E): unknown identifier. Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '217.231' ************** PARI ***************** Host 217.231.108.231 (217.231.108.231) Time: Mon Apr 4 05:10:36 2005 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '217.231' ************** PARI ***************** Host 217.231.108.231 (217.231.108.231) Time: Mon Apr 4 05:10:46 2005 Input: 2+3 = x Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 2+3=x ^-- Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.241.218 (140.247.241.218) Time: Mon Apr 4 05:15:07 2005 Input: ? ?elltors elltors(e,{flag=0}): torsion subgroup of elliptic curve e: order, structure, generators. If flag = 0, use Doud's algorithm; if flag = 1, use Lutz-Nagell. e=ellinit([17,-60,-120,0,0]); elltors(e) 4 = [16, [8, 2], [[30, -90], [-40, 400]]] e.disc 5 = 51438240000 e.disc % 90^2 verify Nagell-Lutz 6 = 0 e.disc % 400^2 verify Nagell-Lutz 7 = 0 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '140.247' ************** PARI ***************** Host 140.247.241.218 (140.247.241.218) Time: Mon Apr 4 05:15:30 2005 Input: elltors(e,{flag=0}): Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: elltors(e,{flag=0}): ^---------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.241.218 (140.247.241.218) Time: Mon Apr 4 05:18:44 2005 Input: e=ellinit([0,0,0,-1,0]) Output: ? [0, 0, 0, -1, 0, 0, -2, 0, -1, 48, 0, 64, 1728, [1.0000000000000000000000000000000000000, 0.E-38, -1.0000000000000000000000000000000000000]~, 2.6220575542921198104648395898911194136, 2.6220575542921198104648395898911194136*I, -0.59907011736779610371996124614016193910, -1.7972103521033883111598837384204858173*I, 6.8751858180203728274900957798105571979] ? Errors (if any) and Timing Info: Timing: real 0m0.071s user 0m0.007s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.241.218 (140.247.241.218) Time: Mon Apr 4 05:20:09 2005 Input: e=ellinit([0,0,0,-1,0]) elltors(e) Output: ? [0, 0, 0, -1, 0, 0, -2, 0, -1, 48, 0, 64, 1728, [1.0000000000000000000000000000000000000, 0.E-38, -1.0000000000000000000000000000000000000]~, 2.6220575542921198104648395898911194136, 2.6220575542921198104648395898911194136*I, -0.59907011736779610371996124614016193910, -1.7972103521033883111598837384204858173*I, 6.8751858180203728274900957798105571979] ? [4, [2, 2], [[1, 0], [0, 0]]] ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.007s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.241.218 (140.247.241.218) Time: Mon Apr 4 05:20:41 2005 Input: e=ellinit([0,0,0,-1,0]); elltors(e) Output: ? ? [4, [2, 2], [[1, 0], [0, 0]]] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.241.218 (140.247.241.218) Time: Mon Apr 4 05:21:52 2005 Input: e = ellinit([0,0,1,-7,6]); elltors(e) Output: ? ? [1, [], []] ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.010s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.241.218 (140.247.241.218) Time: Mon Apr 4 05:22:08 2005 Input: e = ellinit([0,0,1,-1,0]); elltors(e) Output: ? ? [1, [], []] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.012s sys 0m0.003s '140.247' ************** PARI ***************** Host 140.247.241.218 (140.247.241.218) Time: Mon Apr 4 05:22:25 2005 Input: e = ellinit([0,0,0,-1,0]); elltors(e) Output: ? ? [4, [2, 2], [[1, 0], [0, 0]]] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '140.247' ************** PARI ***************** Host 140.247.241.218 (140.247.241.218) Time: Mon Apr 4 05:59:19 2005 Input: e = ellinit([0,0,0,-1,0]); elltors(e) e.disc Output: ? ? [4, [2, 2], [[1, 0], [0, 0]]] ? 64 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '193.54.' ************** PARI ***************** Host 193.54.49.12 (193.54.49.12) Time: Mon Apr 4 08:18:26 2005 Input: simplify(sum('(-1)**j*factorial(2*a-i-j)/(factorial(a-j)*factorial(a-1-j)*factorial(j))', j=0..a-i)); Output: ? ? Errors (if any) and Timing Info: *** variable name expected: simplify(sum('(-1)**j*factorial(2 ^-------------------- Timing: real 0m0.399s user 0m0.013s sys 0m0.008s '169.229' ************** PARI ***************** Host 169.229.36.24 (169.229.36.24) Time: Mon Apr 4 13:46:58 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.189s user 0m0.003s sys 0m0.007s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Mon Apr 4 15:46:04 2005 Input: 1+1; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.006s sys 0m0.006s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:50:26 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x); for(k=1,n,A=intformal(1+A+A^2)); n!*polcoeff(A,n)) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...al(A);if(n<1,n==0,A=O(x); ^ *** Warning: unused characters: ). *** incorrect type in comparison. Timing: real 0m0.025s user 0m0.006s sys 0m0.006s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:50:40 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x);for(k=1,n,A=intformal(1+A+A^2)); n!*polcoeff(A,n)) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.006s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:51:02 2005 Input: a(n)=local(A);if(n<1,n==0,A=O(x);for(k=1,n,A=intformal(1+A+A^2));n!*polcoeff(A,n)) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.003s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:52:15 2005 Input: a(n)=local(A);if(n<1,n==0,A=O(x);for(k=1,n,A=intformal(1+A+A^2));n!*polcoeff(A,n)); a(2) Output: ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.085s user 0m0.006s sys 0m0.009s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:52:30 2005 Input: a(n)=local(A);if(n<1,n==0,A=O(x);for(k=1,n,A=intformal(1+A+A^2));n!*polcoeff(A,n)); a(2);a(3);a(4); Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.009s sys 0m0.002s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:52:41 2005 Input: a(n)=local(A);if(n<1,n==0,A=O(x);for(k=1,n,A=intformal(1+A+A^2));n!*polcoeff(A,n)); a(2),a(3),a(4); Output: ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,a(3),a(4);. Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:52:53 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x);for(k=1,n,A=intformal(1+A+A^2));n!*polcoeff(A,n)); a(2),a(3),a(4); Output: ? ? ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. *** Warning: unused characters: ,a(3),a(4);. Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:53:15 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x);for(k=1,n,A=intformal(1+A+A^2));n!*polcoeff(A,n)); a(2) Output: ? ? ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:53:20 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x);for(k=1,n,A=intformal(1+A+A^2));n!*polcoeff(A,n)); a(2); Output: ? ? ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.016s user 0m0.007s sys 0m0.006s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:53:28 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x);for(k=1,n,A=intformal(1+A+A^2));n!*polcoeff(A,n)); a(2); Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.005s sys 0m0.009s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:54:10 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x);for(k=1,n,A=intformal(1+A+A^2));n!*polcoeff(A,n)); a(2);a(3); Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:54:35 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x);for(k=1,n,A=intformal(1+A+A^2));n!*polcoeff(A,n)) Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.006s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:54:46 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x);for(k=1,n,A=intformal(1+A+A^2));n!*polcoeff(A,n));a(2) Output: ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:54:55 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x);for(k=1,n,A=intformal(1+A+A^2));n!*polcoeff(A,n));a(2);a(3); Output: ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.008s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:55:03 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x);for(k=1,n,A=intformal(1+A+A^2));n!*polcoeff(A,n));a(2);a(3); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.005s sys 0m0.007s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:55:11 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x);for(k=1,n,A=intformal(1+A+A^2));n!*polcoeff(A,n));a(2);a(3); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 16:55:29 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x);for(k=1,n,A=intformal(1+A+A^2));n!*polcoeff(A,n)); a(2);a(3);a(4);a(5); Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 17:08:03 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x); for(k=1,n,A=intformal(1+A+A^2)); n!*polcoeff(A,n)) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...al(A);if(n<1,n==0,A=O(x); ^ *** Warning: unused characters: ). *** incorrect type in comparison. Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 17:08:17 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x); for(k=1,n,A=intformal(1+A+A^2)); n!*polcoeff(A,n)) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 17:08:33 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x); for(k=1,n,A=intformal(1+A+A^2)); n!*polcoeff(A,n)); print a(4); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 17:09:59 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x); for(k=1,n,A=intformal(1+A+A^2)); n!*polcoeff(A,n)); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 17:10:11 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x); for(k=1,n,A=intformal(1+A+A^2)); n!*polcoeff(A,n)); a(5); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 17:10:18 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x); for(k=1,n,A=intformal(1+A+A^2)); n!*polcoeff(A,n)); a(5); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 17:10:24 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x); for(k=1,n,A=intformal(1+A+A^2)); n!*polcoeff(A,n)); a(5): Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 17:12:26 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x); for(k=1,n,A=intformal(1+A+A^2)); n!*polcoeff(A,n)); a(5) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '162.38.' ************** PARI ***************** Host 162.38.126.189 (162.38.126.189) Time: Mon Apr 4 17:12:31 2005 Input: a(n)=local(A); if(n<1,n==0,A=O(x); for(k=1,n,A=intformal(1+A+A^2)); n!*polcoeff(A,n)); a(5) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '18.241.' ************** PARI ***************** Host 18.241.6.152 (18.241.6.152) Time: Mon Apr 4 22:10:14 2005 Input: Input: P:= FunctionField(Rationals()); Q:= PolynomialRing(P); f:=x^6+45*x^5+365*x^4+865*x^3+400*x^2+38*x-4; print(f); G, R:= GaloisGroup(f); print(G); print(Order(G)); Output: ? ? ? ? f ? ? G ? ? Errors (if any) and Timing Info: *** unexpected character: Input:P:=FunctionField(Rati ^-------------------- *** unexpected character: Q:=PolynomialRing(P); ^-------------------- *** unexpected character: f:=x^6+45*x^5+365*x^4+ ^-------------------- *** Warning: unused characters: ,R:=GaloisGroup(f);. *** expected character: '=' instead of: print(Order(G)); ^-- Timing: real 0m0.112s user 0m0.007s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Mon Apr 4 22:54:48 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.189.89 (168.122.189.89) Time: Mon Apr 4 22:55:23 2005 Input: Mod(452,1147)^929 Output: ? Mod(763, 1147) ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.006s sys 0m0.008s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Mon Apr 4 23:14:31 2005 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Errors (if any) and Timing Info: Timing: real 0m0.058s user 0m0.007s sys 0m0.003s '24.177.' ************** PARI ***************** Host 24.177.14.207 (24.177.14.207) Time: Tue Apr 5 01:57:00 2005 Input: Mod(2^9, 9) Output: ? Mod(8, 9) ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.007s sys 0m0.006s '24.177.' ************** PARI ***************** Host 24.177.14.207 (24.177.14.207) Time: Tue Apr 5 02:06:09 2005 Input: factor(341) Output: ? [11 1] [31 1] ? Errors (if any) and Timing Info: Timing: real 0m0.048s user 0m0.004s sys 0m0.009s '24.177.' ************** PARI ***************** Host 24.177.14.207 (24.177.14.207) Time: Tue Apr 5 02:06:43 2005 Input: Mod(2^340 - 1, 341) Output: ? Mod(0, 341) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '24.177.' ************** PARI ***************** Host 24.177.14.207 (24.177.14.207) Time: Tue Apr 5 02:06:51 2005 Input: Mod(2^340 , 341) Output: ? Mod(1, 341) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 5 10:23:04 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.384s user 0m0.006s sys 0m0.006s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 5 10:35:53 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.007s sys 0m0.006s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 5 10:50:05 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.150.168 (128.197.150.168) Time: Tue Apr 5 10:50:20 2005 Input: Mod(3,91)^146 Output: ? Mod(9, 91) ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.008s sys 0m0.003s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 5 10:59:15 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.025s sys 0m0.007s '143.248' ************** PARI ***************** Host 143.248.205.93 (143.248.205.93) Time: Tue Apr 5 12:40:14 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.009s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.189.97 (68.118.189.97) Time: Tue Apr 5 17:44:14 2005 Input: Mod(3,1000)^3841 Output: ? Mod(403, 1000) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '18.53.0' ************** PARI ***************** Host 18.53.0.86 (18.53.0.86) Time: Tue Apr 5 18:15:42 2005 Input: help Output: ? help ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '18.53.0' ************** PARI ***************** Host 18.53.0.86 (18.53.0.86) Time: Tue Apr 5 18:15:49 2005 Input: ? Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '68.173.' ************** PARI ***************** Host 68.173.195.31 (68.173.195.31) Time: Tue Apr 5 21:53:45 2005 Input: 4*4 Output: ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '203.206' ************** PARI ***************** Host 203.206.236.91 (203.206.236.91) Time: Wed Apr 6 11:33:16 2005 Input: print((1844 * 3125) mod 9987); Output: ? 5762500mod9987 ? Errors (if any) and Timing Info: Timing: real 0m0.292s user 0m0.006s sys 0m0.010s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Apr 6 20:39:30 2005 Input: 60! Output: ? 8320987112741390144276341183223364380754172606361245952449277696409600000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.008s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Apr 6 20:40:17 2005 Input: 60!/(19!)*(41!) 59*55*53*47*43*29*23*49*5*9*4 Output: ? 2288279938125352836739124579081263187332067230012400736338750471617813366066581325579955050905600000000000000000000 ? 2044802197953900 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Apr 6 20:40:31 2005 Input: 60!/((19!)*(41!)) 59*55*53*47*43*29*23*49*5*9*4 Output: ? 2044802197953900 ? 2044802197953900 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Thu Apr 7 00:39:41 2005 Input: (x+x^2+x^3+x^4+x^5+x^6)^7 Output: ? x^42 + 7*x^41 + 28*x^40 + 84*x^39 + 210*x^38 + 462*x^37 + 917*x^36 + 1667*x^35 + 2807*x^34 + 4417*x^33 + 6538*x^32 + 9142*x^31 + 12117*x^30 + 15267*x^29 + 18327*x^28 + 20993*x^27 + 22967*x^26 + 24017*x^25 + 24017*x^24 + 22967*x^23 + 20993*x^22 + 18327*x^21 + 15267*x^20 + 12117*x^19 + 9142*x^18 + 6538*x^17 + 4417*x^16 + 2807*x^15 + 1667*x^14 + 917*x^13 + 462*x^12 + 210*x^11 + 84*x^10 + 28*x^9 + 7*x^8 + x^7 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '211.30.' ************** PARI ***************** Host 211.30.207.93 (211.30.207.93) Time: Thu Apr 7 05:55:25 2005 Input: 6a=30 Output: ? 6 ? Errors (if any) and Timing Info: *** Warning: unused characters: a=30. Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '211.30.' ************** PARI ***************** Host 211.30.207.93 (211.30.207.93) Time: Thu Apr 7 05:55:39 2005 Input: 6xa=30 Output: ? 6 ? Errors (if any) and Timing Info: *** Warning: unused characters: xa=30. Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '220.220' ************** PARI ***************** Host 220.220.135.216 (220.220.135.216) Time: Thu Apr 7 12:43:22 2005 Input: factor(1341388) Output: ? [2 2] [335347 1] ? Errors (if any) and Timing Info: Timing: real 0m0.195s user 0m0.004s sys 0m0.010s '220.220' ************** PARI ***************** Host 220.220.135.216 (220.220.135.216) Time: Thu Apr 7 12:43:50 2005 Input: factor(88003028) Output: ? [2 2] [22000757 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '200.204' ************** PARI ***************** Host 200.204.154.117 (200.204.154.117) Time: Thu Apr 7 13:17:00 2005 Input: AlgGrp; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '209.19.' ************** PARI ***************** Host 209.19.49.250 (209.19.49.250) Time: Thu Apr 7 14:36:22 2005 Input: > A := Matrix(2,2,[1,2,3,4]); > A; > SmithForm(A); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: >A:=Matrix(2,2,[1,2, ^-------------------- *** unexpected character: >A; ^--- *** unexpected character: >SmithForm(A); ^-------------- Timing: real 0m0.015s user 0m0.004s sys 0m0.010s '209.19.' ************** PARI ***************** Host 209.19.49.250 (209.19.49.250) Time: Thu Apr 7 14:36:30 2005 Input: A := Matrix(2,2,[1,2,3,4]); A; SmithForm(A); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: A:=Matrix(2,2,[1,2,3,4 ^-------------------- *** expected character: '=' instead of: SmithForm(A); ^- Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '209.19.' ************** PARI ***************** Host 209.19.49.250 (209.19.49.250) Time: Thu Apr 7 14:38:38 2005 Input: A := Matrix(3,3,[11,0,0,0,2,0,0,0,4]); A; SmithForm(A); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: A:=Matrix(3,3,[11,0,0, ^-------------------- *** expected character: '=' instead of: SmithForm(A); ^- Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '209.19.' ************** PARI ***************** Host 209.19.49.250 (209.19.49.250) Time: Thu Apr 7 14:43:22 2005 Input: A := Matrix(2,2,[1,2,3,4]); A; SmithForm(A); Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: A:=Matrix(2,2,[1,2,3,4 ^-------------------- *** expected character: '=' instead of: SmithForm(A); ^- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '158.109' ************** PARI ***************** Host 158.109.66.34 (158.109.66.34) Time: Fri Apr 8 06:05:08 2005 Input: k:=GF(2); l:=GF(3); o:=GF(5); p:=GF(9); [m: m in k]; [m: m in l]; [m: m in o]; [m: m in p]; G25:=ext; P:=PolynomialRing(G25); Output: ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: k:=GF(2); ^------- *** unexpected character: l:=GF(3); ^------- *** unexpected character: o:=GF(5); ^------- *** expected character: '(' instead of: p:=GF(9); ^--------- *** ; or ] expected: [m:mink]; ^------- *** ; or ] expected: [m:minl]; ^------- *** ; or ] expected: [m:mino]; ^------- *** ; or ] expected: [m:minp]; ^------- *** unexpected character: G25:=ext:=PolynomialRing(G25 ^-------------------- Timing: real 0m0.013s user 0m0.005s sys 0m0.006s '158.109' ************** PARI ***************** Host 158.109.66.34 (158.109.66.34) Time: Fri Apr 8 06:32:53 2005 Input: k:=GF(2); l:=GF(3); o:=GF(5); p:=GF(9); [m: m in k]; [m: m in l]; [m: m in o]; [m: m in p]; P:= PolynomialRing(l); pol:=2+2*x+x^2; IsIrreducible(pol); P:= PolynomialRing(k); poli:=1+y+y^4; IsIrreducible(poli); P:= PolynomialRing(o); polin:=3+2*z+z^2; IsIrreducible(polin); P:= PolynomialRing(l); polino:=1+2*w+w^2; IsIrreducible(polino); G9:=ext; G16:=ext; G25:=ext; P:=PolynomialRing(G25); p1:=alpha^2+alpha*x+beta*(x^2); p2:=1+alpha*x; Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: k:=GF(2); ^------- *** unexpected character: l:=GF(3); ^------- *** unexpected character: o:=GF(5); ^------- *** expected character: '(' instead of: p:=GF(9); ^--------- *** ; or ] expected: [m:mink]; ^------- *** ; or ] expected: [m:minl]; ^------- *** ; or ] expected: [m:mino]; ^------- *** ; or ] expected: [m:minp]; ^------- *** unexpected character: P:=PolynomialRing(l); ^-------------------- *** unexpected character: pol:=2+2*x+x^2; ^----------- *** expected character: '=' instead of: IsIrreducible(pol); ^- *** unexpected character: P:=PolynomialRing(k); ^-------------------- *** unexpected character: poli:=1+y+y^4; ^--------- *** expected character: '=' instead of: IsIrreducible(poli); ^- *** unexpected character: P:=PolynomialRing(o); ^-------------------- *** unexpected character: polin:=3+2*z+z^2; ^----------- *** expected character: '=' instead of: IsIrreducible(polin); ^- *** unexpected character: P:=PolynomialRing(l); ^-------------------- *** unexpected character: polino:=1+2*w+w^2; ^----------- *** expected character: '=' instead of: IsIrreducible(polino); ^- *** unexpected character: G9:=ext; ^------------ *** unexpected character: G16:=ext; ^------------- *** unexpected character: G25:=ext; ^--------------- *** unexpected character: P:=PolynomialRing(G25 ^-------------------- *** unexpected character: p1:=alpha^2+alpha*x+bet ^-------------------- *** unexpected character: p2:=1+alpha*x; ^----------- Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '80.229.' ************** PARI ***************** Host 80.229.167.150 (80.229.167.150) Time: Fri Apr 8 17:13:56 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:47:19 2005 Input: prime(123456789012345678901) Output: ? ? Errors (if any) and Timing Info: *** impossible assignment I-->S Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:47:39 2005 Input: isprime(123456789012345678901) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.006s sys 0m0.006s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:47:56 2005 Input: factint(123456789012345678901) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: factint(123456789012 ^-------------------- Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:49:03 2005 Input: factorint(123456789012345678901) Output: ? [11 1] [5471 1] [10000799 1] [205126079 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.007s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:49:34 2005 Input: factorint(1234567890123456789011) Output: ? [19 2] [37 1] [47 1] [1966564491841009 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:49:45 2005 Input: factorint(12345678901234567890111) Output: ? [3 1] [11 1] [1039 1] [87697007 1] [4105827679 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.007s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:49:56 2005 Input: factorint(123456789012345678901111) Output: ? [29 1] [101 1] [214883 1] [196152364176173 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.004s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:50:03 2005 Input: factorint(1234567890123456789011111) Output: ? [7 1] [11 1] [13 1] [37 1] [33333366366699700003 1] ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.008s sys 0m0.005s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:50:15 2005 Input: factorint(12345678901234567890111111) Output: ? [3 1] [223 1] [4099 1] [70571 1] [174829 1] [364897759 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.010s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:50:22 2005 Input: factorint(123456789012345678901111111) Output: ? [11 2] [523 1] [1109 1] [292703 1] [6009927018871 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:50:30 2005 Input: factorint(1234567890123456789011111111) Output: ? [17 1] [37 1] [101 1] [2383 1] [68897 1] [118363719446209 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:50:36 2005 Input: factorint(12345678901234567890111111111) Output: ? [3 2] [11 1] [966431 1] [402601471 1] [320504087789 1] ? Errors (if any) and Timing Info: Timing: real 0m0.072s user 0m0.020s sys 0m0.008s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:50:43 2005 Input: factorint(123456789012345678901111111111) Output: ? [163 1] [191 1] [281 1] [11948184719 1] [1181097519653 1] ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.019s sys 0m0.011s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:50:49 2005 Input: factorint(1234567890123456789011111111111) Output: ? [7 1] [11 1] [13 1] [37 1] [33333366366699700003000003 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.005s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:51:02 2005 Input: factorint(12345678901234567890111111111111) Output: ? [3 1] [101 1] [307 1] [419 1] [991 1] [319629088118814904879 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:51:08 2005 Input: factorint(123456789012345678901111111111111) Output: ? [11 1] [1439 1] [6073961 1] [1284072363835708885619 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.013s sys 0m0.005s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:51:27 2005 Input: factorint(1234567890123456789011111111111111) Output: ? [37 1] [823 1] [9543047 1] [4248409342218184311163 1] ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.039s sys 0m0.015s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:51:34 2005 Input: factorint(12345678901234567890111111111111111) Output: ? [3 1] [11 1] [613 1] [811 1] [23293 1] [32306825202607257079333 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:51:41 2005 Input: factorint(123456789012345678901111111111111111) Output: ? [101 1] [4433131473371 1] [275729346853163655841 1] ? Errors (if any) and Timing Info: Timing: real 0m0.094s user 0m0.082s sys 0m0.014s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:51:51 2005 Input: factorint(1234567890123456789011111111111111111) Output: ? [7 1] [11 1] [13 1] [37 1] [33333366366699700003000003000003 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.008s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:51:58 2005 Input: factorint(12345678901234567890111111111111111111) Output: ? [3 6] [23 1] [1501690022491 1] [490319671789365501563 1] ? Errors (if any) and Timing Info: Timing: real 0m0.092s user 0m0.073s sys 0m0.019s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:52:06 2005 Input: factorint(123456789012345678901111111111111111111) Output: ? [11 1] [83 1] [8388350401661 1] [16120096450833843590627 1] ? Errors (if any) and Timing Info: Timing: real 0m0.116s user 0m0.102s sys 0m0.014s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:52:14 2005 Input: factorint(1234567890123456789011111111111111111111) Output: ? [19 1] [37 1] [67 1] [101 1] [3541 1] [27961 1] [107941 1] [24282780394519101271 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.007s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:52:20 2005 Input: factorint(12345678901234567890111111111111111111111) Output: ? [3 1] [11 1] [5939 1] [8792111891 1] [7164642181922804162785583 1] ? Errors (if any) and Timing Info: Timing: real 0m0.167s user 0m0.149s sys 0m0.018s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:52:26 2005 Input: factorint(123456789012345678901111111111111111111111) Output: ? [433 1] [1780487 1] [160135741013185364052998276087441 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.007s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:52:38 2005 Input: factorint(123456789012345678901111111111111111111111) Output: ? [433 1] [1780487 1] [160135741013185364052998276087441 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.011s sys 0m0.006s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:54:23 2005 Input: factorint(1234567890123456789011) Output: ? [19 2] [37 1] [47 1] [1966564491841009 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '69.70.3' ************** PARI ***************** Host 69.70.3.251 (69.70.3.251) Time: Fri Apr 8 20:56:18 2005 Input: factorint(1234567890123456789011111111111111) Output: ? [37 1] [823 1] [9543047 1] [4248409342218184311163 1] ? Errors (if any) and Timing Info: Timing: real 0m0.056s user 0m0.043s sys 0m0.009s '129.116' ************** PARI ***************** Host 129.116.24.190 (129.116.24.190) Time: Sat Apr 9 05:25:41 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '82.198.' ************** PARI ***************** Host 82.198.63.80 (82.198.63.80) Time: Sat Apr 9 09:23:25 2005 Input: (2+x)^2 Output: ? x^2 + 4*x + 4 ? Errors (if any) and Timing Info: Timing: real 0m0.275s user 0m0.010s sys 0m0.003s '82.198.' ************** PARI ***************** Host 82.198.63.80 (82.198.63.80) Time: Sat Apr 9 09:23:49 2005 Input: (2+x)^2 Output: ? x^2 + 4*x + 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '82.198.' ************** PARI ***************** Host 82.198.63.80 (82.198.63.80) Time: Sat Apr 9 09:27:11 2005 Input: 3+7 Output: ? 10 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '202.39.' ************** PARI ***************** Host 202.39.32.49 (202.39.32.49) Time: Sat Apr 9 11:40:39 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.006s sys 0m0.008s '81.240.' ************** PARI ***************** Host 81.240.14.181 (81.240.14.181) Time: Sat Apr 9 16:40:38 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '219.79.' ************** PARI ***************** Host 219.79.64.254 (219.79.64.254) Time: Sun Apr 10 10:37:15 2005 Input: Factorization(10^100-1) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorization(10^100 ^-------------------- Timing: real 0m0.238s user 0m0.009s sys 0m0.007s '219.79.' ************** PARI ***************** Host 219.79.64.254 (219.79.64.254) Time: Sun Apr 10 10:42:20 2005 Input: Factorization(1111111111111111111111111111111111111111111111111111111111111111111111) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorization(111111 ^-------------------- Timing: real 0m0.021s user 0m0.004s sys 0m0.009s '219.79.' ************** PARI ***************** Host 219.79.64.254 (219.79.64.254) Time: Sun Apr 10 10:42:31 2005 Input: Factorization(1111111111111111111111111111111111111111111111111111111111111111111111) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorization(111111 ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '219.79.' ************** PARI ***************** Host 219.79.64.254 (219.79.64.254) Time: Sun Apr 10 10:42:35 2005 Input: Factorization(111111111111111111111111111111111111111111111111111111111111111111111) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorization(111111 ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '219.79.' ************** PARI ***************** Host 219.79.64.254 (219.79.64.254) Time: Sun Apr 10 10:42:39 2005 Input: Factorization(1111111111111111111111111111111111111111111111111111111111111111111111) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorization(111111 ^-------------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '219.79.' ************** PARI ***************** Host 219.79.64.254 (219.79.64.254) Time: Sun Apr 10 10:42:45 2005 Input: Factorization(11111111111111111111111111111111111111111111111111111111) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorization(111111 ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '219.79.' ************** PARI ***************** Host 219.79.64.254 (219.79.64.254) Time: Sun Apr 10 10:42:49 2005 Input: Factorization(111) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorization(111) ^------------------ Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '219.79.' ************** PARI ***************** Host 219.79.64.254 (219.79.64.254) Time: Sun Apr 10 10:44:47 2005 Input: Factorization(111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorization(111111 ^-------------------- Timing: real 0m0.022s user 0m0.007s sys 0m0.005s '130.123' ************** PARI ***************** Host 130.123.128.117 (130.123.128.117) Time: Sun Apr 10 11:27:22 2005 Input: fib(50) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: fib(50) ^------- Timing: real 0m0.643s user 0m0.008s sys 0m0.008s '130.123' ************** PARI ***************** Host 130.123.128.117 (130.123.128.117) Time: Sun Apr 10 11:27:35 2005 Input: fibonacci(50) Output: ? 12586269025 ? Errors (if any) and Timing Info: Timing: real 0m0.071s user 0m0.006s sys 0m0.012s '151.27.' ************** PARI ***************** Host 151.27.19.67 (151.27.19.67) Time: Sun Apr 10 15:54:13 2005 Input: 2^1000 Output: ? 10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376 ? Errors (if any) and Timing Info: Timing: real 0m0.292s user 0m0.006s sys 0m0.008s '151.27.' ************** PARI ***************** Host 151.27.19.67 (151.27.19.67) Time: Sun Apr 10 15:55:09 2005 Input: 2^1000000 Output: ? 9900656229295898250697923616301903250733624241787567332866396114531709483309486103054614551234648391482431507034583723883510658989416314927422565031572905372314869377232871775494713664238970125842914489614716338412188631103792398056007740136270960553070538667179812336061592179279832732236430322862606574309256916278582042834772001794493190056995140975103125269173943089615493140378429176713780793147953357424131614194925264632270461031051872671543446326415534732828328844476262966391361012119424025100613431716524949459232757177220781095411635556324285623401399844018872126340393003478382714500015263923202290122589106172290370665498223255266570742364678876281944070178196967564313268473039529471786419977305867922878219930648823033450650345967912215239175551092757922030316744363444481760665217392500046261574561285250191078688855985382395910910281904752437827169322142114212392700345639503812353502503119133229035702263721456724737028852183729673865439926655978577772441147113534229818712960636023421248382580720066749580337690655680927014364940044770097986900629915741754905390213872294859512527457258435686930574294331876148804212587070508121098981067309601673311855119053197796894882775023333854740399691742971883475765010217412786166070991380920261381814529687888424435227457227458101653560859482748004650385413813118645127931044092396641676473053009607268165196699855831639249602534508038462262334150604761149537902203721111507607914097574578113395769263576151288262983431551415618254050714509049690835693882437350374813680237901473223489645859363030917593796614865907927235675620625129699427016356478216022433672904344807606952184673828762029275058248015293274931396581899857266679461433306593743364113813692627810553555141318609189614864029747787485088801605497021003450960246787423088192738641626872510869920522778387077213048636102779482608560687963039051922404046465266132189059512323088725564479604746341626862684240276143112253638933142585846098563836632037438775955054200978813776042326316628619102324598113841300603753775993390952276982455476518137898587713078425308571330225253178917068683209419560529835520259023126290003233592710939792988944414652093825497024880577990050489474303866748090608267245501749642844400169343813191709308394603548028963006454622273127795107156202374076438424901060805693079941635557981171624878713897466201262652204378955603898688141184224279952612411255774724283387259399407640486912389154941551570342193966532335975600648916587397746210803262067423480434979262047698622594329836565370079340033961049819673065188275051258918467632999650425329580622773470588731693867109528956563867109447513857323792955119042424439044508858711865043444765898942773529329887549027551330663949351335913390842238721891720761821448281572918436554445910237464143706101581595434557024511357582725139633535893188960025597692385576985841276255385408291268999760677877884215664284885756771798407957836158681048000846324070322554448903671628893605406269440968355872345459470717644718680744770583632389642009521969166278243014024561141637192528456426171652084914747765117608693729555384109074355546509887533273790752687147714623912453461044239297773767990897123738074707[+++] ? Errors (if any) and Timing Info: Timing: real 0m21.691s user 0m19.723s sys 0m0.020s '82.198.' ************** PARI ***************** Host 82.198.63.80 (82.198.63.80) Time: Sun Apr 10 16:39:05 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '82.198.' ************** PARI ***************** Host 82.198.63.80 (82.198.63.80) Time: Sun Apr 10 16:39:35 2005 Input: 2^(1.33) Output: ? 2.5140267490436567043722633786546811127 ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.006s sys 0m0.004s '82.198.' ************** PARI ***************** Host 82.198.63.80 (82.198.63.80) Time: Sun Apr 10 16:39:46 2005 Input: 2^(1.33) Output: ? 2.5140267490436567043722633786546811127 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '130.102' ************** PARI ***************** Host 130.102.2.60 (130.102.2.60) Time: Sun Apr 10 20:27:41 2005 Input: e=ellinit([0,0,0,0,-6]):P=[-3,1]:ellisoncurve(e,P) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.113s user 0m0.011s sys 0m0.007s '130.102' ************** PARI ***************** Host 130.102.128.60 (130.102.128.60) Time: Sun Apr 10 20:28:06 2005 Input: e=ellinit([0,0,0,-6,0]):P=[-3,1]:ellisoncurve(e,P) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '130.102' ************** PARI ***************** Host 130.102.2.60 (130.102.2.60) Time: Sun Apr 10 20:29:57 2005 Input: e=ellinit([0,0,0,-6,0]):P=[-3,3]:ellisoncurve(e,P) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '130.102' ************** PARI ***************** Host 130.102.128.60 (130.102.128.60) Time: Sun Apr 10 20:30:16 2005 Input: e=ellinit([0,0,0,-6,0]):P=[-3,3]:ellisoncurve(e,P) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.008s '130.102' ************** PARI ***************** Host 130.102.2.60 (130.102.2.60) Time: Sun Apr 10 20:30:38 2005 Input: e=ellinit([0,0,0,-6,0]):P=[3,3]:ellisoncurve(e,P) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.010s '130.102' ************** PARI ***************** Host 130.102.128.60 (130.102.128.60) Time: Sun Apr 10 20:31:08 2005 Input: e=ellinit([0,0,0,-6,0]):P=[3,3]:ellpow(e,P,5) Output: ? [2449934787/78198649, -120892771408659/691510653107] ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.008s sys 0m0.002s '158.109' ************** PARI ***************** Host 158.109.66.84 (158.109.66.84) Time: Mon Apr 11 03:37:58 2005 Input: a:=5; Output: ? ? Errors (if any) and Timing Info: *** unexpected character: a:=5; ^--- Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '195.29.' ************** PARI ***************** Host 195.29.121.108 (195.29.121.108) Time: Mon Apr 11 08:07:35 2005 Input: factor(545454) Output: ? [2 1] [3 4] [7 1] [13 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.393s user 0m0.005s sys 0m0.010s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Mon Apr 11 10:38:14 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.331s user 0m0.008s sys 0m0.014s '144.131' ************** PARI ***************** Host 144.131.115.32 (144.131.115.32) Time: Mon Apr 11 22:44:26 2005 Input: lcm(4,6) Output: ? 12 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '144.131' ************** PARI ***************** Host 144.131.115.32 (144.131.115.32) Time: Mon Apr 11 23:30:34 2005 Input: sigma(10*9*8*7*6*5*4*3*2*1) Output: ? 15334088 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.006s sys 0m0.007s '144.131' ************** PARI ***************** Host 144.131.115.32 (144.131.115.32) Time: Mon Apr 11 23:33:32 2005 Input: sigma(factorial(10)) Output: ? ? Errors (if any) and Timing Info: *** not an integer argument in an arithmetic function Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '144.131' ************** PARI ***************** Host 144.131.115.32 (144.131.115.32) Time: Mon Apr 11 23:34:03 2005 Input: x=factorial(10) y=sigma(x) Output: ? 3628800.0000000000000000000000000000000 ? ? Errors (if any) and Timing Info: *** not an integer argument in an arithmetic function Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '144.131' ************** PARI ***************** Host 144.131.115.32 (144.131.115.32) Time: Mon Apr 11 23:34:48 2005 Input: sigma(3628800) Output: ? 15334088 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '217.185' ************** PARI ***************** Host 217.185.234.39 (217.185.234.39) Time: Tue Apr 12 02:23:38 2005 Input: 2^100 Output: ? 1267650600228229401496703205376 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.008s '217.185' ************** PARI ***************** Host 217.185.234.39 (217.185.234.39) Time: Tue Apr 12 02:23:51 2005 Input: 2^10000 Output: ? 19950631168807583848837421626835850838234968318861924548520089498529438830221946631919961684036194597899331129423209124271556491349413781117593785932096323957855730046793794526765246551266059895520550086918193311542508608460618104685509074866089624888090489894838009253941633257850621568309473902556912388065225096643874441046759871626985453222868538161694315775629640762836880760732228535091641476183956381458969463899410840960536267821064621427333394036525565649530603142680234969400335934316651459297773279665775606172582031407994198179607378245683762280037302885487251900834464581454650557929601414833921615734588139257095379769119277800826957735674444123062018757836325502728323789270710373802866393031428133241401624195671690574061419654342324638801248856147305207431992259611796250130992860241708340807605932320161268492288496255841312844061536738951487114256315111089745514203313820202931640957596464756010405845841566072044962867016515061920631004186422275908670900574606417856951911456055068251250406007519842261898059237118054444788072906395242548339221982707404473162376760846613033778706039803413197133493654622700563169937455508241780972810983291314403571877524768509857276937926433221599399876886660808368837838027643282775172273657572744784112294389733810861607423253291974813120197604178281965697475898164531258434135959862784130128185406283476649088690521047580882615823961985770122407044330583075869039319604603404973156583208672105913300903752823415539745394397715257455290510212310947321610753474825740775273986348298498340756937955646638621874569499279016572103701364433135817214311791398222983845847334440270964182851005072927748364550578634501100852987812389473928699540834346158807043959118985815145779177143619698728131459483783202081474982171858011389071228250905826817436220577475921417653715687725614904582904992461028630081535583308130101987675856234343538955409175623400844887526162643568648833519463720377293240094456246923254350400678027273837755376406726898636241037491410966718557050759098100246789880178271925953381282421954028302759408448955014676668389697996886241636313376393903373455801407636741877711055384225739499110186468219696581651485130494222369947714763069155468217682876200362777257723781365331611196811280792669481887201298643660768551639860534602297871557517947385246369446923087894265948217008051120322365496288169035739121368338393591756418733850510970271613915439590991598154654417336311656936031122249937969999226781732358023111862644575299135758175008199839236284615249881088960232244362173771618086357015468484058622329792853875623486556440536962622018963571028812361567512543338303270029097668650568557157505516727518899194129711337690149916181315171544007728650573189557450920330185304847113818315407324053319038462084036421763703911550639789000742853672196280903477974533320468368795868580237952218629120080742819551317948157624448298518461509704888027274721574688131594750409732115080498190455803416826949787141316063210686391511681774304792596709376 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.005s '144.131' ************** PARI ***************** Host 144.131.119.25 (144.131.119.25) Time: Tue Apr 12 04:03:14 2005 Input: chinese(Mod(17,33)),Mod(22,64)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: chinese(Mod(17,33)),Mod(22,64)) ^------------- Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '144.131' ************** PARI ***************** Host 144.131.119.25 (144.131.119.25) Time: Tue Apr 12 04:22:16 2005 Input: chinese(Mod(17,33)),{Mod(22,64)}) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: chinese(Mod(17,33)),{Mod(22,64)}) ^--------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '144.131' ************** PARI ***************** Host 144.131.119.25 (144.131.119.25) Time: Tue Apr 12 04:32:09 2005 Input: chrem(Mod(17,33)),Mod(22,64)) Output: ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,Mod(22,64)). *** unknown function or error in formal parameters: chrem( *** Mod(17,33)),Mod(22,6 ^-------------------- Timing: real 0m0.019s user 0m0.007s sys 0m0.004s '144.131' ************** PARI ***************** Host 144.131.119.25 (144.131.119.25) Time: Tue Apr 12 04:32:28 2005 Input: chrem(Mod(17,33)),{Mod(22,64)}) Output: ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,{Mod(22,64)}). *** unknown function or error in formal parameters: chrem( *** Mod(17,33)),{Mod(22, ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '144.131' ************** PARI ***************** Host 144.131.119.25 (144.131.119.25) Time: Tue Apr 12 04:33:06 2005 Input: chinese(Mod(17,33),Mod(22,64)) Output: ? Mod(1238, 2112) ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.008s sys 0m0.003s '144.131' ************** PARI ***************** Host 144.131.119.25 (144.131.119.25) Time: Tue Apr 12 04:35:00 2005 Input: chinese(Mod(43,101),Mod(25,137)) Output: ? Mod(7012, 13837) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '144.131' ************** PARI ***************** Host 144.131.119.25 (144.131.119.25) Time: Tue Apr 12 04:37:53 2005 Input: x=chinese(Mod(17,33),Mod(22,64)) y=chinese(Mod(43,101),Mod(25,137)) chinese(x,y) Output: ? Mod(1238, 2112) ? Mod(7012, 13837) ? Mod(22063190, 29223744) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 12 19:16:46 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.004s sys 0m0.010s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 12 19:16:51 2005 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x*1)/2);i=i** ); i } collatzlength(360) Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: ...(0,2),x/2,(3*x*1)/2);i=i**);i ^---- *** unknown function or error in formal parameters: collatzlength(360) ^------------------ Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 12 19:17:21 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 12 19:18:36 2005 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(360) Output: ? ? 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 12 19:19:05 2005 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(300) Output: ? ? 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 12 19:19:41 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 12 19:19:53 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(360,16) Output: ? ? [360, 180, 90, 45, 68, 34, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 12 19:20:05 2005 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(360) Output: ? ? 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 12 19:20:15 2005 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: ? ? 75 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 12 19:21:51 2005 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(360) Output: ? ? 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 12 19:22:03 2005 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(360) Output: ? ? 15 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 12 19:22:50 2005 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: ? ? 75 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 12 21:46:45 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '68.90.1' ************** PARI ***************** Host 68.90.158.113 (68.90.158.113) Time: Tue Apr 12 21:46:53 2005 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: ? ? 75 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '220.220' ************** PARI ***************** Host 220.220.135.216 (220.220.135.216) Time: Wed Apr 13 12:21:45 2005 Input: factor(88025824) Output: ? [2 5] [211 1] [13037 1] ? Errors (if any) and Timing Info: Timing: real 0m0.300s user 0m0.004s sys 0m0.009s '62.245.' ************** PARI ***************** Host 62.245.36.123 (62.245.36.123) Time: Wed Apr 13 18:39:23 2005 Input: contfrac(sqrt(3)) Output: ? [1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3] ? Errors (if any) and Timing Info: Timing: real 0m0.102s user 0m0.006s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Apr 13 23:36:46 2005 Input: taylor((x+(m-1)*x^m-m*x^(m-1))/((1-x^m)*(1-x)^2), x) Output: ? ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m0.037s user 0m0.006s sys 0m0.005s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Apr 13 23:45:18 2005 Input: taylor((x+2*x^3-3*x^(2))/((1-x^3)*(1-x)^2), x) Output: ? x - x^2 - x^3 - 2*x^5 - 2*x^6 - x^7 - 3*x^8 - 3*x^9 - 2*x^10 - 4*x^11 - 4*x^12 - 3*x^13 - 5*x^14 - 5*x^15 + O(x^16) ? Errors (if any) and Timing Info: Timing: real 0m0.056s user 0m0.008s sys 0m0.002s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Apr 13 23:46:31 2005 Input: taylor((x+2*x^4-3*x^3)/((1-x^3)*(1-x)^2), x) Output: ? x + 2*x^2 + x^4 + 2*x^5 + x^7 + 2*x^8 + x^10 + 2*x^11 + x^13 + 2*x^14 + O(x^16) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.129.113 (140.247.129.113) Time: Wed Apr 13 23:46:58 2005 Input: taylor((x+3*x^5-4*x^4)/((1-x^4)*(1-x)^2), x) Output: ? x + 2*x^2 + 3*x^3 + x^5 + 2*x^6 + 3*x^7 + x^9 + 2*x^10 + 3*x^11 + x^13 + 2*x^14 + 3*x^15 + O(x^16) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '141.153' ************** PARI ***************** Host 141.153.155.98 (141.153.155.98) Time: Thu Apr 14 00:35:24 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.003s '141.153' ************** PARI ***************** Host 141.153.155.98 (141.153.155.98) Time: Thu Apr 14 00:35:40 2005 Input: james one Output: ? jamesone ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.004s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 14 03:44:56 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=1122043764817953477184538180412899434182334183390016562924074645313304038372684953355862480386165030099850068997062362153704446614306816; ((b*b)-1)/a Output: ? ? ? 1258982210166846893303102575942678332216856134585250543515543931408533022925447565846292014733448904691118237143023157809770445040913431714059498341333026066307037158552967934045972352967093387790348582960067080099348837931124975895651906879346816329078031980736184057855/795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 14 03:45:28 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=241730963211712523635670742244882860678347705246524958475304110630289675521357845571073795086720558180684351393591829733416401113186304; ((b*b)-1)/a Output: ? ? ? 58433858575262313480044092011745074147914609169666533090488254353713332654689401364824302667813350256970551389286204622901119963930736827592400950655036537305933404079715073182205823838673193333855625074667107777507219866254210357400764030292240038216457154947413180415/795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 14 03:46:02 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=241730963211712523635670742244882860678347705246524958475304110630289675521357845571073795086720558180684351393591829733416401113186304; gcd(a,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 14 03:46:16 2005 Input: a=795535258017305167145121871550373005335397768371315887482970506034490852226395158613855712286911706841452612879325276931891140828826431; b=1122043764817953477184538180412899434182334183390016562924074645313304038372684953355862480386165030099850068997062362153704446614306816; gcd(a,b) Output: ? ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 14 04:17:37 2005 Input: a=2535301200456458802993406410751; b=3575855218532327091154132498212; ((b*b)-1)/a Output: ? ? ? 12786740543904876737455904803966131830259270149589072183196943/2535301200456458802993406410751 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 14 04:18:05 2005 Input: a=2535301200456458802993406410751; b=3575855218532327091154132498212; ((b*b)-1)/(a*1.0) Output: ? ? ? 5043479860145506954981338678043.6890607 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 14 04:42:24 2005 Input: gcd(7864575,726140) Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 14 04:42:31 2005 Input: gcd(7864575,726142) Output: ? 19 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '205.175' ************** PARI ***************** Host 205.175.225.22 (205.175.225.22) Time: Thu Apr 14 15:36:12 2005 Input: x^2 + 1 Output: ? x^2 + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.101s user 0m0.008s sys 0m0.007s '205.175' ************** PARI ***************** Host 205.175.225.22 (205.175.225.22) Time: Thu Apr 14 15:37:38 2005 Input: ?X^2 Output: ? ? Errors (if any) and Timing Info: *** X^2: unknown identifier. Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '205.175' ************** PARI ***************** Host 205.175.225.22 (205.175.225.22) Time: Thu Apr 14 15:38:54 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '205.175' ************** PARI ***************** Host 205.175.225.22 (205.175.225.22) Time: Thu Apr 14 15:39:07 2005 Input: x^2 + 1 Output: ? x^2 + 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '205.175' ************** PARI ***************** Host 205.175.225.22 (205.175.225.22) Time: Thu Apr 14 15:43:13 2005 Input: ? x^2 + 1 Output: ? ? ? Errors (if any) and Timing Info: *** x^2+1: user defined variable. Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '205.175' ************** PARI ***************** Host 205.175.225.22 (205.175.225.22) Time: Thu Apr 14 15:49:30 2005 Input: factormod(x^3+x^2+x^1+1,2) Output: ? [Mod(1, 2)*x + Mod(1, 2) 3] ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.008s sys 0m0.006s '205.175' ************** PARI ***************** Host 205.175.225.22 (205.175.225.22) Time: Thu Apr 14 15:49:47 2005 Input: ?factormod(x^3+x^2+x^1+1,2) Output: ? factormod(x,p,{flag=0}): factorization mod p of the polynomial x using Berlekamp. flag is optional, and can be 0: default or 1: simple factormod, same except that only the degrees of the irreducible factors are given. ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.008s sys 0m0.003s '205.175' ************** PARI ***************** Host 205.175.225.22 (205.175.225.22) Time: Thu Apr 14 15:50:15 2005 Input: factormod(x^3+x^2+x^1+1,2) Output: ? [Mod(1, 2)*x + Mod(1, 2) 3] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '205.175' ************** PARI ***************** Host 205.175.225.22 (205.175.225.22) Time: Thu Apr 14 15:50:15 2005 Input: factormod(x^3+x^2+x^1+1,2) Output: ? [Mod(1, 2)*x + Mod(1, 2) 3] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.001s '205.175' ************** PARI ***************** Host 205.175.225.22 (205.175.225.22) Time: Thu Apr 14 15:50:37 2005 Input: factormod(x^8+1,2) Output: ? [Mod(1, 2)*x + Mod(1, 2) 8] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '205.175' ************** PARI ***************** Host 205.175.225.22 (205.175.225.22) Time: Thu Apr 14 15:51:22 2005 Input: factormod(x^16+x^12+x^5+1,2) Output: ? [Mod(1, 2)*x + Mod(1, 2) 1] [Mod(1, 2)*x^15 + Mod(1, 2)*x^14 + Mod(1, 2)*x^13 + Mod(1, 2)*x^12 + Mod(1, 2)*x^4 + Mod(1, 2)*x^3 + Mod(1, 2)*x^2 + Mod(1, 2)*x + Mod(1, 2) 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.062s user 0m0.004s sys 0m0.008s '205.175' ************** PARI ***************** Host 205.175.225.22 (205.175.225.22) Time: Thu Apr 14 15:53:14 2005 Input: factormod(x^32+x^26+x^23+x^22+x^16+x^12+x^11+x^10+x^8+x^7+x^5+x^4+x^2+x+1,2) Output: ? [Mod(1, 2)*x^32 + Mod(1, 2)*x^26 + Mod(1, 2)*x^23 + Mod(1, 2)*x^22 + Mod(1, 2)*x^16 + Mod(1, 2)*x^12 + Mod(1, 2)*x^11 + Mod(1, 2)*x^10 + Mod(1, 2)*x^8 + Mod(1, 2)*x^7 + Mod(1, 2)*x^5 + Mod(1, 2)*x^4 + Mod(1, 2)*x^2 + Mod(1, 2)*x + Mod(1, 2) 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '205.175' ************** PARI ***************** Host 205.175.225.22 (205.175.225.22) Time: Thu Apr 14 15:55:56 2005 Input: factormod(x^16+x^10+x^7+x^6+1,2) Output: ? [Mod(1, 2)*x^16 + Mod(1, 2)*x^10 + Mod(1, 2)*x^7 + Mod(1, 2)*x^6 + Mod(1, 2) 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.002s '205.175' ************** PARI ***************** Host 205.175.225.22 (205.175.225.22) Time: Thu Apr 14 15:56:40 2005 Input: factormod(x^16+x^12+x^5+1,2) Output: ? [Mod(1, 2)*x + Mod(1, 2) 1] [Mod(1, 2)*x^15 + Mod(1, 2)*x^14 + Mod(1, 2)*x^13 + Mod(1, 2)*x^12 + Mod(1, 2)*x^4 + Mod(1, 2)*x^3 + Mod(1, 2)*x^2 + Mod(1, 2)*x + Mod(1, 2) 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '205.175' ************** PARI ***************** Host 205.175.225.22 (205.175.225.22) Time: Thu Apr 14 16:17:20 2005 Input: factormod(x^16+x^12+x^11+x^10+x^8+x^7+x^5+x^4+x^2+x+1,2) Output: ? [Mod(1, 2)*x^4 + Mod(1, 2)*x^3 + Mod(1, 2)*x^2 + Mod(1, 2)*x + Mod(1, 2) 1] [Mod(1, 2)*x^12 + Mod(1, 2)*x^11 + Mod(1, 2)*x^8 + Mod(1, 2)*x^7 + Mod(1, 2)*x^6 + Mod(1, 2)*x^5 + Mod(1, 2)*x^4 + Mod(1, 2)*x^3 + Mod(1, 2) 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '24.35.9' ************** PARI ***************** Host 24.35.92.29 (24.35.92.29) Time: Fri Apr 15 00:10:27 2005 Input: RSAModulus(120); RSAModulus(200); Output: ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: RSAModulus(120); ^---------------- *** unknown function or error in formal parameters: RSAModulus(200); ^---------------- Timing: real 0m0.020s user 0m0.007s sys 0m0.005s '220.220' ************** PARI ***************** Host 220.220.131.174 (220.220.131.174) Time: Sat Apr 16 13:14:54 2005 Input: factor(88030196) Output: ? [2 2] [29 1] [233 1] [3257 1] ? Errors (if any) and Timing Info: Timing: real 0m0.366s user 0m0.005s sys 0m0.011s '220.220' ************** PARI ***************** Host 220.220.131.174 (220.220.131.174) Time: Sat Apr 16 13:15:05 2005 Input: factor(88039196) Output: ? [2 2] [7 1] [3144257 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '62.233.' ************** PARI ***************** Host 62.233.177.118 (62.233.177.118) Time: Sun Apr 17 18:53:53 2005 Input: nextprime(2^102) Output: ? 5070602400912917605986812821771 ? Errors (if any) and Timing Info: Timing: real 0m0.330s user 0m0.010s sys 0m0.010s '62.233.' ************** PARI ***************** Host 62.233.177.118 (62.233.177.118) Time: Sun Apr 17 18:54:04 2005 Input: nextprime(2^102) Output: ? 5070602400912917605986812821771 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '62.233.' ************** PARI ***************** Host 62.233.177.118 (62.233.177.118) Time: Sun Apr 17 18:54:06 2005 Input: nextprime(2^102) Output: ? 5070602400912917605986812821771 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.011s sys 0m0.003s '62.233.' ************** PARI ***************** Host 62.233.177.118 (62.233.177.118) Time: Sun Apr 17 18:54:31 2005 Input: nextprime(2^1002) Output: ? 42860344287450692837937001962400072422456192468221344297750015534814042044997444899727935152627834325103786916702125873007485811427692561743938310298794299215738271099296923941684298420249484567511816728612185899934327765069595070236662175784308251658284785910746168670641719326610497547348822672277831 ? Errors (if any) and Timing Info: Timing: real 0m0.520s user 0m0.513s sys 0m0.008s '24.163.' ************** PARI ***************** Host 24.163.92.132 (24.163.92.132) Time: Mon Apr 18 16:03:15 2005 Input: isprime(5303997074299093151210613111444835358140775949681884238013028415392793884725585478094898416299177103720858422424509705833601542370673273513266455560864372415676692519890385877885071); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.538s user 0m0.025s sys 0m0.011s '24.163.' ************** PARI ***************** Host 24.163.92.132 (24.163.92.132) Time: Mon Apr 18 16:03:44 2005 Input: print(isprime(5303997074299093151210613111444835358140775949681884238013028415392793884725585478094898416299177103720858422424509705833601542370673273513266455560864372415676692519890385877885071)); Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.024s sys 0m0.007s '24.163.' ************** PARI ***************** Host 24.163.92.132 (24.163.92.132) Time: Mon Apr 18 16:09:51 2005 Input: print(isprime(23827457888312558623395242584465016269539774388819751599037460180779090564852996185385763378828548235084665534418717377832050866667966670928951440791360573082750500314083490480680851225326219210714504711947227590565936878773431009720255437687352338946621597288264434171899961960869989950202536935256239303101488619588384133499392240418232965651883904919740481044874698701037331746614654006810482757538099861107531353471874878151045626651289101736015657506398213019480995234415706884129264938887984711850207959128233711069010868140299184822364971161629512252309923508732241783341056790287408894145588653070943959625501323070543802153890520134006013323373415409717896304419013238681486493416627529866405441982798611976696490895844465879291922584604456493274102120507873939022262377601448564458765466882966878136341590379804399543269382185969728001996899268060896295682136505405773302412544650806906440004079924323483756050465963518816616784227135307346697137086462932956570286258938721318356229993725049457177202422165757072051197530761819689788062705619756149916335872025180106793945720944007720436788471047426661560949467980373700750567882884062124012838875581313083353673688412452095762493747230336013652563655985014059149693188656251545723767892361296058813220351458678921836595167091308955578293762797454540045865559067010415254854665357349860550620803012128009964435507121733368109022771596438804242434958071995142930512724895578274912919787580839054458778625931523709249083600027086309713535531174634097276116007304135131655647508543519920549375455387934349425059514912074307713020280777834002991460168511993737343033814519571507107478805327470495008401583269046337221425483734913133151486051651336671241260098446260598170022982459526392054084940208002692993673899055035189815135518456573819173204880540100152552563514155038388625128144638196296554571966753234854105990482607493810943260119889016787731762485600818432705923338371438687926305636332799883022620834864838554758997594639502202388775094480970321952090084577632487508290235429836220404379893524218777079252881721385628105871898622896510723219810638237467711131733167017136302053735599835059305261911287967397823860308796823322006734247647324912162518781010803973714133350765283683773908107372254337129762088677651805067472107892344026191435660893796517697208829616198682939941135538279743471189953836584368024531233064639255294464084712903190234091276623344934238262905489615220503434604508479192715660411767832389405770626158498635567758927653214038207791619890157643776927313945933737068544038887738886336108991027456848016752154160613112653324683512032958272011318925197027794434347480511527213659332480998011740251495544327923139446373066070817197536468093118565404471508579831819087948123370203670366233789835467561792332622873589439095922087599179295533234154847331253106247987315754430176505226325002157537592961729426974805637044469477680194726745003268861673931686751785587630035199340411170502860286345566122710915475436206694602724345166263922310526146239579837521444384684763170279565265747247190533144293086691176701357464366854879)); Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13323 Killed /usr/bin/gp -q -emacs Timing: real 0m22.173s user 0m20.980s sys 0m0.020s '24.163.' ************** PARI ***************** Host 24.163.92.132 (24.163.92.132) Time: Mon Apr 18 16:10:23 2005 Input: print(isprime(23827457888312558623395242584465016269539774388819751599037460180779090564852996185385763378828548235084665534418717377832050866667966670928951440791360573082750500314083490480680851225326219210714504711947227590565936878773431009720255437687352338946621597288264434171899961960869989950202536935256239303101488619588384133499392240418232965651883904919740481044874698701037331746614654006810482757538099861107531353471874878151045626651289101736015657506398213019480995234415706884129264938887984711850207959128233711069010868140299184822364971161629512252309923508732241783341056790287408894145588653070943959625501323070543802153890520134006013323373415409717896304419013238681486493416627529866405441982798611976696490895844465879291922584604456493274102120507873939022262377601448564458765466882966878136341590379804399543269382185969728001996899268060896295682136505405773302412544650806906440004079924323483756050465963518816616784227135307346697137086462932956570286258938721318356229993725049457177202422165757072051197530761819689788062705619756149916335872025180106793945720944007720436788471047426661560949467980373700750567882884062124012838875581313083353673688412452095762493747230336013652563655985014059149693188656251545723767892361296058813220351458678921836595167091308955578293762797454540045865559067010415254854665357349860550620803012128009964435507121733368109022771596438804242434958071995142930512724895578274912919787580839054458778625931523709249083600027086309713535531174634097276116007304135131655647508543519920549375455387934349425059514912074307713020280777834002991460168511993737343033814519571507107478805327470495008401583269046337221425483734913133151486051651336671241260098446260598170022982459526392054084940208002692993673899055035189815135518456573819173204880540100152552563514155038388625128144638196296554571966753234854105990482607493810943260119889016787731762485600818432705923338371438687926305636332799883022620834864838554758997594639502202388775094480970321952090084577632487508290235429836220404379893524218777079252881721385628105871898622896510723219810638237467711131733167017136302053735599835059305261911287967397823860308796823322006734247647324912162518781010803973714133350765283683773908107372254337129762088677651805067472107892344026191435660893796517697208829616198682939941135538279743471189953836584368024531233064639255294464084712903190234091276623344934238262905489615220503434604508479192715660411767832389405770626158498635567758927653214038207791619890157643776927313945933737068544038887738886336108991027456848016752154160613112653324683512032958272011318925197027794434347480511527213659332480998011740251495544327923139446373066070817197536468093118565404471508579831819087948123370203670366233789835467561792332622873589439095922087599179295533234154847331253106247987315754430176505226325002157537592961729426974805637044469477680194726745003268861673931686751785587630035199340411170502860286345566122710915475436206694602724345166263922310526146239579837521444384684763170279565265747247190533144293086691176701357464366854879)); Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13347 Killed /usr/bin/gp -q -emacs Timing: real 0m21.585s user 0m20.979s sys 0m0.022s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Mon Apr 18 16:43:37 2005 Input: 1-1234567^2 Output: ? -1524155677488 ? Errors (if any) and Timing Info: Timing: real 0m0.435s user 0m0.011s sys 0m0.012s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Mon Apr 18 16:44:36 2005 Input: 1+1234567^2 Output: ? 1524155677490 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Mon Apr 18 16:45:07 2005 Input: 2*1234567 Output: ? 2469134 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Mon Apr 18 16:45:58 2005 Input: 2469134^2+1524155677488^2 Output: ? 2323050529225000892700100 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.002s sys 0m0.010s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Mon Apr 18 16:46:33 2005 Input: 1524155677488^2 Output: ? 2323050529218904269990144 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.005s sys 0m0.009s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Mon Apr 18 16:46:47 2005 Input: 1524155677490^2 Output: ? 2323050529225000892700100 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.171.165 (168.122.171.165) Time: Mon Apr 18 16:47:43 2005 Input: 2469134^2+1524155677488^2 Output: ? 2323050529225000892700100 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.87.79 (128.197.87.79) Time: Mon Apr 18 16:56:10 2005 Input: 13^3 Output: ? 2197 ? Errors (if any) and Timing Info: Timing: real 0m0.356s user 0m0.007s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.87.79 (128.197.87.79) Time: Mon Apr 18 16:56:41 2005 Input: 2197+17 Output: ? 2214 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.87.79 (128.197.87.79) Time: Mon Apr 18 16:56:54 2005 Input: 2214^(1/2) Output: ? 47.053161424074365802553969425791015729 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.87.79 (128.197.87.79) Time: Mon Apr 18 16:57:17 2005 Input: 13^3 + 17 Output: ? 2214 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.87.79 (128.197.87.79) Time: Mon Apr 18 16:57:30 2005 Input: 2214^0.5 Output: ? 47.053161424074365802553969425791015729 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.007s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.87.79 (128.197.87.79) Time: Mon Apr 18 16:59:30 2005 Input: 13^3 + 13 - 1 Output: ? 2209 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.87.79 (128.197.87.79) Time: Mon Apr 18 16:59:40 2005 Input: 2209^0.5 Output: ? 46.999999999999999999999999999999999999 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.87.79 (128.197.87.79) Time: Mon Apr 18 16:59:50 2005 Input: 47^2 Output: ? 2209 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.87.79 (128.197.87.79) Time: Mon Apr 18 17:16:17 2005 Input: (23/6)^2 Output: ? 529/36 ? Errors (if any) and Timing Info: Timing: real 0m0.420s user 0m0.009s sys 0m0.016s '128.197' ************** PARI ***************** Host 128.197.87.79 (128.197.87.79) Time: Mon Apr 18 17:16:40 2005 Input: 23*17 Output: ? 391 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.87.79 (128.197.87.79) Time: Mon Apr 18 17:16:57 2005 Input: 391*2 Output: ? 782 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.87.79 (128.197.87.79) Time: Mon Apr 18 17:17:31 2005 Input: (17/6)^2 Output: ? 289/36 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.002s sys 0m0.012s '128.197' ************** PARI ***************** Host 128.197.87.79 (128.197.87.79) Time: Mon Apr 18 17:20:26 2005 Input: 325/13 Output: ? 25 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.87.79 (128.197.87.79) Time: Mon Apr 18 17:22:02 2005 Input: (23/6)*(25/36)-(17/6) Output: ? -37/216 ? Errors (if any) and Timing Info: Timing: real 0m0.052s user 0m0.007s sys 0m0.006s '81.178.' ************** PARI ***************** Host 81.178.117.143 (81.178.117.143) Time: Mon Apr 18 17:23:21 2005 Input: 1 - ( 1 / 2.8 ) Output: ? 0.64285714285714285714285714285714285714 ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.006s sys 0m0.011s '204.156' ************** PARI ***************** Host 204.156.147.62 (204.156.147.62) Time: Mon Apr 18 18:45:28 2005 Input: 2 ^ 1000 Output: ? 10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376 ? Errors (if any) and Timing Info: Timing: real 0m0.373s user 0m0.005s sys 0m0.005s '220.220' ************** PARI ***************** Host 220.220.131.174 (220.220.131.174) Time: Mon Apr 18 18:57:43 2005 Input: factor(88508126) Output: ? [2 1] [7 1] [6322009 1] ? Errors (if any) and Timing Info: Timing: real 0m0.177s user 0m0.008s sys 0m0.008s '18.98.3' ************** PARI ***************** Host 18.98.3.54 (18.98.3.54) Time: Tue Apr 19 02:40:49 2005 Input: e = ellinit([0,-1,1,0,0]) ellglobalred(e) Output: ? [0, -1, 1, 0, 0, -4, 0, 1, -1, 16, -152, -11, -4096/11, [-0.41964337760708056627592628232664330021, 0.70982168880354028313796314116332165010 - 0.30314536460359968462967109851401150147*I, 0.70982168880354028313796314116332165010 + 0.30314536460359968462967109851401150147*I]~, 6.3460465213977671084439730837727365262, -3.1730232606988835542219865418863682631 + 1.4588166169384952293308896129036752571*I, -0.89563194573282844004395254162148111030 - 3.247711662339099984 E-39*I, 0.44781597286641422002197627081074055514 - 0.70093331394394796216199800040425902762*I, 9.2577181172797965885400335591262444436] ? [11, [1, 0, 0, 0], 1] ? Errors (if any) and Timing Info: Timing: real 0m0.429s user 0m0.006s sys 0m0.011s '18.98.3' ************** PARI ***************** Host 18.98.3.54 (18.98.3.54) Time: Tue Apr 19 02:41:26 2005 Input: e = ellinit([0,-1,1,0,0]) elllseries(e, 1, -11 ,1.1) Output: ? [0, -1, 1, 0, 0, -4, 0, 1, -1, 16, -152, -11, -4096/11, [-0.41964337760708056627592628232664330021, 0.70982168880354028313796314116332165010 - 0.30314536460359968462967109851401150147*I, 0.70982168880354028313796314116332165010 + 0.30314536460359968462967109851401150147*I]~, 6.3460465213977671084439730837727365262, -3.1730232606988835542219865418863682631 + 1.4588166169384952293308896129036752571*I, -0.89563194573282844004395254162148111030 - 3.247711662339099984 E-39*I, 0.44781597286641422002197627081074055514 - 0.70093331394394796216199800040425902762*I, 9.2577181172797965885400335591262444436] ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: elllseries(e,1,-11,1.1) ^----- Timing: real 0m0.014s user 0m0.006s sys 0m0.006s '18.98.3' ************** PARI ***************** Host 18.98.3.54 (18.98.3.54) Time: Tue Apr 19 02:41:41 2005 Input: e = ellinit([0,-1,1,0,0]) elllseries(e, 1, -11) Output: ? [0, -1, 1, 0, 0, -4, 0, 1, -1, 16, -152, -11, -4096/11, [-0.41964337760708056627592628232664330021, 0.70982168880354028313796314116332165010 - 0.30314536460359968462967109851401150147*I, 0.70982168880354028313796314116332165010 + 0.30314536460359968462967109851401150147*I]~, 6.3460465213977671084439730837727365262, -3.1730232606988835542219865418863682631 + 1.4588166169384952293308896129036752571*I, -0.89563194573282844004395254162148111030 - 3.247711662339099984 E-39*I, 0.44781597286641422002197627081074055514 - 0.70093331394394796216199800040425902762*I, 9.2577181172797965885400335591262444436] ? ? Errors (if any) and Timing Info: *** cut-off point must be positive in lseriesell. Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '18.98.3' ************** PARI ***************** Host 18.98.3.54 (18.98.3.54) Time: Tue Apr 19 02:41:51 2005 Input: e = ellinit([0,-1,1,0,0]) elllseries(e, 1, 11) Output: ? [0, -1, 1, 0, 0, -4, 0, 1, -1, 16, -152, -11, -4096/11, [-0.41964337760708056627592628232664330021, 0.70982168880354028313796314116332165010 - 0.30314536460359968462967109851401150147*I, 0.70982168880354028313796314116332165010 + 0.30314536460359968462967109851401150147*I]~, 6.3460465213977671084439730837727365262, -3.1730232606988835542219865418863682631 + 1.4588166169384952293308896129036752571*I, -0.89563194573282844004395254162148111030 - 3.247711662339099984 E-39*I, 0.44781597286641422002197627081074055514 - 0.70093331394394796216199800040425902762*I, 9.2577181172797965885400335591262444436] ? 0.25384186085591068433775892335090946103 ? Errors (if any) and Timing Info: Timing: real 0m0.185s user 0m0.179s sys 0m0.008s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Tue Apr 19 09:54:34 2005 Input: Discriminant(x^3-x-1); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Discriminant(x^3-x-1); ^-------- Timing: real 0m0.176s user 0m0.007s sys 0m0.008s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Tue Apr 19 09:54:42 2005 Input: Discriminant(x^3-x-1) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Discriminant(x^3-x-1) ^------- Timing: real 0m0.014s user 0m0.008s sys 0m0.003s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Tue Apr 19 09:55:57 2005 Input: discriminant(x^3-x-1) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: discriminant(x^3-x-1) ^------- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Tue Apr 19 09:56:29 2005 Input: discriminant(x^3-x-1,x) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: discriminant(x^3-x-1,x) ^--------- Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Tue Apr 19 09:56:44 2005 Input: Discriminant(x^3-x-1,x); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Discriminant(x^3-x-1,x); ^---------- Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Tue Apr 19 09:58:04 2005 Input: disc(x^3-x-1,x); Output: ? ? Errors (if any) and Timing Info: *** obsolete function: disc(x^3-x-1,x); ^---------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: disc(x) ===> poldisc(x) poldisc(x,{v}): discriminant of the polynomial x, with respect to main variable if v is omitted, with respect to v otherwise. Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Tue Apr 19 09:58:11 2005 Input: disc(x^3-x-1); Output: ? ? Errors (if any) and Timing Info: *** obsolete function: disc(x^3-x-1); ^-------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: disc(x) ===> poldisc(x) poldisc(x,{v}): discriminant of the polynomial x, with respect to main variable if v is omitted, with respect to v otherwise. Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Tue Apr 19 09:58:20 2005 Input: poldisc(x^3-x-1); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.077s user 0m0.007s sys 0m0.005s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Tue Apr 19 09:58:23 2005 Input: poldisc(x^3-x-1); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Tue Apr 19 09:58:31 2005 Input: poldisc(x^3-x-1) Output: ? -23 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Tue Apr 19 10:13:55 2005 Input: poldisc(x^3-x+1) Output: ? -23 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Tue Apr 19 10:14:00 2005 Input: poldisc(x^3+x+1) Output: ? -31 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Tue Apr 19 10:14:05 2005 Input: poldisc(x^3+x+2) Output: ? -112 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Tue Apr 19 10:14:12 2005 Input: poldisc(x^3+x+3) Output: ? -247 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Tue Apr 19 10:14:25 2005 Input: factorization(poldisc(x^3+x+3)) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: factorization( *** poldisc(x^3+x+3)) ^----------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Tue Apr 19 10:14:39 2005 Input: factor(poldisc(x^3+x+3)) Output: ? [-1 1] [13 1] [19 1] ? Errors (if any) and Timing Info: Timing: real 0m0.045s user 0m0.007s sys 0m0.006s '82.90.1' ************** PARI ***************** Host 82.90.167.146 (82.90.167.146) Time: Tue Apr 19 11:29:06 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 01:57:24 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,223); Output: ? ? ? [2453, 670, 745, 670] ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.008s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 01:57:36 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(2053); Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 01:58:06 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(2047); Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.015s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 01:59:08 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(23*89); Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 01:59:34 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); print([p,x0,x1])} testk(23*89); Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:01:30 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); print([p,x0,x1])} testk(11*239); Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:01:34 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); print([p,x0,x1])} testk(11*239); Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:01:49 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; //x1 = round(abs(polroots(new)[1])); print([p,x0,x1])} testk(11*239); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: ...d)[1]));new=x0+(c-d)/2-x;//x1=round(abs(polro ^-------------------- *** unknown function or error in formal parameters: testk(11*239); ^-------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:02:05 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; /*x1 = round(abs(polroots(new)[1]));*/ print([p,x0,x1])} testk(11*239); Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.015s user 0m0.005s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:03:05 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; /*x1 = round(abs(polroots(new)[1]));*/ print([p,x0,x1])} testk(11*223); Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:06:40 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; /*x1 = round(abs(polroots(new)[1]));*/ print([p,x0,x1])} testk(11*223); Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:06:52 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); print([p,x0,x1])} testk(11*223); Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:07:07 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); print([p,x0,x1])} testk(11*223); Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:07:13 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); print([p,x0,x1])} testk(11*223); Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:09:28 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(23,89); Output: ? ? ? [2047, 622, 622, 548] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:12:10 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(109,89); Output: ? ? ? [9701, 980, 2948, 2588] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:12:56 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(73,89); Output: ? ? ? [6497, 802, 1974, 1744] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:16:27 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(3,1409); Output: ? ? ? [4227, 1408, 1284, 1145] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:18:45 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,223); Output: ? ? ? [2453, 670, 745, 670] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:19:26 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,239); Output: ? ? ? [2629, 716, 799, 699] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:20:34 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(23,191); Output: ? ? ? [4393, 574, 1335, 1171] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.005s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:21:01 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(23,181); Output: ? ? ? [4163, 1266, 1265, 1113] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:21:49 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0+(c-d)/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(23,89); Output: ? ? ? [2047, 622, 622, 548] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:25:34 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(23,89); Output: ? ? ? [2047, 622, 622, 548] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:30:56 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(23,89); Output: ? ? ? [2047, 622, 622, 548] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:31:12 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(223,11); Output: ? ? ? [2453, 670, 745, 670] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:31:36 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(19,521); Output: ? ? ? [9899, 2604, 3008, 2646] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:32:27 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(23,271); Output: ? ? ? [6233, 1356, 1894, 1666] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:33:03 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(23,251); Output: ? ? ? [5773, 252, 1754, 1551] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:33:07 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(23,251); Output: ? ? ? [5773, 252, 1754, 1551] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:33:52 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(23,97); Output: ? ? ? [2231, 484, 678, 594] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:34:24 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(23,97); Output: ? ? ? [2231, 484, 678, 594.21103908299648681968101816506895824] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:34:55 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(23,97); Output: ? ? ? [2231, 484, 677.91018845270822850664075481659396964, 597] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:35:09 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(23,97); Output: ? ? ? [2231, 484, 678, 594] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:35:49 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.088596-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(23,97); Output: ? ? ? [2231, 484, 678, 483] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:37:24 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(19,521); Output: ? ? ? [9899, 2604, 3008, 2646] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:37:43 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.007896-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(19,521); Output: ? ? ? [9899, 2604, 3008, 2601] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:39:17 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(29,79); Output: ? ? ? [2291, 552, 696, 618] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:41:33 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,19); Output: ? ? ? [209, 56, 64, 48] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:57:43 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,47); Output: ? ? ? [1739, 704, 528, 483] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:58:57 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/1.759793; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,47); Output: ? ? ? [1739, 704, 511, 496] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:59:35 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2.01; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,47); Output: ? ? ? [1739, 704, 529, 465] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:59:42 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2.2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,47); Output: ? ? ? [1739, 704, 541, 410] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 02:59:51 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/1.7; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,47); Output: ? ? ? [1739, 704, 506, 497] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:00:09 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.759-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,47); Output: ? ? ? [1739, 704, 528, 533] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.009s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:00:19 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.7-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,47); Output: ? ? ? [1739, 704, 528, 531] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:00:29 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.3-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,47); Output: ? ? ? [1739, 704, 528, 170] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:00:42 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.5-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,47); Output: ? ? ? [1739, 704, 528, 530] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:00:50 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.6-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,47); Output: ? ? ? [1739, 704, 528, 530] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:00:58 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.7-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,47); Output: ? ? ? [1739, 704, 528, 531] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:01:04 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.8-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,47); Output: ? ? ? [1739, 704, 528, 534] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:01:10 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/3-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,47); Output: ? ? ? [1739, 704, 528, 527] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:01:29 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.759793-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,47); Output: ? ? ? [1739, 704, 528, 533] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:01:48 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.759793-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,67); Output: ? ? ? [2479, 334, 753, 756] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:02:03 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.23-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,67); Output: ? ? ? [2479, 334, 753, 340] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:02:24 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.232466-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,67); Output: ? ? ? [2479, 334, 753, 336] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:02:54 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.232466-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,193); Output: ? ? ? [7141, 1738, 2170, 961] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:03:03 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,193); Output: ? ? ? [7141, 1738, 2170, 1906] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:03:51 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(37,239); Output: ? ? ? [8843, 2628, 2687, 2367] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:09:24 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,223); Output: ? ? ? [2453, 670, 745, 670] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:10:15 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,223); Output: ? ? ? [2453, 670, 745.36703898891590502309548602270437243, 656] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:19:11 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,151); Output: ? ? ? [1661, 452, 504.71012192544602315710603095110206666, 444] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:19:21 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,151); Output: ? ? ? [1661, 452, 505, 436] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:22:04 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(337,443); Output: ? ? ? [149291, 39428, 45363, 39961] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:33:34 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.9988-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(337,443); Output: ? ? ? [149291, 39428, 45363, 40064] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:33:44 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.9988-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,223); Output: ? ? ? [2453, 670, 745, 672] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.003s sys 0m0.011s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:33:56 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.9900-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,223); Output: ? ? ? [2453, 670, 745, 688] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:34:09 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.9990-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,223); Output: ? ? ? [2453, 670, 745, 672] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 03:34:16 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.90-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,223); Output: ? ? ? [2453, 670, 745, 771] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:13:03 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,751); Output: ? ? ? [8261, 2254, 2510, 2216] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.005s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:13:31 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.905332-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,751); Output: ? ? ? [8261, 2254, 2510, 2522] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:13:42 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.995332-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,751); Output: ? ? ? [8261, 2254, 2510, 2239] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:13:51 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.985332-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,751); Output: ? ? ? [8261, 2254, 2510, 2287] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:14:23 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.985332-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,733); Output: ? ? ? [8063, 3664, 2450, 2226] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:14:53 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.606549-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,733); Output: ? ? ? [8063, 3664, 2450, 2450] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:15:12 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,733); Output: ? ? ? [8063, 3664, 2450, 2158] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:15:28 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/-1.606549-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,733); Output: ? ? ? [8063, 3664, 2450, 2450] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:15:37 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/-1.676549-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,733); Output: ? ? ? [8063, 3664, 2450, 2450] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.003s sys 0m0.013s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:15:58 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-((c-d))/-1.676549-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,733); Output: ? ? ? [8063, 3664, 2450, 2450] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:16:14 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,733); Output: ? ? ? [8063, 3664, 2450, 2158] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:16:21 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,733); Output: ? ? ? [8063, 3664, 2450, 2450] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:16:49 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,691); Output: ? ? ? [7601, 692, 2310, 2023] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:17:13 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.204479-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,691); Output: ? ? ? [7601, 692, 2310, 1143] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:17:22 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.304479-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,691); Output: ? ? ? [7601, 692, 2310, 709] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:21:17 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); k=(p+x0)/(2*x0); new = x0-abs((c-d))/2.304479-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,691); Output: ? ? ? [7601, 692, 2310, 709] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.004s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:21:27 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); k=(p+x0)/(2*x0) new = x0-abs((c-d))/2.304479-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,691); Output: ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: new=x0-abs((c-d))/2.304479-x;x1=round(abs(polroots(new)[1]));ans=lift(chinese(Mod(1,p1),Mod(-1,p2)));ans=min(ans,p-ans[+++]. Timing: real 0m0.013s user 0m0.009s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:21:56 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); k=(p+x0)/(2*x0); print(k); new = x0-abs((c-d))/2.304479-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,691); Output: ? ? ? 901/420 [7601, 692, 2310, 709] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:22:07 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); k=(p+x0)/(2.0*x0); print(k); new = x0-abs((c-d))/2.304479-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,691); Output: ? ? ? 2.1452380952380952380952380952380952380 [7601, 692, 2310, 709] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:23:01 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); k=(p-x0)/(2.0*x0); print(k); new = x0-abs((c-d))/2.304479-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,691); Output: ? ? ? 1.1452380952380952380952380952380952380 [7601, 692, 2310, 709] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:34:35 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); k=(p+1+x0)/(2.0*x0); print(k); new = x0-abs((c-d))/2.304479-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,691); Output: ? ? ? 2.1454545454545454545454545454545454545 [7601, 692, 2310, 709] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:35:08 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = (abs(polroots(c-d)[1])); k=(p+1+x0)/(2.0*x0); print(k); new = x0-abs((c-d))/2.304479-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,691); Output: ? ? ? 2.1457137933912126064813678425275485547 [7601, 692, 2309.6361076050367880220789941999661866, 711] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:46:29 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = (abs(polroots(c-d)[1])); k=(p+1+x0)/(2.0*x0); print(k); new = x0-abs((c-d))/2.304479-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(7,467); Output: ? ? ? 2.1460010465511640827697070902602522815 [3269, 468, 993.31650087695000279734992534798709721, 306] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.005s sys 0m0.011s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:47:45 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = (abs(polroots(c-d)[1])); k=(p+1+x0)/(2.0*x0); print(k); new = x0-abs((c-d))/2.218424-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(7,467); Output: ? ? ? 2.1460010465511640827697070902602522815 [3269, 468, 993.31650087695000279734992534798709721, 467] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:48:39 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); k=(p+1+x0)/(2.0*x0); print(k); new = x0-abs((c-d))/2.218424-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(7,467); Output: ? ? ? 2.1465256797583081570996978851963746223 [3269, 468, 993, 469] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:48:55 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); k=(p+1+x0)/(2.0*x0); print(k); new = x0-abs((c-d))/2.2177-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(7,467); Output: ? ? ? 2.1465256797583081570996978851963746223 [3269, 468, 993, 471] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:49:07 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); k=(p+1+x0)/(2.0*x0); print(k); new = x0-abs((c-d))/2.2185-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(7,467); Output: ? ? ? 2.1465256797583081570996978851963746223 [3269, 468, 993, 469] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:49:14 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); k=(p+1+x0)/(2.0*x0); print(k); new = x0-abs((c-d))/2.2186-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(7,467); Output: ? ? ? 2.1465256797583081570996978851963746223 [3269, 468, 993, 469] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 05:49:22 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); k=(p+1+x0)/(2.0*x0); print(k); new = x0-abs((c-d))/2.219-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(7,467); Output: ? ? ? 2.1465256797583081570996978851963746223 [3269, 468, 993, 468] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 06:26:06 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.219-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,223); Output: ? ? ? [2453, 670, 745, 352] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 06:26:24 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.937295-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,223); Output: ? ? ? [2453, 670, 745, 745] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 06:26:50 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.463217-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,223); Output: ? ? ? [2453, 670, 745, 9] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 06:27:20 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/-1.595542-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,223); Output: ? ? ? [2453, 670, 745, 745] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 06:27:48 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/-1.936325-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,223); Output: ? ? ? [2453, 670, 745, 745] ? Errors (if any) and Timing Info: Timing: real 0m0.115s user 0m0.007s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 06:27:57 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-((c-d))/-1.936325-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,223); Output: ? ? ? [2453, 670, 745, 746] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 06:28:05 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/-1.936325-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(11,223); Output: ? ? ? [2453, 670, 745, 745] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 06:54:31 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(19,8311); Output: ? ? ? [157909, 41554, 47982, 42256] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 06:54:53 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.0077-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(19,8311); Output: ? ? ? [157909, 41554, 47982, 41561] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 06:55:06 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(19,8311); Output: ? ? ? [157909, 41554, 47982, 24206] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 06:55:19 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.0077-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(19,8311); Output: ? ? ? [157909, 41554, 47982, 41561] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Wed Apr 20 08:04:54 2005 Input: (x+yx)/x Output: ? (x + yx)/x ? Errors (if any) and Timing Info: Timing: real 0m0.441s user 0m0.008s sys 0m0.013s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Wed Apr 20 08:05:05 2005 Input: (x+x^2)/x Output: ? x + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.008s sys 0m0.006s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:43:25 2005 Input: nfinit( (x^2-9-25)^2-60 ) Output: ? [x^4 - 68*x^2 + 1096, [4, 0], 15782400, 8, [[1, -6.4611118774104843517779280047985967938, 20.872983346207416885179265399782399610, -67.431340307585988590430767534438970992; 1, -5.1238689783780738502617630130377083559, 13.127016653792583114820734600217600389, -33.630556705510082198633110240192192261; 1, 5.1238689783780738502617630130377083559, 13.127016653792583114820734600217600389, 33.630556705510082198633110240192192261; 1, 6.4611118774104843517779280047985967938, 20.872983346207416885179265399782399610, 67.431340307585988590430767534438970992], [1, 1, 1, 1; -6.4611118774104843517779280047985967938, -5.1238689783780738502617630130377083559, 5.1238689783780738502617630130377083559, 6.4611118774104843517779280047985967938; 20.872983346207416885179265399782399610, 13.127016653792583114820734600217600389, 13.127016653792583114820734600217600389, 20.872983346207416885179265399782399610; -67.431340307585988590430767534438970992, -33.630556705510082198633110240192192261, 33.630556705510082198633110240192192261, 67.431340307585988590430767534438970992], [4, 0.E-76, 68.000000000000000000000000000000000000, 0.E-75; 0.E-76, 136.00000000000000000000000000000000000, 0.E-74, 1216.0000000000000000000000000000000000; 68.000000000000000000000000000000000000, 0.E-74, 1216.0000000000000000000000000000000000, 0.E-74; 0.E-75, 1216.0000000000000000000000000000000000, 0.E-74, 11356.000000000000000000000000000000000], [4, 0, 68, 0; 0, 136, 0, 1216; 68, 0, 1216, 0; 0, 1216, 0, 11356], [16440, 0, 7672, 0; 0, 60, 0, 56; 0, 0, 4, 0; 0, 0, 0, 4], [79964160, 0, -4471680, 0; 0, 2725440, 0, -291840; -4471680, 0, 263040, 0; 0, -291840, 0, 32640], [3945600, [0, 98880, 0, 1920]~]], [-6.4611118774104843517779280047985967938, -5.1238689783780738502617630130377083559, 5.1238689783780738502617630130377083559, 6.4611118774104843517779280047985967938], [1, x, 1/2*x^2, 1/4*x^3], [1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 2, 0; 0, 0, 0, 4], [1, 0, 0, 0, 0, 0, 0, -274, 0, 0, -274, 0, 0, -274, 0, -4658; 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -137, 0, 0, -137, 0; 0, 0, 1, 0, 0, 2, 0, 34, 1, 0, 34, 0, 0, 34, 0, 441; 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 34, 1, 0, 34, 0]] ? Errors (if any) and Timing Info: Timing: real 0m0.397s user 0m0.012s sys 0m0.006s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:43:43 2005 Input: K=nfinit( (x^2-9-25)^2-60 ) Output: ? [x^4 - 68*x^2 + 1096, [4, 0], 15782400, 8, [[1, -6.4611118774104843517779280047985967938, 20.872983346207416885179265399782399610, -67.431340307585988590430767534438970992; 1, -5.1238689783780738502617630130377083559, 13.127016653792583114820734600217600389, -33.630556705510082198633110240192192261; 1, 5.1238689783780738502617630130377083559, 13.127016653792583114820734600217600389, 33.630556705510082198633110240192192261; 1, 6.4611118774104843517779280047985967938, 20.872983346207416885179265399782399610, 67.431340307585988590430767534438970992], [1, 1, 1, 1; -6.4611118774104843517779280047985967938, -5.1238689783780738502617630130377083559, 5.1238689783780738502617630130377083559, 6.4611118774104843517779280047985967938; 20.872983346207416885179265399782399610, 13.127016653792583114820734600217600389, 13.127016653792583114820734600217600389, 20.872983346207416885179265399782399610; -67.431340307585988590430767534438970992, -33.630556705510082198633110240192192261, 33.630556705510082198633110240192192261, 67.431340307585988590430767534438970992], [4, 0.E-76, 68.000000000000000000000000000000000000, 0.E-75; 0.E-76, 136.00000000000000000000000000000000000, 0.E-74, 1216.0000000000000000000000000000000000; 68.000000000000000000000000000000000000, 0.E-74, 1216.0000000000000000000000000000000000, 0.E-74; 0.E-75, 1216.0000000000000000000000000000000000, 0.E-74, 11356.000000000000000000000000000000000], [4, 0, 68, 0; 0, 136, 0, 1216; 68, 0, 1216, 0; 0, 1216, 0, 11356], [16440, 0, 7672, 0; 0, 60, 0, 56; 0, 0, 4, 0; 0, 0, 0, 4], [79964160, 0, -4471680, 0; 0, 2725440, 0, -291840; -4471680, 0, 263040, 0; 0, -291840, 0, 32640], [3945600, [0, 98880, 0, 1920]~]], [-6.4611118774104843517779280047985967938, -5.1238689783780738502617630130377083559, 5.1238689783780738502617630130377083559, 6.4611118774104843517779280047985967938], [1, x, 1/2*x^2, 1/4*x^3], [1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 2, 0; 0, 0, 0, 4], [1, 0, 0, 0, 0, 0, 0, -274, 0, 0, -274, 0, 0, -274, 0, -4658; 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -137, 0, 0, -137, 0; 0, 0, 1, 0, 0, 2, 0, 34, 1, 0, 34, 0, 0, 34, 0, 441; 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 34, 1, 0, 34, 0]] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.013s sys 0m0.006s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:43:54 2005 Input: K=nfinit( (x^2-9-25)^2-60 ); K Output: ? ? [x^4 - 68*x^2 + 1096, [4, 0], 15782400, 8, [[1, -6.4611118774104843517779280047985967938, 20.872983346207416885179265399782399610, -67.431340307585988590430767534438970992; 1, -5.1238689783780738502617630130377083559, 13.127016653792583114820734600217600389, -33.630556705510082198633110240192192261; 1, 5.1238689783780738502617630130377083559, 13.127016653792583114820734600217600389, 33.630556705510082198633110240192192261; 1, 6.4611118774104843517779280047985967938, 20.872983346207416885179265399782399610, 67.431340307585988590430767534438970992], [1, 1, 1, 1; -6.4611118774104843517779280047985967938, -5.1238689783780738502617630130377083559, 5.1238689783780738502617630130377083559, 6.4611118774104843517779280047985967938; 20.872983346207416885179265399782399610, 13.127016653792583114820734600217600389, 13.127016653792583114820734600217600389, 20.872983346207416885179265399782399610; -67.431340307585988590430767534438970992, -33.630556705510082198633110240192192261, 33.630556705510082198633110240192192261, 67.431340307585988590430767534438970992], [4, 0.E-76, 68.000000000000000000000000000000000000, 0.E-75; 0.E-76, 136.00000000000000000000000000000000000, 0.E-74, 1216.0000000000000000000000000000000000; 68.000000000000000000000000000000000000, 0.E-74, 1216.0000000000000000000000000000000000, 0.E-74; 0.E-75, 1216.0000000000000000000000000000000000, 0.E-74, 11356.000000000000000000000000000000000], [4, 0, 68, 0; 0, 136, 0, 1216; 68, 0, 1216, 0; 0, 1216, 0, 11356], [16440, 0, 7672, 0; 0, 60, 0, 56; 0, 0, 4, 0; 0, 0, 0, 4], [79964160, 0, -4471680, 0; 0, 2725440, 0, -291840; -4471680, 0, 263040, 0; 0, -291840, 0, 32640], [3945600, [0, 98880, 0, 1920]~]], [-6.4611118774104843517779280047985967938, -5.1238689783780738502617630130377083559, 5.1238689783780738502617630130377083559, 6.4611118774104843517779280047985967938], [1, x, 1/2*x^2, 1/4*x^3], [1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 2, 0; 0, 0, 0, 4], [1, 0, 0, 0, 0, 0, 0, -274, 0, 0, -274, 0, 0, -274, 0, -4658; 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -137, 0, 0, -137, 0; 0, 0, 1, 0, 0, 2, 0, 34, 1, 0, 34, 0, 0, 34, 0, 441; 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 34, 1, 0, 34, 0]] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.010s sys 0m0.008s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:44:52 2005 Input: K=nfinit( (x^2-9-25)^2-60 ); nfdisc(K) Output: ? ? ? Errors (if any) and Timing Info: *** incorrect type in nfbasis00. Timing: real 0m0.016s user 0m0.012s sys 0m0.004s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:47:44 2005 Input: K=nfinit( (x^2-9-25)^2-60 ); nfbasis(K) Output: ? ? ? Errors (if any) and Timing Info: *** incorrect type in nfbasis00. Timing: real 0m0.015s user 0m0.009s sys 0m0.005s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:48:00 2005 Input: K=nfinit( (x^2-9-25)^2-60 ); nfbasis( (x^2-9-25)^2-60 ) Output: ? ? [1, x, 1/2*x^2, 1/4*x^3] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.009s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:48:10 2005 Input: K=nfinit( (x^2-9-25)^2-60 ); nfdisc( (x^2-9-25)^2-60 ) Output: ? ? 15782400 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.011s sys 0m0.006s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:48:26 2005 Input: K=nfinit( (x^2-9-25)^2-60 ); factor(nfdisc( (x^2-9-25)^2-60 )) Output: ? ? [2 9] [3 2] [5 2] [137 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:51:57 2005 Input: K=nfinit( (x^2-9-25)^2-60 ); factor(nfdisc( (x^2+3-5)^2-12*x^2 )) Output: ? ? [2 4] [3 2] [5 2] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.009s sys 0m0.007s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:52:25 2005 Input: K=nfinit( (x^2-9-25)^2-60 ); factor(nfdisc( (x^2+3-5)^2-12*x^2 )) poldisc((x^2+3-5)^2-12*x^2 ) Output: ? ? [2 4] [3 2] [5 2] ? 3686400 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:52:33 2005 Input: K=nfinit( (x^2-9-25)^2-60 ); factor(nfdisc( (x^2+3-5)^2-12*x^2 )) factor(poldisc((x^2+3-5)^2-12*x^2 )) Output: ? ? [2 4] [3 2] [5 2] ? [2 14] [3 2] [5 2] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.013s sys 0m0.003s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:56:20 2005 Input: K=nfinit( x^2-3 ); L=rnfinit( K, x^2-5 ); Output: ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.015s user 0m0.007s sys 0m0.006s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:56:28 2005 Input: K=nfinit( x^2-3 ); L=rnfinit( K, x^2-5 ) Output: ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:56:38 2005 Input: K=nfinit( x^2-3 ); L=rnfinit( K, x^2-5 ) Output: ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.013s user 0m0.010s sys 0m0.004s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:57:06 2005 Input: K=nfinit( x^2-3 ); L=rnfinit( K, a^2-5 ) Output: ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:57:12 2005 Input: K=nfinit( x^2-3 ); L=rnfinit( K, A^2-5 ) Output: ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:58:57 2005 Input: y,x; K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,x;. *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.016s user 0m0.009s sys 0m0.005s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:59:18 2005 Input: y; x; K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 10:59:25 2005 Input: x; y; K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.013s user 0m0.006s sys 0m0.005s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:00:09 2005 Input: x; y; K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:00:18 2005 Input: y; x; K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:00:29 2005 Input: y; x; K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:00:32 2005 Input: y; x; K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:01:08 2005 Input: y; x; reorder() K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? [x, y] ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:01:14 2005 Input: y; x; reorder() K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? [x, y] ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:01:20 2005 Input: x; y; reorder() K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? ? [x, y] ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:01:44 2005 Input: y; x; reorder() K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? [x, y] ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.017s user 0m0.010s sys 0m0.004s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:01:46 2005 Input: y; x; reorder() K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? [x, y] ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:02:13 2005 Input: y; x; reorder() K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? [x, y] ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:05:14 2005 Input: y; x; reorder() changevar([y,x]) reorder() K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? [x, y] ? ? [x, y] ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: changevar([y,x]) ^- *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.016s user 0m0.005s sys 0m0.010s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:05:41 2005 Input: y; x; reorder() changevar(,[y,x]) reorder() K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? [x, y] ? ? [x, y] ? ? ? Errors (if any) and Timing Info: *** unexpected character: changevar(,[y,x]) ^------- *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.013s user 0m0.010s sys 0m0.004s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:05:56 2005 Input: y; x; reorder() changevar(x,[y,x]) reorder() K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? [x, y] ? y ? [x, y] ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.017s user 0m0.005s sys 0m0.009s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:06:06 2005 Input: y; x; reorder() changevar(y,[y,x]) reorder() K=nfinit( x^2-3 ); L=rnfinit( K, y^2-5 ) Output: ? ? ? [x, y] ? x ? [x, y] ? ? ? Errors (if any) and Timing Info: *** main variable must be of higher priority in rnfinitalg. Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:06:37 2005 Input: y; x; reorder() changevar(y,[y,x]) reorder() K=nfinit( y^2-3 ); L=rnfinit( K, x^2-5 ) Output: ? ? ? [x, y] ? x ? [x, y] ? ? [x^2 - 5, [[2, 0], [2, 0]], [[5, 0; 0, 5], [5, 0]~], [2, 0; 0, 2], [[[1, -1.2360679774997896964091736687312762354; 1, 3.2360679774997896964091736687312762354], [1, -1.2360679774997896964091736687312762354; 1, 3.2360679774997896964091736687312762354]], [[1, 1; -1.2360679774997896964091736687312762354, 3.2360679774997896964091736687312762354], [1, 1; -1.2360679774997896964091736687312762354, 3.2360679774997896964091736687312762354]], [[2, 2.0000000000000000000000000000000000000; 2.0000000000000000000000000000000000000, 11.999999999999999999999999999999999999], [2, 2.0000000000000000000000000000000000000; 2.0000000000000000000000000000000000000, 11.999999999999999999999999999999999999]], [Mod(2, y^2 - 3), Mod(2, y^2 - 3); Mod(2, y^2 - 3), Mod(12, y^2 - 3)], [;], [;], [;]], [[-2.2360679774997896964091736687312762354, 2.2360679774997896964091736687312762354], [-2.2360679774997896964091736687312762354, 2.2360679774997896964091736687312762354]], [[Mod(1, y^2 - 3), Mod(1, y^2 - 3)*x + Mod(1, y^2 - 3)], [[1, 0; 0, 1], [1/2, 0; 0, 1/2]]], [Mod(1, y^2 - 3), Mod(-1, y^2 - 3); 0, Mod(1, y^2 - 3)], [], [y^2 - 3, [2, 0], 12, 1, [[1, -1.7320508075688772935274463415058723669; 1, 1.7320508075688772935274463415058723669], [1, 1; -1.7320508075688772935274463415058723669, 1.7320508075688772935274463415058723669], [2, 0.E-77; 0.E-77, 6.0000000000000000000000000000000000000], [2, 0; 0, 6], [6, 0; 0, 2], [6, 0; 0, 2], [6, [0, 2]~]], [-1.7320508075688772935274463415058723669, 1.7320508075688772935274463415058723669], [1, y], [1, 0; 0, 1], [1, 0, 0, 3; 0, 1, 1, 0]], [x^4 - 16*x^2 + 4, Mod(-1/4*x^3 + 7/2*x, x^4 - 16*x^2 + 4), -1, [1, x, 1/4*x^2 + 1/2*x + 1/2, 1/8*x^3 - 1/4*x + 1/2], [1, 0, -2, -4; 0, 1, -2, 2; 0, 0, 4, 0; 0, 0, 0, 8]]] ? Errors (if any) and Timing Info: Timing: real 0m0.063s user 0m0.012s sys 0m0.005s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:06:44 2005 Input: K=nfinit( y^2-3 ); L=rnfinit( K, x^2-5 ) Output: ? ? ? [x^2 - 5, [[2, 0], [2, 0]], [[5, 0; 0, 5], [5, 0]~], [2, 0; 0, 2], [[[1, -1.2360679774997896964091736687312762354; 1, 3.2360679774997896964091736687312762354], [1, -1.2360679774997896964091736687312762354; 1, 3.2360679774997896964091736687312762354]], [[1, 1; -1.2360679774997896964091736687312762354, 3.2360679774997896964091736687312762354], [1, 1; -1.2360679774997896964091736687312762354, 3.2360679774997896964091736687312762354]], [[2, 2.0000000000000000000000000000000000000; 2.0000000000000000000000000000000000000, 11.999999999999999999999999999999999999], [2, 2.0000000000000000000000000000000000000; 2.0000000000000000000000000000000000000, 11.999999999999999999999999999999999999]], [Mod(2, y^2 - 3), Mod(2, y^2 - 3); Mod(2, y^2 - 3), Mod(12, y^2 - 3)], [;], [;], [;]], [[-2.2360679774997896964091736687312762354, 2.2360679774997896964091736687312762354], [-2.2360679774997896964091736687312762354, 2.2360679774997896964091736687312762354]], [[Mod(1, y^2 - 3), Mod(1, y^2 - 3)*x + Mod(1, y^2 - 3)], [[1, 0; 0, 1], [1/2, 0; 0, 1/2]]], [Mod(1, y^2 - 3), Mod(-1, y^2 - 3); 0, Mod(1, y^2 - 3)], [], [y^2 - 3, [2, 0], 12, 1, [[1, -1.7320508075688772935274463415058723669; 1, 1.7320508075688772935274463415058723669], [1, 1; -1.7320508075688772935274463415058723669, 1.7320508075688772935274463415058723669], [2, 0.E-77; 0.E-77, 6.0000000000000000000000000000000000000], [2, 0; 0, 6], [6, 0; 0, 2], [6, 0; 0, 2], [6, [0, 2]~]], [-1.7320508075688772935274463415058723669, 1.7320508075688772935274463415058723669], [1, y], [1, 0; 0, 1], [1, 0, 0, 3; 0, 1, 1, 0]], [x^4 - 16*x^2 + 4, Mod(-1/4*x^3 + 7/2*x, x^4 - 16*x^2 + 4), -1, [1, x, 1/4*x^2 + 1/2*x + 1/2, 1/8*x^3 - 1/4*x + 1/2], [1, 0, -2, -4; 0, 1, -2, 2; 0, 0, 4, 0; 0, 0, 0, 8]]] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.012s sys 0m0.003s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:08:22 2005 Input: K=nfinit( y^2-3 ); L=rnfinit( K, x^2-5 ); rnfbasis(L) Output: ? ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: rnfbasis(L) ^- Timing: real 0m0.015s user 0m0.008s sys 0m0.008s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:08:29 2005 Input: K=nfinit( y^2-3 ); L=rnfinit( K, x^2-5 ); rnfbasis(K, x^2-5) Output: ? ? ? ? Errors (if any) and Timing Info: *** please apply bnfinit first. Timing: real 0m0.016s user 0m0.009s sys 0m0.008s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:08:41 2005 Input: K=nfinit( y^2-3 ); L=bnfinit( K, x^2-5 ); rnfbasis(K, x^2-5) Output: ? ? ? ? Errors (if any) and Timing Info: *** this should be an integer: L=bnfinit(K,x^2-5); ^------- *** please apply bnfinit first. Timing: real 0m0.017s user 0m0.006s sys 0m0.009s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:09:00 2005 Input: K=nfinit( y^2-3 ); L=rnfinit( K, x^2-5 ); rnfbasis(K, x^2-5) Output: ? ? ? ? ? Errors (if any) and Timing Info: *** please apply bnfinit first. Timing: real 0m0.015s user 0m0.010s sys 0m0.006s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:09:07 2005 Input: K=nfinit( y^2-3 ); L=rnfinit( K, x^2-5 ); bnfinit(L) rnfbasis(K, x^2-5) Output: ? ? ? ? ? Errors (if any) and Timing Info: *** not a number field in some number field-related function *** please apply bnfinit first. Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:11:27 2005 Input: K=nfinit( y^2-3 ); L=rnfinit( K, x^2-5 ); L.pol Output: ? ? ? ? Errors (if any) and Timing Info: *** incorrect type in .pol: L.pol ^--- Timing: real 0m0.015s user 0m0.012s sys 0m0.003s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:11:35 2005 Input: K=nfinit( y^2-3 ); L=rnfinit( K, x^2-5 ) L.pol Output: ? ? [x^2 - 5, [[2, 0], [2, 0]], [[5, 0; 0, 5], [5, 0]~], [2, 0; 0, 2], [[[1, -1.2360679774997896964091736687312762354; 1, 3.2360679774997896964091736687312762354], [1, -1.2360679774997896964091736687312762354; 1, 3.2360679774997896964091736687312762354]], [[1, 1; -1.2360679774997896964091736687312762354, 3.2360679774997896964091736687312762354], [1, 1; -1.2360679774997896964091736687312762354, 3.2360679774997896964091736687312762354]], [[2, 2.0000000000000000000000000000000000000; 2.0000000000000000000000000000000000000, 11.999999999999999999999999999999999999], [2, 2.0000000000000000000000000000000000000; 2.0000000000000000000000000000000000000, 11.999999999999999999999999999999999999]], [Mod(2, y^2 - 3), Mod(2, y^2 - 3); Mod(2, y^2 - 3), Mod(12, y^2 - 3)], [;], [;], [;]], [[-2.2360679774997896964091736687312762354, 2.2360679774997896964091736687312762354], [-2.2360679774997896964091736687312762354, 2.2360679774997896964091736687312762354]], [[Mod(1, y^2 - 3), Mod(1, y^2 - 3)*x + Mod(1, y^2 - 3)], [[1, 0; 0, 1], [1/2, 0; 0, 1/2]]], [Mod(1, y^2 - 3), Mod(-1, y^2 - 3); 0, Mod(1, y^2 - 3)], [], [y^2 - 3, [2, 0], 12, 1, [[1, -1.7320508075688772935274463415058723669; 1, 1.7320508075688772935274463415058723669], [1, 1; -1.7320508075688772935274463415058723669, 1.7320508075688772935274463415058723669], [2, 0.E-77; 0.E-77, 6.0000000000000000000000000000000000000], [2, 0; 0, 6], [6, 0; 0, 2], [6, 0; 0, 2], [6, [0, 2]~]], [-1.7320508075688772935274463415058723669, 1.7320508075688772935274463415058723669], [1, y], [1, 0; 0, 1], [1, 0, 0, 3; 0, 1, 1, 0]], [x^4 - 16*x^2 + 4, Mod(-1/4*x^3 + 7/2*x, x^4 - 16*x^2 + 4), -1, [1, x, 1/4*x^2 + 1/2*x + 1/2, 1/8*x^3 - 1/4*x + 1/2], [1, 0, -2, -4; 0, 1, -2, 2; 0, 0, 4, 0; 0, 0, 0, 8]]] ? ? Errors (if any) and Timing Info: *** incorrect type in .pol: L.pol ^--- Timing: real 0m0.015s user 0m0.008s sys 0m0.007s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:16:14 2005 Input: K=nfinit( y^2-3 ); L=rnfinit( K, x^2-5 ); L[11] Output: ? ? ? [x^4 - 16*x^2 + 4, Mod(-1/4*x^3 + 7/2*x, x^4 - 16*x^2 + 4), -1, [1, x, 1/4*x^2 + 1/2*x + 1/2, 1/8*x^3 - 1/4*x + 1/2], [1, 0, -2, -4; 0, 1, -2, 2; 0, 0, 4, 0; 0, 0, 0, 8]] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.009s sys 0m0.007s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:16:44 2005 Input: K=nfinit( y^2-3 ); L=rnfinit( K, x^2-5 ); L[11]; M=nfinit(x^4 - 16*x^2 + 4) Output: ? ? ? ? [x^4 - 16*x^2 + 4, [4, 0], 3600, 32, [[1, -3.9681187850686669899366200102371486023, 2.4524322805693749476213226947726255042, -6.3182035813874391316686531861086590870; 1, -0.50401716993091240288172732722540386849, 0.31149974193083535596950363649609826033, 0.60999964888807004244113217991483038072; 1, 0.50401716993091240288172732722540386849, 0.81551691186174775885123096372150212883, 0.39000035111192995755886782008516961927; 1, 3.9681187850686669899366200102371486023, 6.4205510656380419375579427050097741066, 7.3182035813874391316686531861086590870], [1, 1, 1, 1; -3.9681187850686669899366200102371486023, -0.50401716993091240288172732722540386849, 0.50401716993091240288172732722540386849, 3.9681187850686669899366200102371486023; 2.4524322805693749476213226947726255042, 0.31149974193083535596950363649609826033, 0.81551691186174775885123096372150212883, 6.4205510656380419375579427050097741066; -6.3182035813874391316686531861086590870, 0.60999964888807004244113217991483038072, 0.39000035111192995755886782008516961927, 7.3182035813874391316686531861086590870], [4, 3.454467422037777850 E-77, 10.000000000000000000000000000000000000, 2.0000000000000000000000000000000000000; 3.454467422037777850 E-77, 32.000000000000000000000000000000000000, 16.000000000000000000000000000000000000, 54.000000000000000000000000000000000000; 10.000000000000000000000000000000000000, 16.000000000000000000000000000000000000, 48.000000000000000000000000000000000000, 32.000000000000000000000000000000000000; 2.0000000000000000000000000000000000000, 54.000000000000000000000000000000000000, 32.000000000000000000000000000000000000, 94.000000000000000000000000000000000000], [4, 0, 10, 2; 0, 32, 16, 54; 10, 16, 48, 32; 2, 54, 32, 94], [30, 0, 10, 14; 0, 30, 14, 6; 0, 0, 2, 0; 0, 0, 0, 2], [2880, 1920, -600, -960; 1920, 5640, -120, -3240; -600, -120, 240, 0; -960, -3240, 0, 1920], [1800, [600, 840, 120, 0]~]], [-3.9681187850686669899366200102371486023, -0.50401716993091240288172732722540386849, 0.50401716993091240288172732722540386849, 3.9681187850686669899366200102371486023], [1, x, 1/4*x^2 + 1/2*x + 1/2, 1/8*x^3 - 1/4*x + 1/2], [1, 0, -2, -4; 0, 1, -2, 2; 0, 0, 4, 0; 0, 0, 0, 8], [1, 0, 0, 0, 0, -2, -2, -4, 0, -2, -4, -4, 0, -4, -4, -7; 0, 1, 0, 0, 1, -2, 0, -3, 0, 0, -2, -1, 0, -3, -1, -6; 0, 0, 1, 0, 0, 4, 2, 7, 1, 2, 6, 4, 0, 7, 4, 12; 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 4, 1, 0, 4, 1]] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.013s sys 0m0.007s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:16:53 2005 Input: K=nfinit( y^2-3 ); L=rnfinit( K, x^2-5 ); L[11]; M=nfbasis(x^4 - 16*x^2 + 4) Output: ? ? ? ? [1, x, 1/4*x^2 + 1/2*x + 1/2, 1/8*x^3 - 1/4*x + 1/2] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.011s sys 0m0.006s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:17:03 2005 Input: K=nfinit( y^2-3 ); L=rnfinit( K, x^2-5 ); L[11]; M=nfdisc(x^4 - 16*x^2 + 4) Output: ? ? ? ? 3600 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.009s sys 0m0.005s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:17:14 2005 Input: K=nfinit( y^2-3 ); L=rnfinit( K, x^2-5 ); L[11]; factor(nfdisc(x^4 - 16*x^2 + 4)) Output: ? ? ? ? [2 4] [3 2] [5 2] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.009s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:26:09 2005 Input: K=nfinit( y^2-13 ); L=rnfinit( K, x^2-5 ); L[11] factor(nfdisc(x^4 - 16*x^2 + 4)) Output: ? ? ? [x^4 - 36*x^2 + 64, Mod(1/16*x^3 - 11/4*x, x^4 - 36*x^2 + 64), -1, [1, 1/2*x, 1/8*x^2 + 1/4*x, 1/32*x^3 + 1/8*x + 1/2], [1, 0, 0, -16; 0, 2, -4, -8; 0, 0, 8, 0; 0, 0, 0, 32]] ? [2 4] [3 2] [5 2] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.012s sys 0m0.004s '212.201' ************** PARI ***************** Host 212.201.44.249 (212.201.44.249) Time: Wed Apr 20 11:26:19 2005 Input: K=nfinit( y^2-13 ); L=rnfinit( K, x^2-5 ); L[11] factor(nfdisc(x^4 - 36*x^2 + 64)) Output: ? ? ? [x^4 - 36*x^2 + 64, Mod(1/16*x^3 - 11/4*x, x^4 - 36*x^2 + 64), -1, [1, 1/2*x, 1/8*x^2 + 1/4*x, 1/32*x^3 + 1/8*x + 1/2], [1, 0, 0, -16; 0, 2, -4, -8; 0, 0, 8, 0; 0, 0, 0, 32]] ? [5 2] [13 2] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Wed Apr 20 13:47:32 2005 Input: factor(144) Output: ? [2 4] [3 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '165.106' ************** PARI ***************** Host 165.106.23.212 (165.106.23.212) Time: Wed Apr 20 15:23:18 2005 Input: hi Output: ? hi ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '165.106' ************** PARI ***************** Host 165.106.23.212 (165.106.23.212) Time: Wed Apr 20 15:23:34 2005 Input: 1+2 Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '69.154.' ************** PARI ***************** Host 69.154.30.117 (69.154.30.117) Time: Wed Apr 20 18:07:08 2005 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: ? 366,378,582,594,846,1026,1374,1386, ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.004s '69.154.' ************** PARI ***************** Host 69.154.30.117 (69.154.30.117) Time: Wed Apr 20 18:07:23 2005 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 19:06:41 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.144-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(19,8311); Output: ? ? ? [157909, 41554, 47982, 29259] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 19:06:56 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.0-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(19,8311); Output: ? ? ? [157909, 41554, 47982, 42256] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.010s sys 0m0.003s '154.20.' ************** PARI ***************** Host 154.20.103.1 (154.20.103.1) Time: Wed Apr 20 20:42:30 2005 Input: E:=EllipticCurve([-133^2, 0]);E; RankBounds(E); IntegralPoints(E); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: E:=EllipticCurve([-133 ^-------------------- *** expected character: '=' instead of: RankBounds(E); ^- *** expected character: '=' instead of: IntegralPoints(E); ^- Timing: real 0m0.016s user 0m0.007s sys 0m0.005s '141.132' ************** PARI ***************** Host 141.132.11.3 (141.132.11.3) Time: Wed Apr 20 20:47:04 2005 Input: 2*5 Output: ? 10 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '200.146' ************** PARI ***************** Host 200.146.131.140 (200.146.131.140) Time: Wed Apr 20 21:58:07 2005 Input: factor(2^(2^5)+1) Output: ? [641 1] [6700417 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '200.146' ************** PARI ***************** Host 200.146.131.140 (200.146.131.140) Time: Wed Apr 20 22:03:00 2005 Input: factor(x^6-1) Output: ? [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '172.181' ************** PARI ***************** Host 172.181.219.121 (172.181.219.121) Time: Wed Apr 20 22:03:20 2005 Input: pploth(1,10,x) Output: WARNING: PARI command contains unsafe command 'plot', so it will not be executed. '172.181' ************** PARI ***************** Host 172.181.219.121 (172.181.219.121) Time: Wed Apr 20 22:03:46 2005 Input: ploth(1,10,x) Output: WARNING: PARI command contains unsafe command 'plot', so it will not be executed. '200.146' ************** PARI ***************** Host 200.146.131.140 (200.146.131.140) Time: Wed Apr 20 22:04:07 2005 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '172.181' ************** PARI ***************** Host 172.181.219.121 (172.181.219.121) Time: Wed Apr 20 22:04:41 2005 Input: x+y Output: ? x + y ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '172.181' ************** PARI ***************** Host 172.181.219.121 (172.181.219.121) Time: Wed Apr 20 22:05:30 2005 Input: (x+3)/x Output: ? (x + 3)/x ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:05:41 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; p=2053; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.0-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(19,8311); Output: ? ? ? [2053, -39501, 624, 544] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '172.181' ************** PARI ***************** Host 172.181.219.121 (172.181.219.121) Time: Wed Apr 20 22:06:07 2005 Input: 5+8 Output: ? 13 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:06:11 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; p=2051; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.0-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(19,8311); Output: ? ? ? [2051, -39503, 623, 556] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:06:24 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; p=2049; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.0-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(19,8311); Output: ? ? ? [2049, -39505, 623, 537] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:06:50 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; p=2047; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.0-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(19,8311); Output: ? ? ? [2047, -39507, 622, 548] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:07:00 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.0-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(19,8311); Output: ? ? ? [157909, 41554, 47982, 42256] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '200.146' ************** PARI ***************** Host 200.146.131.140 (200.146.131.140) Time: Wed Apr 20 22:07:46 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.007s sys 0m0.005s '200.146' ************** PARI ***************** Host 200.146.131.140 (200.146.131.140) Time: Wed Apr 20 22:07:47 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/was.css Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...(x,2)==Mod(0,2),x/was.css ^ Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '200.146' ************** PARI ***************** Host 200.146.131.140 (200.146.131.140) Time: Wed Apr 20 22:21:13 2005 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: ? ? 75 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '200.146' ************** PARI ***************** Host 200.146.131.140 (200.146.131.140) Time: Wed Apr 20 22:21:13 2005 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/was.css Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...(x,2)==Mod(0,2),x/was.css ^ Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:40:02 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = round(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.0-x; x1 = round(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? ? Errors (if any) and Timing Info: *** precision loss in truncation Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:40:37 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.0-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 21801206812891614112132530110561314528161404177521565248313676126679976579908840670855138224992451529447938569452799656210189978098881420317798104411675193952168350839998516, 5.7186001329446843902787286628050776568 E172, 5.0356177482329135433611135921463760466 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:42:25 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.118-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 21801206812891614112132530110561314528161404177521565248313676126679976579908840670855138224992451529447938569452799656210189978098881420317798104411675193952168350839998516, 5.7186001329446843902787286628050776568 E172, 3.7666200382539569871916122060621045096 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:42:37 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/1.99-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 21801206812891614112132530110561314528161404177521565248313676126679976579908840670855138224992451529447938569452799656210189978098881420317798104411675193952168350839998516, 5.7186001329446843902787286628050776568 E172, 5.1431599270446895226975120146958905837 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:42:46 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.4-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 21801206812891614112132530110561314528161404177521565248313676126679976579908840670855138224992451529447938569452799656210189978098881420317798104411675193952168350839998516, 5.7186001329446843902787286628050776568 E172, 7.3393059576187436990517669016579456511 E171] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:44:50 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.4-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 7.3393059576187436990517669016579456511 E171] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:44:59 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.1-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 3.9601959601151537499971293666512306762 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:45:07 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.11-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 3.8526537813033777706607309441017161391 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:45:16 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.8847741719973939566331451411560853059 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:45:22 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.22-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.6696898143738419979603482960570562315 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:45:30 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.29-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 1.9168945626914101426055593382104544724 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:45:38 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.27-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1319789203149621012783561833094835464 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:45:46 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.2395210991267380806147546058589980836 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.011s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:45:53 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1857500097208500909465553945842408151 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:46:02 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1803729007802612919797354734567650882 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:46:11 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2656-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1792974789921435321863714892312699428 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:46:24 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1803729007802612919797354734567650882 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.004s sys 0m0.011s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:46:30 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26555-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1798351898862024120830534813440175153 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:46:38 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26551-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1802653586014495160003990750342155736 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:46:45 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265511-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1802546043835683384024654351919606221 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:46:54 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26552-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801578164226377400210626766116660591 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:47:03 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26553-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1800502742438259640417262781891165445 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:47:10 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265525-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801040453332318520313944774003913019 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.011s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:47:18 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265524-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801147995511130296293281172426462534 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:47:25 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801255537689942072272617570849012048 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:47:33 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655231-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801244783472060894674683931006757096 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:47:42 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655232-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801234029254179717076750291164502143 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:47:50 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655233-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801223275036298539478816651322247193 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:47:57 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655234-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801212520818417361880883011479992242 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:48:03 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655235-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801201766600536184282949371637737290 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:48:11 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26552345-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801207143709476773081916191558864766 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:48:18 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26552346-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206068287688655322122827574639273 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:48:29 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26552345-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801207143709476773081916191558864766 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:48:36 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523455-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206605998582714202019509566752019 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:48:44 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523454-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206713540761525977998845965174568 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:48:51 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206821082940337753978182363597116 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:48:59 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655234535-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206767311850931865988514164385842 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:49:06 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655234533-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206788820286694221184381444070353 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:49:13 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655234531-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206810328722456576380248723754861 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:49:22 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26552345305-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206815705831397165179215543675989 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:49:32 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26552345309-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206811404144244694140042087739087 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:49:40 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26552345308-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812479566032811899835451723313 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:49:49 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26552345307-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206813554987820929659628815707538 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:50:06 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453071-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206813447445642117883649479309117 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:50:13 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453072-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206813339903463306107670142910693 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 22:50:22 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453073-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206813232361284494331690806512272 E172] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:03:15 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453073-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, ans-x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206813232361284494331690806512272 E172, -3.4074717236180158024519774487032291982 E161] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:03:25 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453072-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, ans-x1])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206813339903463306107670142910693 E172, -4.4828935117357755958159616531136286853 E161] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:03:44 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453072-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206813339903463306107670142910693 E172, 4.4828935117357755958159616531136286853 E161] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:03:52 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453074-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206813124819105682555711470113850 E172, 2.3320499355002560090879932206705711714 E161] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:03:59 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453075-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206813017276926870779732133715426 E172, 1.2566281473824962157240089799182354695 E161] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:04:05 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453076-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812909734748059003752797317004 E172, 1.8120635926473642236002476097106149644 E160] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:04:15 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453075-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206813017276926870779732133715426 E172, 1.2566281473824962157240089799182354695 E161] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:04:22 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453076-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812909734748059003752797317004 E172, 1.8120635926473642236002476097106149644 E160] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:04:34 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453077-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812802192569247227773460918582 E172, -8.9421542885302337100395945343337044978 E160] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:04:44 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655234530765-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812855963658653115763129117792 E172, -3.5650453479414347432196735259099331425 E160] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:04:52 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655234530763-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812877472094415470958996397476 E172, -1.4142017717059151564917051225404246004 E160] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:05:00 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655234530762-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812888226312296648556930037321 E172, -3.3877998358815536312772069371856898704 E159] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:05:07 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655234530761-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812898980530177826154863677162 E172, 7.3664180452960443023626348979521717661 E159] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:05:14 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26552345307615-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812893603421237237355896857240 E172, 1.9893091047072453355427128901251545044 E159] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:05:22 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26552345307616-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812892527999449119596103493257 E172, 9.1388731658948554217872943345009263635 E158] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:05:30 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26552345307617-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812891452577661001836310129271 E172, -1.6153447152827425118525674887018534022 E158] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:05:38 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453076165-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812891990288555060716206811263 E172, 3.7617642253060564549673566087864962093 E158] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:05:46 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453076166-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812891882746376248940227474866 E172, 2.6863424371882966616033826918696907211 E158] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:05:53 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453076167-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812891775204197437164248138468 E172, 1.6109206490705368682394051407592637548 E158] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:06:02 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453076168-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812891667662018625388268802068 E172, 5.3549886095277707487540669303551328994 E157] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:06:11 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453076169-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812891560119839813612289465670 E172, -5.3992292716498271848857812646215663236 E157] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:06:19 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655234530761685-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812891613890929219500279133869 E172, -2.2120331061028218065879880843350949815 E155] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:06:26 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655234530761684-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812891624645147100677877067510 E172, 1.0533014570567315752982221413986116391 E157] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:06:34 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26552345307616845-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812891619268038160089078100690 E172, 5.1559056299785167861619838672979142990 E156] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:06:41 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.26552345307616849-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812891614966351007618038927234 E172, 8.5421847750747761270690225900190342593 E155] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:06:52 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453076168499-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812891613998471398312055113204 E172, -1.1366113179850620132315542106344510452 E155] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:06:58 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453076168495-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812891614428640113559159030550 E172, 3.1650758344859771602296146719775355355 E155] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.011s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:07:05 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453076168497-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812891614213555755935607071878 E172, 1.0142322582504575735013016016849660166 E155] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:07:11 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.265523453076168498-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812891614106013577123831092542 E172, -6.1189529867302219853315175204938902344 E153] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Wed Apr 20 23:07:19 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p = p1*p2; a =(p+1-x)/2; b = a*(a-1)/p; c = b+x/2; d = 8*b-(p-x); x0 = /*round*/(abs(polroots(c-d)[1])); new = x0-abs((c-d))/2.2655234530761684975-x; x1 = /*round*/(abs(polroots(new)[1])); ans = lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); print([p,ans*1.0,x0,x1, x1-ans])} testk(472772146107435302536223071973048224632914695302097116459852171130520711256363590397527,398075086424064937397125500550386491199064362342526708406385189575946388957261768583317); Output: ? ? ? [188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059, 2.1801206812891614112132530110561314528 E172, 5.7186001329446843902787286628050776568 E172, 2.1801206812891614159784666529719082210 E172, 4.7652136419157767682035901961853552270 E154] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.009s '69.154.' ************** PARI ***************** Host 69.154.30.117 (69.154.30.117) Time: Thu Apr 21 00:36:15 2005 Input: decimalcycle(p0,q0)= { local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans } decimalcycle(7,17) Output: ? ? [4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '195.128' ************** PARI ***************** Host 195.128.67.199 (195.128.67.199) Time: Thu Apr 21 04:20:28 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '195.128' ************** PARI ***************** Host 195.128.67.199 (195.128.67.199) Time: Thu Apr 21 04:20:45 2005 Input: factor(8) Output: ? [2 3] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '195.128' ************** PARI ***************** Host 195.128.67.199 (195.128.67.199) Time: Thu Apr 21 04:26:57 2005 Input: factor(873426282083472237420227951981) Output: ? [882522887823547 1] [989692498783223 1] ? Errors (if any) and Timing Info: Timing: real 0m0.110s user 0m0.046s sys 0m0.010s '195.128' ************** PARI ***************** Host 195.128.67.199 (195.128.67.199) Time: Thu Apr 21 04:27:38 2005 Input: factor(759204344728748305361209735427408110317842298754894530555817) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 15716 Killed /usr/bin/gp -q -emacs Timing: real 0m21.275s user 0m20.964s sys 0m0.038s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:33:14 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=10^4; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [5, 7, 35, 6, 11, 6] [5, 13, 65, 14, 20, 14] [11, 41, 451, 122, 137, 122] [11, 47, 517, 142, 157, 142] [11, 173, 1903, 518, 578, 518] [11, 179, 1969, 538, 598, 538] [11, 223, 2453, 670, 745, 670] [19, 103, 1957, 514, 595, 514] [41, 317, 12997, 3486, 3949, 3486] [41, 503, 20623, 5534, 6266, 5534] [71, 101, 7171, 1918, 2179, 1918] [71, 467, 33157, 8874, 10075, 8874] [71, 751, 53321, 14270, 16202, 14270] [71, 953, 67663, 18106, 20560, 18106] [71, 1237, 87827, 23502, 26687, 23502] [71, 1319, 93649, 25062, 28456, 25062] [71, 2089, 148319, 39690, 45068, 39690] [71, 2657, 188647, 50482, 57322, 50482] [71, 3023, 214633, 57438, 65218, 57438] [71, 3307, 234797, 62834, 71345, 62834] [71, 3793, 269303, 72066, 81830, 72066] [71, 4159, 295289, 79022, 89726, 79022] [71, 5011, 355781, 95210, 108107, 95210] [79, 109, 8611, 2290, 2617, 2290] Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 15961 Killed /usr/bin/gp -q -emacs Timing: real 0m21.016s user 0m20.983s sys 0m0.018s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:34:00 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+abs(c-d)/2-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=10^4; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 5, 15, 4, 4, 4] [3, 11, 33, 10, 10, 10] [23, 89, 2047, 622, 622, 622] [79, 283, 22357, 6793, 6793, 6793] Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 15967 Killed /usr/bin/gp -q -emacs Timing: real 0m21.002s user 0m20.993s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:34:50 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0-(c-d)/2-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=10^4; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 5, 15, 4, 4, 4] [3, 11, 33, 10, 10, 10] [23, 89, 2047, 622, 622, 622] [79, 283, 22357, 6793, 6793, 6793] Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 15973 Killed /usr/bin/gp -q -emacs Timing: real 0m21.016s user 0m20.986s sys 0m0.013s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:35:27 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=10^4; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [5, 7, 35, 6, 11, 6] [5, 13, 65, 14, 20, 14] [11, 41, 451, 122, 137, 122] [11, 47, 517, 142, 157, 142] [11, 173, 1903, 518, 578, 518] [11, 179, 1969, 538, 598, 538] [11, 223, 2453, 670, 745, 670] [19, 103, 1957, 514, 595, 514] [41, 317, 12997, 3486, 3949, 3486] [41, 503, 20623, 5534, 6266, 5534] [71, 101, 7171, 1918, 2179, 1918] [71, 467, 33157, 8874, 10075, 8874] [71, 751, 53321, 14270, 16202, 14270] [71, 953, 67663, 18106, 20560, 18106] [71, 1237, 87827, 23502, 26687, 23502] [71, 1319, 93649, 25062, 28456, 25062] [71, 2089, 148319, 39690, 45068, 39690] [71, 2657, 188647, 50482, 57322, 50482] [71, 3023, 214633, 57438, 65218, 57438] [71, 3307, 234797, 62834, 71345, 62834] [71, 3793, 269303, 72066, 81830, 72066] [71, 4159, 295289, 79022, 89726, 79022] [71, 5011, 355781, 95210, 108107, 95210] [79, 109, 8611, 2290, 2617, 2290] Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 15979 Killed /usr/bin/gp -q -emacs Timing: real 0m21.030s user 0m20.986s sys 0m0.015s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:36:03 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(d-c)/2-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=10^4; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 5, 15, 4, 4, 4] [3, 11, 33, 10, 10, 10] [23, 89, 2047, 622, 622, 622] [79, 283, 22357, 6793, 6793, 6793] Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 15988 Killed /usr/bin/gp -q -emacs Timing: real 0m21.012s user 0m20.983s sys 0m0.016s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:36:40 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.118-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=10^4; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [5, 83, 415, 84, 126, 84] [5, 227, 1135, 226, 345, 226] [5, 443, 2215, 444, 673, 444] [5, 487, 2435, 486, 740, 486] [5, 797, 3985, 796, 1211, 796] [5, 1013, 5065, 1014, 1539, 1014] [5, 1063, 5315, 1064, 1615, 1064] [5, 1373, 6865, 1374, 2086, 1374] [5, 1423, 7115, 1424, 2162, 1424] [5, 1733, 8665, 1734, 2633, 1734] [5, 1777, 8885, 1776, 2700, 1776] [5, 1993, 9965, 1994, 3028, 1994] [5, 2087, 10435, 2086, 3171, 2086] [5, 2347, 11735, 2346, 3566, 2346] [5, 2657, 13285, 2656, 4037, 2656] [5, 2663, 13315, 2664, 4046, 2664] [5, 2707, 13535, 2706, 4113, 2706] [5, 3593, 17965, 3594, 5459, 3594] [5, 3637, 18185, 3636, 5526, 3636] [5, 3803, 19015, 3804, 5778, 3804] [5, 3853, 19265, 3854, 5854, 3854] [5, 3947, 19735, 3946, 5997, 3946] [5, 4423, 22115, 4424, 6720, 4424] [5, 4517, 22585, 4516, 6863, 4516] [5, 4523, 22615, 4524, 6872, 4524] [5, 4567, 22835, 4566, 6939, 4566] [5, 4733, 23665, 4734, 7191, 4734] [5, 4783, 23915, 4784, 7267, 4784] [5, 4877, 24385, 4876, 7410, 4876] [5, 5237, 26185, 5236, 7957, 5236] [5, 5807, 29035, 5806, 8823, 5806] [5, 5857, 29285, 5856, 8899, 5856] [5, 6067, 30335, 6066, 9218, 6066] [5, 6073, 30365, 6074, 9227, 6074] [5, 6427, 32135, 6426, 9765, 6426] [5, 6737, 33685, 6736, 10236, 6736] [5, 6997, 34985, 6996, 10631, 6996] [5, 7213, 36065, 7214, 10959, 7214] [5, 7307, 36535, 7306, 11102, 7306] [5, 7573, 37865, 7574, 11506, 7574] [5, 7883, 39415, 7884, 11977, 7884] [5, 7933, 39665, 7934, 12053, 7934] [5, 8243, 41215, 8244, 12524, 8244] [5, 8863, 44315, 8864, 13466, 8864] [5, 9173, 45865, 9174, 13937, 9174] [5, 9433, 47165, 9434, 14332, 9434] [5, 9743, 48715, 9744, 14803, 9744] Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 15994 Killed /usr/bin/gp -q -emacs Timing: real 0m21.005s user 0m20.996s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:37:45 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.118-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=10^4; {nc=0;nt=0; forprime(p1=11,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 16001 Killed /usr/bin/gp -q -emacs Timing: real 0m21.010s user 0m20.980s sys 0m0.021s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:39:19 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.1178-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=10^4; {nc=0;nt=0; forprime(p1=11,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 16012 Killed /usr/bin/gp -q -emacs Timing: real 0m21.008s user 0m20.994s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:40:03 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.1178-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=10^4; {nc=0;nt=0; forprime(p1=7,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 16026 Killed /usr/bin/gp -q -emacs Timing: real 0m21.015s user 0m20.982s sys 0m0.019s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:40:35 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.118-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=400; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [5, 83, 415, 84, 126, 84] [5, 227, 1135, 226, 345, 226] Kevin: 2/3003 in 1994 ms ? Errors (if any) and Timing Info: Timing: real 0m2.010s user 0m2.002s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:40:53 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.118-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=500; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [5, 83, 415, 84, 126, 84] [5, 227, 1135, 226, 345, 226] [5, 443, 2215, 444, 673, 444] [5, 487, 2435, 486, 740, 486] Kevin: 4/4465 in 2975 ms ? Errors (if any) and Timing Info: Timing: real 0m2.988s user 0m2.981s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:41:15 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.118-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=600; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [5, 83, 415, 84, 126, 84] [5, 227, 1135, 226, 345, 226] [5, 443, 2215, 444, 673, 444] [5, 487, 2435, 486, 740, 486] Kevin: 4/5886 in 3894 ms ? Errors (if any) and Timing Info: Timing: real 0m3.906s user 0m3.899s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:41:36 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.118-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [5, 83, 415, 84, 126, 84] [5, 227, 1135, 226, 345, 226] [5, 443, 2215, 444, 673, 444] [5, 487, 2435, 486, 740, 486] Kevin: 4/7750 in 5191 ms ? Errors (if any) and Timing Info: Timing: real 0m5.207s user 0m5.196s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:41:53 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.123-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? Kevin: 0/7750 in 5187 ms ? Errors (if any) and Timing Info: Timing: real 0m5.199s user 0m5.191s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:42:09 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.01-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [5, 7, 35, 6, 11, 6] [5, 13, 65, 14, 20, 14] [23, 383, 8809, 2299, 2677, 2299] [569, 653, 371557, 97298, 112901, 97298] Kevin: 4/7750 in 5196 ms ? Errors (if any) and Timing Info: Timing: real 0m5.214s user 0m5.203s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:42:32 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.99-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 17, 51, 16, 15, 16] [5, 7, 35, 6, 11, 6] [5, 13, 65, 14, 20, 14] [7, 41, 287, 83, 87, 83] [11, 283, 3113, 848, 946, 848] Kevin: 5/7750 in 5214 ms ? Errors (if any) and Timing Info: Timing: real 0m5.231s user 0m5.218s sys 0m0.011s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:42:46 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.995-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 17, 51, 16, 15, 16] [5, 7, 35, 6, 11, 6] [5, 13, 65, 14, 20, 14] [7, 41, 287, 83, 87, 83] [7, 97, 679, 195, 206, 195] Kevin: 5/7750 in 5148 ms ? Errors (if any) and Timing Info: Timing: real 0m5.160s user 0m5.156s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:43:10 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.985-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 17, 51, 16, 15, 16] [5, 7, 35, 6, 11, 6] [5, 13, 65, 14, 20, 14] [7, 127, 889, 253, 270, 253] Kevin: 4/7750 in 5205 ms ? Errors (if any) and Timing Info: Timing: real 0m5.228s user 0m5.214s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:43:28 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.945-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10] [3, 17, 51, 16, 15, 16] [17, 541, 9197, 2704, 2795, 2704] [73, 199, 14527, 4379, 4414, 4379] Kevin: 4/7750 in 5169 ms ? Errors (if any) and Timing Info: Timing: real 0m5.182s user 0m5.177s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:43:42 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.745-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [2, 3, 6, 1, 2, 1] [3, 7, 21, 8, 6, 8] [3, 11, 33, 10, 10, 10] [3, 31, 93, 32, 28, 32] [3, 53, 159, 52, 48, 52] [13, 71, 923, 285, 280, 285] [23, 89, 2047, 622, 622, 622] [23, 233, 5359, 1632, 1628, 1632] [79, 349, 27571, 8375, 8378, 8375] Kevin: 9/7750 in 5201 ms ? Errors (if any) and Timing Info: Timing: real 0m5.220s user 0m5.208s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:44:01 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.75-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [2, 3, 6, 1, 2, 1] [3, 7, 21, 8, 6, 8] [3, 11, 33, 10, 10, 10] [3, 31, 93, 32, 28, 32] [3, 53, 159, 52, 48, 52] [13, 71, 923, 285, 280, 285] [23, 89, 2047, 622, 622, 622] [23, 233, 5359, 1632, 1628, 1632] [79, 349, 27571, 8375, 8378, 8375] Kevin: 9/7750 in 5196 ms ? Errors (if any) and Timing Info: Timing: real 0m5.212s user 0m5.200s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:44:15 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.65-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [2, 3, 6, 1, 2, 1] [3, 7, 21, 8, 6, 8] [3, 11, 33, 10, 10, 10] [3, 19, 57, 20, 17, 20] [3, 41, 123, 40, 37, 40] [23, 89, 2047, 622, 622, 622] Kevin: 6/7750 in 5192 ms ? Errors (if any) and Timing Info: Timing: real 0m5.205s user 0m5.200s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:44:32 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.65-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [2, 3, 6, 1, 2, 1] [2, 5, 10, 1, 3, 1] [2, 7, 14, 1, 4, 1] [337, 491, 165467, 17186, 50279, 17186] Kevin: 4/7750 in 5170 ms ? Errors (if any) and Timing Info: Timing: real 0m5.183s user 0m5.174s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:44:49 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.00118-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [5, 7, 35, 6, 11, 6] [5, 13, 65, 14, 20, 14] [11, 41, 451, 122, 137, 122] [11, 47, 517, 142, 157, 142] Kevin: 4/7750 in 5204 ms ? Errors (if any) and Timing Info: Timing: real 0m5.224s user 0m5.210s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:45:48 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.02-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [5, 7, 35, 6, 11, 6] [7, 43, 301, 85, 91, 85] Kevin: 2/7750 in 5142 ms ? Errors (if any) and Timing Info: Timing: real 0m5.155s user 0m5.148s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:46:02 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.125-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [5, 137, 685, 136, 208, 136] [5, 307, 1535, 306, 466, 306] Kevin: 2/7750 in 5190 ms ? Errors (if any) and Timing Info: Timing: real 0m5.204s user 0m5.197s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:46:17 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+abs(c-d)/2.125-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 5, 15, 4, 4, 4] [3, 11, 33, 10, 10, 10] [23, 89, 2047, 622, 622, 622] [79, 283, 22357, 6793, 6793, 6793] Kevin: 4/7750 in 5199 ms ? Errors (if any) and Timing Info: Timing: real 0m5.217s user 0m5.205s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:46:40 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+abs(c-d)/2-x; x1=/*round*/(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10.000000000000000000000000000000000000] [23, 89, 2047, 622, 622, 622.00000000000000000000000000000000000] Kevin: 2/7750 in 5234 ms ? Errors (if any) and Timing Info: Timing: real 0m5.248s user 0m5.236s sys 0m0.011s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:47:03 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+abs(c-d)/2.118-x; x1=/*round*/(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? Kevin: 0/7750 in 5149 ms ? Errors (if any) and Timing Info: Timing: real 0m5.162s user 0m5.154s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:47:21 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+abs(c-d)/1.95-x; x1=/*round*/(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10.000000000000000000000000000000000000] Kevin: 1/7750 in 5212 ms ? Errors (if any) and Timing Info: Timing: real 0m5.225s user 0m5.218s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:47:38 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.95-x; x1=/*round*/(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? Kevin: 0/7750 in 5198 ms ? Errors (if any) and Timing Info: Timing: real 0m5.214s user 0m5.203s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:47:56 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.047-x; x1=/*round*/(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? Kevin: 0/7750 in 5193 ms ? Errors (if any) and Timing Info: Timing: real 0m5.206s user 0m5.198s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:48:11 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.118-x; x1=/*round*/(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? Kevin: 0/7750 in 5188 ms ? Errors (if any) and Timing Info: Timing: real 0m5.207s user 0m5.198s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:48:29 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.878-x; x1=/*round*/(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? Kevin: 0/7750 in 5141 ms ? Errors (if any) and Timing Info: Timing: real 0m5.155s user 0m5.150s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:48:42 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.878-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10] [3, 41, 123, 40, 37, 40] [7, 83, 581, 167, 177, 167] [11, 19, 209, 56, 64, 56] [13, 19, 247, 77, 75, 77] [13, 59, 767, 235, 233, 235] [13, 97, 1261, 389, 383, 389] [13, 137, 1781, 547, 541, 547] [23, 89, 2047, 622, 622, 622] [23, 601, 13823, 4208, 4200, 4208] [79, 191, 15089, 4583, 4585, 4583] [79, 599, 47321, 14377, 14379, 14377] Kevin: 12/7750 in 5211 ms ? Errors (if any) and Timing Info: Timing: real 0m5.225s user 0m5.218s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:49:27 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.879-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=700; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10] [3, 41, 123, 40, 37, 40] [7, 83, 581, 167, 177, 167] [11, 19, 209, 56, 64, 56] [13, 19, 247, 77, 75, 77] [13, 59, 767, 235, 233, 235] [23, 89, 2047, 622, 622, 622] [79, 191, 15089, 4583, 4585, 4583] [79, 599, 47321, 14377, 14379, 14377] Kevin: 9/7750 in 5212 ms ? Errors (if any) and Timing Info: Timing: real 0m5.231s user 0m5.219s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:50:11 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.879-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=800; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10] [3, 41, 123, 40, 37, 40] [7, 83, 581, 167, 177, 167] [11, 19, 209, 56, 64, 56] [13, 19, 247, 77, 75, 77] [13, 59, 767, 235, 233, 235] [23, 89, 2047, 622, 622, 622] [79, 191, 15089, 4583, 4585, 4583] [79, 599, 47321, 14377, 14379, 14377] [181, 701, 126881, 38554, 38554, 38554] Kevin: 10/9591 in 6379 ms ? Errors (if any) and Timing Info: Timing: real 0m6.390s user 0m6.385s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:50:37 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.889-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=800; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10] [3, 29, 87, 28, 26, 28] [3, 41, 123, 40, 37, 40] [23, 89, 2047, 622, 622, 622] [43, 281, 12083, 3654, 3672, 3654] [181, 701, 126881, 38554, 38554, 38554] Kevin: 6/9591 in 6440 ms ? Errors (if any) and Timing Info: Timing: real 0m6.458s user 0m6.446s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:50:51 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.881-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=800; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10] [3, 29, 87, 28, 26, 28] [3, 41, 123, 40, 37, 40] [11, 19, 209, 56, 64, 56] [13, 19, 247, 77, 75, 77] [13, 59, 767, 235, 233, 235] [23, 89, 2047, 622, 622, 622] [79, 191, 15089, 4583, 4585, 4583] [79, 599, 47321, 14377, 14379, 14377] [181, 701, 126881, 38554, 38554, 38554] Kevin: 10/9591 in 6433 ms ? Errors (if any) and Timing Info: Timing: real 0m6.448s user 0m6.441s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:51:16 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.954-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=800; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10] [3, 17, 51, 16, 15, 16] Kevin: 2/9591 in 6389 ms ? Errors (if any) and Timing Info: Timing: real 0m6.403s user 0m6.396s sys 0m0.005s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:51:45 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.12-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=800; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [5, 83, 415, 84, 126, 84] [5, 127, 635, 126, 193, 126] [5, 563, 2815, 564, 855, 564] [5, 607, 3035, 606, 922, 606] [5, 613, 3065, 614, 931, 614] [5, 773, 3865, 774, 1174, 774] [19, 29, 551, 115, 167, 115] Kevin: 7/9591 in 6433 ms ? Errors (if any) and Timing Info: Timing: real 0m6.453s user 0m6.439s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:51:59 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.125-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=800; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [5, 137, 685, 136, 208, 136] [5, 307, 1535, 306, 466, 306] Kevin: 2/9591 in 6356 ms ? Errors (if any) and Timing Info: Timing: real 0m6.368s user 0m6.365s sys 0m0.003s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:52:12 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/2.135-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=800; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [5, 103, 515, 104, 156, 104] [11, 43, 473, 87, 144, 87] Kevin: 2/9591 in 6368 ms ? Errors (if any) and Timing Info: Timing: real 0m6.382s user 0m6.373s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:52:28 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.878-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=800; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10] [3, 41, 123, 40, 37, 40] [7, 83, 581, 167, 177, 167] [11, 19, 209, 56, 64, 56] [13, 19, 247, 77, 75, 77] [13, 59, 767, 235, 233, 235] [13, 97, 1261, 389, 383, 389] [13, 137, 1781, 547, 541, 547] [23, 89, 2047, 622, 622, 622] [23, 601, 13823, 4208, 4200, 4208] [79, 191, 15089, 4583, 4585, 4583] [79, 599, 47321, 14377, 14379, 14377] [181, 701, 126881, 38554, 38554, 38554] Kevin: 13/9591 in 6445 ms ? Errors (if any) and Timing Info: Timing: real 0m6.469s user 0m6.450s sys 0m0.017s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:54:33 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.996617-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=800; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 17, 51, 16, 15, 16] [5, 7, 35, 6, 11, 6] [5, 13, 65, 14, 20, 14] [7, 41, 287, 83, 87, 83] [7, 97, 679, 195, 206, 195] Kevin: 5/9591 in 6440 ms ? Errors (if any) and Timing Info: Timing: real 0m6.455s user 0m6.444s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:54:47 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.9966-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=800; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 17, 51, 16, 15, 16] [5, 7, 35, 6, 11, 6] [5, 13, 65, 14, 20, 14] [7, 41, 287, 83, 87, 83] [7, 97, 679, 195, 206, 195] Kevin: 5/9591 in 6446 ms ? Errors (if any) and Timing Info: Timing: real 0m6.467s user 0m6.455s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:55:02 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.877-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=800; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10] [3, 41, 123, 40, 37, 40] [7, 83, 581, 167, 177, 167] [11, 19, 209, 56, 64, 56] [13, 19, 247, 77, 75, 77] [13, 59, 767, 235, 233, 235] [13, 97, 1261, 389, 383, 389] [13, 137, 1781, 547, 541, 547] [23, 89, 2047, 622, 622, 622] [23, 601, 13823, 4208, 4200, 4208] [53, 139, 7367, 2225, 2239, 2225] [79, 191, 15089, 4583, 4585, 4583] [79, 599, 47321, 14377, 14379, 14377] [181, 701, 126881, 38554, 38554, 38554] Kevin: 14/9591 in 6450 ms ? Errors (if any) and Timing Info: Timing: real 0m6.468s user 0m6.458s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:55:29 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.877-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=1000; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10] [3, 41, 123, 40, 37, 40] [7, 83, 581, 167, 177, 167] [11, 19, 209, 56, 64, 56] [13, 19, 247, 77, 75, 77] [13, 59, 767, 235, 233, 235] [13, 97, 1261, 389, 383, 389] [13, 137, 1781, 547, 541, 547] [23, 89, 2047, 622, 622, 622] [23, 601, 13823, 4208, 4200, 4208] [53, 139, 7367, 2225, 2239, 2225] [79, 191, 15089, 4583, 4585, 4583] [79, 599, 47321, 14377, 14379, 14377] [181, 701, 126881, 38554, 38554, 38554] Kevin: 14/14028 in 9436 ms ? Errors (if any) and Timing Info: Timing: real 0m9.455s user 0m9.443s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:56:09 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.877-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=1500; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10] [3, 41, 123, 40, 37, 40] [7, 83, 581, 167, 177, 167] [11, 19, 209, 56, 64, 56] [13, 19, 247, 77, 75, 77] [13, 59, 767, 235, 233, 235] [13, 97, 1261, 389, 383, 389] [13, 137, 1781, 547, 541, 547] [23, 89, 2047, 622, 622, 622] [23, 601, 13823, 4208, 4200, 4208] [53, 139, 7367, 2225, 2239, 2225] [79, 191, 15089, 4583, 4585, 4583] [79, 599, 47321, 14377, 14379, 14377] [181, 701, 126881, 38554, 38554, 38554] Kevin: 14/28441 in 18942 ms ? Errors (if any) and Timing Info: Timing: real 0m22.055s user 0m18.948s sys 0m0.006s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:56:41 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.887-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=1500; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10] [3, 29, 87, 28, 26, 28] [3, 41, 123, 40, 37, 40] [23, 89, 2047, 622, 622, 622] [79, 191, 15089, 4583, 4585, 4583] [79, 599, 47321, 14377, 14379, 14377] [181, 701, 126881, 38554, 38554, 38554] Kevin: 7/28441 in 19145 ms ? Errors (if any) and Timing Info: Timing: real 0m20.224s user 0m19.152s sys 0m0.027s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:57:09 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.889-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=1500; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10] [3, 29, 87, 28, 26, 28] [3, 41, 123, 40, 37, 40] [23, 89, 2047, 622, 622, 622] [43, 281, 12083, 3654, 3672, 3654] [181, 701, 126881, 38554, 38554, 38554] Kevin: 6/28441 in 19159 ms ? Errors (if any) and Timing Info: Timing: real 0m19.216s user 0m19.165s sys 0m0.016s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:57:39 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.87-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=1500; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10] [3, 41, 123, 40, 37, 40] [3, 53, 159, 52, 48, 52] [7, 83, 581, 167, 177, 167] [11, 19, 209, 56, 64, 56] [13, 19, 247, 77, 75, 77] [13, 59, 767, 235, 233, 235] [23, 89, 2047, 622, 622, 622] [79, 191, 15089, 4583, 4585, 4583] [79, 599, 47321, 14377, 14379, 14377] [181, 701, 126881, 38554, 38554, 38554] Kevin: 11/28441 in 19109 ms ? Errors (if any) and Timing Info: Timing: real 0m19.160s user 0m19.112s sys 0m0.024s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:58:21 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=x0+(c-d)/1.56-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=1500; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [2, 3, 6, 1, 2, 1] [3, 11, 33, 10, 10, 10] [3, 29, 87, 28, 26, 28] [23, 89, 2047, 622, 622, 622] [23, 227, 5221, 1588, 1586, 1588] [181, 701, 126881, 38554, 38554, 38554] Kevin: 6/28441 in 19149 ms ? Errors (if any) and Timing Info: Timing: real 0m19.171s user 0m19.154s sys 0m0.013s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:58:56 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=(2*x0)+(c-d)-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=1500; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [2, 5, 10, 1, 3, 1] [2, 7, 14, 1, 4, 1] [2, 11, 22, 1, 7, 1] [13, 67, 871, 66, 265, 66] Kevin: 4/28441 in 19175 ms ? Errors (if any) and Timing Info: Timing: real 0m19.193s user 0m19.179s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 05:59:44 2005 Input: {testk(p1,p2)=local(p,a,b,c,d,new,x0,x1,ans); p=p1*p2; a=(p+1-x)/2; b=a*(a-1)/p; c=b+x/2; d=8*b-(p-x); x0=round(abs(polroots(c-d)[1])); new=(2*x0)+(c-d)/2-x; x1=round(abs(polroots(new)[1])); ans=lift(chinese(Mod(1,p1),Mod(-1,p2))); ans=min(ans,p-ans); [p1,p2,p,ans,x0,x1]} mp=1500; {nc=0;nt=0; forprime(p1=2,mp,forprime(p2=p1+1,mp, t=testk(p1,p2);nt=nt+1; if(t[4]==t[6],nc=nc+1;print(t)))); print("Kevin: "nc"/"nt " in "gettime" ms")} Output: ? ? ? ? ? [3, 11, 33, 10, 10, 10] [23, 89, 2047, 622, 622, 622] [79, 283, 22357, 6793, 6793, 6793] [181, 701, 126881, 38554, 38554, 38554] Kevin: 4/28441 in 19260 ms ? Errors (if any) and Timing Info: Timing: real 0m19.296s user 0m19.266s sys 0m0.014s '81.184.' ************** PARI ***************** Host 81.184.31.88 (81.184.31.88) Time: Thu Apr 21 18:41:21 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.171s user 0m0.008s sys 0m0.007s '81.184.' ************** PARI ***************** Host 81.184.31.88 (81.184.31.88) Time: Thu Apr 21 18:45:34 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.007s sys 0m0.003s '24.213.' ************** PARI ***************** Host 24.213.136.229 (24.213.136.229) Time: Thu Apr 21 20:12:50 2005 Input: zeta(2) Output: ? 1.6449340668482264364724151666460251892 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.005s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 22:56:33 2005 Input: { n=2; print(n); } Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 23:02:05 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 23:02:42 2005 Input: { n=2; print(n); } Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 23:15:03 2005 Input: { h=0; for(a=1,52, for(b=2,52,if(b>a, for(c=3,52,if(c>b, for(d=4,52,if(d>c, for(e=5,52,if(e>d, h=h+1; )) )) )) )) ) print(h); } Output: ? @ Euler I List Mat Mod O Pi Pol Polrev Qfb Ser Set Str Vec abs acos acosh addhelp addprimes agm algdep alias allocatemem arg asin asinh atan atanh bernfrac bernreal bernvec besseljh besselk bestappr bezout bezoutres bigomega binary binomial bitand bitneg bitnegimply bitor bittest bitxor bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark break ceil centerlift changevar charpoly chinese component concat conj conjvec content contfrac contfracpnqn core coredisc cos cosh cotan default denominator deriv dilog dirdiv direuler dirmul dirzetak divisors divrem eint1 elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint erfc error eta eulerphi eval exp extern factor factorback factorcantor factorff factorial factorint factormod factornf factorpadic ffinit fibonacci floor for fordiv forprime forstep forsubgroup forvec frac galoisfixedfield galoisinit galoispermtopol galoissubcyclo gamma gammah gcd getheap getrand getstack gettime global hilbert hyperu idealadd idealaddtoone idealappr idealchinese idealcoprime idealdiv idealfactor idealhnf idealintersect idealinv ideallist ideallistarch ideallog idealmin idealmul idealnorm idealpow idealprimedec idealprincipal idealred idealstar idealtwoelt idealval ideleprincipal if imag incgam incgamc input install intformal intnum isfundamental isprime ispseudoprime issquare issquarefree kill kronecker lcm length lex lift lindep listcreate listinsert listkill listput listsort lngamma log matadjoint matalgtobasis matbasistoalg matcompanion matdet matdetint matdiagonal mateigen mathess mathilbert mathnf mathnfmod mathnfmodid matid matimage matimagecompl matindexrank matintersect matinverseimage matisdiagonal matker matkerint matmuldiagonal matmultodiagonal matpascal matrank matrix matrixqz matsize matsnf matsolve matsolvemod matsupplement mattranspose max min modreverse moebius newtonpoly next nextprime nfalgtobasis nfbasis nfbasistoalg nfdetint nfdisc nfeltdiv nfeltdiveuc nfeltdivmodpr nfeltdivrem nfeltmod nfeltmul nfeltmulmodpr nfeltpow nfeltpowmodpr nfeltreduce nfeltreducemodpr nfeltval nffactor nffactormod nfgaloisapply nfgaloisconj nfhilbert nfhnf nfhnfmod nfinit nfisideal nfisincl nfisisom nfkermodpr nfmodprinit nfnewprec nfroots nfrootsof1 nfsnf nfsolvemodpr nfsubfields norm norml2 numdiv numerator numtoperm omega padicappr padicprec permtonum plot plotbox plotclip plotcolor plotcopy plotcursor plotdraw plotfile ploth plothraw plothsizes plotinit plotkill plotlines plotlinetype plotmove plotpoints plotpointsize plotpointtype plotrbox plotrecth plotrecthraw plotrline plotrmove plotrpoint plotscale plotstring plotterm polcoeff polcompositum polcyclo poldegree poldisc poldiscreduced polgalois polhensellift polinterpolate polisirreducible pollead pollegendre polrecip polred polredabs polredord polresultant polroots polrootsmod polrootspadic polsturm polsubcyclo polsylvestermatrix polsym poltchebi poltschirnhaus polylog polzagier precision precprime prime primes print print1 printp printp1 printtex prod prodeuler prodinf psdraw psi psploth psplothraw qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfgaussred qfjacobi qflll qflllgram qfminim qfperfection qfsign quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit quit random read real removeprimes reorder return rnfalgtobasis rnfbasis rnfbasistoalg rnfcharpoly rnfconductor rnfdedekind rnfdet rnfdisc rnfeltabstorel rnfeltdown rnfeltreltoabs rnfeltup rnfequation rnfhnfbasis rnfidealabstorel rnfidealdown rnfidealhnf rnfidealmul rnfidealnormabs rnfidealnormrel rnfidealreltoabs rnfidealtwoelt rnfidealup rnfinit rnfisfree rnfisnorm rnfkummer rnflllgram rnfnormgroup rnfpolred rnfpolredabs rnfpseudobasis rnfsteinitz round serconvol serlaplace serreverse setintersect setisset setminus setrand setsearch setunion shift shiftmul sigma sign simplify sin sinh sizebyte sizedigit solve sqr sqrt sqrtint sqrtn subgrouplist subst sum sumalt sumdiv suminf sumpos system tan tanh taylor teichmuller theta thetanullk thue thueinit trace trap truncate type until valuation variable vecextract vecmax vecmin vecsort vector vectorv weber whatnow while write write1 writetex x zeta zetak zetakinit znlog znorder znprimroot znstar @E_N_D@ Euler I List Mat Mod O Pi Pol Polrev Qfb Ser Set Str Vec abs acos acosh addhelp addprimes agm algdep alias allocatemem arg asin asinh atan atanh bernfrac bernreal bernvec besseljh besselk bestappr bezout bezoutres bigomega binary binomial bitand bitneg bitnegimply bitor bittest bitxor bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark break ceil centerlift changevar charpoly chinese component concat conj conjvec content contfrac contfracpnqn core coredisc cos cosh cotan default denominator deri ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** unexpected character: h=0;for(a=1,52,_for(b=2,52,if(b>a,_ ^-------------------- Timing: real 0m0.022s user 0m0.014s sys 0m0.006s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 23:16:38 2005 Input: { h=2; print(h); } Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 23:18:01 2005 Input: { h=0; for(a=1,52, for(b=2,52,if(b>a, for(c=3,52,if(c>b, for(d=4,52,if(d>c, for(e=5,52,if(e>d, h=h+1 )) )) )) )) ) print(h); } Output: ? @ Euler I List Mat Mod O Pi Pol Polrev Qfb Ser Set Str Vec abs acos acosh addhelp addprimes agm algdep alias allocatemem arg asin asinh atan atanh bernfrac bernreal bernvec besseljh besselk bestappr bezout bezoutres bigomega binary binomial bitand bitneg bitnegimply bitor bittest bitxor bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark break ceil centerlift changevar charpoly chinese component concat conj conjvec content contfrac contfracpnqn core coredisc cos cosh cotan default denominator deriv dilog dirdiv direuler dirmul dirzetak divisors divrem eint1 elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint erfc error eta eulerphi eval exp extern factor factorback factorcantor factorff factorial factorint factormod factornf factorpadic ffinit fibonacci floor for fordiv forprime forstep forsubgroup forvec frac galoisfixedfield galoisinit galoispermtopol galoissubcyclo gamma gammah gcd getheap getrand getstack gettime global hilbert hyperu idealadd idealaddtoone idealappr idealchinese idealcoprime idealdiv idealfactor idealhnf idealintersect idealinv ideallist ideallistarch ideallog idealmin idealmul idealnorm idealpow idealprimedec idealprincipal idealred idealstar idealtwoelt idealval ideleprincipal if imag incgam incgamc input install intformal intnum isfundamental isprime ispseudoprime issquare issquarefree kill kronecker lcm length lex lift lindep listcreate listinsert listkill listput listsort lngamma log matadjoint matalgtobasis matbasistoalg matcompanion matdet matdetint matdiagonal mateigen mathess mathilbert mathnf mathnfmod mathnfmodid matid matimage matimagecompl matindexrank matintersect matinverseimage matisdiagonal matker matkerint matmuldiagonal matmultodiagonal matpascal matrank matrix matrixqz matsize matsnf matsolve matsolvemod matsupplement mattranspose max min modreverse moebius newtonpoly next nextprime nfalgtobasis nfbasis nfbasistoalg nfdetint nfdisc nfeltdiv nfeltdiveuc nfeltdivmodpr nfeltdivrem nfeltmod nfeltmul nfeltmulmodpr nfeltpow nfeltpowmodpr nfeltreduce nfeltreducemodpr nfeltval nffactor nffactormod nfgaloisapply nfgaloisconj nfhilbert nfhnf nfhnfmod nfinit nfisideal nfisincl nfisisom nfkermodpr nfmodprinit nfnewprec nfroots nfrootsof1 nfsnf nfsolvemodpr nfsubfields norm norml2 numdiv numerator numtoperm omega padicappr padicprec permtonum plot plotbox plotclip plotcolor plotcopy plotcursor plotdraw plotfile ploth plothraw plothsizes plotinit plotkill plotlines plotlinetype plotmove plotpoints plotpointsize plotpointtype plotrbox plotrecth plotrecthraw plotrline plotrmove plotrpoint plotscale plotstring plotterm polcoeff polcompositum polcyclo poldegree poldisc poldiscreduced polgalois polhensellift polinterpolate polisirreducible pollead pollegendre polrecip polred polredabs polredord polresultant polroots polrootsmod polrootspadic polsturm polsubcyclo polsylvestermatrix polsym poltchebi poltschirnhaus polylog polzagier precision precprime prime primes print print1 printp printp1 printtex prod prodeuler prodinf psdraw psi psploth psplothraw qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfgaussred qfjacobi qflll qflllgram qfminim qfperfection qfsign quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit quit random read real removeprimes reorder return rnfalgtobasis rnfbasis rnfbasistoalg rnfcharpoly rnfconductor rnfdedekind rnfdet rnfdisc rnfeltabstorel rnfeltdown rnfeltreltoabs rnfeltup rnfequation rnfhnfbasis rnfidealabstorel rnfidealdown rnfidealhnf rnfidealmul rnfidealnormabs rnfidealnormrel rnfidealreltoabs rnfidealtwoelt rnfidealup rnfinit rnfisfree rnfisnorm rnfkummer rnflllgram rnfnormgroup rnfpolred rnfpolredabs rnfpseudobasis rnfsteinitz round serconvol serlaplace serreverse setintersect setisset setminus setrand setsearch setunion shift shiftmul sigma sign simplify sin sinh sizebyte sizedigit solve sqr sqrt sqrtint sqrtn subgrouplist subst sum sumalt sumdiv suminf sumpos system tan tanh taylor teichmuller theta thetanullk thue thueinit trace trap truncate type until valuation variable vecextract vecmax vecmin vecsort vector vectorv weber whatnow while write write1 writetex x zeta zetak zetakinit znlog znorder znprimroot znstar @E_N_D@ Euler I List Mat Mod O Pi Pol Polrev Qfb Ser Set Str Vec abs acos acosh addhelp addprimes agm algdep alias allocatemem arg asin asinh atan atanh bernfrac bernreal bernvec besseljh besselk bestappr bezout bezoutres bigomega binary binomial bitand bitneg bitnegimply bitor bittest bitxor bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark break ceil centerlift changevar charpoly chinese component concat conj conjvec content contfrac contfracpnqn core coredisc cos cosh cotan default denominator deri ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** unexpected character: h=0;for(a=1,52,_for(b=2,52,if(b>a,_ ^-------------------- Timing: real 0m0.023s user 0m0.018s sys 0m0.004s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 23:22:23 2005 Input: { h=0; for(a=1,52, for(b=2,52,if(b>a, h=h+1 )) ) print(h); } Output: ? @ Euler I List Mat Mod O Pi Pol Polrev Qfb Ser Set Str Vec abs acos acosh addhelp addprimes agm algdep alias allocatemem arg asin asinh atan atanh bernfrac bernreal bernvec besseljh besselk bestappr bezout bezoutres bigomega binary binomial bitand bitneg bitnegimply bitor bittest bitxor bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark break ceil centerlift changevar charpoly chinese component concat conj conjvec content contfrac contfracpnqn core coredisc cos cosh cotan default denominator deriv dilog dirdiv direuler dirmul dirzetak divisors divrem eint1 elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint erfc error eta eulerphi eval exp extern factor factorback factorcantor factorff factorial factorint factormod factornf factorpadic ffinit fibonacci floor for fordiv forprime forstep forsubgroup forvec frac galoisfixedfield galoisinit galoispermtopol galoissubcyclo gamma gammah gcd getheap getrand getstack gettime global hilbert hyperu idealadd idealaddtoone idealappr idealchinese idealcoprime idealdiv idealfactor idealhnf idealintersect idealinv ideallist ideallistarch ideallog idealmin idealmul idealnorm idealpow idealprimedec idealprincipal idealred idealstar idealtwoelt idealval ideleprincipal if imag incgam incgamc input install intformal intnum isfundamental isprime ispseudoprime issquare issquarefree kill kronecker lcm length lex lift lindep listcreate listinsert listkill listput listsort lngamma log matadjoint matalgtobasis matbasistoalg matcompanion matdet matdetint matdiagonal mateigen mathess mathilbert mathnf mathnfmod mathnfmodid matid matimage matimagecompl matindexrank matintersect matinverseimage matisdiagonal matker matkerint matmuldiagonal matmultodiagonal matpascal matrank matrix matrixqz matsize matsnf matsolve matsolvemod matsupplement mattranspose max min modreverse moebius newtonpoly next nextprime nfalgtobasis nfbasis nfbasistoalg nfdetint nfdisc nfeltdiv nfeltdiveuc nfeltdivmodpr nfeltdivrem nfeltmod nfeltmul nfeltmulmodpr nfeltpow nfeltpowmodpr nfeltreduce nfeltreducemodpr nfeltval nffactor nffactormod nfgaloisapply nfgaloisconj nfhilbert nfhnf nfhnfmod nfinit nfisideal nfisincl nfisisom nfkermodpr nfmodprinit nfnewprec nfroots nfrootsof1 nfsnf nfsolvemodpr nfsubfields norm norml2 numdiv numerator numtoperm omega padicappr padicprec permtonum plot plotbox plotclip plotcolor plotcopy plotcursor plotdraw plotfile ploth plothraw plothsizes plotinit plotkill plotlines plotlinetype plotmove plotpoints plotpointsize plotpointtype plotrbox plotrecth plotrecthraw plotrline plotrmove plotrpoint plotscale plotstring plotterm polcoeff polcompositum polcyclo poldegree poldisc poldiscreduced polgalois polhensellift polinterpolate polisirreducible pollead pollegendre polrecip polred polredabs polredord polresultant polroots polrootsmod polrootspadic polsturm polsubcyclo polsylvestermatrix polsym poltchebi poltschirnhaus polylog polzagier precision precprime prime primes print print1 printp printp1 printtex prod prodeuler prodinf psdraw psi psploth psplothraw qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfgaussred qfjacobi qflll qflllgram qfminim qfperfection qfsign quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit quit random read real removeprimes reorder return rnfalgtobasis rnfbasis rnfbasistoalg rnfcharpoly rnfconductor rnfdedekind rnfdet rnfdisc rnfeltabstorel rnfeltdown rnfeltreltoabs rnfeltup rnfequation rnfhnfbasis rnfidealabstorel rnfidealdown rnfidealhnf rnfidealmul rnfidealnormabs rnfidealnormrel rnfidealreltoabs rnfidealtwoelt rnfidealup rnfinit rnfisfree rnfisnorm rnfkummer rnflllgram rnfnormgroup rnfpolred rnfpolredabs rnfpseudobasis rnfsteinitz round serconvol serlaplace serreverse setintersect setisset setminus setrand setsearch setunion shift shiftmul sigma sign simplify sin sinh sizebyte sizedigit solve sqr sqrt sqrtint sqrtn subgrouplist subst sum sumalt sumdiv suminf sumpos system tan tanh taylor teichmuller theta thetanullk thue thueinit trace trap truncate type until valuation variable vecextract vecmax vecmin vecsort vector vectorv weber whatnow while write write1 writetex x zeta zetak zetakinit znlog znorder znprimroot znstar @E_N_D@ Euler I List Mat Mod O Pi Pol Polrev Qfb Ser Set Str Vec abs acos acosh addhelp addprimes agm algdep alias allocatemem arg asin asinh atan atanh bernfrac bernreal bernvec besseljh besselk bestappr bezout bezoutres bigomega binary binomial bitand bitneg bitnegimply bitor bittest bitxor bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark break ceil centerlift changevar charpoly chinese component concat conj conjvec content contfrac contfracpnqn core coredisc cos cosh cotan default denominator deri ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** unexpected character: h=0;for(a=1,52,_for(b=2,52,if(b>a,_ ^-------------------- Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 23:24:32 2005 Input: { h=0; for(a=1,52, for(b=2,52,if(b>a, h=h+1 )) ); print(h); } Output: ? @ Euler I List Mat Mod O Pi Pol Polrev Qfb Ser Set Str Vec abs acos acosh addhelp addprimes agm algdep alias allocatemem arg asin asinh atan atanh bernfrac bernreal bernvec besseljh besselk bestappr bezout bezoutres bigomega binary binomial bitand bitneg bitnegimply bitor bittest bitxor bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark break ceil centerlift changevar charpoly chinese component concat conj conjvec content contfrac contfracpnqn core coredisc cos cosh cotan default denominator deriv dilog dirdiv direuler dirmul dirzetak divisors divrem eint1 elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint erfc error eta eulerphi eval exp extern factor factorback factorcantor factorff factorial factorint factormod factornf factorpadic ffinit fibonacci floor for fordiv forprime forstep forsubgroup forvec frac galoisfixedfield galoisinit galoispermtopol galoissubcyclo gamma gammah gcd getheap getrand getstack gettime global hilbert hyperu idealadd idealaddtoone idealappr idealchinese idealcoprime idealdiv idealfactor idealhnf idealintersect idealinv ideallist ideallistarch ideallog idealmin idealmul idealnorm idealpow idealprimedec idealprincipal idealred idealstar idealtwoelt idealval ideleprincipal if imag incgam incgamc input install intformal intnum isfundamental isprime ispseudoprime issquare issquarefree kill kronecker lcm length lex lift lindep listcreate listinsert listkill listput listsort lngamma log matadjoint matalgtobasis matbasistoalg matcompanion matdet matdetint matdiagonal mateigen mathess mathilbert mathnf mathnfmod mathnfmodid matid matimage matimagecompl matindexrank matintersect matinverseimage matisdiagonal matker matkerint matmuldiagonal matmultodiagonal matpascal matrank matrix matrixqz matsize matsnf matsolve matsolvemod matsupplement mattranspose max min modreverse moebius newtonpoly next nextprime nfalgtobasis nfbasis nfbasistoalg nfdetint nfdisc nfeltdiv nfeltdiveuc nfeltdivmodpr nfeltdivrem nfeltmod nfeltmul nfeltmulmodpr nfeltpow nfeltpowmodpr nfeltreduce nfeltreducemodpr nfeltval nffactor nffactormod nfgaloisapply nfgaloisconj nfhilbert nfhnf nfhnfmod nfinit nfisideal nfisincl nfisisom nfkermodpr nfmodprinit nfnewprec nfroots nfrootsof1 nfsnf nfsolvemodpr nfsubfields norm norml2 numdiv numerator numtoperm omega padicappr padicprec permtonum plot plotbox plotclip plotcolor plotcopy plotcursor plotdraw plotfile ploth plothraw plothsizes plotinit plotkill plotlines plotlinetype plotmove plotpoints plotpointsize plotpointtype plotrbox plotrecth plotrecthraw plotrline plotrmove plotrpoint plotscale plotstring plotterm polcoeff polcompositum polcyclo poldegree poldisc poldiscreduced polgalois polhensellift polinterpolate polisirreducible pollead pollegendre polrecip polred polredabs polredord polresultant polroots polrootsmod polrootspadic polsturm polsubcyclo polsylvestermatrix polsym poltchebi poltschirnhaus polylog polzagier precision precprime prime primes print print1 printp printp1 printtex prod prodeuler prodinf psdraw psi psploth psplothraw qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfgaussred qfjacobi qflll qflllgram qfminim qfperfection qfsign quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit quit random read real removeprimes reorder return rnfalgtobasis rnfbasis rnfbasistoalg rnfcharpoly rnfconductor rnfdedekind rnfdet rnfdisc rnfeltabstorel rnfeltdown rnfeltreltoabs rnfeltup rnfequation rnfhnfbasis rnfidealabstorel rnfidealdown rnfidealhnf rnfidealmul rnfidealnormabs rnfidealnormrel rnfidealreltoabs rnfidealtwoelt rnfidealup rnfinit rnfisfree rnfisnorm rnfkummer rnflllgram rnfnormgroup rnfpolred rnfpolredabs rnfpseudobasis rnfsteinitz round serconvol serlaplace serreverse setintersect setisset setminus setrand setsearch setunion shift shiftmul sigma sign simplify sin sinh sizebyte sizedigit solve sqr sqrt sqrtint sqrtn subgrouplist subst sum sumalt sumdiv suminf sumpos system tan tanh taylor teichmuller theta thetanullk thue thueinit trace trap truncate type until valuation variable vecextract vecmax vecmin vecsort vector vectorv weber whatnow while write write1 writetex x zeta zetak zetakinit znlog znorder znprimroot znstar @E_N_D@ Euler I List Mat Mod O Pi Pol Polrev Qfb Ser Set Str Vec abs acos acosh addhelp addprimes agm algdep alias allocatemem arg asin asinh atan atanh bernfrac bernreal bernvec besseljh besselk bestappr bezout bezoutres bigomega binary binomial bitand bitneg bitnegimply bitor bittest bitxor bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark break ceil centerlift changevar charpoly chinese component concat conj conjvec content contfrac contfracpnqn core coredisc cos cosh cotan default denominator deri ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** unexpected character: h=0;for(a=1,52,_for(b=2,52,if(b>a,_ ^-------------------- Timing: real 0m0.014s user 0m0.009s sys 0m0.004s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 23:25:52 2005 Input: { h=0; for(a=1,52,print(a)) } Output: ? @ Euler I List Mat Mod O Pi Pol Polrev Qfb Ser Set Str Vec abs acos acosh addhelp addprimes agm algdep alias allocatemem arg asin asinh atan atanh bernfrac bernreal bernvec besseljh besselk bestappr bezout bezoutres bigomega binary binomial bitand bitneg bitnegimply bitor bittest bitxor bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark break ceil centerlift changevar charpoly chinese component concat conj conjvec content contfrac contfracpnqn core coredisc cos cosh cotan default denominator deriv dilog dirdiv direuler dirmul dirzetak divisors divrem eint1 elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint erfc error eta eulerphi eval exp extern factor factorback factorcantor factorff factorial factorint factormod factornf factorpadic ffinit fibonacci floor for fordiv forprime forstep forsubgroup forvec frac galoisfixedfield galoisinit galoispermtopol galoissubcyclo gamma gammah gcd getheap getrand getstack gettime global hilbert hyperu idealadd idealaddtoone idealappr idealchinese idealcoprime idealdiv idealfactor idealhnf idealintersect idealinv ideallist ideallistarch ideallog idealmin idealmul idealnorm idealpow idealprimedec idealprincipal idealred idealstar idealtwoelt idealval ideleprincipal if imag incgam incgamc input install intformal intnum isfundamental isprime ispseudoprime issquare issquarefree kill kronecker lcm length lex lift lindep listcreate listinsert listkill listput listsort lngamma log matadjoint matalgtobasis matbasistoalg matcompanion matdet matdetint matdiagonal mateigen mathess mathilbert mathnf mathnfmod mathnfmodid matid matimage matimagecompl matindexrank matintersect matinverseimage matisdiagonal matker matkerint matmuldiagonal matmultodiagonal matpascal matrank matrix matrixqz matsize matsnf matsolve matsolvemod matsupplement mattranspose max min modreverse moebius newtonpoly next nextprime nfalgtobasis nfbasis nfbasistoalg nfdetint nfdisc nfeltdiv nfeltdiveuc nfeltdivmodpr nfeltdivrem nfeltmod nfeltmul nfeltmulmodpr nfeltpow nfeltpowmodpr nfeltreduce nfeltreducemodpr nfeltval nffactor nffactormod nfgaloisapply nfgaloisconj nfhilbert nfhnf nfhnfmod nfinit nfisideal nfisincl nfisisom nfkermodpr nfmodprinit nfnewprec nfroots nfrootsof1 nfsnf nfsolvemodpr nfsubfields norm norml2 numdiv numerator numtoperm omega padicappr padicprec permtonum plot plotbox plotclip plotcolor plotcopy plotcursor plotdraw plotfile ploth plothraw plothsizes plotinit plotkill plotlines plotlinetype plotmove plotpoints plotpointsize plotpointtype plotrbox plotrecth plotrecthraw plotrline plotrmove plotrpoint plotscale plotstring plotterm polcoeff polcompositum polcyclo poldegree poldisc poldiscreduced polgalois polhensellift polinterpolate polisirreducible pollead pollegendre polrecip polred polredabs polredord polresultant polroots polrootsmod polrootspadic polsturm polsubcyclo polsylvestermatrix polsym poltchebi poltschirnhaus polylog polzagier precision precprime prime primes print print1 printp printp1 printtex prod prodeuler prodinf psdraw psi psploth psplothraw qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfgaussred qfjacobi qflll qflllgram qfminim qfperfection qfsign quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit quit random read real removeprimes reorder return rnfalgtobasis rnfbasis rnfbasistoalg rnfcharpoly rnfconductor rnfdedekind rnfdet rnfdisc rnfeltabstorel rnfeltdown rnfeltreltoabs rnfeltup rnfequation rnfhnfbasis rnfidealabstorel rnfidealdown rnfidealhnf rnfidealmul rnfidealnormabs rnfidealnormrel rnfidealreltoabs rnfidealtwoelt rnfidealup rnfinit rnfisfree rnfisnorm rnfkummer rnflllgram rnfnormgroup rnfpolred rnfpolredabs rnfpseudobasis rnfsteinitz round serconvol serlaplace serreverse setintersect setisset setminus setrand setsearch setunion shift shiftmul sigma sign simplify sin sinh sizebyte sizedigit solve sqr sqrt sqrtint sqrtn subgrouplist subst sum sumalt sumdiv suminf sumpos system tan tanh taylor teichmuller theta thetanullk thue thueinit trace trap truncate type until valuation variable vecextract vecmax vecmin vecsort vector vectorv weber whatnow while write write1 writetex x zeta zetak zetakinit znlog znorder znprimroot znstar @E_N_D1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 ? Errors (if any) and Timing Info: *** Warning: unused characters: _. Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 23:25:59 2005 Input: { h=0; for(a=1,52,print(a)); } Output: ? @ Euler I List Mat Mod O Pi Pol Polrev Qfb Ser Set Str Vec abs acos acosh addhelp addprimes agm algdep alias allocatemem arg asin asinh atan atanh bernfrac bernreal bernvec besseljh besselk bestappr bezout bezoutres bigomega binary binomial bitand bitneg bitnegimply bitor bittest bitxor bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark break ceil centerlift changevar charpoly chinese component concat conj conjvec content contfrac contfracpnqn core coredisc cos cosh cotan default denominator deriv dilog dirdiv direuler dirmul dirzetak divisors divrem eint1 elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint erfc error eta eulerphi eval exp extern factor factorback factorcantor factorff factorial factorint factormod factornf factorpadic ffinit fibonacci floor for fordiv forprime forstep forsubgroup forvec frac galoisfixedfield galoisinit galoispermtopol galoissubcyclo gamma gammah gcd getheap getrand getstack gettime global hilbert hyperu idealadd idealaddtoone idealappr idealchinese idealcoprime idealdiv idealfactor idealhnf idealintersect idealinv ideallist ideallistarch ideallog idealmin idealmul idealnorm idealpow idealprimedec idealprincipal idealred idealstar idealtwoelt idealval ideleprincipal if imag incgam incgamc input install intformal intnum isfundamental isprime ispseudoprime issquare issquarefree kill kronecker lcm length lex lift lindep listcreate listinsert listkill listput listsort lngamma log matadjoint matalgtobasis matbasistoalg matcompanion matdet matdetint matdiagonal mateigen mathess mathilbert mathnf mathnfmod mathnfmodid matid matimage matimagecompl matindexrank matintersect matinverseimage matisdiagonal matker matkerint matmuldiagonal matmultodiagonal matpascal matrank matrix matrixqz matsize matsnf matsolve matsolvemod matsupplement mattranspose max min modreverse moebius newtonpoly next nextprime nfalgtobasis nfbasis nfbasistoalg nfdetint nfdisc nfeltdiv nfeltdiveuc nfeltdivmodpr nfeltdivrem nfeltmod nfeltmul nfeltmulmodpr nfeltpow nfeltpowmodpr nfeltreduce nfeltreducemodpr nfeltval nffactor nffactormod nfgaloisapply nfgaloisconj nfhilbert nfhnf nfhnfmod nfinit nfisideal nfisincl nfisisom nfkermodpr nfmodprinit nfnewprec nfroots nfrootsof1 nfsnf nfsolvemodpr nfsubfields norm norml2 numdiv numerator numtoperm omega padicappr padicprec permtonum plot plotbox plotclip plotcolor plotcopy plotcursor plotdraw plotfile ploth plothraw plothsizes plotinit plotkill plotlines plotlinetype plotmove plotpoints plotpointsize plotpointtype plotrbox plotrecth plotrecthraw plotrline plotrmove plotrpoint plotscale plotstring plotterm polcoeff polcompositum polcyclo poldegree poldisc poldiscreduced polgalois polhensellift polinterpolate polisirreducible pollead pollegendre polrecip polred polredabs polredord polresultant polroots polrootsmod polrootspadic polsturm polsubcyclo polsylvestermatrix polsym poltchebi poltschirnhaus polylog polzagier precision precprime prime primes print print1 printp printp1 printtex prod prodeuler prodinf psdraw psi psploth psplothraw qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfgaussred qfjacobi qflll qflllgram qfminim qfperfection qfsign quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit quit random read real removeprimes reorder return rnfalgtobasis rnfbasis rnfbasistoalg rnfcharpoly rnfconductor rnfdedekind rnfdet rnfdisc rnfeltabstorel rnfeltdown rnfeltreltoabs rnfeltup rnfequation rnfhnfbasis rnfidealabstorel rnfidealdown rnfidealhnf rnfidealmul rnfidealnormabs rnfidealnormrel rnfidealreltoabs rnfidealtwoelt rnfidealup rnfinit rnfisfree rnfisnorm rnfkummer rnflllgram rnfnormgroup rnfpolred rnfpolredabs rnfpseudobasis rnfsteinitz round serconvol serlaplace serreverse setintersect setisset setminus setrand setsearch setunion shift shiftmul sigma sign simplify sin sinh sizebyte sizedigit solve sqr sqrt sqrtint sqrtn subgrouplist subst sum sumalt sumdiv suminf sumpos system tan tanh taylor teichmuller theta thetanullk thue thueinit trace trap truncate type until valuation variable vecextract vecmax vecmin vecsort vector vectorv weber whatnow while write write1 writetex x zeta zetak zetakinit znlog znorder znprimroot znstar @E_N_D? Errors (if any) and Timing Info: *** unexpected character: h=0;for(a=1,52,print(a));_ ^- Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 23:26:20 2005 Input: { for(a=1,52,print(a)); } Output: ? @ Euler I List Mat Mod O Pi Pol Polrev Qfb Ser Set Str Vec abs acos acosh addhelp addprimes agm algdep alias allocatemem arg asin asinh atan atanh bernfrac bernreal bernvec besseljh besselk bestappr bezout bezoutres bigomega binary binomial bitand bitneg bitnegimply bitor bittest bitxor bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark break ceil centerlift changevar charpoly chinese component concat conj conjvec content contfrac contfracpnqn core coredisc cos cosh cotan default denominator deriv dilog dirdiv direuler dirmul dirzetak divisors divrem eint1 elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint erfc error eta eulerphi eval exp extern factor factorback factorcantor factorff factorial factorint factormod factornf factorpadic ffinit fibonacci floor for fordiv forprime forstep forsubgroup forvec frac galoisfixedfield galoisinit galoispermtopol galoissubcyclo gamma gammah gcd getheap getrand getstack gettime global hilbert hyperu idealadd idealaddtoone idealappr idealchinese idealcoprime idealdiv idealfactor idealhnf idealintersect idealinv ideallist ideallistarch ideallog idealmin idealmul idealnorm idealpow idealprimedec idealprincipal idealred idealstar idealtwoelt idealval ideleprincipal if imag incgam incgamc input install intformal intnum isfundamental isprime ispseudoprime issquare issquarefree kill kronecker lcm length lex lift lindep listcreate listinsert listkill listput listsort lngamma log matadjoint matalgtobasis matbasistoalg matcompanion matdet matdetint matdiagonal mateigen mathess mathilbert mathnf mathnfmod mathnfmodid matid matimage matimagecompl matindexrank matintersect matinverseimage matisdiagonal matker matkerint matmuldiagonal matmultodiagonal matpascal matrank matrix matrixqz matsize matsnf matsolve matsolvemod matsupplement mattranspose max min modreverse moebius newtonpoly next nextprime nfalgtobasis nfbasis nfbasistoalg nfdetint nfdisc nfeltdiv nfeltdiveuc nfeltdivmodpr nfeltdivrem nfeltmod nfeltmul nfeltmulmodpr nfeltpow nfeltpowmodpr nfeltreduce nfeltreducemodpr nfeltval nffactor nffactormod nfgaloisapply nfgaloisconj nfhilbert nfhnf nfhnfmod nfinit nfisideal nfisincl nfisisom nfkermodpr nfmodprinit nfnewprec nfroots nfrootsof1 nfsnf nfsolvemodpr nfsubfields norm norml2 numdiv numerator numtoperm omega padicappr padicprec permtonum plot plotbox plotclip plotcolor plotcopy plotcursor plotdraw plotfile ploth plothraw plothsizes plotinit plotkill plotlines plotlinetype plotmove plotpoints plotpointsize plotpointtype plotrbox plotrecth plotrecthraw plotrline plotrmove plotrpoint plotscale plotstring plotterm polcoeff polcompositum polcyclo poldegree poldisc poldiscreduced polgalois polhensellift polinterpolate polisirreducible pollead pollegendre polrecip polred polredabs polredord polresultant polroots polrootsmod polrootspadic polsturm polsubcyclo polsylvestermatrix polsym poltchebi poltschirnhaus polylog polzagier precision precprime prime primes print print1 printp printp1 printtex prod prodeuler prodinf psdraw psi psploth psplothraw qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfgaussred qfjacobi qflll qflllgram qfminim qfperfection qfsign quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit quit random read real removeprimes reorder return rnfalgtobasis rnfbasis rnfbasistoalg rnfcharpoly rnfconductor rnfdedekind rnfdet rnfdisc rnfeltabstorel rnfeltdown rnfeltreltoabs rnfeltup rnfequation rnfhnfbasis rnfidealabstorel rnfidealdown rnfidealhnf rnfidealmul rnfidealnormabs rnfidealnormrel rnfidealreltoabs rnfidealtwoelt rnfidealup rnfinit rnfisfree rnfisnorm rnfkummer rnflllgram rnfnormgroup rnfpolred rnfpolredabs rnfpseudobasis rnfsteinitz round serconvol serlaplace serreverse setintersect setisset setminus setrand setsearch setunion shift shiftmul sigma sign simplify sin sinh sizebyte sizedigit solve sqr sqrt sqrtint sqrtn subgrouplist subst sum sumalt sumdiv suminf sumpos system tan tanh taylor teichmuller theta thetanullk thue thueinit trace trap truncate type until valuation variable vecextract vecmax vecmin vecsort vector vectorv weber whatnow while write write1 writetex x zeta zetak zetakinit znlog znorder znprimroot znstar @E_N_D? Errors (if any) and Timing Info: *** unexpected character: for(a=1,52,print(a));_ ^- Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 23:28:00 2005 Input: { h=0; for(a=1,52,h=h+1); print(h); } Output: ? 52 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.003s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 23:29:45 2005 Input: { h=0; for(a=1,52, for(b=2,52,if(b>a, h=h+1 )) ); print(h); } Output: ? @ Euler I List Mat Mod O Pi Pol Polrev Qfb Ser Set Str Vec abs acos acosh addhelp addprimes agm algdep alias allocatemem arg asin asinh atan atanh bernfrac bernreal bernvec besseljh besselk bestappr bezout bezoutres bigomega binary binomial bitand bitneg bitnegimply bitor bittest bitxor bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark break ceil centerlift changevar charpoly chinese component concat conj conjvec content contfrac contfracpnqn core coredisc cos cosh cotan default denominator deriv dilog dirdiv direuler dirmul dirzetak divisors divrem eint1 elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint erfc error eta eulerphi eval exp extern factor factorback factorcantor factorff factorial factorint factormod factornf factorpadic ffinit fibonacci floor for fordiv forprime forstep forsubgroup forvec frac galoisfixedfield galoisinit galoispermtopol galoissubcyclo gamma gammah gcd getheap getrand getstack gettime global hilbert hyperu idealadd idealaddtoone idealappr idealchinese idealcoprime idealdiv idealfactor idealhnf idealintersect idealinv ideallist ideallistarch ideallog idealmin idealmul idealnorm idealpow idealprimedec idealprincipal idealred idealstar idealtwoelt idealval ideleprincipal if imag incgam incgamc input install intformal intnum isfundamental isprime ispseudoprime issquare issquarefree kill kronecker lcm length lex lift lindep listcreate listinsert listkill listput listsort lngamma log matadjoint matalgtobasis matbasistoalg matcompanion matdet matdetint matdiagonal mateigen mathess mathilbert mathnf mathnfmod mathnfmodid matid matimage matimagecompl matindexrank matintersect matinverseimage matisdiagonal matker matkerint matmuldiagonal matmultodiagonal matpascal matrank matrix matrixqz matsize matsnf matsolve matsolvemod matsupplement mattranspose max min modreverse moebius newtonpoly next nextprime nfalgtobasis nfbasis nfbasistoalg nfdetint nfdisc nfeltdiv nfeltdiveuc nfeltdivmodpr nfeltdivrem nfeltmod nfeltmul nfeltmulmodpr nfeltpow nfeltpowmodpr nfeltreduce nfeltreducemodpr nfeltval nffactor nffactormod nfgaloisapply nfgaloisconj nfhilbert nfhnf nfhnfmod nfinit nfisideal nfisincl nfisisom nfkermodpr nfmodprinit nfnewprec nfroots nfrootsof1 nfsnf nfsolvemodpr nfsubfields norm norml2 numdiv numerator numtoperm omega padicappr padicprec permtonum plot plotbox plotclip plotcolor plotcopy plotcursor plotdraw plotfile ploth plothraw plothsizes plotinit plotkill plotlines plotlinetype plotmove plotpoints plotpointsize plotpointtype plotrbox plotrecth plotrecthraw plotrline plotrmove plotrpoint plotscale plotstring plotterm polcoeff polcompositum polcyclo poldegree poldisc poldiscreduced polgalois polhensellift polinterpolate polisirreducible pollead pollegendre polrecip polred polredabs polredord polresultant polroots polrootsmod polrootspadic polsturm polsubcyclo polsylvestermatrix polsym poltchebi poltschirnhaus polylog polzagier precision precprime prime primes print print1 printp printp1 printtex prod prodeuler prodinf psdraw psi psploth psplothraw qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfgaussred qfjacobi qflll qflllgram qfminim qfperfection qfsign quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit quit random read real removeprimes reorder return rnfalgtobasis rnfbasis rnfbasistoalg rnfcharpoly rnfconductor rnfdedekind rnfdet rnfdisc rnfeltabstorel rnfeltdown rnfeltreltoabs rnfeltup rnfequation rnfhnfbasis rnfidealabstorel rnfidealdown rnfidealhnf rnfidealmul rnfidealnormabs rnfidealnormrel rnfidealreltoabs rnfidealtwoelt rnfidealup rnfinit rnfisfree rnfisnorm rnfkummer rnflllgram rnfnormgroup rnfpolred rnfpolredabs rnfpseudobasis rnfsteinitz round serconvol serlaplace serreverse setintersect setisset setminus setrand setsearch setunion shift shiftmul sigma sign simplify sin sinh sizebyte sizedigit solve sqr sqrt sqrtint sqrtn subgrouplist subst sum sumalt sumdiv suminf sumpos system tan tanh taylor teichmuller theta thetanullk thue thueinit trace trap truncate type until valuation variable vecextract vecmax vecmin vecsort vector vectorv weber whatnow while write write1 writetex x zeta zetak zetakinit znlog znorder znprimroot znstar @E_N_D@ Euler I List Mat Mod O Pi Pol Polrev Qfb Ser Set Str Vec abs acos acosh addhelp addprimes agm algdep alias allocatemem arg asin asinh atan atanh bernfrac bernreal bernvec besseljh besselk bestappr bezout bezoutres bigomega binary binomial bitand bitneg bitnegimply bitor bittest bitxor bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark break ceil centerlift changevar charpoly chinese component concat conj conjvec content contfrac contfracpnqn core coredisc cos cosh cotan default denominator deri ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** unexpected character: h=0;for(a=1,52,_for(b=2,52,if(b>a,_ ^-------------------- Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 23:31:29 2005 Input: { h=0; for(a=1,52,for(b=2,52,if(b>a,h=h+1))); print(h); } Output: ? 1326 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.009s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 23:34:02 2005 Input: { h=0; for(a=1,52,for(b=2,52,if(b>a,for(c=3,52,if(c>b,for(d=4,52,if(d>c,for(e=5,52,if(e>d,h=h+1))))))))); print(h); } Output: ? 2598960 ? Errors (if any) and Timing Info: Timing: real 0m15.461s user 0m15.454s sys 0m0.005s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 23:37:10 2005 Input: { h=0; for(a=1,52,for(b=2,52,if(b>a,for(c=3,52,if(c>b,for(d=4,52,if(d>c,for(e=5,52,if(e>d,for(f=6,52,if(f>e,h=h+1))))))))))); print(h); } Output: ? @ }Euler }I }List }Mat }Mod }O }Pi }Pol }Polrev }Qfb }Ser }Set }Str }Vec }abs }acos }acosh }addhelp }addprimes }agm }algdep }alias }allocatemem }arg }asin }asinh }atan }atanh }bernfrac }bernreal }bernvec }besseljh }besselk }bestappr }bezout }bezoutres }bigomega }binary }binomial }bitand }bitneg }bitnegimply }bitor }bittest }bitxor }bnfcertify }bnfclassunit }bnfclgp }bnfdecodemodule }bnfinit }bnfisintnorm }bnfisnorm }bnfisprincipal }bnfissunit }bnfisunit }bnfmake }bnfnarrow }bnfreg }bnfsignunit }bnfsunit }bnfunit }bnrL1 }bnrclass }bnrclassno }bnrclassnolist }bnrconductor }bnrconductorofchar }bnrdisc }bnrdisclist }bnrinit }bnrisconductor }bnrisprincipal }bnrrootnumber }bnrstark }break }ceil }centerlift }changevar }charpoly }chinese }component }concat }conj }conjvec }content }contfrac }contfracpnqn }core }coredisc }cos }cosh }cotan }default }denominator }deriv }dilog }dirdiv }direuler }dirmul }dirzetak }divisors }divrem }eint1 }elladd }ellak }ellan }ellap }ellbil }ellchangecurve }ellchangepoint }elleisnum }elleta }ellglobalred }ellheight }ellheightmatrix }ellinit }ellisoncurve }ellj }elllocalred }elllseries }ellorder }ellordinate }ellpointtoz }ellpow }ellrootno }ellsigma }ellsub }elltaniyama }elltors }ellwp }ellzeta }ellztopoint }erfc }error }eta }eulerphi }eval }exp }extern }factor }factorback }factorcantor }factorff }factorial }factorint }factormod }factornf }factorpadic }ffinit }fibonacci }floor }for }fordiv }forprime }forstep }forsubgroup }forvec }frac }galoisfixedfield }galoisinit }galoispermtopol }galoissubcyclo }gamma }gammah }gcd }getheap }getrand }getstack }gettime }global }hilbert }hyperu }idealadd }idealaddtoone }idealappr }idealchinese }idealcoprime }idealdiv }idealfactor }idealhnf }idealintersect }idealinv }ideallist }ideallistarch }ideallog }idealmin }idealmul }idealnorm }idealpow }idealprimedec }idealprincipal }idealred }idealstar }idealtwoelt }idealval }ideleprincipal }if }imag }incgam }incgamc }input }install }intformal }intnum }isfundamental }isprime }ispseudoprime }issquare }issquarefree }kill }kronecker }lcm }length }lex }lift }lindep }listcreate }listinsert }listkill }listput }listsort }lngamma }log }matadjoint }matalgtobasis }matbasistoalg }matcompanion }matdet }matdetint }matdiagonal }mateigen }mathess }mathilbert }mathnf }mathnfmod }mathnfmodid }matid }matimage }matimagecompl }matindexrank }matintersect }matinverseimage }matisdiagonal }matker }matkerint }matmuldiagonal }matmultodiagonal }matpascal }matrank }matrix }matrixqz }matsize }matsnf }matsolve }matsolvemod }matsupplement }mattranspose }max }min }modreverse }moebius }newtonpoly }next }nextprime }nfalgtobasis }nfbasis }nfbasistoalg }nfdetint }nfdisc }nfeltdiv }nfeltdiveuc }nfeltdivmodpr }nfeltdivrem }nfeltmod }nfeltmul }nfeltmulmodpr }nfeltpow }nfeltpowmodpr }nfeltreduce }nfeltreducemodpr }nfeltval }nffactor }nffactormod }nfgaloisapply }nfgaloisconj }nfhilbert }nfhnf }nfhnfmod }nfinit }nfisideal }nfisincl }nfisisom }nfkermodpr }nfmodprinit }nfnewprec }nfroots }nfrootsof1 }nfsnf }nfsolvemodpr }nfsubfields }norm }norml2 }numdiv }numerator }numtoperm }omega }padicappr }padicprec }permtonum }plot }plotbox }plotclip }plotcolor }plotcopy }plotcursor }plotdraw }plotfile }ploth }plothraw }plothsizes }plotinit }plotkill }plotlines }plotlinetype }plotmove }plotpoints }plotpointsize }plotpointtype }plotrbox }plotrecth }plotrecthraw }plotrline }plotrmove }plotrpoint }plotscale }plotstring }plotterm }polcoeff }polcompositum }polcyclo }poldegree }poldisc }poldiscreduced }polgalois }polhensellift }polinterpolate }polisirreducible }pollead }pollegendre }polrecip }polred }polredabs }polredord }polresultant }polroots }polrootsmod }polrootspadic }polsturm }polsubcyclo }polsylvestermatrix }polsym }poltchebi }poltschirnhaus }polylog }polzagier }precision }precprime }prime }primes }print }print1 }printp }printp1 }printtex }prod }prodeuler }prodinf }psdraw }psi }psploth }psplothraw }qfbclassno }qfbcompraw }qfbhclassno }qfbnucomp }qfbnupow }qfbpowraw }qfbprimeform }qfbred }qfgaussred }qfjacobi }qflll }qflllgram }qfminim }qfperfection }qfsign }quadclassunit }quaddisc }quadgen }quadhilbert }quadpoly }quadray }quadregulator }quadunit }quit }random }read }real }removeprimes }reorder }return }rnfalgtobasis }rnfbasis }rnfbasistoalg }rnfcharpoly }rnfconductor }rnfdedekind }rnfdet }rnfdisc }rnfeltabstorel }rnfeltdown }rnfeltreltoabs }rnfeltup }rnfequation }rnfhnfbasis }rnfidealabstorel }rnfidealdown }rnfidealhnf }rnfidealmul }rnfidealnormabs }rnfidealnormrel }rnfidealreltoabs }rnfidealtwoelt }rnfidealup }rnfinit }rnfisfree }rnfisnorm }rnfkummer }rnflllgram }rnfnormgroup }rnfpolred }rnfpolredabs }rnfpseudobasis }rnfsteinitz }round }serconvol }serlaplace }serreverse }setintersect }setisset }setminus }setrand }setsearch }setunion }shift }shiftmul }sigma }sign }simplify }sin }sinh }sizebyte }sizedigit }solve }sqr }sqrt }sqrtint }sqrtn }subgrouplist }subst }sum }sumalt }sumdiv }suminf }sumpos }system }tan }tanh }taylor }teichmuller }theta }thetanullk }thue }thueinit }trace }trap }truncate }type }until }valuation }variable }vecextract }vecmax }vecmin }vecsort }vector }vectorv }weber }whatnow }while }write }write1 }writetex }x }zeta }zetak }zetakinit }znlog }znorder }znprimroot }znstar @E_N_D? Errors (if any) and Timing Info: *** unexpected character: ...=h+1)))))))))));print(h);_ ^- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.117.' ************** PARI ***************** Host 68.117.198.191 (68.117.198.191) Time: Thu Apr 21 23:39:57 2005 Input: { h=0; for(a=1,52,for(b=2,52,if(b>a,for(c=3,52,if(c>b,for(d=4,52,if(d>c,for(e=5,52,if(e>d,h=h+1))))))))); print(h); } Output: ? 2598960 ? Errors (if any) and Timing Info: Timing: real 0m16.298s user 0m16.270s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Apr 21 23:57:48 2005 Input: p=2453; m=659; e=809; gcd(p-m,p-e) Output: ? ? ? ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.005s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:49:51 2005 Input: Mod(4,8)^(-1) Output: ? ? Errors (if any) and Timing Info: *** impossible inverse modulo: Mod(4, 8). Timing: real 0m0.320s user 0m0.007s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:49:57 2005 Input: Mod(4,9)^(-1) Output: ? Mod(7, 9) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:50:03 2005 Input: Mod(2^2,9)^(-1) Output: ? Mod(7, 9) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:50:11 2005 Input: Mod(2^2,3^2)^(-1) Output: ? Mod(7, 9) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:50:16 2005 Input: Mod(2,3^2)^(-1) Output: ? Mod(5, 9) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:50:27 2005 Input: Mod(2^(1/2),3^2)^(-1) Output: ? ? Errors (if any) and Timing Info: *** forbidden division t_REAL % t_INT. Timing: real 0m0.026s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:51:01 2005 Input: Mod(√4,3^2)^(-1) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: Mod(√4,3^2)^(-1) ^----------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:51:02 2005 Input: Mod(√4,3^2)^(-1) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: Mod(√4,3^2)^(-1) ^----------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:51:13 2005 Input: Mod(√4,11)^(-1) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: Mod(√4,11)^(-1) ^---------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:51:20 2005 Input: Mod(√4,√17)^(-1) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: Mod(√4,√17)^( ^-------------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:51:21 2005 Input: Mod(√4,√17)^(-1) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: Mod(√4,√17)^( ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:51:22 2005 Input: Mod(√4,√17)^(-1) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: Mod(√4,√17)^( ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:51:29 2005 Input: Mod(1+√4,√17)^(-1) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: Mod(1+√4,√17)^( ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:51:35 2005 Input: Mod(1+i,√17)^(-1) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: Mod(1+i,√17)^(-1) ^-------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:51:39 2005 Input: Mod(1+i,17)^(-1) Output: ? ? Errors (if any) and Timing Info: *** forbidden division t_POL % t_INT. Timing: real 0m0.022s user 0m0.007s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:51:44 2005 Input: Mod(1+i,2+17)^(-1) Output: ? ? Errors (if any) and Timing Info: *** forbidden division t_POL % t_INT. Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.183.57 (168.122.183.57) Time: Fri Apr 22 11:51:45 2005 Input: Mod(1+i,2+17)^(-1) Output: ? ? Errors (if any) and Timing Info: *** forbidden division t_POL % t_INT. Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '62.42.2' ************** PARI ***************** Host 62.42.22.165 (62.42.22.165) Time: Fri Apr 22 16:19:34 2005 Input: Smokey := function(n, p, f, m) InitialPreserve := [ Random(0,1) : i in [1..n] ]; treeGrowIgnite := func< F | [ x eq 0 select Floor(1+p-Random(0,1)) else Floor(2+f-Random(0,1)) : x in F ] >; forestIgnite := function(F) ignite := func< n1, a, n2 | a eq 1 and (n1 eq 2 or n2 eq 2) select 2 else a >; next := func< F | [ ignite(F[#F], F[1], F[2]) ] cat [ ignite(F[i-1], F[i], F[i+1]) : i in [2..#F-1] ] cat [ ignite(F[#F-1], F[#F], F[1]) ] >; // compute the result of forestIgnite as a fixed point return func< F1,F2 | F1 eq F2 select F1 else $$(F2, next(F2)) >(F, next(F)); end function; destroy := func< F | [ x eq 2 select 0 else x : x in F ] >; return [ i eq 1 select InitialPreserve else destroy(forestIgnite(treeGrowIgnite(Self(i-1)))) : i in [1..m]]; end function; F := Smokey(25, 0.2, 0.4, 200); Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: Smokey:=function(n,p,f,m) ^------------------ *** unexpected character: InitialPreserve:=[Random(0,1):iin[1. ^-------------------- *** unexpected character: treeGrowIgnite:=func; ^-------------------- *** unexpected character: forestIgnite:=function(F) ^------------ *** unexpected character: ignite:=func;. *** expected character: '=' instead of: aeq1and(n1eq2orn2eq2)select2elsea>; ^-------------- *** unexpected character: next:=func; ^-------------------- *** unexpected character: //computetheresultof ^-------------------- *** Warning: unused characters: ,F2|. *** incorrect type in comparison. *** Warning: unused characters: $$(F2,next(F2))>(F,next(F));. *** unexpected character: destroy:=func Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.013s user 0m0.003s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 01:38:11 2005 Input: isprime(11) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.038s user 0m0.005s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 01:38:19 2005 Input: isprime(11) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 01:38:34 2005 Input: isprime(10) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 01:38:58 2005 Input: isprime(11) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 01:39:13 2005 Input: isprime(12) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 01:39:32 2005 Input: Mod(16,5) Output: ? Mod(1, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 01:45:24 2005 Input: isprime(11); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 01:45:30 2005 Input: isprime(11) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 01:45:40 2005 Input: isprime(11) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 02:03:16 2005 Input: gcd(55,128) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 02:03:29 2005 Input: gcd(55,128,73,237) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: gcd(55,128,73,237) ^----- Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 02:04:01 2005 Input: gcd(55,73) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 02:04:08 2005 Input: gcd(55,75) Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 02:05:00 2005 Input: chrem([46,37,10,118],[55,128,72,237]) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: chrem([46,37,10,118] ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 02:07:01 2005 Input: chrem( [46,37,10,118],[55,128,72,237] ) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: chrem([46,37,10,118] ^-------------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '64.81.5' ************** PARI ***************** Host 64.81.58.231 (64.81.58.231) Time: Sun Apr 24 03:03:43 2005 Input: solve(2*x=6,x) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: solve(2*x=6,x) ^-------- Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '64.81.5' ************** PARI ***************** Host 64.81.58.231 (64.81.58.231) Time: Sun Apr 24 03:03:50 2005 Input: solve(2*x=6) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: solve(2*x=6) ^------ Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '64.81.5' ************** PARI ***************** Host 64.81.58.231 (64.81.58.231) Time: Sun Apr 24 03:03:55 2005 Input: 2x Output: ? 2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x. Timing: real 0m0.052s user 0m0.006s sys 0m0.005s '64.81.5' ************** PARI ***************** Host 64.81.58.231 (64.81.58.231) Time: Sun Apr 24 03:03:58 2005 Input: 2x=6 Output: ? 2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x=6. Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '64.81.5' ************** PARI ***************** Host 64.81.58.231 (64.81.58.231) Time: Sun Apr 24 03:04:05 2005 Input: 2*x=6 Output: ? 12 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '64.81.5' ************** PARI ***************** Host 64.81.58.231 (64.81.58.231) Time: Sun Apr 24 03:05:12 2005 Input: 2*3 Output: ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:20:01 2005 Input: factor (3540) Output: ? [2 2] [3 1] [5 1] [59 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.005s sys 0m0.009s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:20:57 2005 Input: factor(3539 Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: factor(3539 ^ Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:21:31 2005 Input: factor(3539) Output: ? [3539 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:21:58 2005 Input: factor(3541) Output: ? [3541 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:22:48 2005 Input: factor(45879521356895215456899665585213541) Output: ? [3 1] [137 1] [181146013 1] [616237718323605814726987 1] ? Errors (if any) and Timing Info: Timing: real 0m0.138s user 0m0.070s sys 0m0.019s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:23:15 2005 Input: factor(458795213568952154568996655852135411) Output: ? [29 1] [7232405612851 1] [2187449854542867214709 1] ? Errors (if any) and Timing Info: Timing: real 0m0.124s user 0m0.108s sys 0m0.017s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:23:26 2005 Input: factor(45879521356895215456899665585213541171) Output: ? [3 1] [18433 1] [38796011 1] [2314470029 1] [9239808397790591 1] ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.036s sys 0m0.006s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:23:39 2005 Input: factor(4587952135689521545689966558521354171) Output: ? [23 1] [67 1] [821 1] [323647 1] [11204732606593008670138013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.011s sys 0m0.004s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:23:46 2005 Input: factor(4587952135689521545689966558521354171) Output: ? [23 1] [67 1] [821 1] [323647 1] [11204732606593008670138013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.006s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:23:57 2005 Input: factor(458795213568952154568996655852135417111) Output: ? [2087 1] [3298201 1] [21611565156239 1] [3084132939593527 1] ? Errors (if any) and Timing Info: Timing: real 0m0.051s user 0m0.034s sys 0m0.017s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:24:06 2005 Input: factor(4587952135689521545689966558521354171111) Output: ? [3631 1] [364056677 1] [8674366007 1] [400115970080575379 1] ? Errors (if any) and Timing Info: Timing: real 0m0.062s user 0m0.048s sys 0m0.014s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:24:16 2005 Input: factor(458795213568952154568996655852135417111171) Output: ? [7 1] [191 1] [491 1] [99259 1] [2139047 1] [1353054047 1] [2432767536083323 1] ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.027s sys 0m0.009s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:24:36 2005 Input: factor(4587952135689521545689966558521354171111711) Output: ? [17 1] [23 1] [30591006776797867 1] [383573283997045411648763 1] ? Errors (if any) and Timing Info: Timing: real 0m0.400s user 0m0.375s sys 0m0.021s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:24:45 2005 Input: factor(45879521356895215456899665585213541711117111) Output: ? [3 3] [47 1] [839 1] [5395751 1] [38588117 1] [41208015437 1] [5022363121499 1] ? Errors (if any) and Timing Info: Timing: real 0m0.042s user 0m0.037s sys 0m0.005s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:24:59 2005 Input: factor(458795213568952154568996655852135417111171111) Output: ? [67 1] [463 1] [4344037 1] [3404627235943870826267717047991143 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.015s sys 0m0.002s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:25:56 2005 Input: factor(3404627235943870826267717047991143) Output: ? [3404627235943870826267717047991143 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:42:08 2005 Input: factor(3404627235943870826267) Output: ? [7 1] [486375319420552975181 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:42:54 2005 Input: factor(3539627235943870826267) Output: ? [257 1] [13772868622349691931 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:43:23 2005 Input: factor(3539627235943870826269) Output: ? [131 1] [2508871909 1] [10769802611 1] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.018s sys 0m0.003s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:43:39 2005 Input: factor(3539627235943870826271) Output: ? [3 1] [11 1] [17 1] [53 1] [61 1] [1069 1] [2207 1] [827196949 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:43:53 2005 Input: factor(3539627235943870826273) Output: ? [73197559 1] [48357175899047 1] ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.014s sys 0m0.011s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:44:13 2005 Input: factor(3539627235943870826277) Output: ? [3 4] [23 1] [433261 1] [4385257252639 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:44:27 2005 Input: factor(3539627235943870826279) Output: ? [7 1] [14144297 1] [35750170807801 1] ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.016s sys 0m0.006s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:44:45 2005 Input: factor(3539627235943870826281) Output: ? [73 1] [281 1] [1777 1] [97104849686681 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:44:58 2005 Input: factor(3539627235943870826283) Output: ? [3 1] [1179875745314623608761 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:45:27 2005 Input: factor(3539627235943870826287) Output: ? [13 1] [29 1] [161125763 1] [58270828237 1] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.013s sys 0m0.009s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:45:50 2005 Input: factor(3539627235943870826289) Output: ? [3 1] [10456909 1] [112832171085607 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.004s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:46:04 2005 Input: factor(3539627235943870826291) Output: ? [487 1] [7268228410562363093 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:46:19 2005 Input: factor(3539627235943870826293) Output: ? [7 2] [11 1] [19 1] [18593 1] [669107 1] [27782423 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.002s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:46:53 2005 Input: factor(3539627235943870826297) Output: ? [1811 1] [1954515315264423427 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 03:47:20 2005 Input: factor(3539627235943870826299) Output: ? [3539627235943870826299 1] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.010s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 03:49:32 2005 Input: 10! Output: ? 3628800 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 03:50:11 2005 Input: factor(10) Output: ? [2 1] [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 03:50:25 2005 Input: factor(3628800) Output: ? [2 8] [3 4] [5 2] [7 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '81.182.' ************** PARI ***************** Host 81.182.183.186 (81.182.183.186) Time: Sun Apr 24 04:40:11 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Sun Apr 24 07:09:41 2005 Input: msolved(9*x=12,15) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: msolved(9*x=12,15) ^------------------ Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '202.7.1' ************** PARI ***************** Host 202.7.183.130 (202.7.183.130) Time: Sun Apr 24 10:09:17 2005 Input: chinese(chinese(Mod(1,3),Mod(2,5)),Mod(3,7)) Output: ? Mod(52, 105) ? Errors (if any) and Timing Info: Timing: real 0m0.325s user 0m0.006s sys 0m0.008s '202.7.1' ************** PARI ***************** Host 202.7.183.130 (202.7.183.130) Time: Sun Apr 24 10:10:21 2005 Input: chinese(Mod(4,6),Mod(13,15)) Output: ? Mod(28, 30) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '202.7.1' ************** PARI ***************** Host 202.7.183.130 (202.7.183.130) Time: Sun Apr 24 10:12:58 2005 Input: chinese(chinese(chinese((Mod(17,33),Mod(22,64)),Mod(41,101)),Mod(25,137)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...inese(chinese((Mod(17,33) *** ,Mod(22,64)),Mod(41, ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.003s '202.7.1' ************** PARI ***************** Host 202.7.183.130 (202.7.183.130) Time: Sun Apr 24 10:13:10 2005 Input: chinese(chinese(chinese(Mod(17,33),Mod(22,64)),Mod(41,101)),Mod(25,137)) Output: ? Mod(8174678, 29223744) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '202.7.1' ************** PARI ***************** Host 202.7.183.130 (202.7.183.130) Time: Sun Apr 24 10:14:10 2005 Input: chinese(chinese(chinese(Mod(17,33),Mod(22,64)),Mod(41,101)),Mod(25,137)) isPrime(137) Output: ? Mod(8174678, 29223744) ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: isPrime(137) ^------------ Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '202.7.1' ************** PARI ***************** Host 202.7.183.130 (202.7.183.130) Time: Sun Apr 24 10:14:24 2005 Input: chinese(chinese(chinese(Mod(17,33),Mod(22,64)),Mod(41,101)),Mod(25,137)) Prime(137) Output: ? Mod(8174678, 29223744) ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Prime(137) ^---------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '202.7.1' ************** PARI ***************** Host 202.7.183.130 (202.7.183.130) Time: Sun Apr 24 10:14:34 2005 Input: chinese(chinese(chinese(Mod(17,33),Mod(22,64)),Mod(41,101)),Mod(25,137)) isprime(137) Output: ? Mod(8174678, 29223744) ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.007s sys 0m0.005s '202.7.1' ************** PARI ***************** Host 202.7.183.130 (202.7.183.130) Time: Sun Apr 24 10:14:43 2005 Input: chinese(chinese(chinese(Mod(17,33),Mod(22,64)),Mod(41,101)),Mod(25,137)) Output: ? Mod(8174678, 29223744) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '202.7.1' ************** PARI ***************** Host 202.7.183.130 (202.7.183.130) Time: Sun Apr 24 10:30:15 2005 Input: chinese(chinese(chinese(Mod(17,33),Mod(22,64)),Mod(41,101)),Mod(25,137)) Mod(17,33) Output: ? Mod(8174678, 29223744) ? ? Mod(17, 33) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '81.66.1' ************** PARI ***************** Host 81.66.170.9 (81.66.170.9) Time: Sun Apr 24 10:52:46 2005 Input: factor(123456789123456789123456789123456789123456789123456789) Output: ? [3 3] [7 1] [11 1] [13 1] [19 1] [757 1] [3607 1] [3803 1] [52579 1] [70541929 1] [14175966169 1] [440334654777631 1] ? Errors (if any) and Timing Info: Timing: real 0m0.094s user 0m0.039s sys 0m0.013s '80.58.3' ************** PARI ***************** Host 80.58.32.171 (80.58.32.171) Time: Sun Apr 24 11:11:19 2005 Input: print("---------------------1.1--------------"); k:=FiniteField(3); M:=KMatrixSpace(k,4,7); G:= M ! [1,2,0,0,0,0,0, 0,2,1,0,1,1,0, 1,1,2,0,0,1,1, 0,0,0,2,0,1,1]; G; Output: ? ---------------------1.1-------------- ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: k:=FiniteField(3); ^---------------- *** unexpected character: M:=KMatrixSpace(k,4,7) ^-------------------- *** unexpected character: G:=M![1,2,0,0,0,0,0,0, ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '24.5.19' ************** PARI ***************** Host 24.5.192.7 (24.5.192.7) Time: Sun Apr 24 20:52:22 2005 Input: E = ellint([0,-1,-1,0,0]) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: E=ellint([0,-1,-1,0,0] ^-------------------- Timing: real 0m0.025s user 0m0.007s sys 0m0.003s '24.5.19' ************** PARI ***************** Host 24.5.192.7 (24.5.192.7) Time: Sun Apr 24 20:52:52 2005 Input: E = ellinit([0,-1,-1,0,0]) Output: ? [0, -1, -1, 0, 0, -4, 0, 1, -1, 16, -152, -11, -4096/11, [-0.41964337760708056627592628232664330021, 0.70982168880354028313796314116332165010 - 0.30314536460359968462967109851401150147*I, 0.70982168880354028313796314116332165010 + 0.30314536460359968462967109851401150147*I]~, 6.3460465213977671084439730837727365262, -3.1730232606988835542219865418863682631 + 1.4588166169384952293308896129036752571*I, -0.89563194573282844004395254162148111030 - 3.247711662339099984 E-39*I, 0.44781597286641422002197627081074055514 - 0.70093331394394796216199800040425902762*I, 9.2577181172797965885400335591262444436] ? Errors (if any) and Timing Info: Timing: real 0m0.134s user 0m0.007s sys 0m0.008s '24.5.19' ************** PARI ***************** Host 24.5.192.7 (24.5.192.7) Time: Sun Apr 24 20:55:32 2005 Input: E = ellinit([0,-1,-1,0,0]) P = [0,0] elladd(E,P,P) Output: ? [0, -1, -1, 0, 0, -4, 0, 1, -1, 16, -152, -11, -4096/11, [-0.41964337760708056627592628232664330021, 0.70982168880354028313796314116332165010 - 0.30314536460359968462967109851401150147*I, 0.70982168880354028313796314116332165010 + 0.30314536460359968462967109851401150147*I]~, 6.3460465213977671084439730837727365262, -3.1730232606988835542219865418863682631 + 1.4588166169384952293308896129036752571*I, -0.89563194573282844004395254162148111030 - 3.247711662339099984 E-39*I, 0.44781597286641422002197627081074055514 - 0.70093331394394796216199800040425902762*I, 9.2577181172797965885400335591262444436] ? ? [0, 0] ? [1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.005s '24.5.19' ************** PARI ***************** Host 24.5.192.7 (24.5.192.7) Time: Sun Apr 24 20:56:08 2005 Input: E = ellinit([0,-1,-1,0,0]) P = [0,0] ellnmult(E,P,5) Output: ? [0, -1, -1, 0, 0, -4, 0, 1, -1, 16, -152, -11, -4096/11, [-0.41964337760708056627592628232664330021, 0.70982168880354028313796314116332165010 - 0.30314536460359968462967109851401150147*I, 0.70982168880354028313796314116332165010 + 0.30314536460359968462967109851401150147*I]~, 6.3460465213977671084439730837727365262, -3.1730232606988835542219865418863682631 + 1.4588166169384952293308896129036752571*I, -0.89563194573282844004395254162148111030 - 3.247711662339099984 E-39*I, 0.44781597286641422002197627081074055514 - 0.70093331394394796216199800040425902762*I, 9.2577181172797965885400335591262444436] ? ? [0, 0] ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: ellnmult(E,P,5) ^--------------- Timing: real 0m0.020s user 0m0.008s sys 0m0.005s '24.5.19' ************** PARI ***************** Host 24.5.192.7 (24.5.192.7) Time: Sun Apr 24 20:56:32 2005 Input: E = ellinit([0,-1,-1,0,0]) P = [0,0] ellnmult(E,5,P) Output: ? [0, -1, -1, 0, 0, -4, 0, 1, -1, 16, -152, -11, -4096/11, [-0.41964337760708056627592628232664330021, 0.70982168880354028313796314116332165010 - 0.30314536460359968462967109851401150147*I, 0.70982168880354028313796314116332165010 + 0.30314536460359968462967109851401150147*I]~, 6.3460465213977671084439730837727365262, -3.1730232606988835542219865418863682631 + 1.4588166169384952293308896129036752571*I, -0.89563194573282844004395254162148111030 - 3.247711662339099984 E-39*I, 0.44781597286641422002197627081074055514 - 0.70093331394394796216199800040425902762*I, 9.2577181172797965885400335591262444436] ? ? [0, 0] ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: ellnmult(E,5,P) ^--------------- Timing: real 0m0.020s user 0m0.010s sys 0m0.003s '24.5.19' ************** PARI ***************** Host 24.5.192.7 (24.5.192.7) Time: Sun Apr 24 20:56:54 2005 Input: E = ellinit([0,-1,-1,0,0]) P = [0,0] ellmultn(E,P,5) Output: ? [0, -1, -1, 0, 0, -4, 0, 1, -1, 16, -152, -11, -4096/11, [-0.41964337760708056627592628232664330021, 0.70982168880354028313796314116332165010 - 0.30314536460359968462967109851401150147*I, 0.70982168880354028313796314116332165010 + 0.30314536460359968462967109851401150147*I]~, 6.3460465213977671084439730837727365262, -3.1730232606988835542219865418863682631 + 1.4588166169384952293308896129036752571*I, -0.89563194573282844004395254162148111030 - 3.247711662339099984 E-39*I, 0.44781597286641422002197627081074055514 - 0.70093331394394796216199800040425902762*I, 9.2577181172797965885400335591262444436] ? ? [0, 0] ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: ellmultn(E,P,5) ^--------------- Timing: real 0m0.014s user 0m0.009s sys 0m0.006s '24.5.19' ************** PARI ***************** Host 24.5.192.7 (24.5.192.7) Time: Sun Apr 24 20:58:51 2005 Input: E = ellinit([0,-1,-1,0,0]) P = [0,0] elltors(E) ellmultn(E,P,5) Output: ? [0, -1, -1, 0, 0, -4, 0, 1, -1, 16, -152, -11, -4096/11, [-0.41964337760708056627592628232664330021, 0.70982168880354028313796314116332165010 - 0.30314536460359968462967109851401150147*I, 0.70982168880354028313796314116332165010 + 0.30314536460359968462967109851401150147*I]~, 6.3460465213977671084439730837727365262, -3.1730232606988835542219865418863682631 + 1.4588166169384952293308896129036752571*I, -0.89563194573282844004395254162148111030 - 3.247711662339099984 E-39*I, 0.44781597286641422002197627081074055514 - 0.70093331394394796216199800040425902762*I, 9.2577181172797965885400335591262444436] ? ? [0, 0] ? [5, [5], [[0, 1]]] ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: ellmultn(E,P,5) ^--------------- Timing: real 0m0.014s user 0m0.009s sys 0m0.006s '24.5.19' ************** PARI ***************** Host 24.5.192.7 (24.5.192.7) Time: Sun Apr 24 21:03:13 2005 Input: E = ellinit([0,-1,-1,0,0]) P = [0,0] elltors(E) ellpow(E,P,5) Output: ? [0, -1, -1, 0, 0, -4, 0, 1, -1, 16, -152, -11, -4096/11, [-0.41964337760708056627592628232664330021, 0.70982168880354028313796314116332165010 - 0.30314536460359968462967109851401150147*I, 0.70982168880354028313796314116332165010 + 0.30314536460359968462967109851401150147*I]~, 6.3460465213977671084439730837727365262, -3.1730232606988835542219865418863682631 + 1.4588166169384952293308896129036752571*I, -0.89563194573282844004395254162148111030 - 3.247711662339099984 E-39*I, 0.44781597286641422002197627081074055514 - 0.70093331394394796216199800040425902762*I, 9.2577181172797965885400335591262444436] ? ? [0, 0] ? [5, [5], [[0, 1]]] ? [0] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.008s sys 0m0.004s '24.5.19' ************** PARI ***************** Host 24.5.192.7 (24.5.192.7) Time: Sun Apr 24 21:04:49 2005 Input: E = ellinit([0,0,0,0,1]) Output: ? [0, 0, 0, 0, 1, 0, 0, 4, 0, 0, -864, -432, 0, [-1.0000000000000000000000000000000000000, 0.50000000000000000000000000000000000000 - 0.86602540378443864676372317075293618346*I, 0.50000000000000000000000000000000000000 + 0.86602540378443864676372317075293618346*I]~, 4.2065463159763627835250572371508824064, -2.1032731579881813917625286185754412032 + 1.2143253239437908059099708448904656242*I, -1.2935547796148952674767575125656058188 + 3.359966980742911939 E-39*I, 0.64677738980744763373837875628280290940 - 1.1202513003332802196552063208342852345*I, 5.1081157178325565351221945057517738028] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.004s '4.5.245' ************** PARI ***************** Host 4.5.245.39 (4.5.245.39) Time: Sun Apr 24 22:50:44 2005 Input: 2; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '80.58.3' ************** PARI ***************** Host 80.58.32.107 (80.58.32.107) Time: Mon Apr 25 05:47:06 2005 Input: K:=FiniteField(3); HammingCode(K,2); Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: K:=FiniteField(3); ^---------------- *** unknown function or error in formal parameters: HammingCode(K,2); ^----------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '158.109' ************** PARI ***************** Host 158.109.70.226 (158.109.70.226) Time: Mon Apr 25 09:51:46 2005 Input: Z3:=GF(3); P3:=PolynomialRing(Z3); K4:=VectorSpace(Z3,4); Gx:=2 + 2*x + 2*x^3 + x^4; //[2,2,0,2,1,0,0,0] M:=KMatrixSpace(Z3,4,8); G:=M![2,2,0,2,1,0,0,0, 0,2,2,0,2,1,0,0, 0,0,2,2,0,2,1,0, 0,0,0,2,2,0,2,1]; C1:=CyclicCode(8,Gx); Paraula1:=K4![2,0,2,1]; Paraula1*GeneratorMatrix(C1); Paraula1; Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: Z3:=GF(3); ^------- *** unexpected character: P3:=PolynomialRing(Z3) ^-------------------- *** unexpected character: K4:=VectorSpace(Z3,4); ^------------------- *** unexpected character: Gx:=2+2*x+2*x^3+x^4;//[ ^-------------------- *** unexpected character: M:=KMatrixSpace(Z3,4,8 ^-------------------- *** unexpected character: G:=M![2,2,0,2,1,0,0,0, ^-------------------- *** unexpected character: C1:=CyclicCode(8,Gx); ^------------------ *** unexpected character: Paraula1:=K4![2,0,2,1]; ^-------------- *** expected character: '=' instead of: ...aula1*GeneratorMatrix(C1); ^- Timing: real 0m0.302s user 0m0.006s sys 0m0.011s '18.95.5' ************** PARI ***************** Host 18.95.5.102 (18.95.5.102) Time: Mon Apr 25 11:32:21 2005 Input: MonomialToPowerSumMatrix(4) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: MonomialToPowerSumMa ^-------------------- Timing: real 0m0.020s user 0m0.006s sys 0m0.007s '152.78.' ************** PARI ***************** Host 152.78.65.145 (152.78.65.145) Time: Mon Apr 25 13:00:16 2005 Input: 6*zeta(2) Output: ? 9.8696044010893586188344909998761511352 ? Errors (if any) and Timing Info: Timing: real 0m0.292s user 0m0.006s sys 0m0.007s '152.78.' ************** PARI ***************** Host 152.78.65.145 (152.78.65.145) Time: Mon Apr 25 13:00:38 2005 Input: 6*zeta(2)/Pi^2 Output: ? 0.99999999999999999999999999999999999999 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.004s '152.78.' ************** PARI ***************** Host 152.78.65.145 (152.78.65.145) Time: Mon Apr 25 13:29:49 2005 Input: 6*zeta(2)/Pi^2 Mod(14152019010605^127, 123456791) Output: ? 0.99999999999999999999999999999999999999 ? Mod(104120308, 123456791) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '152.78.' ************** PARI ***************** Host 152.78.65.145 (152.78.65.145) Time: Mon Apr 25 13:30:11 2005 Input: 6*zeta(2)/Pi^2 Mod(14152019010605^127, 123456791) Mod(7,3) Output: ? 0.99999999999999999999999999999999999999 ? Mod(104120308, 123456791) ? Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '152.78.' ************** PARI ***************** Host 152.78.65.145 (152.78.65.145) Time: Mon Apr 25 13:32:13 2005 Input: 6*zeta(2)/Pi^2 Mod(14152019010605^127, 123456791) Mod(7,3) Mod(14152019010605^127, 987654323) Output: ? 0.99999999999999999999999999999999999999 ? Mod(104120308, 123456791) ? Mod(1, 3) ? Mod(812538893, 987654323) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.002s '152.78.' ************** PARI ***************** Host 152.78.65.145 (152.78.65.145) Time: Mon Apr 25 13:36:06 2005 Input: 6*zeta(2)/Pi^2 Mod(14152019010605^127, 123456791) Mod(7,3) Mod(14152019010605^127, 987654323) gcd(3,6) Output: ? 0.99999999999999999999999999999999999999 ? Mod(104120308, 123456791) ? Mod(1, 3) ? Mod(812538893, 987654323) ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.261s user 0m0.008s sys 0m0.004s '152.78.' ************** PARI ***************** Host 152.78.65.145 (152.78.65.145) Time: Mon Apr 25 13:36:15 2005 Input: 6*zeta(2)/Pi^2 Mod(14152019010605^127, 123456791) Mod(7,3) Mod(14152019010605^127, 987654323) gcd(3,6) gcd(3,7) Output: ? 0.99999999999999999999999999999999999999 ? Mod(104120308, 123456791) ? Mod(1, 3) ? Mod(812538893, 987654323) ? 3 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.006s sys 0m0.006s '152.78.' ************** PARI ***************** Host 152.78.65.145 (152.78.65.145) Time: Mon Apr 25 13:36:37 2005 Input: 6*zeta(2)/Pi^2 Mod(14152019010605^127, 123456791) Mod(7,3) Mod(14152019010605^127, 987654323) gcd(3,6) gcd(3,7) gcd(123456791, 987654323) Output: ? 0.99999999999999999999999999999999999999 ? Mod(104120308, 123456791) ? Mod(1, 3) ? Mod(812538893, 987654323) ? 3 ? 1 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.005s '152.78.' ************** PARI ***************** Host 152.78.65.145 (152.78.65.145) Time: Mon Apr 25 13:40:38 2005 Input: 6*zeta(2)/Pi^2 Mod(14152019010605^127, 123456791) Mod(7,3) Mod(14152019010605^127, 987654323) gcd(3,6) gcd(3,7) 123456791*987654323 Output: ? 0.99999999999999999999999999999999999999 ? Mod(104120308, 123456791) ? Mod(1, 3) ? Mod(812538893, 987654323) ? 3 ? 1 ? 121932633334857493 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.008s sys 0m0.004s '152.78.' ************** PARI ***************** Host 152.78.65.145 (152.78.65.145) Time: Mon Apr 25 13:40:53 2005 Input: 6*zeta(2)/Pi^2 Mod(14152019010605^127, 123456791) Mod(7,3) Mod(14152019010605^127, 987654323) gcd(3,6) gcd(3,7) 123456791*987654323 Mod(14152019010605^127,121932633334857493) Output: ? 0.99999999999999999999999999999999999999 ? Mod(104120308, 123456791) ? Mod(1, 3) ? Mod(812538893, 987654323) ? 3 ? 1 ? 121932633334857493 ? Mod(18001903071439991, 121932633334857493) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '152.78.' ************** PARI ***************** Host 152.78.65.145 (152.78.65.145) Time: Mon Apr 25 13:42:25 2005 Input: 6*zeta(2)/Pi^2 Mod(14152019010605^127, 123456791) Mod(7,3) Mod(14152019010605^127, 987654323) gcd(3,6) gcd(3,7) 123456791*987654323 Mod(14152019010605^127,121932633334857493) Mod(18001903071439991,987654323) Output: ? 0.99999999999999999999999999999999999999 ? Mod(104120308, 123456791) ? Mod(1, 3) ? Mod(812538893, 987654323) ? 3 ? 1 ? 121932633334857493 ? Mod(18001903071439991, 121932633334857493) ? Mod(812538893, 987654323) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.007s '152.78.' ************** PARI ***************** Host 152.78.65.145 (152.78.65.145) Time: Mon Apr 25 13:42:46 2005 Input: 6*zeta(2)/Pi^2 Mod(14152019010605^127, 123456791) Mod(7,3) Mod(14152019010605^127, 987654323) gcd(3,6) gcd(3,7) 123456791*987654323 Mod(14152019010605^127,121932633334857493) Mod(18001903071439991,123456791) Output: ? 0.99999999999999999999999999999999999999 ? Mod(104120308, 123456791) ? Mod(1, 3) ? Mod(812538893, 987654323) ? 3 ? 1 ? 121932633334857493 ? Mod(18001903071439991, 121932633334857493) ? Mod(104120308, 123456791) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.005s sys 0m0.008s '210.98.' ************** PARI ***************** Host 210.98.29.3 (210.98.29.3) Time: Mon Apr 25 20:01:20 2005 Input: oE := Order(Poly(Zx, [1,0,5]); OE := OrderMaximal(oE); OrderClassGroup(OE); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: oE:=Order(Poly(Zx,[1,0, ^-------------------- *** unexpected character: OE:=OrderMaximal(oE); ^------------------ *** expected character: '=' instead of: OrderClassGroup(OE); ^- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '210.98.' ************** PARI ***************** Host 210.98.29.3 (210.98.29.3) Time: Mon Apr 25 20:01:39 2005 Input: oE := Order(Poly(Zx, [1,0,5]); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: oE:=Order(Poly(Zx,[1,0, ^-------------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '210.98.' ************** PARI ***************** Host 210.98.29.3 (210.98.29.3) Time: Mon Apr 25 20:01:59 2005 Input: oE := Order(Poly(Zx,[1,0,5])); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: oE:=Order(Poly(Zx,[1,0, ^-------------------- Timing: real 0m0.015s user 0m0.009s sys 0m0.002s '210.98.' ************** PARI ***************** Host 210.98.29.3 (210.98.29.3) Time: Mon Apr 25 20:02:03 2005 Input: oE := Order(Poly(Zx,[1,0,5])); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: oE:=Order(Poly(Zx,[1,0, ^-------------------- Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:06:00 2005 Input: isprime(1169) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.007s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:06:17 2005 Input: gcd(70,245) Output: ? 35 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:06:41 2005 Input: chinese(mod(1,3), mod(2,5)) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: chinese(mod(1,3),mod(2,5)) ^------------------ For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:07:02 2005 Input: chinese(mod(1,3),mod(2,5)) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: chinese(mod(1,3),mod(2,5)) ^------------------ For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:07:18 2005 Input: chinese(Mod(1,3),Mod(2,5)) Output: ? Mod(7, 15) ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.009s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:08:35 2005 Input: chinese(Mod(3,7),(chinese(Mod(1,3),Mod(2,5))) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...inese(Mod(1,3),Mod(2,5))) ^ Timing: real 0m0.017s user 0m0.005s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:08:44 2005 Input: chinese((Mod(3,7),(chinese(Mod(1,3),Mod(2,5))) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: chinese((Mod(3,7) *** ,(chinese(Mod(1,3),M ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:08:54 2005 Input: chinese((Mod(3,7),chinese(Mod(1,3),Mod(2,5))) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: chinese((Mod(3,7) *** ,chinese(Mod(1,3),Mo ^-------------------- Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:08:57 2005 Input: chinese((Mod(3,7),chinese(Mod(1,3),Mod(2,5))) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: chinese((Mod(3,7) *** ,chinese(Mod(1,3),Mo ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:09:02 2005 Input: chinese((Mod(3,7),chinese(Mod(1,3),Mod(2,5)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: chinese((Mod(3,7) *** ,chinese(Mod(1,3),Mo ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:09:22 2005 Input: chinese(Mod(3,7),chinese(Mod(1,3),Mod(2,5)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...hinese(Mod(1,3),Mod(2,5)) ^ Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:10:59 2005 Input: chinese(Mod(3,7),chinese(Mod(1,3),Mod(2,5)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...hinese(Mod(1,3),Mod(2,5)) ^ Timing: real 0m0.021s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:11:18 2005 Input: chinese(Mod(3,7), chinese((Mod(1,3),Mod(2,5)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...od(3,7),chinese((Mod(1,3) *** ,Mod(2,5)) ^---------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:11:32 2005 Input: chinese(Mod(3,7),chinese((Mod(1,3),Mod(2,5))) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...od(3,7),chinese((Mod(1,3) *** ,Mod(2,5))) ^----------- Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:11:53 2005 Input: chinese Mod(3,7),chinese((Mod(1,3),Mod(2,5))) Output: ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,chinese((Mod(1,3),Mod(2,5))). *** unknown function or error in formal parameters: chineseMod(3,7),chin ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:12:14 2005 Input: chinese ((Mod(3,7)),chinese((Mod(1,3),Mod(2,5))) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...d(3,7)),chinese((Mod(1,3) *** ,Mod(2,5))) ^----------- Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:12:20 2005 Input: chinese ((Mod(3,7)),chinese((Mod(1,3),Mod(2,5))) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...d(3,7)),chinese((Mod(1,3) *** ,Mod(2,5))) ^----------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:15:18 2005 Input: sigma(10) Output: ? 18 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:15:30 2005 Input: sigma(35) Output: ? 48 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:15:41 2005 Input: sigma(10!) Output: ? 15334088 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.005s '210.98.' ************** PARI ***************** Host 210.98.29.3 (210.98.29.3) Time: Mon Apr 25 20:16:20 2005 Input: qfbclassno(5) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.006s sys 0m0.006s '210.98.' ************** PARI ***************** Host 210.98.29.3 (210.98.29.3) Time: Mon Apr 25 20:16:30 2005 Input: qfbclassno(5); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.005s '210.98.' ************** PARI ***************** Host 210.98.29.3 (210.98.29.3) Time: Mon Apr 25 20:16:43 2005 Input: qfbclassno(7) Output: ? ? Errors (if any) and Timing Info: *** discriminant not congruent to 0 or 1 mod 4 in classno2. Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '210.98.' ************** PARI ***************** Host 210.98.29.3 (210.98.29.3) Time: Mon Apr 25 20:16:56 2005 Input: qfbclassno(9) Output: ? ? Errors (if any) and Timing Info: *** square argument in regula. Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '210.98.' ************** PARI ***************** Host 210.98.29.3 (210.98.29.3) Time: Mon Apr 25 20:17:05 2005 Input: qfbclassno(13) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:17:43 2005 Input: sigma(3628800) Output: ? 15334088 ? ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.008s sys 0m0.004s '210.98.' ************** PARI ***************** Host 210.98.29.3 (210.98.29.3) Time: Mon Apr 25 20:17:56 2005 Input: qfbclassno(-15) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:24:04 2005 Input: numdiv(10!) Output: ? 270 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:32:13 2005 Input: chrem(Mod(1,3), Mod(2,5), Mod(3,7)) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: chrem( *** Mod(1,3),Mod(2,5),Mo ^-------------------- Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:32:27 2005 Input: chrem(Mod(1,3), Mod(2,5)) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: chrem( *** Mod(1,3),Mod(2,5)) ^------------------ Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:32:36 2005 Input: chinese(Mod(1,3), Mod(2,5)) Output: ? Mod(7, 15) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:32:48 2005 Input: chinese(Mod(1,3), Mod(2,5), Mod (3,7)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: chinese(Mod(1,3),Mod(2,5),Mod(3,7)) ^---------- Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:33:22 2005 Input: chinese(Mod(1,3), Mod(2,5)) Output: ? Mod(7, 15) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:33:47 2005 Input: chinese(Mod(3,7), Mod(7,15)) Output: ? Mod(52, 105) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:34:51 2005 Input: chinese(Mod(0,27), Mod(-1,8)) Output: ? Mod(135, 216) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:36:40 2005 Input: chinese(4*Mod(2,33), 3*Mod(2,64)) Output: ? Mod(2054, 2112) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:37:32 2005 Input: chinese(5*Mod(3, 101), Mod(2054, 2112) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...Mod(3,101),Mod(2054,2112) ^ Timing: real 0m0.029s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:37:37 2005 Input: chinese(5*Mod(3, 101), Mod(2054, 2112)) Output: ? Mod(101318, 213312) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:38:16 2005 Input: chinese(6*Mod(13, 137), Mod(101318, 213312)) Output: ? Mod(314630, 29223744) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:39:43 2005 Input: chinese(mod(2,3), Mod(3,4)) Output: ? ? ? Errors (if any) and Timing Info: *** obsolete function: chinese(mod(2,3),Mod(3,4)) ^------------------ For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.022s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:39:49 2005 Input: chinese(Mod(2,3), Mod(3,4)) Output: ? Mod(11, 12) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:40:02 2005 Input: chinese(Mod(4,5), Mod(11,12)) Output: ? Mod(59, 60) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:41:36 2005 Input: chinese(2*Mod(2,3), 3*Mod(3,4)) Output: ? Mod(1, 12) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:41:59 2005 Input: chinese(4*Mod(4,5), Mod(1,12)) Output: ? Mod(1, 60) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:42:41 2005 Input: chinese(4Mod(2,33), 3Mod(2,64)) Output: ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: chinese(4Mod(2,33),3Mod(2,64) ^-------------------- Timing: real 0m0.022s user 0m0.010s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:42:52 2005 Input: chinese(4*Mod(2,33), 3*Mod(2,64)) Output: ? Mod(2054, 2112) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:43:16 2005 Input: chinese(5*Mod(3,101), Mod(2054, 2112)) Output: ? Mod(101318, 213312) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:43:43 2005 Input: chinese(6*Mod(13, 137), Mod(101318, 213312)) Output: ? Mod(314630, 29223744) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:49:37 2005 Input: Mod(16, 5); Output: ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:49:41 2005 Input: Mod(16, 5) Output: ? Mod(1, 5) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:51:14 2005 Input: 7*Mod(16, 5) Output: ? Mod(2, 5) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:51:26 2005 Input: 7*Mod(8,9) Output: ? Mod(2, 9) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:51:42 2005 Input: 8*Mod(7,9) Output: ? Mod(2, 9) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:51:47 2005 Input: 8*Mod(7,9) Output: ? Mod(2, 9) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:52:02 2005 Input: 7*Mod(8,9) Output: ? Mod(2, 9) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Mon Apr 25 20:52:12 2005 Input: 7*Mod(6,9) Output: ? Mod(6, 9) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 05:45:14 2005 Input: chinese(chinese(Mod(1,3),Mod(2,5)),Mod(3,7) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...d(1,3),Mod(2,5)),Mod(3,7) ^ Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 05:45:49 2005 Input: print(chinese(chinese(Mod(1,3),Mod(2,5)),Mod(3,7)); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...(1,3),Mod(2,5)),Mod(3,7)); ^- Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 05:46:55 2005 Input: print(chinese(Mod(1,3),Mod(2,5))); Output: ? Mod(7, 15) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 05:54:17 2005 Input: print(chinese(Mod(1,3),Mod(2,5),Mod(3,7))); Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...chinese(Mod(1,3),Mod(2,5) *** ,Mod(3,7))); ^------------ Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 05:54:44 2005 Input: print(chinese(Mod(1,3),Mod(2,5)),Mod(3,7))); Output: ? Mod(7, 15)Mod(3, 7) ? Errors (if any) and Timing Info: *** Warning: unused characters: );. Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 05:55:28 2005 Input: print(chinese(Mod(1,3),Mod(2,5)),Mod(3,7)); Output: ? Mod(7, 15)Mod(3, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.005s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 05:56:45 2005 Input: print(chinese(chinese(Mod(1,3),Mod(2,5)),Mod(3,7))); Output: ? Mod(52, 105) ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.006s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 06:00:25 2005 Input: print(gcd(6,10)); print(chinese(chinese(Mod(1,3),Mod(2,5)),Mod(3,7))); Output: ? 2 ? ? Mod(52, 105) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 06:02:23 2005 Input: print(gcd(885568,33)); print(gcd(456621,64)); print(gcd(289344,101)); print(gcd(213312,137)); print(chinese(chinese(Mod(1,3),Mod(2,5)),Mod(3,7))); Output: ? 1 ? 1 ? 1 ? 1 ? Mod(52, 105) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '203.166' ************** PARI ***************** Host 203.166.57.138 (203.166.57.138) Time: Tue Apr 26 07:45:48 2005 Input: help Output: ? help ? Errors (if any) and Timing Info: Timing: real 0m0.389s user 0m0.005s sys 0m0.008s '203.28.' ************** PARI ***************** Host 203.28.159.153 (203.28.159.153) Time: Tue Apr 26 07:48:37 2005 Input: chinese Output: ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: chinese ^ Timing: real 0m0.242s user 0m0.009s sys 0m0.012s '203.23.' ************** PARI ***************** Host 203.23.22.152 (203.23.22.152) Time: Tue Apr 26 07:52:27 2005 Input: chinese(2,3) Output: ? ? Errors (if any) and Timing Info: *** incompatible arguments in chinois. Timing: real 0m0.098s user 0m0.007s sys 0m0.006s '203.166' ************** PARI ***************** Host 203.166.57.138 (203.166.57.138) Time: Tue Apr 26 08:09:47 2005 Input: gcd(99,64) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.432s user 0m0.007s sys 0m0.011s '203.23.' ************** PARI ***************** Host 203.23.22.152 (203.23.22.152) Time: Tue Apr 26 08:17:21 2005 Input: divisors(35) Output: ? [1, 5, 7, 35] ? Errors (if any) and Timing Info: Timing: real 0m0.193s user 0m0.006s sys 0m0.012s '203.23.' ************** PARI ***************** Host 203.23.22.151 (203.23.22.151) Time: Tue Apr 26 08:17:49 2005 Input: sum(divisors(35)) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: sum(divisors(35)) ^------------- Timing: real 0m0.016s user 0m0.006s sys 0m0.008s '203.166' ************** PARI ***************** Host 203.166.57.135 (203.166.57.135) Time: Tue Apr 26 08:23:35 2005 Input: divisors(10!) Output: ? [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 50, 54, 56, 60, 63, 64, 70, 72, 75, 80, 81, 84, 90, 96, 100, 105, 108, 112, 120, 126, 128, 135, 140, 144, 150, 160, 162, 168, 175, 180, 189, 192, 200, 210, 216, 224, 225, 240, 252, 256, 270, 280, 288, 300, 315, 320, 324, 336, 350, 360, 378, 384, 400, 405, 420, 432, 448, 450, 480, 504, 525, 540, 560, 567, 576, 600, 630, 640, 648, 672, 675, 700, 720, 756, 768, 800, 810, 840, 864, 896, 900, 945, 960, 1008, 1050, 1080, 1120, 1134, 1152, 1200, 1260, 1280, 1296, 1344, 1350, 1400, 1440, 1512, 1575, 1600, 1620, 1680, 1728, 1792, 1800, 1890, 1920, 2016, 2025, 2100, 2160, 2240, 2268, 2304, 2400, 2520, 2592, 2688, 2700, 2800, 2835, 2880, 3024, 3150, 3200, 3240, 3360, 3456, 3600, 3780, 3840, 4032, 4050, 4200, 4320, 4480, 4536, 4725, 4800, 5040, 5184, 5376, 5400, 5600, 5670, 5760, 6048, 6300, 6400, 6480, 6720, 6912, 7200, 7560, 8064, 8100, 8400, 8640, 8960, 9072, 9450, 9600, 10080, 10368, 10800, 11200, 11340, 11520, 12096, 12600, 12960, 13440, 14175, 14400, 15120, 16128, 16200, 16800, 17280, 18144, 18900, 19200, 20160, 20736, 21600, 22400, 22680, 24192, 25200, 25920, 26880, 28350, 28800, 30240, 32400, 33600, 34560, 36288, 37800, 40320, 43200, 44800, 45360, 48384, 50400, 51840, 56700, 57600, 60480, 64800, 67200, 72576, 75600, 80640, 86400, 90720, 100800, 103680, 113400, 120960, 129600, 134400, 145152, 151200, 172800, 181440, 201600, 226800, 241920, 259200, 302400, 362880, 403200, 453600, 518400, 604800, 725760, 907200, 1209600, 1814400, 3628800] ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.007s sys 0m0.007s '203.23.' ************** PARI ***************** Host 203.23.22.153 (203.23.22.153) Time: Tue Apr 26 08:42:38 2005 Input: gcd(10560,101) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.006s sys 0m0.005s '203.23.' ************** PARI ***************** Host 203.23.22.154 (203.23.22.154) Time: Tue Apr 26 08:52:04 2005 Input: gcd(1279872,137) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '203.23.' ************** PARI ***************** Host 203.23.22.152 (203.23.22.152) Time: Tue Apr 26 09:05:30 2005 Input: isprime(67) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.362s user 0m0.006s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.9.138 (129.143.9.138) Time: Tue Apr 26 09:05:38 2005 Input: 1+1 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.006s '203.166' ************** PARI ***************** Host 203.166.57.135 (203.166.57.135) Time: Tue Apr 26 09:05:55 2005 Input: factor(67) Output: ? [67 1] ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 09:27:54 2005 Input: print(gcd(885568,33)); print(gcd(456621,64)); print(gcd(289344,101)); print(gcd(213312,137)); print(chinese(chinese(chinese(Mod(2,33),Mod(2,64)),Mod(3,101)),Mod(13,137))); Output: ? 1 ? 1 ? 1 ? 1 ? Mod(27208898, 29223744) ? Errors (if any) and Timing Info: Timing: real 0m0.159s user 0m0.009s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 09:35:07 2005 Input: print(chinese(chinese(chinese(Mod(2,33),Mod(2,64)),Mod(3,101)),Mod(13,137))); print(Mod(157,105)); Output: ? Mod(27208898, 29223744) ? Mod(52, 105) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 09:36:05 2005 Input: print(chinese(chinese(chinese(Mod(2,33),Mod(2,64)),Mod(3,101)),Mod(13,137))); print(Mod(750740964000,29223744)); Output: ? Mod(27208898, 29223744) ? Mod(12204384, 29223744) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 10:03:27 2005 Input: print(chinese(chinese(chinese(Mod(2,33),Mod(2,64)),Mod(3,101)),Mod(13,137))); print(Mod(750740964000,29223744)); Output: ? Mod(27208898, 29223744) ? Mod(12204384, 29223744) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 10:05:44 2005 Input: print(chinese(chinese(chinese(Mod(2,33),Mod(2,64)),Mod(3,101)),Mod(13,137))); print(Mod(66622166,29223744)); Output: ? Mod(27208898, 29223744) ? Mod(8174678, 29223744) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '219.164' ************** PARI ***************** Host 219.164.19.110 (219.164.19.110) Time: Tue Apr 26 13:13:48 2005 Input: factor(88054688) Output: ? [2 5] [47 1] [127 1] [461 1] ? Errors (if any) and Timing Info: Timing: real 0m0.210s user 0m0.009s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 22:57:32 2005 Input: chinese(chinese(chinese(Mod(17,33),Mod(22,64)),Mod(41,101)),Mod(25,137)) Output: ? Mod(8174678, 29223744) ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:02:36 2005 Input: sigma(10!) Output: ? 15334088 ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:05:31 2005 Input: chinese(chinese(chinese(Mod(17,33),Mod(22,64)),Mod(41,101)),Mod(25,137)) Output: ? Mod(8174678, 29223744) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:10:30 2005 Input: chinese(chinese(Mod(5,6),Mod(4,5)),Mod(3,4)) Output: ? Mod(59, 60) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:20:58 2005 Input: chinese(Mod(4,5),Mod(3,4) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: chinese(Mod(4,5),Mod(3,4) ^ Timing: real 0m0.027s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:21:04 2005 Input: chinese(Mod(4,5),Mod(3,4)) Output: ? Mod(19, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:22:31 2005 Input: sigma(11) Output: ? 12 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:22:39 2005 Input: sigma(10!) Output: ? 15334088 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:22:49 2005 Input: sigma(10*9) Output: ? 234 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.008s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:23:03 2005 Input: sigma(10*9*8*7*6*5*4*3*2) Output: ? 15334088 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:24:02 2005 Input: chinese( Mod(3,4), Mod(4,5)) Output: ? Mod(19, 20) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.003s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:24:28 2005 Input: chinese( Mod(2,3), Mod(19,20)) Output: ? Mod(59, 60) ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:25:03 2005 Input: chinese( 4*Mod(2,33), 3*Mod(2,64)) Output: ? Mod(2054, 2112) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.005s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:25:26 2005 Input: chinese( 5*Mod(3,101), Mod(2054,2112)) Output: ? Mod(101318, 213312) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:25:50 2005 Input: chinese( 6*Mod(13,137), Mod(101318, 213312)) Output: ? Mod(314630, 29223744) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.002s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:26:39 2005 Input: 64! Output: ? 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:26:56 2005 Input: 2(64!) Output: ? 2 ? Errors (if any) and Timing Info: *** Warning: unused characters: (64!). Timing: real 0m0.022s user 0m0.003s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:27:05 2005 Input: 2*(64!) Output: ? 253773864371768328206866778670322961605731032349090384397603788750429408460800000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.005s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:27:10 2005 Input: 2*(64!) +1 Output: ? 253773864371768328206866778670322961605731032349090384397603788750429408460800000000000001 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:27:21 2005 Input: 314630-13 Output: ? 314617 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:27:34 2005 Input: factor(253773864371768328206866778670322961605731032349090384397603788750429408460800000000000001) Output: ? [67 1] [127 1] [433 1] [2741 1] [84871 1] [1438891073 1] [55170223013 1] [3729747748300229314695687876891629543976653546969201147 1] ? Errors (if any) and Timing Info: Timing: real 0m1.990s user 0m1.928s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:27:35 2005 Input: 314617/137 Output: ? 314617/137 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:27:53 2005 Input: 2*(64!) + 1 Output: ? 253773864371768328206866778670322961605731032349090384397603788750429408460800000000000001 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:28:11 2005 Input: (2*(64!) + 1)/67 Output: ? 3787669617489079525475623562243626292622851229090901259665728190304916544191044776119403 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:28:14 2005 Input: (2*(64!) + 1)/67 Output: ? 3787669617489079525475623562243626292622851229090901259665728190304916544191044776119403 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:28:20 2005 Input: (2*(64!) + 1) Output: ? 253773864371768328206866778670322961605731032349090384397603788750429408460800000000000001 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:28:32 2005 Input: factor(256252345234623453412512345641361356155134513451345613451234513451346134563773864371768328206866778670322961605731032349090384397603788750429408460800000000000001) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13427 Killed /usr/bin/gp -q -emacs Timing: real 0m21.507s user 0m20.984s sys 0m0.016s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:28:55 2005 Input: (4*314630 - 2)/33 Output: ? 419506/11 ? Errors (if any) and Timing Info: Timing: real 0m0.113s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:29:02 2005 Input: factor(2562523452346434513451345613451234513451346134563773864371768328206866778670322961605731032349090384397603788750429408460800000000000001) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 13738 Killed /usr/bin/gp -q -emacs Timing: real 0m21.457s user 0m20.993s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:29:09 2005 Input: factor(256252328206866778670322961605731032349090384397603788750429408460800000000000001) Output: ? [3 2] [12569 1] [2265294049795058200248609556189664450889670215058245495977134293904756853281 1] ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.017s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:29:13 2005 Input: 419506/11 Output: ? 419506/11 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:29:44 2005 Input: factor(25622352352328206866778670322961605731032349090384397603788750429408460800000000000001) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 14161 Killed /usr/bin/gp -q -emacs Timing: real 0m21.599s user 0m20.989s sys 0m0.011s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:30:13 2005 Input: factor(2562235235232820778670322961605731032349090384397603788750429408460800000000000001) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 14531 Killed /usr/bin/gp -q -emacs Timing: real 0m21.578s user 0m20.994s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:30:36 2005 Input: factor(256357357333572346246241605731032349090384397603788750429408460800000000000001) Output: ? [7 1] [1583 1] [20902397 1] [926967822903442643 1] [96832375129808402179 1] [12330636509005285401114054869 1] ? Errors (if any) and Timing Info: Timing: real 0m14.032s user 0m13.489s sys 0m0.056s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:30:52 2005 Input: factor(2563573573335723462462416057310323490903843976037887504294084608800000000000001) Output: ? [3 1] [7 1] [53 1] [22093871 1] [104250658699586678735454062837381807327671283023979232333379990896487 1] ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.020s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:31:09 2005 Input: factor(2563573573335723462462416057310323490903843976037887504294084608800000000000001) Output: ? [3 1] [7 1] [53 1] [22093871 1] [104250658699586678735454062837381807327671283023979232333379990896487 1] ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.020s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:31:15 2005 Input: factor(25635735733357234624624160573103234909038543976037887504294084608800000000000001) Output: ? [103 1] [185684657 1] [1340394204933875159884232594722431524618337989004800177295746360836231 1] ? Errors (if any) and Timing Info: Timing: real 0m0.131s user 0m0.127s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:31:20 2005 Input: factor(2563573573335723462462416054773103234909038543976037887504294084608800000000000001) Output: ? [11 1] [67 1] [859 1] [76777 1] [264997217 1] [199027314430838279348982021053185575924612652685060425236105883 1] ? Errors (if any) and Timing Info: Timing: real 0m0.155s user 0m0.148s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue Apr 26 23:31:50 2005 Input: factor(92563573573335723462462416054773103234909038543976037887504294084608800000000000001) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 15779 Killed /usr/bin/gp -q -emacs Timing: real 0m21.465s user 0m20.991s sys 0m0.009s '66.185.' ************** PARI ***************** Host 66.185.84.73 (66.185.84.73) Time: Wed Apr 27 06:18:37 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.004s '216.28.' ************** PARI ***************** Host 216.28.79.228 (216.28.79.228) Time: Wed Apr 27 09:10:28 2005 Input: 2^5 2 + 2 Output: ? 32 ? 4 ? ? Errors (if any) and Timing Info: Timing: real 0m0.692s user 0m0.007s sys 0m0.006s '216.28.' ************** PARI ***************** Host 216.28.79.228 (216.28.79.228) Time: Wed Apr 27 09:10:28 2005 Input: 2^5 2 + 2 Output: ? 32 ? 4 ? ? Errors (if any) and Timing Info: Timing: real 0m0.688s user 0m0.006s sys 0m0.006s '128.178' ************** PARI ***************** Host 128.178.73.83 (128.178.73.83) Time: Wed Apr 27 11:28:42 2005 Input: Factorization(21312321480802) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorization(213123 ^-------------------- Timing: real 0m0.062s user 0m0.005s sys 0m0.006s '66.240.' ************** PARI ***************** Host 66.240.9.82 (66.240.9.82) Time: Wed Apr 27 12:03:46 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.005s '212.130' ************** PARI ***************** Host 212.130.130.128 (212.130.130.128) Time: Wed Apr 27 13:09:09 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.078s user 0m0.005s sys 0m0.007s '212.130' ************** PARI ***************** Host 212.130.130.128 (212.130.130.128) Time: Wed Apr 27 13:09:21 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '128.135' ************** PARI ***************** Host 128.135.197.118 (128.135.197.118) Time: Wed Apr 27 13:09:34 2005 Input: E^0.001 Output: ? ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m0.038s user 0m0.007s sys 0m0.003s '128.135' ************** PARI ***************** Host 128.135.197.118 (128.135.197.118) Time: Wed Apr 27 13:09:39 2005 Input: e^0.001 Output: ? ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m0.013s user 0m0.007s sys 0m0.003s '61.197.' ************** PARI ***************** Host 61.197.87.238 (61.197.87.238) Time: Wed Apr 27 14:38:17 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '140.247' ************** PARI ***************** Host 140.247.161.30 (140.247.161.30) Time: Wed Apr 27 20:32:15 2005 Input: L := NumberField(x^3+x+1); M := SplittingField(L); Discriminant(RingOfIntegers(M)); Factorization(Discriminant(RingOfIntegers(M))); OM := RingOfIntegers(M); Factorization(2*OM); Output: ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: L:=NumberField(x^3+x+1 ^-------------------- *** unexpected character: M:=SplittingField(L); ^------------------- *** unknown function or error in formal parameters: Discriminant( *** RingOfIntegers(M)); ^------------------- *** unknown function or error in formal parameters: Factorization( *** Discriminant(RingOfI ^-------------------- *** unexpected character: OM:=RingOfIntegers(M); ^------------------- *** unknown function or error in formal parameters: Factorization(2*OM); ^-------------------- Timing: real 0m0.036s user 0m0.008s sys 0m0.003s '206.112' ************** PARI ***************** Host 206.112.75.208 (206.112.75.208) Time: Thu Apr 28 08:32:03 2005 Input: 00110111101 Output: ? 110111101 ? Errors (if any) and Timing Info: Timing: real 0m0.381s user 0m0.004s sys 0m0.014s '206.112' ************** PARI ***************** Host 206.112.75.208 (206.112.75.208) Time: Thu Apr 28 08:40:02 2005 Input: Factorial(18) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorial(18) ^------------- Timing: real 0m0.017s user 0m0.006s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.87.79 (128.197.87.79) Time: Thu Apr 28 13:12:37 2005 Input: 3.14*2^(1/2) Output: ? 4.4406305858515184532373025940184519666 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.87.79 (128.197.87.79) Time: Thu Apr 28 13:13:12 2005 Input: 3.14*(4/3)^(1/2) Output: ? 3.6257596905108498011174543415522928214 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '63.149.' ************** PARI ***************** Host 63.149.68.2 (63.149.68.2) Time: Thu Apr 28 16:24:29 2005 Input: matker(Mat([x,x]),1) Output: ? [x] [x] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '63.149.' ************** PARI ***************** Host 63.149.68.2 (63.149.68.2) Time: Thu Apr 28 16:26:54 2005 Input: nfisincl(nfinit(y),vector(9,x,x)) Output: ? ? Errors (if any) and Timing Info: *** constant polynomial in nfiso or nfincl. Timing: real 0m0.037s user 0m0.005s sys 0m0.009s '67.100.' ************** PARI ***************** Host 67.100.204.64 (67.100.204.64) Time: Fri Apr 29 01:54:53 2005 Input: for(i=2,7,print(i)) Output: ? 2 3 4 5 6 7 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.007s '141.76.' ************** PARI ***************** Host 141.76.75.171 (141.76.75.171) Time: Fri Apr 29 05:21:25 2005 Input: if(n<1,0,direuler(p=2,n,1/(1-X)/(1-p*X))[n]) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.017s user 0m0.008s sys 0m0.008s '141.76.' ************** PARI ***************** Host 141.76.75.171 (141.76.75.171) Time: Fri Apr 29 05:22:03 2005 Input: a(n)=if(n<1,0,direuler(p=2,n,1/(1-X)/(1-p*X))[n]); a(5) Output: ? ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '141.76.' ************** PARI ***************** Host 141.76.75.171 (141.76.75.171) Time: Fri Apr 29 05:22:09 2005 Input: a(n)=if(n<1,0,direuler(p=2,n,1/(1-X)/(1-p*X))[n]) a(5) Output: ? ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '141.76.' ************** PARI ***************** Host 141.76.75.171 (141.76.75.171) Time: Fri Apr 29 05:22:14 2005 Input: a(n)=if(n<1,0,direuler(p=2,n,1/(1-X)/(1-p*X))[n]), a(5) Output: ? ? 6 ? Errors (if any) and Timing Info: *** Warning: unused characters: ,. Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '141.76.' ************** PARI ***************** Host 141.76.75.171 (141.76.75.171) Time: Fri Apr 29 05:23:40 2005 Input: for(n=1,7,print(if(n<1,0,direuler(p=2,n,1/(1-X)/(1-p*X))[n])) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...2,n,1/(1-X)/(1-p*X))[n])) ^ Timing: real 0m0.019s user 0m0.006s sys 0m0.008s '141.76.' ************** PARI ***************** Host 141.76.75.171 (141.76.75.171) Time: Fri Apr 29 05:23:58 2005 Input: for(n=1,7,print(if(n<1,0,direuler(p=2,n,1/(1-X)/(1-p*X))[n]))) Output: ? 1 3 4 7 6 12 8 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '63.149.' ************** PARI ***************** Host 63.149.68.2 (63.149.68.2) Time: Fri Apr 29 15:16:46 2005 Input: bnfunit(nfbasis(x^10+1)) Output: ? ? Errors (if any) and Timing Info: *** bug in GP (Segmentation Fault), please report Timing: real 0m0.137s user 0m0.005s sys 0m0.008s '63.149.' ************** PARI ***************** Host 63.149.68.2 (63.149.68.2) Time: Fri Apr 29 15:17:18 2005 Input: bnfunit(nfbasis(x^10+1)) Output: ? ? Errors (if any) and Timing Info: *** bug in GP (Segmentation Fault), please report Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '85.96.2' ************** PARI ***************** Host 85.96.207.208 (85.96.207.208) Time: Fri Apr 29 16:08:02 2005 Input: y^q-y=x^q_0(x^q-x) Output: ? ? Errors (if any) and Timing Info: *** negative exponent in glog. Timing: real 0m0.034s user 0m0.005s sys 0m0.008s '205.250' ************** PARI ***************** Host 205.250.249.214 (205.250.249.214) Time: Sun May 1 00:47:14 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.172s user 0m0.005s sys 0m0.008s '205.250' ************** PARI ***************** Host 205.250.249.214 (205.250.249.214) Time: Sun May 1 00:47:29 2005 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.008s sys 0m0.005s '205.250' ************** PARI ***************** Host 205.250.249.214 (205.250.249.214) Time: Sun May 1 00:47:48 2005 Input: 2+300! Output: ? 306057512216440636035370461297268629388588804173576999416776741259476533176716867465515291422477573349939147888701726368864263907759003154226842927906974559841225476930271954604008012215776252176854255965356903506788725264321896264299365204576448830388909753943489625436053225980776521270822437639449120128678675368305712293681943649956460498166450227716500185176546469340112226034729724066333258583506870150169794168850353752137554910289126407157154830282284937952636580145235233156936482233436799254594095276820608062232812387383880817049600000000000000000000000000000000000000000000000000000000000000000000000002 ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.010s sys 0m0.002s '205.250' ************** PARI ***************** Host 205.250.249.214 (205.250.249.214) Time: Sun May 1 00:48:19 2005 Input: 12! Output: ? 479001600 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '205.250' ************** PARI ***************** Host 205.250.249.214 (205.250.249.214) Time: Sun May 1 00:48:29 2005 Input: 4! Output: ? 24 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '84.109.' ************** PARI ***************** Host 84.109.153.14 (84.109.153.14) Time: Sun May 1 03:34:18 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '84.109.' ************** PARI ***************** Host 84.109.153.14 (84.109.153.14) Time: Sun May 1 03:35:08 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!"haim Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: *** Warning: unused characters: haim. Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '60.34.5' ************** PARI ***************** Host 60.34.53.175 (60.34.53.175) Time: Sun May 1 04:23:46 2005 Input: Factorize(x*(y-z)^5+y*(z-x)^5+z*(x-y)^5); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Factorize(x*(y-z)^5+y*(z-x)^5+z ^-------------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '60.34.5' ************** PARI ***************** Host 60.34.53.175 (60.34.53.175) Time: Sun May 1 04:24:36 2005 Input: x*(y-z)^5+y*(z-x)^5+z*(x-y)^5; (x-y)*(y-z)*(z-x)*((x+y+z)*(x^2+y^2+z^2)-9*x*y*z); Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.006s sys 0m0.006s '84.58.1' ************** PARI ***************** Host 84.58.136.33 (84.58.136.33) Time: Sun May 1 05:22:53 2005 Input: G:=SymmetricGroup(7); CharacterTable(G); Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: G:=SymmetricGroup(7); ^------------------- *** expected character: '=' instead of: CharacterTable(G); ^- Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '137.165' ************** PARI ***************** Host 137.165.195.51 (137.165.195.51) Time: Sun May 1 16:16:11 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.290s user 0m0.007s sys 0m0.009s '68.196.' ************** PARI ***************** Host 68.196.169.191 (68.196.169.191) Time: Sun May 1 21:01:38 2005 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.007s sys 0m0.010s '68.196.' ************** PARI ***************** Host 68.196.169.191 (68.196.169.191) Time: Sun May 1 21:02:21 2005 Input: 200! Output: ? 788657867364790503552363213932185062295135977687173263294742533244359449963403342920304284011984623904177212138919638830257642790242637105061926624952829931113462857270763317237396988943922445621451664240254033291864131227428294853277524242407573903240321257405579568660226031904170324062351700858796178922222789623703897374720000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.011s sys 0m0.003s '157.158' ************** PARI ***************** Host 157.158.0.30 (157.158.0.30) Time: Mon May 2 12:13:38 2005 Input: E1 := EllipticCurve([FldRat | 0, 0, 0, 1, 0]); E2 := EllipticCurve([GF(13) | 0, 0, 0, 1, 4]); IsIsomorphic(E1, E2); Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: E1:=EllipticCurve([FldR ^-------------------- *** unexpected character: E2:=EllipticCurve([GF(1 ^-------------------- *** expected character: '=' instead of: IsIsomorphic(E1,E2); ^- Timing: real 0m0.103s user 0m0.009s sys 0m0.003s '219.164' ************** PARI ***************** Host 219.164.19.110 (219.164.19.110) Time: Mon May 2 12:32:26 2005 Input: factor(88524480) Output: ? [2 6] [3 1] [5 1] [11 1] [83 1] [101 1] ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.008s sys 0m0.007s '219.164' ************** PARI ***************** Host 219.164.19.110 (219.164.19.110) Time: Mon May 2 13:54:50 2005 Input: factor(88063676) Output: ? [2 2] [22015919 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '157.158' ************** PARI ***************** Host 157.158.0.30 (157.158.0.30) Time: Mon May 2 14:16:23 2005 Input: E1 := EllipticCurve([FiniteField(11) | 1, 2]); E2 := EllipticCurve([FiniteField(11) | 1, 2]); kk:=IsIsomorphic(E1,E2):Map; Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: E1:=EllipticCurve([Fini ^-------------------- *** unexpected character: E2:=EllipticCurve([Fini ^-------------------- *** unexpected character: kk:=IsIsomorphic(E1,E2) ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '165.21.' ************** PARI ***************** Host 165.21.154.109 (165.21.154.109) Time: Tue May 3 06:02:03 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.212s user 0m0.006s sys 0m0.010s '131.111' ************** PARI ***************** Host 131.111.229.148 (131.111.229.148) Time: Tue May 3 09:46:06 2005 Input: contfrac((sqrt(55)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: contfrac((sqrt(55)) ^ Timing: real 0m0.310s user 0m0.005s sys 0m0.011s '131.111' ************** PARI ***************** Host 131.111.229.148 (131.111.229.148) Time: Tue May 3 09:46:56 2005 Input: contfrac(sqrt(55)) Output: ? [7, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2] ? Errors (if any) and Timing Info: Timing: real 0m0.075s user 0m0.005s sys 0m0.007s '131.111' ************** PARI ***************** Host 131.111.229.148 (131.111.229.148) Time: Tue May 3 09:47:01 2005 Input: contfrac(sqrt(55)) Output: ? [7, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '131.111' ************** PARI ***************** Host 131.111.229.148 (131.111.229.148) Time: Tue May 3 09:47:42 2005 Input: contfrac(sqrt(97)) Output: ? [9, 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18, 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18, 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18, 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18, 1, 5, 1, 1, 1, 1, 2] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue May 3 15:22:07 2005 Input: factor(3721) Output: ? [61 2] ? Errors (if any) and Timing Info: Timing: real 0m0.048s user 0m0.007s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue May 3 15:22:22 2005 Input: factor(10573) Output: ? [97 1] [109 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.004s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue May 3 15:32:35 2005 Input: factor(340667) Output: ? [443 1] [769 1] ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.009s sys 0m0.003s '213.64.' ************** PARI ***************** Host 213.64.138.160 (213.64.138.160) Time: Wed May 4 14:48:03 2005 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.006s '139.78.' ************** PARI ***************** Host 139.78.115.225 (139.78.115.225) Time: Wed May 4 14:48:26 2005 Input: decimalcycle(p0,q0)= { local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans } decimalcycle(7,17) Output: ? ? [4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9] ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.007s sys 0m0.005s '81.228.' ************** PARI ***************** Host 81.228.242.44 (81.228.242.44) Time: Thu May 5 06:05:13 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '128.119' ************** PARI ***************** Host 128.119.47.86 (128.119.47.86) Time: Thu May 5 14:37:58 2005 Input: factor(Random(10^20)) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: factor(Random(10^20)) ^-------------- Timing: real 0m0.381s user 0m0.010s sys 0m0.007s '128.119' ************** PARI ***************** Host 128.119.47.86 (128.119.47.86) Time: Thu May 5 14:38:17 2005 Input: A=Random(10^20); factor(A) Output: ? ? [A 1] ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: A=Random(10^20); ^-------------- Timing: real 0m0.071s user 0m0.009s sys 0m0.003s '128.119' ************** PARI ***************** Host 128.119.47.86 (128.119.47.86) Time: Thu May 5 14:38:30 2005 Input: A=Random(10^20) Output: ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: A=Random(10^20) ^------------- Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '128.119' ************** PARI ***************** Host 128.119.47.86 (128.119.47.86) Time: Thu May 5 14:38:45 2005 Input: A=random(10^20) Output: ? 91935484484434818391 ? ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.009s sys 0m0.005s '128.119' ************** PARI ***************** Host 128.119.47.86 (128.119.47.86) Time: Thu May 5 14:38:52 2005 Input: A=random(10^20) factor(A) Output: ? 91935484484434818391 ? [30553 1] [10163339 1] [296068973 1] ? Errors (if any) and Timing Info: Timing: real 0m0.047s user 0m0.010s sys 0m0.006s '128.119' ************** PARI ***************** Host 128.119.47.86 (128.119.47.86) Time: Thu May 5 14:38:54 2005 Input: A=random(10^20) factor(A) Output: ? 91935484484434818391 ? [30553 1] [10163339 1] [296068973 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.010s sys 0m0.006s '128.119' ************** PARI ***************** Host 128.119.47.86 (128.119.47.86) Time: Thu May 5 14:38:55 2005 Input: A=random(10^20) factor(A) Output: ? 91935484484434818391 ? [30553 1] [10163339 1] [296068973 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.006s '128.119' ************** PARI ***************** Host 128.119.47.86 (128.119.47.86) Time: Thu May 5 14:38:55 2005 Input: A=random(10^20) factor(A) Output: ? 91935484484434818391 ? [30553 1] [10163339 1] [296068973 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.012s sys 0m0.003s '128.119' ************** PARI ***************** Host 128.119.47.86 (128.119.47.86) Time: Thu May 5 14:38:56 2005 Input: A=random(10^20) factor(A) Output: ? 91935484484434818391 ? [30553 1] [10163339 1] [296068973 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.011s sys 0m0.004s '128.119' ************** PARI ***************** Host 128.119.47.86 (128.119.47.86) Time: Thu May 5 14:38:59 2005 Input: A=random(10^20) factor(A) Output: ? 91935484484434818391 ? [30553 1] [10163339 1] [296068973 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.009s sys 0m0.007s '165.170' ************** PARI ***************** Host 165.170.128.65 (165.170.128.65) Time: Thu May 5 16:04:25 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.007s sys 0m0.007s '151.100' ************** PARI ***************** Host 151.100.50.6 (151.100.50.6) Time: Fri May 6 05:43:35 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '67.136.' ************** PARI ***************** Host 67.136.35.67 (67.136.35.67) Time: Fri May 6 12:20:34 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.315s user 0m0.007s sys 0m0.005s '218.41.' ************** PARI ***************** Host 218.41.181.201 (218.41.181.201) Time: Sat May 7 01:44:53 2005 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.079s user 0m0.005s sys 0m0.011s '201.252' ************** PARI ***************** Host 201.252.163.10 (201.252.163.10) Time: Sat May 7 16:42:44 2005 Input: 9999^9999 Output: ? 3678978362165515792692625984783565804550254385734776186401856613845616360874750523676165256293320372567032110928366569599432699044419901243683670414060788244958198542680024242555554443351351009201406913420042334263191360440293163925263158121905901809215111676734097618278012767257225075955830464560320325882929419607338700417637982216741626089370630527817919858248244425067882107032040504992133693942984257209267233391108496072474133573230329041350621303555562644061581689489773346475812382861630761542671206427399665195254818870660761299953367109234343296185246620947655303971825992891467766505449702800439539931629360781232287044852497103043500184438484564204069490370009909530341317336334459448625114891862723875368733284186382707049409415586173190187044779587133413954719164091602407423040277644116344823196694780496108829093860394544019077913975064195661487863596355153601977696894647060796078336789818901664700936711780540601588027849120357502804206125775390530395449721795143559185701130989019673973414458162432452044153141771428470077266579671902890598334369757628149907925325804486123759313657431199276911296909988206875045039284204307223007631041398551718017194485506118265217378424353090327768422839936661234797187668662233022432765913802940812930832473399186457600442171772676827615589458775748985986943115616079918481062535783932761746719296095626506175157728984170030971916674508316799683778054082276816688275906538543217866233253802344032652736891976377022470188077093942589570091121680352119736644969204407030630301158396442464636963861919447633190882306922903255230862361035382856766851117326908414263376550446343025959082668379320746709766639152173593543645174998642666861898469093179065202738980674585838269877494546529628303732456318069369239643468584292202923520521843654345394564312954036612437941581404860167933009913560237592337540921596701085678500505207755925095414568272811484781341240031790752673345533742323049977749836527251232204614844529896829235256775947568362574019368797193312608151988595835341331987263683085114693074364277007707975208628852485313299912715708207480967112315919293149969754093821366914768573101984753671149697664696427061732195557936683529744972934672549510900881858985774146689241975618277136688446771946216425556661883998990043133641594285532514785010400951091060253788904076362048542387172565421872193317750093239328348968888759727286751396577155938041423726595410490273125365223664256870411016155290271383386269763833610637527679643386430615158198911094509969103962663060068622172753207212153606813868060367150723684376668129656888542614348374746217699029039834049200407834976530457104740679693998861278920967480901247610862684317640321368218626295038436251501630287464327906726270234208560271152269105899657094135246671184697222281406209293748345352552744017910479812490132919915153120767115137225635886145189519931750150629199709199246358542547706324512413730715983303961218777018316650860242362705920223695303294292054527056124929199921380822588923362245497206479695923327141351853527169422607934639903986697742072846910922708797302177552521537198273335418617482504927534477283613110327139979008043467741332003969949024947500695665[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.566s user 0m0.358s sys 0m0.012s '201.252' ************** PARI ***************** Host 201.252.163.10 (201.252.163.10) Time: Sat May 7 16:43:28 2005 Input: 9999^9999 Output: ? 3678978362165515792692625984783565804550254385734776186401856613845616360874750523676165256293320372567032110928366569599432699044419901243683670414060788244958198542680024242555554443351351009201406913420042334263191360440293163925263158121905901809215111676734097618278012767257225075955830464560320325882929419607338700417637982216741626089370630527817919858248244425067882107032040504992133693942984257209267233391108496072474133573230329041350621303555562644061581689489773346475812382861630761542671206427399665195254818870660761299953367109234343296185246620947655303971825992891467766505449702800439539931629360781232287044852497103043500184438484564204069490370009909530341317336334459448625114891862723875368733284186382707049409415586173190187044779587133413954719164091602407423040277644116344823196694780496108829093860394544019077913975064195661487863596355153601977696894647060796078336789818901664700936711780540601588027849120357502804206125775390530395449721795143559185701130989019673973414458162432452044153141771428470077266579671902890598334369757628149907925325804486123759313657431199276911296909988206875045039284204307223007631041398551718017194485506118265217378424353090327768422839936661234797187668662233022432765913802940812930832473399186457600442171772676827615589458775748985986943115616079918481062535783932761746719296095626506175157728984170030971916674508316799683778054082276816688275906538543217866233253802344032652736891976377022470188077093942589570091121680352119736644969204407030630301158396442464636963861919447633190882306922903255230862361035382856766851117326908414263376550446343025959082668379320746709766639152173593543645174998642666861898469093179065202738980674585838269877494546529628303732456318069369239643468584292202923520521843654345394564312954036612437941581404860167933009913560237592337540921596701085678500505207755925095414568272811484781341240031790752673345533742323049977749836527251232204614844529896829235256775947568362574019368797193312608151988595835341331987263683085114693074364277007707975208628852485313299912715708207480967112315919293149969754093821366914768573101984753671149697664696427061732195557936683529744972934672549510900881858985774146689241975618277136688446771946216425556661883998990043133641594285532514785010400951091060253788904076362048542387172565421872193317750093239328348968888759727286751396577155938041423726595410490273125365223664256870411016155290271383386269763833610637527679643386430615158198911094509969103962663060068622172753207212153606813868060367150723684376668129656888542614348374746217699029039834049200407834976530457104740679693998861278920967480901247610862684317640321368218626295038436251501630287464327906726270234208560271152269105899657094135246671184697222281406209293748345352552744017910479812490132919915153120767115137225635886145189519931750150629199709199246358542547706324512413730715983303961218777018316650860242362705920223695303294292054527056124929199921380822588923362245497206479695923327141351853527169422607934639903986697742072846910922708797302177552521537198273335418617482504927534477283613110327139979008043467741332003969949024947500695665[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.366s user 0m0.357s sys 0m0.007s '68.201.' ************** PARI ***************** Host 68.201.85.82 (68.201.85.82) Time: Sun May 8 00:52:29 2005 Input: 2+1 Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.005s '68.201.' ************** PARI ***************** Host 68.201.85.82 (68.201.85.82) Time: Sun May 8 00:52:35 2005 Input: 2+1=? Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 2+1=? ^-- Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.239.48 (168.122.239.48) Time: Mon May 9 00:00:55 2005 Input: (8^9)^3(Mod12) Output: ? 2417851639229258349412352 ? Errors (if any) and Timing Info: *** Warning: unused characters: (Mod12). Timing: real 0m0.182s user 0m0.007s sys 0m0.005s '168.122' ************** PARI ***************** Host 168.122.239.48 (168.122.239.48) Time: Mon May 9 00:01:03 2005 Input: (8^9)^3(Mod,12) Output: ? 2417851639229258349412352 ? Errors (if any) and Timing Info: *** Warning: unused characters: (Mod,12). Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.239.48 (168.122.239.48) Time: Mon May 9 00:01:09 2005 Input: (8^9)^3(Mod,12) Output: ? 2417851639229258349412352 ? Errors (if any) and Timing Info: *** Warning: unused characters: (Mod,12). Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.239.48 (168.122.239.48) Time: Mon May 9 00:02:17 2005 Input: Mod((8^9)^3,12) Output: ? Mod(8, 12) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '202.58.' ************** PARI ***************** Host 202.58.86.3 (202.58.86.3) Time: Mon May 9 04:51:07 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.005s sys 0m0.006s '220.236' ************** PARI ***************** Host 220.236.11.53 (220.236.11.53) Time: Mon May 9 07:38:27 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.107s user 0m0.007s sys 0m0.006s '220.236' ************** PARI ***************** Host 220.236.11.53 (220.236.11.53) Time: Mon May 9 07:39:37 2005 Input: 4+3+2*9 Output: ? 25 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.006s sys 0m0.006s '220.236' ************** PARI ***************** Host 220.236.11.53 (220.236.11.53) Time: Mon May 9 07:40:03 2005 Input: 4+3+2*9 Output: ? 25 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '168.122' ************** PARI ***************** Host 168.122.128.59 (168.122.128.59) Time: Mon May 9 11:05:32 2005 Input: factor(1147) Output: ? [31 1] [37 1] ? Errors (if any) and Timing Info: Timing: real 0m0.308s user 0m0.006s sys 0m0.006s '168.122' ************** PARI ***************** Host 168.122.128.59 (168.122.128.59) Time: Mon May 9 11:11:11 2005 Input: factor(7081) Output: ? [73 1] [97 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '168.122' ************** PARI ***************** Host 168.122.128.59 (168.122.128.59) Time: Mon May 9 11:15:25 2005 Input: Mod(1789, 6912)^(-1) Output: ? Mod(85, 6912) ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.008s sys 0m0.005s '80.238.' ************** PARI ***************** Host 80.238.13.231 (80.238.13.231) Time: Mon May 9 15:34:15 2005 Input: 1000! Output: ? 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.011s sys 0m0.003s '80.238.' ************** PARI ***************** Host 80.238.13.231 (80.238.13.231) Time: Mon May 9 15:34:52 2005 Input: factor(x^100-1) Output: ? [x - 1 1] [x + 1 1] [x^2 + 1 1] [x^4 - x^3 + x^2 - x + 1 1] [x^4 + x^3 + x^2 + x + 1 1] [x^8 - x^6 + x^4 - x^2 + 1 1] [x^20 - x^15 + x^10 - x^5 + 1 1] [x^20 + x^15 + x^10 + x^5 + 1 1] [x^40 - x^30 + x^20 - x^10 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.083s user 0m0.020s sys 0m0.005s '80.238.' ************** PARI ***************** Host 80.238.13.231 (80.238.13.231) Time: Mon May 9 15:36:08 2005 Input: f(x)=x^2+10; f(3456) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '80.238.' ************** PARI ***************** Host 80.238.13.231 (80.238.13.231) Time: Mon May 9 15:36:18 2005 Input: f(x)=x^2+10 Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '80.238.' ************** PARI ***************** Host 80.238.13.231 (80.238.13.231) Time: Mon May 9 15:36:34 2005 Input: f(39) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: f(39) ^----- Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '80.238.' ************** PARI ***************** Host 80.238.13.231 (80.238.13.231) Time: Mon May 9 15:37:01 2005 Input: f(x):=x^2+10 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: f(x):=x^2+10 ^------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '80.238.' ************** PARI ***************** Host 80.238.13.231 (80.238.13.231) Time: Mon May 9 15:37:04 2005 Input: f(x):=x^2+10 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: f(x):=x^2+10 ^------- Timing: real 0m0.012s user 0m0.002s sys 0m0.011s '80.238.' ************** PARI ***************** Host 80.238.13.231 (80.238.13.231) Time: Mon May 9 15:37:24 2005 Input: factor(x^100-1) Output: ? [x - 1 1] [x + 1 1] [x^2 + 1 1] [x^4 - x^3 + x^2 - x + 1 1] [x^4 + x^3 + x^2 + x + 1 1] [x^8 - x^6 + x^4 - x^2 + 1 1] [x^20 - x^15 + x^10 - x^5 + 1 1] [x^20 + x^15 + x^10 + x^5 + 1 1] [x^40 - x^30 + x^20 - x^10 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.022s sys 0m0.006s '80.238.' ************** PARI ***************** Host 80.238.13.231 (80.238.13.231) Time: Mon May 9 15:37:24 2005 Input: 1000! Output: ? 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '24.235.' ************** PARI ***************** Host 24.235.163.229 (24.235.163.229) Time: Mon May 9 18:26:53 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '150.250' ************** PARI ***************** Host 150.250.41.249 (150.250.41.249) Time: Mon May 9 19:28:05 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '216.31.' ************** PARI ***************** Host 216.31.252.2 (216.31.252.2) Time: Tue May 10 22:56:59 2005 Input: factor 21 Output: ? factor21 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.004s sys 0m0.008s '216.31.' ************** PARI ***************** Host 216.31.252.2 (216.31.252.2) Time: Tue May 10 22:57:20 2005 Input: factor(21) Output: ? [3 1] [7 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.004s sys 0m0.010s '216.31.' ************** PARI ***************** Host 216.31.252.2 (216.31.252.2) Time: Tue May 10 22:58:30 2005 Input: factor(2799783391122132787082946763872260162107044678695542853756000992932612840010760934567105295536085606182235191095136578863716786955428537560009929326128400107609345671052955360856061822351910951365788637105954482006576775098580557613579098734950144178863178946295187237869221823983) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 17230 Killed /usr/bin/gp -q -emacs Timing: real 0m21.044s user 0m20.992s sys 0m0.008s '216.31.' ************** PARI ***************** Host 216.31.252.2 (216.31.252.2) Time: Tue May 10 22:59:22 2005 Input: factor(2799783391122132787082946763872260162107044678695542853756000992932612840010760934567105295536085606182235191095136578863716786955428537560009929326128400107609345671052955360856061822351910951365788637105954482006576775098580557613579098734950144178863178946295187237869221823983) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 17242 Killed /usr/bin/gp -q -emacs Timing: real 0m21.017s user 0m20.994s sys 0m0.006s '82.225.' ************** PARI ***************** Host 82.225.162.107 (82.225.162.107) Time: Wed May 11 08:24:00 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.496s user 0m0.009s sys 0m0.010s '82.225.' ************** PARI ***************** Host 82.225.162.107 (82.225.162.107) Time: Wed May 11 08:24:38 2005 Input: 1/a+1/b Output: ? (1/b*a + 1)/a ? Errors (if any) and Timing Info: Timing: real 0m0.137s user 0m0.005s sys 0m0.006s '82.225.' ************** PARI ***************** Host 82.225.162.107 (82.225.162.107) Time: Wed May 11 08:25:21 2005 Input: f:=atan(x)+x diff(f) Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: f:=atan(x)+x ^---------- *** expected character: '=' instead of: diff(f) ^ Timing: real 0m0.095s user 0m0.007s sys 0m0.007s '131.155' ************** PARI ***************** Host 131.155.145.153 (131.155.145.153) Time: Wed May 11 11:57:24 2005 Input: Q := RationalField(); P := PolynomialRing(Q,2); I := ideal; GroebnerBasis(I); Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: Q:=RationalField(); ^----------------- *** Warning: unused characters: ,y>:=PolynomialRing(Q,2);. *** incorrect type in comparison. *** unexpected character: I:=ideal qfjacobi(x) qfjacobi(x): eigenvalues and orthogonal matrix of eigenvectors of the Timing: real symmetric matrix x. Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '203.28.' ************** PARI ***************** Host 203.28.159.137 (203.28.159.137) Time: Tue May 17 06:05:46 2005 Input: jacobi([7 11]) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: jacobi([711]) ^------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: jacobi(x) ===> qfjacobi(x) qfjacobi(x): eigenvalues and orthogonal matrix of eigenvectors of the Timing: real symmetric matrix x. Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '203.28.' ************** PARI ***************** Host 203.28.159.135 (203.28.159.135) Time: Tue May 17 06:06:05 2005 Input: ?jacobi Output: ? ? Errors (if any) and Timing Info: *** obsolete function: jacobi ^------ For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: jacobi(x) ===> qfjacobi(x) qfjacobi(x): eigenvalues and orthogonal matrix of eigenvectors of the Timing: real symmetric matrix x. Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '203.28.' ************** PARI ***************** Host 203.28.159.136 (203.28.159.136) Time: Tue May 17 06:06:15 2005 Input: ?qfjacobi Output: ? qfjacobi(x): eigenvalues and orthogonal matrix of eigenvectors of the real symmetric matrix x. ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '203.23.' ************** PARI ***************** Host 203.23.22.154 (203.23.22.154) Time: Tue May 17 06:06:35 2005 Input: ?qfjacobi(7) Output: ? qfjacobi(x): eigenvalues and orthogonal matrix of eigenvectors of the real symmetric matrix x. ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '203.28.' ************** PARI ***************** Host 203.28.159.138 (203.28.159.138) Time: Tue May 17 06:28:09 2005 Input: gcd(97,101) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.007s '220.240' ************** PARI ***************** Host 220.240.168.46 (220.240.168.46) Time: Tue May 17 09:12:01 2005 Input: isprime(79) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.360s user 0m0.006s sys 0m0.006s '220.240' ************** PARI ***************** Host 220.240.168.46 (220.240.168.46) Time: Tue May 17 09:12:18 2005 Input: isprime(101) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.007s '220.240' ************** PARI ***************** Host 220.240.168.46 (220.240.168.46) Time: Tue May 17 09:12:34 2005 Input: isprime(89) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.007s '203.28.' ************** PARI ***************** Host 203.28.159.138 (203.28.159.138) Time: Tue May 17 09:23:09 2005 Input: kronecker(7,79) Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.004s sys 0m0.010s '203.28.' ************** PARI ***************** Host 203.28.159.154 (203.28.159.154) Time: Tue May 17 09:23:24 2005 Input: kronecker(15,101) Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '203.28.' ************** PARI ***************** Host 203.28.159.137 (203.28.159.137) Time: Tue May 17 09:23:35 2005 Input: kronecker(11,35) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '203.23.' ************** PARI ***************** Host 203.23.22.138 (203.23.22.138) Time: Tue May 17 09:24:59 2005 Input: chrem(sd) Output: ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: chrem(sd) ^ Timing: real 0m0.022s user 0m0.005s sys 0m0.007s '203.28.' ************** PARI ***************** Host 203.28.159.152 (203.28.159.152) Time: Tue May 17 09:25:33 2005 Input: chinese([11,11],[5,7]) Output: ? ? Errors (if any) and Timing Info: *** incompatible arguments in chinois. Timing: real 0m0.021s user 0m0.002s sys 0m0.010s '203.28.' ************** PARI ***************** Host 203.28.159.151 (203.28.159.151) Time: Tue May 17 09:25:50 2005 Input: chinese([11,7],[11,5]) Output: ? ? Errors (if any) and Timing Info: *** incompatible arguments in chinois. Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '203.28.' ************** PARI ***************** Host 203.28.159.137 (203.28.159.137) Time: Tue May 17 09:27:14 2005 Input: chinese(Mod(11,7),Mod(11,5)) Output: ? Mod(11, 35) ? Errors (if any) and Timing Info: Timing: real 0m0.041s user 0m0.004s sys 0m0.009s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 19:59:46 2005 Input: print(isprime(79)); Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 20:10:15 2005 Input: print(kronecker(7,79)); Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 20:19:51 2005 Input: print(kronecker(3,101)); Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 20:19:55 2005 Input: print(kronecker(3,101)); Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 20:26:52 2005 Input: print(kronecker(3,101)); print(kronecker(2,3)); Output: ? -1 ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 21:02:20 2005 Input: print(kronecker(97,101)); print(kronecker(2,3)); Output: ? 1 ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 21:04:45 2005 Input: print(kronecker(97,101)); print(kronecker(97,69)); Output: ? 1 ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 21:24:59 2005 Input: print(kronecker(97,101)); print(kronecker(11,35)); Output: ? 1 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 21:47:41 2005 Input: print(chinese(Mod(1,3),Mod(2,5))); Output: ? Mod(7, 15) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 21:48:14 2005 Input: print(chinese(Mod(4,5),Mod(5,7))); Output: ? Mod(19, 35) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.002s sys 0m0.011s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 21:53:49 2005 Input: prime(4919) Output: ? 47713 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 21:53:58 2005 Input: prime(4919) Output: ? 47713 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 21:54:24 2005 Input: isprime(4919) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '220.240' ************** PARI ***************** Host 220.240.168.46 (220.240.168.46) Time: Tue May 17 21:56:18 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '220.240' ************** PARI ***************** Host 220.240.168.46 (220.240.168.46) Time: Tue May 17 21:56:34 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" isprime(19) Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '220.240' ************** PARI ***************** Host 220.240.168.46 (220.240.168.46) Time: Tue May 17 21:56:43 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" isprime(97) Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:12:42 2005 Input: kronecker(97,101) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:16:56 2005 Input: chinese(Mod(4,5),Mod(5,7)) Output: ? Mod(19, 35) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:17:43 2005 Input: Mod(19^2,35) Output: ? Mod(11, 35) ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.008s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:18:52 2005 Input: 19^2 Output: ? 361 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:22:23 2005 Input: Mod(19^2,5) Output: ? Mod(1, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.010s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:23:50 2005 Input: Mod(121,5) Output: ? Mod(1, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:24:05 2005 Input: Mod(121,35) Output: ? Mod(16, 35) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:27:58 2005 Input: Mod(26^2,35) Output: ? Mod(11, 35) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:43:44 2005 Input: Mod(16^2,35) Output: ? Mod(11, 35) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:43:47 2005 Input: Mod(16^2,35) Output: ? Mod(11, 35) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:45:10 2005 Input: fuck Output: ? fuck ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.007s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:45:40 2005 Input: Mod(fuck,shit) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.012s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:45:53 2005 Input: Mod(shit,cunt) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:46:00 2005 Input: Mod(shit,shit) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:46:08 2005 Input: Mod(shit,shitshit) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:46:14 2005 Input: shit^2 Output: ? shit^2 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:46:26 2005 Input: shit*fuck+cunt Output: ? fuck*shit + cunt ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:46:30 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Tue May 17 22:47:06 2005 Input: kronecker(3,11) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '192.43.' ************** PARI ***************** Host 192.43.227.18 (192.43.227.18) Time: Wed May 18 00:19:37 2005 Input: 2^4919 Output: ? 58418267242802372854733467471265335866204099588314926852143038330604907800721211985172904821571811418284417114623199021139745583594080813159493596804154672239472381342510089729663854518461790093849678283645109701573536921075157822647287521242789251423451300387986195372076682742271464498050840954399477078061296566990546633116997486918834091476005376434033391400116590178940617107327173228948390879947594751509877873348967171609434138579111404592147575016585299390476414372690768723109875288856828454539542306882362390762007020543628134041667576185583595846548083973537262090396012242842846239595238099222029147169586276395808365885221239460902630829303627768266090520435972374444555186899304890382671637779841352466055969918057614729136124681229402591832722658718021899061148285395901118187639790327265029246397173726029119204399080894946526690440335822215784249519568079695438494356253557804113643644469618171160292210608118948033449675803228610684307896959929689739127971723469814927689498709838320609875123418927548577138469284978475343255046846310742922181704401201682595551921594344373335384790984350986836531033161887093846680820268213647008425654945699026334295517452441150252106431609577386168942826465000140441618507716940096871867977455243477825124309721439042206362913093166968209741496395388809067330026049891831019759899161264371158339741446396047486958133640155195071212362903761425248019587297085008066054679101822700324931674229333863731683206676499237077451276288 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 00:54:37 2005 Input: a = Mod(11711,11903); b = Mod(1681, 11903); d = -64*a^3-27*16*b^2 Output: ? ? ? Mod(11483, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 00:58:12 2005 Input: a = Mod(11711,11903); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 00:58:22 2005 Input: a = Mod(11711,11903); a Output: ? ? Mod(11711, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 00:58:28 2005 Input: a = Mod(11711,11903); a; Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 00:58:50 2005 Input: a = Mod(11711,11903); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 00:59:02 2005 Input: Mod(11711,11903); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 00:59:05 2005 Input: Mod(11711,11903); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 00:59:08 2005 Input: Mod(11711,11903); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 00:59:11 2005 Input: Mod(11711,11903); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 00:59:14 2005 Input: Mod(11711,11903); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 00:59:15 2005 Input: Mod(11711,11903); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:03:20 2005 Input: a = Mod(11711,11903); b = Mod(1681,11903); d = -64*a^3 - 27*16*b^2; Output: ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.010s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:03:29 2005 Input: a = Mod(11711,11903); b = Mod(1681,11903); d = -64*a^3 - 27*16*b^2; Output: ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:03:42 2005 Input: a = Mod(11711,11903); b = Mod(1681,11903); d = -64*a^3 - 27*16*b^2 Output: ? ? ? Mod(11483, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:04:01 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*a^3 - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(11483, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:04:44 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*a^3 - 27*16*b^2 %d Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:04:50 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*a^3 - 27*16*b^2 d Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(11483, 11903) ? ? Mod(11483, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:05:00 2005 Input: a = Mod(11711,11903) a b = Mod(1681,11903) b d = -64*a^3 - 27*16*b^2 d Output: ? Mod(11711, 11903) ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(1681, 11903) ? Mod(11483, 11903) ? ? Mod(11483, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:05:43 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*a^3 e = - 27*16*b^2 Output: ? Mod(11711, 11903) ? ? Mod(1681, 11903) ? ? Mod(4264, 11903) ? Mod(7219, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:09:19 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*a^3 e = - 27*16*b^2 Output: ? Mod(11711, 11903) ? ? Mod(1681, 11903) ? ? Mod(4264, 11903) ? Mod(7219, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:09:27 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*a^3 e = - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4264, 11903) ? Mod(7219, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:10:36 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*a^3 e = - 27*16*b^2 f = -64*a^3 - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4264, 11903) ? Mod(7219, 11903) ? ? Mod(11483, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:10:40 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*a^3 e = - 27*16*b^2 f = -64*a^3 - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4264, 11903) ? Mod(7219, 11903) ? ? Mod(11483, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '220.240' ************** PARI ***************** Host 220.240.168.46 (220.240.168.46) Time: Wed May 18 01:21:08 2005 Input: kronecker(-15,71) Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '220.240' ************** PARI ***************** Host 220.240.168.46 (220.240.168.46) Time: Wed May 18 01:23:38 2005 Input: kronecker(-5,6)) Output: ? -1 ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '220.240' ************** PARI ***************** Host 220.240.168.46 (220.240.168.46) Time: Wed May 18 01:23:48 2005 Input: kronecker(-5,6) Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:48:12 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*-11711^3 e = - 27*16*b^2 f = -64*a^3 - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? 102792615579584 ? Mod(7219, 11903) ? ? Mod(11483, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:48:22 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*192^3 e = - 27*16*b^2 f = -64*a^3 - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? -452984832 ? Mod(7219, 11903) ? ? Mod(11483, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:48:35 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*a^3 e = - 27*16*b^2 f = -64*a^3 - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4264, 11903) ? Mod(7219, 11903) ? ? Mod(11483, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:52:47 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*1711^3 e = - 27*16*b^2 f = -64*a^3 - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? -320575259584 ? Mod(7219, 11903) ? ? Mod(11483, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:53:20 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*a^3 e = - 27*16*b^2 f = -64*a^3 - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4264, 11903) ? Mod(7219, 11903) ? ? Mod(11483, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 01:59:54 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*192^3 e = - 27*16*b^2 f = -64*a^3 - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? -452984832 ? Mod(7219, 11903) ? ? Mod(11483, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 02:00:22 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*1711^3 e = - 27*16*b^2 f = -64*a^3 - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? -320575259584 ? Mod(7219, 11903) ? ? Mod(11483, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 02:00:28 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*1^3 e = - 27*16*b^2 f = -64*a^3 - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? -64 ? Mod(7219, 11903) ? ? Mod(11483, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 02:01:16 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*-192^3 e = - 27*16*b^2 f = -64*a^3 - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? 452984832 ? Mod(7219, 11903) ? ? Mod(11483, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 02:02:22 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*a^3 e = - 27*16*b^2 f = -64*a^3 - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4264, 11903) ? Mod(7219, 11903) ? ? Mod(11483, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 02:02:35 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*4264^3 e = - 27*16*b^2 f = -64*a^3 - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? -4961712111616 ? Mod(7219, 11903) ? ? Mod(11483, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 02:06:32 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*4264^3 e = - 27*7219*b^2 f = -64*a^3 - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? -4961712111616 ? Mod(2396, 11903) ? ? Mod(11483, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 02:06:49 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*4264^3 e = - 27*7219^2 f = -64*a^3 - 27*16*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? -4961712111616 ? -1407076947 ? ? Mod(11483, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 02:07:15 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*4264^3 e = - 27*7219^2 f = e + d Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? -4961712111616 ? -1407076947 ? ? -4963119188563 ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 02:07:37 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) d = -64*4264^3 e = - 27*7219^2 f = Mod(e + d,11903) Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? -4961712111616 ? -1407076947 ? ? Mod(6306, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 03:20:59 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 03:23:45 2005 Input: e = ellinit([0,0,0,50,0,12]) e.disc Output: ? [0, 0, 0, 50, 0, 0, 100, 0, -2500, -2400, 0, -8000000, 1728, [0.E-38, 0.E-38 - 7.0710678118654752440084436210484903928*I, 0.E-38 + 7.0710678118654752440084436210484903928*I]~, 1.3944877932545392513094460578332838984, -0.69724389662726962565472302891664194922 + 0.69724389662726962565472302891664194922*I, -2.2528649363489628512388674105190381857 + 0.E-38*I, 1.1264324681744814256194337052595190928 - 3.3792974045234442768583011157785572786*I, 0.97229810276795730332277690846907309383] ? -8000000 ? Errors (if any) and Timing Info: Timing: real 0m0.081s user 0m0.009s sys 0m0.009s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 03:24:00 2005 Input: e = ellinit([0,0,0,7,0,3]) e.disc Output: ? [0, 0, 0, 7, 0, 0, 14, 0, -49, -336, 0, -21952, 1728, [0.E-38, 0.E-38 - 2.6457513110645905905016157536392604257*I, 0.E-38 + 2.6457513110645905905016157536392604257*I]~, 2.2797262925836439195308405778060532534, -1.1398631462918219597654202889030266267 + 1.1398631462918219597654202889030266267*I, -1.3780569464895651082295680104313910799 + 0.E-38*I, 0.68902847324478255411478400521569553998 - 2.0670854197343476623443520156470866199*I, 2.5985759845485830206907096824875924344] ? -21952 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 03:24:12 2005 Input: e = ellinit([0,0,0,5,0,1]) e.disc Output: ? [0, 0, 0, 5, 0, 0, 10, 0, -25, -240, 0, -8000, 1728, [0.E-38, 0.E-38 - 2.2360679774997896964091736687312762354*I, 0.E-38 + 2.2360679774997896964091736687312762354*I]~, 2.4797889302951614108285261418130523687, -1.2398944651475807054142630709065261843 + 1.2398944651475807054142630709065261843*I, -1.2668790537813472010294975779050892277 + 0.E-38*I, 0.63343952689067360051474878895254461386 - 1.9003185806720208015442463668576338416*I, 3.0746765694072104491793213839047603881] ? -8000 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 03:26:09 2005 Input: e = ellinit([0,0,0,5,0,1]) Output: ? [0, 0, 0, 5, 0, 0, 10, 0, -25, -240, 0, -8000, 1728, [0.E-38, 0.E-38 - 2.2360679774997896964091736687312762354*I, 0.E-38 + 2.2360679774997896964091736687312762354*I]~, 2.4797889302951614108285261418130523687, -1.2398944651475807054142630709065261843 + 1.2398944651475807054142630709065261843*I, -1.2668790537813472010294975779050892277 + 0.E-38*I, 0.63343952689067360051474878895254461386 - 1.9003185806720208015442463668576338416*I, 3.0746765694072104491793213839047603881] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 03:26:14 2005 Input: e = ellinit([0,0,0,5,0,1]) Output: ? [0, 0, 0, 5, 0, 0, 10, 0, -25, -240, 0, -8000, 1728, [0.E-38, 0.E-38 - 2.2360679774997896964091736687312762354*I, 0.E-38 + 2.2360679774997896964091736687312762354*I]~, 2.4797889302951614108285261418130523687, -1.2398944651475807054142630709065261843 + 1.2398944651475807054142630709065261843*I, -1.2668790537813472010294975779050892277 + 0.E-38*I, 0.63343952689067360051474878895254461386 - 1.9003185806720208015442463668576338416*I, 3.0746765694072104491793213839047603881] ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 03:26:21 2005 Input: e = ellinit([0,0,0,5,0,1]) 2.2 e.disc Output: ? [0, 0, 0, 5, 0, 0, 10, 0, -25, -240, 0, -8000, 1728, [0.E-38, 0.E-38 - 2.2360679774997896964091736687312762354*I, 0.E-38 + 2.2360679774997896964091736687312762354*I]~, 2.4797889302951614108285261418130523687, -1.2398944651475807054142630709065261843 + 1.2398944651475807054142630709065261843*I, -1.2668790537813472010294975779050892277 + 0.E-38*I, 0.63343952689067360051474878895254461386 - 1.9003185806720208015442463668576338416*I, 3.0746765694072104491793213839047603881] ? 2.1999999999999999999999999999999999999 ? -8000 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 03:26:26 2005 Input: e = ellinit([0,0,0,1,0,1]) 2.2 e.disc Output: ? [0, 0, 0, 1, 0, 0, 2, 0, -1, -48, 0, -64, 1728, [0.E-38, 0.E-38 - 1.0000000000000000000000000000000000000*I, 0.E-38 + 1.0000000000000000000000000000000000000*I]~, 3.7081493546027438368677006943905200924, -1.8540746773013719184338503471952600462 + 1.8540746773013719184338503471952600462*I, -0.84721308479397908660649912348219163647 + 0.E-39*I, 0.42360654239698954330324956174109581823 - 1.2708196271909686299097486852232874547*I, 6.8751858180203728274900957798105571978] ? 2.1999999999999999999999999999999999999 ? -64 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 03:29:02 2005 Input: e = ellinit([0,3,3,4,4]) e.disc Output: ? [0, 3, 3, 4, 4, 12, 8, 25, 59, -48, -3672, -7867, 110592/7867, [-2.4152642235612098685359293628203932034, -0.29236788821939506573203531858980339827 - 1.5818437397130083372533384678068221009*I, -0.29236788821939506573203531858980339827 + 1.5818437397130083372533384678068221009*I]~, 3.1743827205222969549510932688377384063, -1.5871913602611484774755466344188692031 + 0.99074066559284181143241718668618450726*I, -1.6369609976577484965275689488067650582 - 5.015557493762104928 E-39*I, 0.81848049882887424826378447440338252911 - 1.5005740962372073611425063113137105605*I, 3.1449900493766764346899242257718046181] ? -7867 ? Errors (if any) and Timing Info: Timing: real 0m0.038s user 0m0.007s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 03:29:59 2005 Input: e = ellinit([0,0,0,4,4]) e.disc Output: ? [0, 0, 0, 4, 4, 0, 8, 16, -16, -192, -3456, -11008, 27648/43, [-0.84770759813956654275608012525103046735, 0.42385379906978327137804006262551523367 - 2.1304826047066576861372545391184851671*I, 0.42385379906978327137804006262551523367 + 2.1304826047066576861372545391184851671*I]~, 2.7525869610791663760796733421463827732, -1.3762934805395831880398366710731913866 + 1.0680769505910142539186462566048404825*I, -1.5547095492086261399062086764272337240 + 0.E-38*I, 0.77735477460431306995310433821361686204 - 1.7445923256428446083132185846115004717*I, 2.9399746876260228606541277576721301116] ? -11008 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.009s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 03:30:21 2005 Input: e = ellinit([0,0,0,4,4]) lift(e.disc,%7) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 03:31:10 2005 Input: e = ellinit([0,0,0,4,4]) Mod(e.disc,7) Output: ? [0, 0, 0, 4, 4, 0, 8, 16, -16, -192, -3456, -11008, 27648/43, [-0.84770759813956654275608012525103046735, 0.42385379906978327137804006262551523367 - 2.1304826047066576861372545391184851671*I, 0.42385379906978327137804006262551523367 + 2.1304826047066576861372545391184851671*I]~, 2.7525869610791663760796733421463827732, -1.3762934805395831880398366710731913866 + 1.0680769505910142539186462566048404825*I, -1.5547095492086261399062086764272337240 + 0.E-38*I, 0.77735477460431306995310433821361686204 - 1.7445923256428446083132185846115004717*I, 2.9399746876260228606541277576721301116] ? Mod(3, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.004s sys 0m0.011s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 03:33:40 2005 Input: e = ellinit([0,0,0,5,5]) Mod(e.disc,7) Output: ? [0, 0, 0, 5, 5, 0, 10, 20, -25, -240, -4320, -18800, 34560/47, [-0.86883002034147494866578591160926232551, 0.43441501017073747433289295580463116275 - 2.3592687857013930810587340987551895932*I, 0.43441501017073747433289295580463116275 + 2.3592687857013930810587340987551895932*I]~, 2.6094489873190035524712047492438917789, -1.3047244936595017762356023746219458894 + 1.0295453254886101039438238687530188141*I, -1.6103968283991592263845026586392851682 + 4.417168269825323510 E-39*I, 0.80519841419957961319225132931964258410 - 1.8393037011928704934971703524819774273*I, 2.6865460069952675320351653048572363875] ? Mod(2, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 03:34:37 2005 Input: e = ellinit([0,0,0,46,5]) Mod(e.disc,13) Output: ? [0, 0, 0, 46, 5, 0, 92, 20, -2116, -2208, -4320, -6240304, 672786432/390019, [-0.10866775602418399277882645991720381159, 0.054333878012091996389413229958601905796 - 6.7829828623474715869199033116311556848*I, 0.054333878012091996389413229958601905796 + 6.7829828623474715869199033116311556848*I]~, 1.4315058179805940576822456106244955664, -0.71575290899029702884112280531224778323 + 0.70793735970265872347334810688099507743*I, -2.2260965903264132221712530944902002225 + 5.713138448031281241 E-39*I, 1.1130482951632066110856265472451001112 - 3.2955015180053691292527146689463186712*I, 1.0134164491801765211535778470574872934] ? Mod(8, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.011s sys 0m0.003s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 03:34:44 2005 Input: e = ellinit([0,0,0,46,5]); Mod(e.disc,13) Output: ? ? Mod(8, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 03:36:33 2005 Input: e1 = ellinit([0,0,0,46,5]); Mod(e1.disc,13) e2 = ellinit([0,0,0,12,17]); Mod(e2.disc,17) e3 = ellinit([0,0,0,6,3]); Mod(e3.disc,5) e4 = ellinit([0,0,0,46,5]); Mod(e4.disc,23) e5 = ellinit([0,0,0,46,5]); Mod(e5.disc,29) e6 = ellinit([0,0,0,46,5]); Mod(e6.disc,31) e7 = ellinit([0,0,0,46,5]); Mod(e7.disc,7) e8 = ellinit([0,0,0,46,5]); Mod(e8.disc,37) Output: ? ? Mod(8, 13) ? ? Mod(10, 17) ? ? Mod(3, 5) ? ? Mod(10, 23) ? ? Mod(3, 29) ? ? Mod(27, 31) ? ? Mod(0, 7) ? ? Mod(5, 37) ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.015s sys 0m0.009s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 04:45:37 2005 Input: e1 = ellinit([0,0,0,46,5]); Mod(e1.disc,13) p = 11903 alpha = 3^3 + 11711 * 3 + 1681 Mod(3^((p - 1) / 2), p) Output: ? ? Mod(8, 13) ? 11903 ? 36841 ? Mod(1, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 04:50:10 2005 Input: e1 = ellinit([0,0,0,46,5]); Mod(e1.disc,13) p = 11903 alpha = 3^3 + 11711 * 3 + 1681 Mod(alpha^((p - 1) / 2), p) Output: ? ? Mod(8, 13) ? 11903 ? 36841 ? Mod(1, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 04:50:13 2005 Input: e1 = ellinit([0,0,0,46,5]); Mod(e1.disc,13) p = 11903 alpha = 3^3 + 11711 * 3 + 1681 Mod(alpha^((p - 1) / 2), p) Output: ? ? Mod(8, 13) ? 11903 ? 36841 ? Mod(1, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.008s sys 0m0.009s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 04:50:38 2005 Input: e1 = ellinit([0,0,0,46,5]); Mod(e1.disc,13) p = 11903 (p-1)/2 alpha = 3^3 + 11711 * 3 + 1681 Mod(alpha^((p - 1) / 2), p) Output: ? ? Mod(8, 13) ? 11903 ? 5951 ? 36841 ? Mod(1, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.010s '147.173' ************** PARI ***************** Host 147.173.98.48 (147.173.98.48) Time: Wed May 18 05:11:37 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '152.81.' ************** PARI ***************** Host 152.81.8.128 (152.81.8.128) Time: Wed May 18 08:05:58 2005 Input: exp(2.0) Output: ? 7.3890560989306502272304274605750078131 ? Errors (if any) and Timing Info: Timing: real 0m0.640s user 0m0.011s sys 0m0.014s '129.199' ************** PARI ***************** Host 129.199.224.112 (129.199.224.112) Time: Wed May 18 08:44:16 2005 Input: mathhilbert(3) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: mathhilbert(3) ^-------------- Timing: real 0m0.371s user 0m0.010s sys 0m0.009s '129.199' ************** PARI ***************** Host 129.199.224.112 (129.199.224.112) Time: Wed May 18 08:44:23 2005 Input: mathilbert(3) Output: ? [1 1/2 1/3] [1/2 1/3 1/4] [1/3 1/4 1/5] ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.006s sys 0m0.007s '38.112.' ************** PARI ***************** Host 38.112.73.66 (38.112.73.66) Time: Wed May 18 08:54:04 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.006s sys 0m0.007s '132.216' ************** PARI ***************** Host 132.216.180.111 (132.216.180.111) Time: Wed May 18 16:06:21 2005 Input: {pollard2(a,n,q)= local(d,e); d = gcd(a,n); if(d!=1, return(d)); e = gcd((Mod(a,n)^q)-1,n); return(e);} pollard2(2,3,6) Output: ? ? ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.006s sys 0m0.008s '132.216' ************** PARI ***************** Host 132.216.180.111 (132.216.180.111) Time: Wed May 18 16:06:37 2005 Input: {pollard2(a,n,q)= local(d,e); d = gcd(a,n); if(d!=1, return(d)); e = gcd((Mod(a,n)^q)-1,n); return(e);} Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '132.216' ************** PARI ***************** Host 132.216.180.111 (132.216.180.111) Time: Wed May 18 16:07:08 2005 Input: {pollard2(a,n,q)= local(d,e); d = gcd(a,n); if(d!=1, return(d)); e = gcd((Mod(a,n)^q)-1,n); return(e);} pollard2(1242154236,1536236427,1653523626) Output: ? ? ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '132.216' ************** PARI ***************** Host 132.216.180.111 (132.216.180.111) Time: Wed May 18 16:07:11 2005 Input: {pollard2(a,n,q)= local(d,e); d = gcd(a,n); if(d!=1, return(d)); e = gcd((Mod(a,n)^q)-1,n); return(e);} pollard2(1242154236,1536236427,1653523626) Output: ? ? ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '132.216' ************** PARI ***************** Host 132.216.180.111 (132.216.180.111) Time: Wed May 18 16:07:12 2005 Input: {pollard2(a,n,q)= local(d,e); d = gcd(a,n); if(d!=1, return(d)); e = gcd((Mod(a,n)^q)-1,n); return(e);} pollard2(1242154236,1536236427,1653523626) Output: ? ? ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '132.216' ************** PARI ***************** Host 132.216.180.111 (132.216.180.111) Time: Wed May 18 16:07:13 2005 Input: {pollard2(a,n,q)= local(d,e); d = gcd(a,n); if(d!=1, return(d)); e = gcd((Mod(a,n)^q)-1,n); return(e);} pollard2(1242154236,1536236427,1653523626) Output: ? ? ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.005s '132.216' ************** PARI ***************** Host 132.216.180.111 (132.216.180.111) Time: Wed May 18 16:07:28 2005 Input: {pollard2(a,n,q)= local(d,e); d = gcd(a,n); if(d!=1, return(d)); e = gcd((Mod(a,n)^q)-1,n); return(e);} pollard2(1242154236,1536236427,1653523626) Output: ? ? ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:34:17 2005 Input: a = Mod(11711,11903); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:34:24 2005 Input: a = Mod(11711,11903) Output: ? Mod(11711, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:34:42 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:35:09 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) a^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? ? Mod(4397, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:35:41 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) -64*a^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? ? Mod(4264, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:43:51 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) -64*4397^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? ? -5440632241472 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:44:01 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) -64*11711^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? ? -102792615579584 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:44:10 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) -64*(11711^3) Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? ? -102792615579584 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:44:37 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) -64*4264^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? ? -4961712111616 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:44:56 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) -64*a^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? ? Mod(4264, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:45:37 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) a; -64*a^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? ? Mod(4264, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:45:43 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) a -64*a^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(11711, 11903) ? Mod(4264, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:56:27 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) a^3 -64*a^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4397, 11903) ? ? Mod(4264, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:56:29 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) a^3 - a -64*a^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4589, 11903) ? Mod(4264, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:56:59 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) a^3 -64*a^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4397, 11903) ? ? Mod(4264, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:57:17 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) a^3 - a -64*a^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4589, 11903) ? Mod(4264, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:58:28 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) a^3 -64*a^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4397, 11903) ? Mod(4264, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 18 21:58:32 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) 2a - a -64*a^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? 2 ? Mod(4264, 11903) ? Errors (if any) and Timing Info: *** Warning: unused characters: a-a. Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu May 19 02:26:24 2005 Input: a = Mod(11711,11903) a^3 Output: ? Mod(11711, 11903) ? Mod(4397, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.004s sys 0m0.009s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu May 19 02:29:26 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) a^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4397, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu May 19 02:29:40 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) -64*a^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4264, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu May 19 02:31:13 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) a^3 -64*a^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4397, 11903) ? Mod(4264, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.007s sys 0m0.004s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu May 19 02:31:44 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) a^3 (-64*4397)%11903 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu May 19 02:32:06 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) a^3 -64*a^3 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4397, 11903) ? Mod(4264, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu May 19 02:35:40 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) a^3 -64*a^3-27*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4397, 11903) ? Mod(6947, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu May 19 02:35:54 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) a^3 -64*a^3+27*b^2 Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4397, 11903) ? Mod(1581, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu May 19 02:37:20 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) -16*(4*a^3+27*b^2) Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(11483, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.005s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu May 19 02:37:44 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) 4*a^3 27*b^2 -16*(4*a^3+27*b^2) Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(5685, 11903) ? Mod(9220, 11903) ? Mod(11483, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu May 19 02:39:06 2005 Input: a = Mod(11711,11903) b = Mod(1681,11903) a^3 4*a^3 27*b^2 -16*(4*a^3+27*b^2) Output: ? Mod(11711, 11903) ? Mod(1681, 11903) ? Mod(4397, 11903) ? Mod(5685, 11903) ? Mod(9220, 11903) ? Mod(11483, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '130.123' ************** PARI ***************** Host 130.123.128.117 (130.123.128.117) Time: Thu May 19 18:42:10 2005 Input: FindGroupOrder2 := function (p, s) K := GF(p); v := K ! (4*s); u := K ! (s^2-5); x := u^3; b := 4*x*v; a := (v-u)^3*(3*u+v); A := a/b-2; x := x/v^3; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); return FactoredOrder(E); end function; p:=8609003047812738970231959229; s:=948982508630324; FindGroupOrder2(p,s); Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: FindGroupOrder2:=function(p,s) ^-------------- *** unexpected character: K:=GF(p); ^------- *** unexpected character: v:=K!(4*s); ^--------- *** unexpected character: u:=K!(s^2-5); ^----------- *** unexpected character: x:=u^3; ^----- *** unexpected character: b:=4*x*v; ^------- *** unexpected character: a:=(v-u)^3*(3*u+v); ^----------------- *** unexpected character: A:=a/b-2; ^------- *** unexpected character: x:=x/v^3; ^------- *** unexpected character: b:=x^3+A*x^2+x; ^------------- *** unexpected character: E:=EllipticCurve([0,b* ^-------------------- *** expected character: '=' instead of: returnFactoredOrder(E); ^- *** unexpected character: p:=8609003047812738970 ^-------------------- *** unexpected character: s:=948982508630324; ^----------------- *** expected character: '=' instead of: FindGroupOrder2(p,s); ^- Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '12.30.1' ************** PARI ***************** Host 12.30.121.5 (12.30.121.5) Time: Thu May 19 19:51:37 2005 Input: 2^2^2^2^2 Output: ? 2003529930406846464979072351560255750447825475569751419265016973710894059556311453089506130880933348101038234342907263181822949382118812668869506364761547029165041871916351587966347219442930927982084309104855990570159318959639524863372367203002916969592156108764948889254090805911457037675208500206671563702366126359747144807111774815880914135742720967190151836282560618091458852699826141425030123391108273603843767876449043205960379124490905707560314035076162562476031863793126484703743782954975613770981604614413308692118102485959152380195331030292162800160568670105651646750568038741529463842244845292537361442533614373729088303794601274724958414864915930647252015155693922628180691650796381064132275307267143998158508811292628901134237782705567421080070065283963322155077831214288551675554073345107213112427399562982719769150054883905223804357045848197956393157853510018992000024141963706813559840464039472194016069517690156119726982337890017641517190051133466306898140219383481435426387306539552969691388024158161859561100640362119796101859534802787167200122604642492385111393400464351623867567078745259464670903886547743483217897012764455529409092021959585751622973333576159552394885297579954028471943529913543763705986928913757153740001986394332464890052543106629669165243419174691389632476560289415199775477703138064781342309596190960654591300890188887588084733625956065444888501447335706058817090162108499714529568344061979690565469813631162053579369791403236328496233046421066136200220175787851857409162050489711781820400187282939943446186224328009837323764931814789848119452713007440220765680910376203999203492023906626264491909167985461515778839060397720759279378852241294301017458086862263369284725851403039615558564330385450688652213114813638408384778263790459607186876728509763471271988890680478243230394718650525660978150729861141430305816927924971409161059417185352275887504477592218301158780701975535722241400019548102005661773589781499532325208589753463547007786690406429016763808161740550405117670093673202804549339027992491867306539931640720492238474815280619166900933805732120816350707634351669869625020969023162859350071874190579161241536897514808261904847946571736601005892476655445840838334790544144817684255327207315586349347605137419779525190365032198020108764738368682531025183377533908861426184800374008082238104076468878471647552945326947661700424461063311238021134588694532200116564076327023074292426051582811070387018345324567635625951430032037432740780879056283663406965030844225855967039271869461158513793386475699748568670079823960604393478850861649260304945061743412365828352144806726676841807083754862211408236579802961200027441324438432402331257403545019352428776430880232850855886089962774458164680857875115807014743763867976955049991643998284357290415378143438847303484261903388841494031366139854257635577105335580206622185577060082551288893332226436281984838613239570676191409638533832374343758830859233722284644287996245605476932428998432652677378373173288063210753211238680604674708428051166488709084770291208161104912555598322366244868556651402684641209694982590565519216188104341226838996283071654868525536914850299539675503954938371853405900096[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.198s user 0m0.090s sys 0m0.012s '12.30.1' ************** PARI ***************** Host 12.30.121.5 (12.30.121.5) Time: Thu May 19 19:51:51 2005 Input: 2^2^2^2 Output: ? 65536 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '12.30.1' ************** PARI ***************** Host 12.30.121.5 (12.30.121.5) Time: Thu May 19 19:51:54 2005 Input: 2^2^2^2^2 Output: ? 2003529930406846464979072351560255750447825475569751419265016973710894059556311453089506130880933348101038234342907263181822949382118812668869506364761547029165041871916351587966347219442930927982084309104855990570159318959639524863372367203002916969592156108764948889254090805911457037675208500206671563702366126359747144807111774815880914135742720967190151836282560618091458852699826141425030123391108273603843767876449043205960379124490905707560314035076162562476031863793126484703743782954975613770981604614413308692118102485959152380195331030292162800160568670105651646750568038741529463842244845292537361442533614373729088303794601274724958414864915930647252015155693922628180691650796381064132275307267143998158508811292628901134237782705567421080070065283963322155077831214288551675554073345107213112427399562982719769150054883905223804357045848197956393157853510018992000024141963706813559840464039472194016069517690156119726982337890017641517190051133466306898140219383481435426387306539552969691388024158161859561100640362119796101859534802787167200122604642492385111393400464351623867567078745259464670903886547743483217897012764455529409092021959585751622973333576159552394885297579954028471943529913543763705986928913757153740001986394332464890052543106629669165243419174691389632476560289415199775477703138064781342309596190960654591300890188887588084733625956065444888501447335706058817090162108499714529568344061979690565469813631162053579369791403236328496233046421066136200220175787851857409162050489711781820400187282939943446186224328009837323764931814789848119452713007440220765680910376203999203492023906626264491909167985461515778839060397720759279378852241294301017458086862263369284725851403039615558564330385450688652213114813638408384778263790459607186876728509763471271988890680478243230394718650525660978150729861141430305816927924971409161059417185352275887504477592218301158780701975535722241400019548102005661773589781499532325208589753463547007786690406429016763808161740550405117670093673202804549339027992491867306539931640720492238474815280619166900933805732120816350707634351669869625020969023162859350071874190579161241536897514808261904847946571736601005892476655445840838334790544144817684255327207315586349347605137419779525190365032198020108764738368682531025183377533908861426184800374008082238104076468878471647552945326947661700424461063311238021134588694532200116564076327023074292426051582811070387018345324567635625951430032037432740780879056283663406965030844225855967039271869461158513793386475699748568670079823960604393478850861649260304945061743412365828352144806726676841807083754862211408236579802961200027441324438432402331257403545019352428776430880232850855886089962774458164680857875115807014743763867976955049991643998284357290415378143438847303484261903388841494031366139854257635577105335580206622185577060082551288893332226436281984838613239570676191409638533832374343758830859233722284644287996245605476932428998432652677378373173288063210753211238680604674708428051166488709084770291208161104912555598322366244868556651402684641209694982590565519216188104341226838996283071654868525536914850299539675503954938371853405900096[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.101s user 0m0.090s sys 0m0.011s '12.30.1' ************** PARI ***************** Host 12.30.121.5 (12.30.121.5) Time: Thu May 19 19:51:57 2005 Input: 2^^2 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 2^^2 ^-- Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '217.185' ************** PARI ***************** Host 217.185.234.94 (217.185.234.94) Time: Thu May 19 23:36:15 2005 Input: 2^100 Output: ? 1267650600228229401496703205376 ? Errors (if any) and Timing Info: Timing: real 0m0.321s user 0m0.003s sys 0m0.010s '217.231' ************** PARI ***************** Host 217.231.84.134 (217.231.84.134) Time: Fri May 20 02:00:09 2005 Input: 5*0.437847823647862384623849275829048092384902348290384239084902384 Output: ? 2.1892391182393119231192463791452404619 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.009s sys 0m0.003s '81.152.' ************** PARI ***************** Host 81.152.192.136 (81.152.192.136) Time: Fri May 20 02:47:08 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '81.152.' ************** PARI ***************** Host 81.152.192.136 (81.152.192.136) Time: Fri May 20 02:47:19 2005 Input: 2*2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '81.152.' ************** PARI ***************** Host 81.152.192.136 (81.152.192.136) Time: Fri May 20 02:47:43 2005 Input: 2*2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '84.139.' ************** PARI ***************** Host 84.139.59.28 (84.139.59.28) Time: Fri May 20 09:44:42 2005 Input: x+3=10 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: x+3=10 ^--- Timing: real 0m0.247s user 0m0.006s sys 0m0.008s '84.139.' ************** PARI ***************** Host 84.139.59.28 (84.139.59.28) Time: Fri May 20 09:44:54 2005 Input: 6+3 Output: ? 9 ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.006s sys 0m0.006s '84.139.' ************** PARI ***************** Host 84.139.59.28 (84.139.59.28) Time: Fri May 20 09:45:39 2005 Input: 9^0,5 Output: ? 1 ? Errors (if any) and Timing Info: *** Warning: unused characters: ,5. Timing: real 0m0.019s user 0m0.005s sys 0m0.008s '84.139.' ************** PARI ***************** Host 84.139.59.28 (84.139.59.28) Time: Fri May 20 09:45:45 2005 Input: 9^0.5 Output: ? 2.9999999999999999999999999999999999999 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.003s sys 0m0.009s '84.139.' ************** PARI ***************** Host 84.139.59.28 (84.139.59.28) Time: Fri May 20 09:46:13 2005 Input: 9^0.6 Output: ? 3.7371928188465519779000410099209152427 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '84.139.' ************** PARI ***************** Host 84.139.59.28 (84.139.59.28) Time: Fri May 20 09:46:21 2005 Input: 9^0.50000001 Output: ? 3.0000000659167380442559632751397706317 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '84.139.' ************** PARI ***************** Host 84.139.59.28 (84.139.59.28) Time: Fri May 20 09:46:28 2005 Input: 9^0.5000000000000000000000001 Output: ? 3.0000000000000000000000006591673732008 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '84.139.' ************** PARI ***************** Host 84.139.59.28 (84.139.59.28) Time: Fri May 20 09:46:35 2005 Input: 9^0.500000000000000000000000000000000000001 Output: ? 3.0000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '84.139.' ************** PARI ***************** Host 84.139.59.28 (84.139.59.28) Time: Fri May 20 09:46:49 2005 Input: 9^0.5000000000000000000000000000000000001 Output: ? 3.0000000000000000000000000000000000006 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '84.139.' ************** PARI ***************** Host 84.139.59.28 (84.139.59.28) Time: Fri May 20 09:46:53 2005 Input: 9^0.50000000000000000000000000000000000001 Output: ? 3.0000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '84.139.' ************** PARI ***************** Host 84.139.59.28 (84.139.59.28) Time: Fri May 20 09:47:12 2005 Input: 9^7 Output: ? 4782969 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '84.139.' ************** PARI ***************** Host 84.139.59.28 (84.139.59.28) Time: Fri May 20 09:47:28 2005 Input: sin60 Output: ? sin60 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '84.139.' ************** PARI ***************** Host 84.139.59.28 (84.139.59.28) Time: Fri May 20 09:47:39 2005 Input: duhastdoofeohren Output: ? duhastdoofeohren ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '62.77.2' ************** PARI ***************** Host 62.77.247.89 (62.77.247.89) Time: Fri May 20 14:08:36 2005 Input: x^3-2x=4 Output: ? x^3 - 2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x=4. Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '140.247' ************** PARI ***************** Host 140.247.29.104 (140.247.29.104) Time: Sat May 21 15:17:58 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.144s user 0m0.009s sys 0m0.008s '80.224.' ************** PARI ***************** Host 80.224.227.254 (80.224.227.254) Time: Sun May 22 11:37:10 2005 Input: P:=PolynomialRing(GF(2)); G16:=ext; f:=x^4+x+1; C:=BCHCode(G16,15,7); C; g:=GeneratorPolynomial(C); g; m11:=MinimalPolynomial(alpha); m33:=MinimalPolynomial(alpha^3); m55:=MinimalPolynomial(alpha^5); g2:=m11*m33*m55; g2; Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: P:=PolynomialRing(GF( ^-------------------- *** unexpected character: G16:=ext ^-------------------- *** unexpected character: f:=x^4+x+1; ^--------- *** unexpected character: C:=BCHCode(G16,15,7); ^------------------- *** unexpected character: g:=GeneratorPolynomia ^-------------------- *** unexpected character: m11:=MinimalPolynomial(a ^-------------------- *** unexpected character: m33:=MinimalPolynomial(a ^-------------------- *** unexpected character: m55:=MinimalPolynomial(a ^-------------------- *** unexpected character: g2:=m11*m33*m55; ^------------- Timing: real 0m0.038s user 0m0.010s sys 0m0.008s '80.58.5' ************** PARI ***************** Host 80.58.50.107 (80.58.50.107) Time: Sun May 22 11:46:20 2005 Input: P:=PolynomialRing(GF(3)); g:=P![2,2,0,2,1,0,0,0]; g; C1:=CyclicCode(8,g); G:=GeneratorMatrix(C1); IC:=InformationSpace(C1); W:=IC![2,0,2,1]; paraula:=W*G; paraula; grau:=Degree(g); pol_g:= x^grau; w:=P![2,0,2,1]; pol_w:=pol_g*w; residu:=pol_w mod g; pol_paraula:=pol_w-residu; paraula2:=Coefficients(pol_paraula); paraula2; pol_h:=CheckPolynomial(C1); pol_h; g*pol_h mod (x^8 - 1); Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: P:=PolynomialRing(GF( ^-------------------- *** unexpected character: g:=P![2,2,0,2,1,0,0,0] ^-------------------- *** unexpected character: C1:=CyclicCode(8,g); ^----------------- *** unexpected character: G:=GeneratorMatrix(C1) ^-------------------- *** unexpected character: IC:=InformationSpace(C1 ^-------------------- *** unexpected character: W:=IC![2,0,2,1]; ^-------------- *** unexpected character: paraula:=W*G; ^----- *** unexpected character: grau:=Degree(g); ^----------- *** unexpected character: pol_g:=x^grau; ^-------- *** unexpected character: w:=P![2,0,2,1]; ^------------- *** unexpected character: pol_w:=pol_g*w; ^--------- *** unexpected character: residu:=pol_wmodg; ^----------- *** unexpected character: pol_paraula:=pol_w-residu; ^-------------- *** unexpected character: paraula2:=Coefficients(pol_pa ^-------------------- *** unexpected character: pol_h:=CheckPolynomial(C1) ^-------------------- *** expected character: ',' instead of: g*pol_hmod(x^8-1); ^------ Timing: real 0m0.019s user 0m0.008s sys 0m0.011s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Mon May 23 00:17:18 2005 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.074s user 0m0.009s sys 0m0.010s '158.109' ************** PARI ***************** Host 158.109.66.87 (158.109.66.87) Time: Mon May 23 05:22:07 2005 Input: M := KMatrixSpace(FiniteField(3), 4, 8); G := M ! [2,2,0,2,1,0,0,0 ,0,2,2,0,2,1,0,0 ,0,0,2,2,0,2,1,0 ,0,0,0,2,2,0,2,1]; C1 := LinearCode(G); P3:=PolynomialRing(FiniteField(3)); GF3:=FiniteField(3); G2:=P3![2,2,0,2,1,0,0,0]; C2:=CyclicCode(8,G2); C2; C2 eq C1; Output: ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: M:=KMatrixSpace(Finite ^-------------------- *** unexpected character: G:=M![2,2,0,2,1,0,0,0, ^-------------------- *** unexpected character: C1:=LinearCode(G); ^--------------- *** unexpected character: P3:=PolynomialRing(Fin ^-------------------- *** unexpected character: GF3:=FiniteField(3); ^---------------- *** unexpected character: G2:=P3![2,2,0,2,1,0,0,0 ^-------------------- *** unexpected character: C2:=CyclicCode(8,G2); ^------------------ Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '158.109' ************** PARI ***************** Host 158.109.66.23 (158.109.66.23) Time: Mon May 23 07:12:49 2005 Input: P:=PolynomialRing(GF(3)); g:=2+2*x+2*x^3+x^4; G:=KMatrixSpace(GF(3),4,8)! [2,2,0,2,1,0,0,0, 0,2,2,0,2,1,0,0, 0,0,2,2,0,2,1,0, 0,0,0,2,2,0,2,1]; C1a:=LinearCode(G); C1b:=CyclicCode(8,g); [x:x in C1a] eq [x:x in C1b]; ux:=x^7+2*x^6+2*x^4; q,r:=Quotrem(ux,g); v:=Coefficients(r+ux); v; u:=VectorSpace(GF(3),4)![2,0,2,1]; u*GeneratorMatrix(C1a); h:=(x^8-1)/g; h; K:=GF(2^4); P:=PolynomialRing(K); C2:=ReedSolomonCode(K,5); Length(C2); Dimension(C2); MinimumDistance(C2); IsMaximumDistanceSeparable(C2); GeneratorPolynomial(C2); g:=&*[(x-alpha^i): i in [1..4]]; g; i:=P![1,0,0,alpha^7,0,0,alpha,0,alpha^7,0,1]; i:=i*x^4; q,r:=Quotrem(i,g); v:=Coefficients(r+i); v; Syndrome(C2,v); Output: ? ? ? ? ? 0 ? 0 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: P:=PolynomialRing(GF( ^-------------------- *** unexpected character: g:=2+2*x+2*x^3+x^4; ^----------------- *** unexpected character: G:=KMatrixSpace(GF(3), ^-------------------- *** unexpected character: [2,2,0,2,1,0,0,0, ^ *** Warning: unused characters: ,2,2,0,2,1,0,0,. *** Warning: unused characters: ,0,2,2,0,2,1,0,. *** Warning: unused characters: ,0,0,2,2,0,2,1];. *** unexpected character: C1a:=LinearCode(G); ^--------------- *** unexpected character: C1b:=CyclicCode(8,g); ^----------------- *** ; or ] expected: [x:xinC1a]eq[x:xinC1b] ^-------------------- *** unexpected character: ux:=x^7+2*x^6+2*x^4; ^----------------- *** Warning: unused characters: ,r:=Quotrem(ux,g);. *** unexpected character: v:=Coefficients(r+ux); ^-------------------- *** unexpected character: u:=VectorSpace(GF(3),4 ^-------------------- *** expected character: '=' instead of: u*GeneratorMatrix(C1a); ^- *** unexpected character: h:=(x^8-1)/g; ^----------- *** unexpected character: K:=GF(2^4); ^---------- *** unexpected character: P:=PolynomialRing(K); ^-------------------- *** unexpected character: C2:=ReedSolomonCode(K,5 ^-------------------- *** expected character: '=' instead of: Length(C2); ^- *** expected character: '=' instead of: Dimension(C2); ^- *** expected character: '=' instead of: MinimumDistance(C2); ^- *** expected character: '=' instead of: ...imumDistanceSeparable(C2); ^- *** expected character: '=' instead of: GeneratorPolynomial(C2); ^- *** unexpected character: g:=&*[(x-alpha^i):iin[ ^-------------------- *** unexpected character: i:=P![1,0,0,alpha^7,0, ^-------------------- *** unexpected character: i:=i*x^4; ^------- *** Warning: unused characters: ,r:=Quotrem(i,g);. *** unexpected character: v:=Coefficients(r+i); ^------------------- *** expected character: '=' instead of: Syndrome(C2,v); ^- Timing: real 0m3.842s user 0m0.009s sys 0m0.018s '158.109' ************** PARI ***************** Host 158.109.66.23 (158.109.66.23) Time: Mon May 23 07:14:24 2005 Input: P:=PolynomialRing(GF(3)); g:=2+2*x+2*x^3+x^4; G:=KMatrixSpace(GF(3),4,8)! [2,2,0,2,1,0,0,0, 0,2,2,0,2,1,0,0, 0,0,2,2,0,2,1,0, 0,0,0,2,2,0,2,1]; C1a:=LinearCode(G); C1b:=CyclicCode(8,g); [x:x in C1a] eq [x:x in C1b]; ux:=x^7+2*x^6+2*x^4; q,r:=Quotrem(ux,g); v:=Coefficients(r+ux); v; u:=VectorSpace(GF(3),4)![2,0,2,1]; u*GeneratorMatrix(C1a); h:=(x^8-1)/g; h; K:=GF(2^4); P:=PolynomialRing(K); C2:=ReedSolomonCode(K,5); Length(C2); Dimension(C2); MinimumDistance(C2); IsMaximumDistanceSeparable(C2); GeneratorPolynomial(C2); g:=&*[(x-alpha^i): i in [1..4]]; g; i:=P![1,0,0,alpha^7,0,0,alpha,0,alpha^7,0,1]; i:=i*x^4; q,r:=Quotrem(i,g); v:=Coefficients(r+i); v; Syndrome(C2,v); Output: ? ? ? ? ? 0 ? 0 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: P:=PolynomialRing(GF( ^-------------------- *** unexpected character: g:=2+2*x+2*x^3+x^4; ^----------------- *** unexpected character: G:=KMatrixSpace(GF(3), ^-------------------- *** unexpected character: [2,2,0,2,1,0,0,0, ^ *** Warning: unused characters: ,2,2,0,2,1,0,0,. *** Warning: unused characters: ,0,2,2,0,2,1,0,. *** Warning: unused characters: ,0,0,2,2,0,2,1];. *** unexpected character: C1a:=LinearCode(G); ^--------------- *** unexpected character: C1b:=CyclicCode(8,g); ^----------------- *** ; or ] expected: [x:xinC1a]eq[x:xinC1b] ^-------------------- *** unexpected character: ux:=x^7+2*x^6+2*x^4; ^----------------- *** Warning: unused characters: ,r:=Quotrem(ux,g);. *** unexpected character: v:=Coefficients(r+ux); ^-------------------- *** unexpected character: u:=VectorSpace(GF(3),4 ^-------------------- *** expected character: '=' instead of: u*GeneratorMatrix(C1a); ^- *** unexpected character: h:=(x^8-1)/g; ^----------- *** unexpected character: K:=GF(2^4); ^---------- *** unexpected character: P:=PolynomialRing(K); ^-------------------- *** unexpected character: C2:=ReedSolomonCode(K,5 ^-------------------- *** expected character: '=' instead of: Length(C2); ^- *** expected character: '=' instead of: Dimension(C2); ^- *** expected character: '=' instead of: MinimumDistance(C2); ^- *** expected character: '=' instead of: ...imumDistanceSeparable(C2); ^- *** expected character: '=' instead of: GeneratorPolynomial(C2); ^- *** unexpected character: g:=&*[(x-alpha^i):iin[ ^-------------------- *** unexpected character: i:=P![1,0,0,alpha^7,0, ^-------------------- *** unexpected character: i:=i*x^4; ^------- *** Warning: unused characters: ,r:=Quotrem(i,g);. *** unexpected character: v:=Coefficients(r+i); ^------------------- *** expected character: '=' instead of: Syndrome(C2,v); ^- Timing: real 0m0.998s user 0m0.012s sys 0m0.012s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Mon May 23 12:32:58 2005 Input: factor(948) Output: ? [2 2] [3 1] [79 1] ? Errors (if any) and Timing Info: Timing: real 0m0.256s user 0m0.007s sys 0m0.015s '158.109' ************** PARI ***************** Host 158.109.40.8 (158.109.40.8) Time: Mon May 23 13:19:03 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.005s sys 0m0.013s '140.247' ************** PARI ***************** Host 140.247.28.226 (140.247.28.226) Time: Mon May 23 17:15:25 2005 Input: factor(90832094802384) Output: ? [2 4] [3 1] [13 1] [145564254491 1] ? Errors (if any) and Timing Info: Timing: real 0m0.143s user 0m0.012s sys 0m0.007s '137.153' ************** PARI ***************** Host 137.153.0.25 (137.153.0.25) Time: Tue May 24 00:34:16 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.322s user 0m0.008s sys 0m0.017s '137.153' ************** PARI ***************** Host 137.153.0.34 (137.153.0.34) Time: Tue May 24 00:34:26 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.008s '137.153' ************** PARI ***************** Host 137.153.0.36 (137.153.0.36) Time: Tue May 24 00:34:34 2005 Input: 27*37 Output: ? 999 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '137.153' ************** PARI ***************** Host 137.153.0.37 (137.153.0.37) Time: Tue May 24 00:34:50 2005 Input: (x+1)^4 Output: ? x^4 + 4*x^3 + 6*x^2 + 4*x + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.011s sys 0m0.006s '131.170' ************** PARI ***************** Host 131.170.90.4 (131.170.90.4) Time: Tue May 24 01:08:21 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.011s sys 0m0.007s '212.242' ************** PARI ***************** Host 212.242.216.237 (212.242.216.237) Time: Tue May 24 05:07:39 2005 Input: f(x)=a_5*x^5 + a_4*x^4 + a_3*x^3 + a_2*x^2 + a_1*x + a_0 Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '212.242' ************** PARI ***************** Host 212.242.216.237 (212.242.216.237) Time: Tue May 24 05:07:48 2005 Input: f(x)=a_5*x^5 + a_4*x^4 + a_3*x^3 + a_2*x^2 + a_1*x + a_0; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '212.242' ************** PARI ***************** Host 212.242.216.237 (212.242.216.237) Time: Tue May 24 05:08:00 2005 Input: 465*4646 Output: ? 2160390 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue May 24 06:09:38 2005 Input: numdiv(1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.050s user 0m0.011s sys 0m0.007s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue May 24 06:09:49 2005 Input: numdiv(2) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.011s sys 0m0.006s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue May 24 06:09:59 2005 Input: numdiv(4) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue May 24 06:10:30 2005 Input: n=2 numdiv(n^2)/numdiv(n) Output: ? 2 ? 3/2 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue May 24 06:10:57 2005 Input: n=1 numdiv(n^2)/numdiv(n) Output: ? 1 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue May 24 06:13:00 2005 Input: for(n=1,10,numdiv(n^2)/numdiv(n)) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.011s sys 0m0.007s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue May 24 06:13:54 2005 Input: for(n=1,10,? numdiv(n^2)/numdiv(n)) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: for(n=1,10,?numdiv(n^2)/numdiv( ^-------------------- Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '84.109.' ************** PARI ***************** Host 84.109.104.157 (84.109.104.157) Time: Tue May 24 11:41:13 2005 Input: sin(5) Output: ? -0.95892427466313846889315440615599397334 ? Errors (if any) and Timing Info: Timing: real 0m0.288s user 0m0.006s sys 0m0.015s '84.109.' ************** PARI ***************** Host 84.109.104.157 (84.109.104.157) Time: Tue May 24 11:41:27 2005 Input: taylor(sin(x)( Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: taylor(sin(x)( ^- Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '84.109.' ************** PARI ***************** Host 84.109.104.157 (84.109.104.157) Time: Tue May 24 11:41:32 2005 Input: taylor(sin(x)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: taylor(sin(x)) ^- Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '84.109.' ************** PARI ***************** Host 84.109.104.157 (84.109.104.157) Time: Tue May 24 11:41:36 2005 Input: taylor(sin(x),0) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: taylor(sin(x),0) ^-- Timing: real 0m0.044s user 0m0.007s sys 0m0.011s '84.109.' ************** PARI ***************** Host 84.109.104.157 (84.109.104.157) Time: Tue May 24 11:41:44 2005 Input: taylor(sin(x),x,0,0) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: taylor(sin(x),x,0,0) ^----- Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '84.109.' ************** PARI ***************** Host 84.109.104.157 (84.109.104.157) Time: Tue May 24 11:41:49 2005 Input: taylor(sin(x),x,0) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: taylor(sin(x),x,0) ^--- Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '84.109.' ************** PARI ***************** Host 84.109.104.157 (84.109.104.157) Time: Tue May 24 11:41:53 2005 Input: taylor(sin(x),x) Output: ? x - 1/6*x^3 + 1/120*x^5 - 1/5040*x^7 + 1/362880*x^9 - 1/39916800*x^11 + 1/6227020800*x^13 - 1/1307674368000*x^15 + O(x^16) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '203.144' ************** PARI ***************** Host 203.144.160.242 (203.144.160.242) Time: Tue May 24 11:49:23 2005 Input: n=2^16*3^10*5^8 numdiv(n^2)/numdiv(n) Output: ? 1511654400000000 ? 7 ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.009s sys 0m0.011s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Tue May 24 20:50:49 2005 Input: e = ellinit([0,0,0,a4,a6]) e.disc p = [0, 0] ellisoncurve(e, p) ellapdd(e, p, p) Output: ? [0, 0, 0, a4, a6, 0, 2*a4, 4*a6, -a4^2, -48*a4, -864*a6, -64*a4^3 - 432*a6^2, -6912*a4^3/(-4*a4^3 - 27*a6^2), 0, 0, 0, 0, 0, 0] ? -64*a4^3 - 432*a6^2 ? [0, 0] ? 0 ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: ellapdd(e,p,p) ^ Timing: real 0m0.318s user 0m0.011s sys 0m0.011s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Tue May 24 20:51:27 2005 Input: e = ellinit([0,0,0,a4,a6]) e.disc p = [0, 0] ellisoncurve(e, p) Output: ? [0, 0, 0, a4, a6, 0, 2*a4, 4*a6, -a4^2, -48*a4, -864*a6, -64*a4^3 - 432*a6^2, -6912*a4^3/(-4*a4^3 - 27*a6^2), 0, 0, 0, 0, 0, 0] ? -64*a4^3 - 432*a6^2 ? [0, 0] ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Tue May 24 20:51:43 2005 Input: e = ellinit([0,0,0,a4,a6]) e.disc p = [0, 0] ellisoncurve(e, p) elladd(e, p, p) Output: ? [0, 0, 0, a4, a6, 0, 2*a4, 4*a6, -a4^2, -48*a4, -864*a6, -64*a4^3 - 432*a6^2, -6912*a4^3/(-4*a4^3 - 27*a6^2), 0, 0, 0, 0, 0, 0] ? -64*a4^3 - 432*a6^2 ? [0, 0] ? 0 ? [0] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.011s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Tue May 24 20:52:02 2005 Input: e = ellinit([0,0,0,a4,a6]) e.disc p = [0, 0] ellisoncurve(e, p) elladd(e, p, p) Output: ? [0, 0, 0, a4, a6, 0, 2*a4, 4*a6, -a4^2, -48*a4, -864*a6, -64*a4^3 - 432*a6^2, -6912*a4^3/(-4*a4^3 - 27*a6^2), 0, 0, 0, 0, 0, 0] ? -64*a4^3 - 432*a6^2 ? [0, 0] ? 0 ? [0] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Tue May 24 20:52:09 2005 Input: e = ellinit([0,0,0,a4,a6]) e.disc p = [3, 2330] ellisoncurve(e, p) elladd(e, p, p) Output: ? [0, 0, 0, a4, a6, 0, 2*a4, 4*a6, -a4^2, -48*a4, -864*a6, -64*a4^3 - 432*a6^2, -6912*a4^3/(-4*a4^3 - 27*a6^2), 0, 0, 0, 0, 0, 0] ? -64*a4^3 - 432*a6^2 ? [3, 2330] ? 0 ? [1/21715600*a4^2 + 27/10857800*a4 - 130292871/21715600, -1/101194696000*a4^3 - 81/101194696000*a4^2 + 195438213/101194696000*a4 - 235778364808883/101194696000] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.013s sys 0m0.004s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Tue May 24 20:52:40 2005 Input: e = ellinit([0,0,0,11711,1681]) e.disc p = [3, 2330] ellisoncurve(e, p) elladd(e, p, p) Output: ? [0, 0, 0, 11711, 1681, 0, 23422, 6724, -137147521, -562128, -1452384, -102793836308336, 11101602482595072/6424614769271, [-0.14354000875585559952786981691953114335, 0.071770004377927799763934908459765571677 - 108.21744523319974043438428139957432674*I, 0.071770004377927799763934908459765571677 + 108.21744523319974043438428139957432674*I]~, 0.35662003442814887732751006527963270632, -0.17831001721407443866375503263981635316 + 0.17814798165875702685711694222663204523*I, -8.8197586059461463851339993469869318320 + 0.E-37*I, 4.4098793029730731925669996734934659160 - 13.215227393249777426995641096319039092*I, 0.063531139352451165660882632446065337870] ? -102793836308336 ? [3, 2330] ? 0 ? [1871761/5428900, -29388353933009/12649337000] ? Errors (if any) and Timing Info: Timing: real 0m0.064s user 0m0.016s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Tue May 24 20:52:56 2005 Input: e = ellinit([0,0,0,11711,1681]); e.disc p = [3, 2330] ellisoncurve(e, p) elladd(e, p, p) Output: ? ? -102793836308336 ? [3, 2330] ? 0 ? [1871761/5428900, -29388353933009/12649337000] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.014s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Tue May 24 20:53:17 2005 Input: e = ellinit([0,0,0,11711,1681]); mod(e.disc, 11903) p = [3, 2330] ellisoncurve(e, p) elladd(e, p, p) Output: ? ? ? [3, 2330] ? 0 ? [1871761/5428900, -29388353933009/12649337000] ? Errors (if any) and Timing Info: *** obsolete function: mod(e.disc,11903) ^----------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.021s user 0m0.011s sys 0m0.010s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Tue May 24 20:53:42 2005 Input: e = ellinit([0,0,0,11711,1681]); Mod(e.disc, 11903) p = [3, 2330] ellisoncurve(e, p) elladd(e, p, p) Output: ? ? Mod(11483, 11903) ? [3, 2330] ? 0 ? [1871761/5428900, -29388353933009/12649337000] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.014s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Tue May 24 20:54:30 2005 Input: e = ellinit([0,0,0,11711,1681]); Mod(e.disc, 11903) p = [3, 2330] ellisoncurve(e, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) Output: ? ? Mod(11483, 11903) ? [3, 2330] ? 0 ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.013s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Tue May 24 20:54:43 2005 Input: e = ellinit([0,0,0,11711,1681]); Mod(e.disc, 11903) p = [3, 2330] ellisoncurve(e, p) q = elladd(e, p, p) elladd(e, p, q) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) elladd(e, p, p) Output: ? ? Mod(11483, 11903) ? [3, 2330] ? 0 ? [1871761/5428900, -29388353933009/12649337000] ? [638186362039049361563/207790466373721, -16122087689051138009386739619190/2995286897558739418019] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? [1871761/5428900, -29388353933009/12649337000] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.010s sys 0m0.011s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Tue May 24 20:55:22 2005 Input: e = ellinit([0,0,0,11711,1681]); Mod(e.disc, 11903) p = [3, 2330] ellisoncurve(e, p) q = elladd(e, p, p) q = elladd(e, p, q) q = elladd(e, p, q) q = elladd(e, p, q) q = elladd(e, p, q) q = elladd(e, p, q) q = elladd(e, p, q) q = elladd(e, p, q) q = elladd(e, p, q) q = elladd(e, p, q) q = elladd(e, p, q) q = elladd(e, p, q) q = elladd(e, p, q) q = elladd(e, p, q) q = elladd(e, p, q) Output: ? ? Mod(11483, 11903) ? [3, 2330] ? 0 ? [1871761/5428900, -29388353933009/12649337000] ? [638186362039049361563/207790466373721, -16122087689051138009386739619190/2995286897558739418019] ? [106208397036479242482615541514316641/18755228362963692793975744345363600, 6001908621598600023312009890897627977273150678049235439/2568523447789366712064012941955976250705525357384000] ? [-27642546249582912693863098017758859453980947645833017717/12003796517755991330774262233949042819364409788669164361, -96346069966279818447965356036242097030732991806289056242526019912625011104868000052650/41588948226818673880617849080478224141740250010967086754077553968803814704865180859] ? [41469622707336546849501326512962398390225003026507460567969151780835780543041183441/54009253643569000682557071950641976832805745656235884804539456927108045948100, -8444912042093217339697954208168223404008483207187307855066089083551929748533461920653432267445812880994745516526928393122511/12551691708561875511617821842516905402858955823033058759005099554866844722050210999831934510248447853859515438621000] ? [1193883278034188744110522014276761247453691181753859341082040982128580555085195142128318761060320114282770817363/143264355282186554280306734820194594864777969718822218115530883944298808349634265166101875914354705996108778321, 4018546424258096310106685835078097503396182507507418678106643455080644450264311171772968168155542592429162703586495329349398104024475340348748753532638465084273744752890/1714775321167253431320749666341048953640015216206443014244358076685456250293859631288149910978323673529990959625770504992701406745130832956785583218188709590296062119] ? [-13357701070617735021467650786747608488034877179996285977865731763419411259541506212969703025913666979706105124336048136909276277110304312616179839/2702471395984817500882391925405652923224535230997556374995559036484899950268300241640862313575189000769247832909274301762203290710851454425422400, -10262159536542808589392820384006921220351519524646376351440992822450837428141496290642692408159129218584620289382207068532729956350477875673680978960961266572392656571845200332690624817770412732396018216258691793208276159/4442645486469460353003803294801788899344738099019158219844119980508966157679219602462743135403453623960575729751174470329127883022947725138796080224814073276801463546254867071472010655982127147021204687447188306368000] ? [1097507970977264591625913264507901341595518537714474447354346653016640479203154504642831544929949894452776345398628078804515179062621897420961635178410904751079455033748947394386020599603/3216090786548063344607364154978507334594714503833066729580895379741916799820832835158697922020739695009383868241519271742875574831007062073317131682518972722221249648222704289425201, -1149771519033329553066723595669970350789106405589242723443493752081025952460707078490044833007715366665239656250928804521615203096649496221323164417413492778077757340332902897881264202816178067180494406848316162457833798333195022516956290348837954792052591069000667780083520953030/5767564364411515419946866395768563787806957791018271055381623955835862058301882745040403605004588807610714455570077394130656159706792310350270920191266295400798318593797826005271220645223425215459401122691370891480488045842032179355062461894738645011040843840819744277801] ? 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[-1877092307474938387073487103127806137179755816381950675030383103989241378727839908226718510964874603170079610009992745105034541600320763551593301546973561479613436565081449417810219726350028967915290571250444056289133901485990747325904059865674431700131809597460660843640080597/247799270246929081704621603541399575350190130870911238308165592146464588940825178815979065538228750284019536958483219405013209696090865330233738805745040803304093134725071053818116718486835001803617996139277844185989870608838017373411792545678909841970323170187175535235277801, -284103186914463046498999565686306271162425467866757116407264512249454261203704439806554910518936622705366761389890966831876003866330797256949829950012441829085979510893722363764128420600268167202452308966453453819631824575885333398741712985594999336777795580290931226176640205184537629398994662006497890270310276257427063246619933778997640002019859977901462384698763756724353032383965101846804122078968388555953643370/123353090440751470331086310693492511044082493788755903564430177019786464044469559941722065161215588594148604288193164566119258443608766948014565646042562941752837326674102958627237813606499099039840092395168834581377239910577523187722858984234970963731188935378591148087427706605334087122759672373380450791834887480311881119723849728120457946668648073231429281518447988242250155288741056106779430815834035895731701] ? [2957469805096517776163588788152124867738601929137418598668630536546484545128438869472227035919840994984892779410693619282699103720843383341499425621410308144730433705594913242508391573460018566960117056196572410723255258168002092027539258317662019176610654361133697211706517362424678260771052496854876974320421400193888512126411361/15407012261461943718720719900845982865647765583500963351304466729466441710394497250312162068635012877356612003549200166523866283727622897933250826369990635640323244472232900158230435568416915688689879104777152529842630427426278594371157057223191472055813259792886044973456467289417973848925276849786166713067357831807656880400, -5086049095986089689392173001103224490939660843036311336429841325889062123795727228299755091233747848494253444373707120348024773849170136993673539888672428071775799854589771286149420012597254796679305652785857472150946712616686683039033875950625724144271048042229116019505129514145352159186475010689854966208155668126510535251030743021274750995082958923439197458093924269804977625232471058899993376709074875913832726344137846825252851296848553304871959519848224005557724397737352244530717718634641/60475245810723322462154889752759747352939013155363773672140443886053036652648332850387084350878914920750369593408003456359331185283149318827974271781515157593874407396215346862645193222554827133503837212836033327516673765677462401628541917946277156824587295112068347095530511729297213552017732434615360741518649555489757300934963744954681455432157916033115668657491620961085256213436234102122365561865634234927936134244551695471685051844347486491963898511975888351772239345022986976408000] ? [483484281785087440473429055233183901475672403938687366468169617419998783341797315835037240484599318829054741598209465383630785498352654804550364784612057154286740844747221616235972878792947123537703329614934865395013542523817968795099232705982288540850192953857094349258166022698903276664857219460846220550086201502341401644233662985229752227347398579880150713165378640562599227132864763/35296125960488418547368341311897722408080705266008118451401257059501888769199099433281307796753910218682993868570706857303508135315237362958764524143487894161450801650076669023644174158008473762295577284661201633580498498880290068389725499219458570834075323132768549427422992361397900144002932714017033284974947991447293691707236677915626740268816353318700256873173264190658891283752121, 494310781541384560746025608099219215079716862477645532098336502699600099231503249564580564218418308107233755453666575563142548851988132251106937215738857550296973334253753455078106555877775416130746377157543856949729360390801042625678600500170020591252461674749836191114547815954114555506007351274697355215872404834898064566361739003530920890141819463670390523194445404025530134625470565162287037592071809162479194634670835608546353115674500674961079312497438401574541831605474211023916433441817179952761511982690442667907955622343381972259995519861532581980838544353705593285900490/209696200212649028467650561327804404084543032857872979911805789231958477571832687814755598162218513186383215656818691441458492592991358715090136589687956597151546820005384433685846868203556304337629666068029702888103653722656746526216116892826700477670614663725267306099685550767367611875089489444427131844852401917935694574985307467574942388280044982697568700845119482520020927511230956071684977325404653004132148376609025087387127539228608821715331777043767893287770010405216183245972227308648875750730076158437108472367390971037248383702863405666090349405892071723100666065581] ? [-23597113214152084384123764575183166475736352755806697459683124079696234102080721589480355129434021980580688205401887273257339459107170897848359743923526790060026734154768810896498546404811444724719295406548360347880852332068103341348364323548679005712690922789160565801062621145472355319124222605793552785004838967326231663553678830913055347134769677668997648078837472453396230247116046896764441519259079360842467272112242279830180048637559093842159/2313535295247185808841324560126848599410456968189373308206028771367307105537942180968513406019 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.024s sys 0m0.009s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Tue May 24 20:55:51 2005 Input: e = ellinit([0,0,0,11711,1681]); Mod(e.disc, 11903) p = [3, 2330] ellisoncurve(e, p) q = elladd(e, p, p) Output: ? ? Mod(11483, 11903) ? [3, 2330] ? 0 ? [1871761/5428900, -29388353933009/12649337000] ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.015s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 00:21:23 2005 Input: p = 11903; x = Mod(3,p); y = Mod(2330,p); a4 = Mod(11711,p); lambda = (Mod(3,p)*x^2+a4)/(Mod(2,p)*y); print(lambda); Output: ? ? ? ? ? ? Mod(2848, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.010s sys 0m0.010s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 00:22:37 2005 Input: p = 11903; x = Mod(3,p); y = Mod(2330,p); a4 = Mod(11711,p); lambda = (Mod(3,p)*x^2+a4)/(Mod(2,p)*y); xx = lambda^2 - Mod(2,p)*x; yy = lambda*(x-xx) - y; print(xx," ",yy); Output: ? ? ? ? ? ? ? ? Mod(5155, 11903) Mod(1173, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.011s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 01:39:26 2005 Input: e = ellinit([0,0,0,11711,1681])*Mod(1,11903); e.disc Output: ? ? ? Errors (if any) and Timing Info: *** forbidden multiplication t_REAL * t_INTMOD. *** incorrect type in .disc: e.disc ^---- Timing: real 0m0.020s user 0m0.010s sys 0m0.010s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 01:39:41 2005 Input: e = ellinit([0,0,0,11711,1681])*Mod(1,11903); Output: ? ? Errors (if any) and Timing Info: *** forbidden multiplication t_REAL * t_INTMOD. Timing: real 0m0.020s user 0m0.013s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 01:39:53 2005 Input: e = ellinit([0,0,0,11711,1681]) Output: ? [0, 0, 0, 11711, 1681, 0, 23422, 6724, -137147521, -562128, -1452384, -102793836308336, 11101602482595072/6424614769271, [-0.14354000875585559952786981691953114335, 0.071770004377927799763934908459765571677 - 108.21744523319974043438428139957432674*I, 0.071770004377927799763934908459765571677 + 108.21744523319974043438428139957432674*I]~, 0.35662003442814887732751006527963270632, -0.17831001721407443866375503263981635316 + 0.17814798165875702685711694222663204523*I, -8.8197586059461463851339993469869318320 + 0.E-37*I, 4.4098793029730731925669996734934659160 - 13.215227393249777426995641096319039092*I, 0.063531139352451165660882632446065337870] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.012s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 01:39:59 2005 Input: e = ellinit([0,0,0,11711,1681]) e.disc Output: ? [0, 0, 0, 11711, 1681, 0, 23422, 6724, -137147521, -562128, -1452384, -102793836308336, 11101602482595072/6424614769271, [-0.14354000875585559952786981691953114335, 0.071770004377927799763934908459765571677 - 108.21744523319974043438428139957432674*I, 0.071770004377927799763934908459765571677 + 108.21744523319974043438428139957432674*I]~, 0.35662003442814887732751006527963270632, -0.17831001721407443866375503263981635316 + 0.17814798165875702685711694222663204523*I, -8.8197586059461463851339993469869318320 + 0.E-37*I, 4.4098793029730731925669996734934659160 - 13.215227393249777426995641096319039092*I, 0.063531139352451165660882632446065337870] ? -102793836308336 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.013s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 01:40:13 2005 Input: e = ellinit([0,0,0,11711,1681]) Mod(e.disc,p) Output: ? [0, 0, 0, 11711, 1681, 0, 23422, 6724, -137147521, -562128, -1452384, -102793836308336, 11101602482595072/6424614769271, [-0.14354000875585559952786981691953114335, 0.071770004377927799763934908459765571677 - 108.21744523319974043438428139957432674*I, 0.071770004377927799763934908459765571677 + 108.21744523319974043438428139957432674*I]~, 0.35662003442814887732751006527963270632, -0.17831001721407443866375503263981635316 + 0.17814798165875702685711694222663204523*I, -8.8197586059461463851339993469869318320 + 0.E-37*I, 4.4098793029730731925669996734934659160 - 13.215227393249777426995641096319039092*I, 0.063531139352451165660882632446065337870] ? Mod(-102793836308336, p) ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.014s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 01:40:55 2005 Input: p = 11903 a4 = 11711 a6 = 1681 e = ellinit([0,0,0,a4,a6]*Mod(1,p)) Mod(e.disc,p) Output: ? 11903 ? 11711 ? 1681 ? [Mod(0, 11903), Mod(0, 11903), Mod(0, 11903), Mod(11711, 11903), Mod(1681, 11903), Mod(0, 11903), Mod(11519, 11903), Mod(6724, 11903), Mod(10748, 11903), Mod(9216, 11903), Mod(11685, 11903), Mod(11483, 11903), Mod(3542, 11903), 0, 0, 0, 0, 0, 0] ? ? Errors (if any) and Timing Info: *** forbidden division t_INTMOD % t_INT. Timing: real 0m0.017s user 0m0.009s sys 0m0.009s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 01:41:04 2005 Input: p = 11903 a4 = 11711 a6 = 1681 e = ellinit([0,0,0,a4,a6]*Mod(1,p)); Mod(e.disc,p) Output: ? 11903 ? 11711 ? 1681 ? ? ? Errors (if any) and Timing Info: *** forbidden division t_INTMOD % t_INT. Timing: real 0m0.018s user 0m0.013s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 01:41:25 2005 Input: p = 11903 a4 = 11711 a6 = 1681 e = ellinit([0,0,0,a4,a6]*Mod(1,p)); e.disc Output: ? 11903 ? 11711 ? 1681 ? ? Mod(11483, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 01:42:16 2005 Input: p = 11903 a4 = 11711 a6 = 1681 e = ellinit([0,0,0,a4,a6]*Mod(1,p)); e.disc P = [3,2330] ellisoncurve(e,P) Q = elladd(e,P,P) Output: ? 11903 ? 11711 ? 1681 ? ? Mod(11483, 11903) ? [3, 2330] ? 1 ? [Mod(5155, 11903), Mod(1173, 11903)] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 01:42:24 2005 Input: p = 11903; a4 = 11711; a6 = 1681; e = ellinit([0,0,0,a4,a6]*Mod(1,p)); e.disc P = [3,2330]; ellisoncurve(e,P) Q = elladd(e,P,P) Output: ? ? ? ? ? Mod(11483, 11903) ? ? 1 ? [Mod(5155, 11903), Mod(1173, 11903)] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 01:43:11 2005 Input: p = 11903; a4 = 11711; a6 = 1681; e = ellinit([0,0,0,a4,a6]*Mod(1,p)); e.disc P = [3,2330]; ellisoncurve(e,P) Q = elladd(e,P,P) Q = elladd(e,Q,Q) Q = elladd(e,Q,Q) Q = elladd(e,Q,Q) Output: ? ? ? ? ? Mod(11483, 11903) ? ? 1 ? [Mod(5155, 11903), Mod(1173, 11903)] ? [Mod(2848, 11903), Mod(8021, 11903)] ? [Mod(6192, 11903), Mod(699, 11903)] ? [Mod(9517, 11903), Mod(4600, 11903)] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '138.130' ************** PARI ***************** Host 138.130.2.244 (138.130.2.244) Time: Wed May 25 02:55:28 2005 Input: 7+9 Output: ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.008s '138.130' ************** PARI ***************** Host 138.130.2.244 (138.130.2.244) Time: Wed May 25 02:55:48 2005 Input: 4689650+899-6745735*5 Output: ? -29038126 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '138.130' ************** PARI ***************** Host 138.130.2.244 (138.130.2.244) Time: Wed May 25 02:55:54 2005 Input: 4689650+899-67457355 Output: ? -62766806 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '138.130' ************** PARI ***************** Host 138.130.2.244 (138.130.2.244) Time: Wed May 25 02:56:01 2005 Input: 4689650+899-674573 Output: ? 4015976 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '138.130' ************** PARI ***************** Host 138.130.2.244 (138.130.2.244) Time: Wed May 25 02:56:06 2005 Input: 4689650+899-674573 Output: ? 4015976 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 04:00:09 2005 Input: p = 11903 a4 = 11711 a6 = 1681 e = ellint([-,0,0,a4,a6]*Mod(1,p)); e.disc P = [3,2330] ellisoncurve(e, P) Q = elladd(e, P, P) Output: ? 11903 ? 11711 ? 1681 ? ? ? [3, 2330] ? ? ? Errors (if any) and Timing Info: *** unexpected character: e=ellint([-,0,0,a4,a6]*Mod(1,p) ^-------------------- *** incorrect type in .disc: e.disc ^---- *** bad argument for an elliptic curve related function *** bad argument for an elliptic curve related function Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 04:00:19 2005 Input: p = 11903 a4 = 11711 a6 = 1681 e = ellinit([-,0,0,a4,a6]*Mod(1,p)); e.disc P = [3,2330] ellisoncurve(e, P) Q = elladd(e, P, P) Output: ? 11903 ? 11711 ? 1681 ? ? ? [3, 2330] ? ? ? Errors (if any) and Timing Info: *** unexpected character: e=ellinit([-,0,0,a4,a6]*Mod(1,p) ^-------------------- *** incorrect type in .disc: e.disc ^---- *** bad argument for an elliptic curve related function *** bad argument for an elliptic curve related function Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 04:00:33 2005 Input: p = 11903 a4 = 11711 a6 = 1681 e = ellinit([0,0,0,a4,a6]*Mod(1,p)); e.disc P = [3,2330] ellisoncurve(e, P) Q = elladd(e, P, P) Output: ? 11903 ? 11711 ? 1681 ? ? Mod(11483, 11903) ? [3, 2330] ? 1 ? [Mod(5155, 11903), Mod(1173, 11903)] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 04:02:20 2005 Input: p = 11903 a4 = 11711 a6 = 1681 e = ellinit([0,0,0,a4,a6]*Mod(1,p)); e.disc P = [3,2330] ellisoncurve(e, P) Q = elladd(e, P, P) R = [9517, 4600] ellisoncurve(e, R) Output: ? 11903 ? 11711 ? 1681 ? ? Mod(11483, 11903) ? [3, 2330] ? 1 ? [Mod(5155, 11903), Mod(1173, 11903)] ? [9517, 4600] ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 04:02:38 2005 Input: p = 11903; a4 = 11711; a6 = 1681; e = ellinit([0,0,0,a4,a6]*Mod(1,p)); e.disc P = [3,2330]; ellisoncurve(e, P) Q = elladd(e, P, P) R = [9517, 4600]; ellisoncurve(e, R) Output: ? ? ? ? ? Mod(11483, 11903) ? ? 1 ? [Mod(5155, 11903), Mod(1173, 11903)] ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 04:02:59 2005 Input: p = 11903; a4 = 11711; a6 = 1681; e = ellinit([0,0,0,a4,a6]*Mod(1,p)); e.disc P = [3,2330]; ellisoncurve(e, P) Q = elladd(e, P, P) R = [9517, 4600]; ellisoncurve(e, Q) Output: ? ? ? ? ? Mod(11483, 11903) ? ? 1 ? [Mod(5155, 11903), Mod(1173, 11903)] ? ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed May 25 04:09:19 2005 Input: p = 11903; a4 = 11711; a6 = 1681; e = ellinit([0,0,0,a4,a6]*Mod(1,p)); e.disc P = [3,2330]; ellisoncurve(e, P) Q = elladd(e, P, P) R = [9517, 4600]; ellisoncurve(e, Q) Mod(4660*2957, p) Output: ? ? ? ? ? Mod(11483, 11903) ? ? 1 ? [Mod(5155, 11903), Mod(1173, 11903)] ? ? 1 ? ? Mod(7849, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '203.101' ************** PARI ***************** Host 203.101.47.155 (203.101.47.155) Time: Wed May 25 07:47:34 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.277s user 0m0.013s sys 0m0.007s '207.102' ************** PARI ***************** Host 207.102.176.15 (207.102.176.15) Time: Wed May 25 15:35:32 2005 Input: h=8_9 Output: ? 8 ? Errors (if any) and Timing Info: *** Warning: unused characters: _9. Timing: real 0m0.116s user 0m0.009s sys 0m0.009s '207.102' ************** PARI ***************** Host 207.102.176.15 (207.102.176.15) Time: Wed May 25 15:35:42 2005 Input: h=89 Output: ? 89 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '207.102' ************** PARI ***************** Host 207.102.176.15 (207.102.176.15) Time: Wed May 25 15:35:55 2005 Input: 89 +3 Output: ? 89 ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.011s sys 0m0.006s '207.102' ************** PARI ***************** Host 207.102.176.15 (207.102.176.15) Time: Wed May 25 15:36:07 2005 Input: 89+3= Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 89+3= ^- Timing: real 0m0.023s user 0m0.010s sys 0m0.006s '207.102' ************** PARI ***************** Host 207.102.176.15 (207.102.176.15) Time: Wed May 25 15:36:11 2005 Input: 89+3=h Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 89+3=h ^-- Timing: real 0m0.026s user 0m0.009s sys 0m0.008s '207.102' ************** PARI ***************** Host 207.102.176.15 (207.102.176.15) Time: Wed May 25 15:37:04 2005 Input: 89+h=92 Output: ? 181 ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.010s sys 0m0.008s '171.161' ************** PARI ***************** Host 171.161.224.10 (171.161.224.10) Time: Thu May 26 12:10:29 2005 Input: erfc(1) Output: ? 0.15729920705028513065877936491739074077 ? Errors (if any) and Timing Info: Timing: real 0m0.184s user 0m0.008s sys 0m0.011s '171.161' ************** PARI ***************** Host 171.161.224.10 (171.161.224.10) Time: Thu May 26 12:11:38 2005 Input: erfc(1) default(realprecision, 40) erfc(1) Output: WARNING: PARI command contains unsafe command 'default', so it will not be executed. '83.70.6' ************** PARI ***************** Host 83.70.68.233 (83.70.68.233) Time: Thu May 26 15:33:29 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '82.52.1' ************** PARI ***************** Host 82.52.106.213 (82.52.106.213) Time: Fri May 27 00:29:14 2005 Input: 10!+1 Output: ? 3628801 ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.010s sys 0m0.009s '82.52.1' ************** PARI ***************** Host 82.52.106.213 (82.52.106.213) Time: Fri May 27 00:29:34 2005 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.008s '82.64.2' ************** PARI ***************** Host 82.64.222.229 (82.64.222.229) Time: Fri May 27 12:18:31 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '216.118' ************** PARI ***************** Host 216.118.213.30 (216.118.213.30) Time: Fri May 27 15:42:56 2005 Input: hi Output: ? hi ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '194.51.' ************** PARI ***************** Host 194.51.93.46 (194.51.93.46) Time: Fri May 27 15:43:38 2005 Input: K := PolynomialRing(GF(2)); algo:= function(r,n,g,C); d:=MinimumDistance(C); t:=Truncate((d-1)/2); s:=r mod g; i:=0; S:= (T^i)*s mod g; if #(Terms(S)) gt t then i:=i+1; else i:=i; end if; e:= (T^(n-i)) * S mod ((T^n)-1); print e; end function; gex := (T^5 - 1)*(T^3 + T + 1); nex:=15; Cex := CyclicCode(nex,gex); c:=Random(Cex); transforme := function(l); L:=OverDimension(l); m:=0; i:=1; while L-i ne 0 do if l[i] eq 1 then m:=m+T^(i-1); end if; i:=i+1; end while; return m; end function; d:=transforme(c); Output: ? ? ? ? ? ? ? ? ? ? else ? ? ? ? ? ? ? ? ? ? ? ? ? ? whileL - ine0 ? do ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: K:=PolynomialRing(GF( ^-------------------- *** unexpected character: algo:=function(r,n,g,C); ^------------------- *** unexpected character: d:=MinimumDistance(C); ^-------------------- *** unexpected character: t:=Truncate((d-1)/2); ^------------------- *** unexpected character: s:=rmodg; ^------- *** unexpected character: i:=0; ^--- *** unexpected character: S:=(T^i)*smodg; ^------------- *** expected character: '(' instead of: if#(Terms(S))gttthen ^------------------ *** unexpected character: i:=i+1; ^----- *** unexpected character: i:=i; ^--- *** unexpected character: e:=(T^(n-i))*Smod((T^n ^-------------------- *** unexpected character: gex:=(T^5-1)*(T^3+T+1); ^------------------- *** unexpected character: nex:=15; ^---- *** unexpected character: Cex:=CyclicCode(nex,gex) ^-------------------- *** unexpected character: c:=Random(Cex); ^------------- *** unexpected character: transforme:=function(l); ^------------- *** unexpected character: L:=OverDimension(l); ^------------------ *** unexpected character: m:=0; ^--- *** unexpected character: i:=1; ^--- *** Warning: unused characters: eq1thenm:=m+T^(i-1);. *** unexpected character: ifl[i]eq1thenm:=m+T^(i- ^-------------------- *** unexpected character: endif;i:=i+1;endwhile; ^-------------- *** unexpected character: d:=transforme(c); ^--------------- Timing: real 0m0.053s user 0m0.011s sys 0m0.009s '221.186' ************** PARI ***************** Host 221.186.0.23 (221.186.0.23) Time: Sat May 28 14:53:23 2005 Input: 1956838260564091438065319057901820337*171437647252353405893256996766843366184204177221854529669 Output: ? 335475747444495528670349694508008734509501229024370827423027602677845706870178177844074078453 ? Errors (if any) and Timing Info: Timing: real 0m0.285s user 0m0.011s sys 0m0.013s '70.110.' ************** PARI ***************** Host 70.110.155.172 (70.110.155.172) Time: Sat May 28 17:44:10 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.007s sys 0m0.011s '70.110.' ************** PARI ***************** Host 70.110.155.172 (70.110.155.172) Time: Sat May 28 17:44:26 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.009s '70.110.' ************** PARI ***************** Host 70.110.155.172 (70.110.155.172) Time: Sat May 28 18:11:39 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '70.110.' ************** PARI ***************** Host 70.110.155.172 (70.110.155.172) Time: Sat May 28 18:12:04 2005 Input: 1+1 Output: ? 2 ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '70.110.' ************** PARI ***************** Host 70.110.155.172 (70.110.155.172) Time: Sat May 28 18:12:09 2005 Input: 1+1 Output: ? 2 ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '70.110.' ************** PARI ***************** Host 70.110.155.172 (70.110.155.172) Time: Sat May 28 18:13:32 2005 Input: 5*7 Output: ? 35 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '70.110.' ************** PARI ***************** Host 70.110.155.172 (70.110.155.172) Time: Sat May 28 18:13:57 2005 Input: 1/7 Output: ? 1/7 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '70.110.' ************** PARI ***************** Host 70.110.155.172 (70.110.155.172) Time: Sat May 28 18:14:07 2005 Input: 1/7 Output: ? 1/7 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '70.110.' ************** PARI ***************** Host 70.110.155.172 (70.110.155.172) Time: Sat May 28 18:14:37 2005 Input: 17 Output: ? 17 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '213.179' ************** PARI ***************** Host 213.179.251.247 (213.179.251.247) Time: Sun May 29 07:24:52 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m3.363s user 0m0.011s sys 0m0.016s '193.204' ************** PARI ***************** Host 193.204.167.87 (193.204.167.87) Time: Mon May 30 08:45:12 2005 Input: factor(33) Output: ? [3 1] [11 1] ? Errors (if any) and Timing Info: Timing: real 0m0.319s user 0m0.012s sys 0m0.006s '221.186' ************** PARI ***************** Host 221.186.0.23 (221.186.0.23) Time: Mon May 30 12:00:37 2005 Input: factor(88537224) Output: ? [2 3] [3 1] [17 1] [217003 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '203.144' ************** PARI ***************** Host 203.144.160.247 (203.144.160.247) Time: Mon May 30 13:04:14 2005 Input: polgalois(x^6+4*x^5+3*x^4-4*x^3-2*x^2+2*x+1) Output: ? [18, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.178s user 0m0.028s sys 0m0.012s '221.186' ************** PARI ***************** Host 221.186.0.23 (221.186.0.23) Time: Mon May 30 17:36:42 2005 Input: factor(88537970) Output: ? [2 1] [5 1] [8853797 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.008s '203.194' ************** PARI ***************** Host 203.194.42.162 (203.194.42.162) Time: Mon May 30 22:09:00 2005 Input: 6x-9y+3x= Output: ? 6 ? Errors (if any) and Timing Info: *** Warning: unused characters: x-9y+3x=. Timing: real 0m0.017s user 0m0.009s sys 0m0.009s '203.194' ************** PARI ***************** Host 203.194.42.162 (203.194.42.162) Time: Mon May 30 22:09:23 2005 Input: 9+21= Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 9+21= ^- Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '203.194' ************** PARI ***************** Host 203.194.42.162 (203.194.42.162) Time: Mon May 30 22:09:38 2005 Input: 21+9 Output: ? 30 ? Errors (if any) and Timing Info: Timing: real 0m0.076s user 0m0.010s sys 0m0.007s '203.194' ************** PARI ***************** Host 203.194.42.162 (203.194.42.162) Time: Mon May 30 22:13:07 2005 Input: 80%+y=124 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '203.194' ************** PARI ***************** Host 203.194.42.162 (203.194.42.162) Time: Mon May 30 22:14:06 2005 Input: 5y + 3 =4y-5 Output: ? 5 ? Errors (if any) and Timing Info: *** Warning: unused characters: y+3=4y-5. Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '203.194' ************** PARI ***************** Host 203.194.42.162 (203.194.42.162) Time: Mon May 30 22:15:31 2005 Input: 3a/4+6=12 Output: ? 3 ? Errors (if any) and Timing Info: *** Warning: unused characters: a/4+6=12. Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '203.194' ************** PARI ***************** Host 203.194.42.162 (203.194.42.162) Time: Mon May 30 22:16:47 2005 Input: -6--8 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '203.194' ************** PARI ***************** Host 203.194.42.162 (203.194.42.162) Time: Mon May 30 22:17:37 2005 Input: 3pt-6pr+9p Output: ? 3 ? Errors (if any) and Timing Info: *** Warning: unused characters: pt-6pr+9p. Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '203.194' ************** PARI ***************** Host 203.194.42.162 (203.194.42.162) Time: Mon May 30 22:18:49 2005 Input: 12ab/4ac Output: ? 12 ? Errors (if any) and Timing Info: *** Warning: unused characters: ab/4ac. Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '203.194' ************** PARI ***************** Host 203.194.42.162 (203.194.42.162) Time: Mon May 30 22:21:14 2005 Input: 18-3y=3 Output: ? 15 ? Errors (if any) and Timing Info: *** Warning: unused characters: y=3. Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue May 31 04:06:50 2005 Input: polgalois(X^6 + 4*X^5 + 3*X^4 - 4*X^3 - 2*X^2 + 2*X + 1) Output: ? [18, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.027s sys 0m0.009s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue May 31 04:08:05 2005 Input: polgalois(x^6+3*x^3+3) Output: ? [18, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.043s user 0m0.032s sys 0m0.007s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue May 31 04:08:14 2005 Input: polgalois(x^6+3*x^3+2) Output: ? ? Errors (if any) and Timing Info: *** sorry, galois of reducible polynomial is not yet implemented. Timing: real 0m0.018s user 0m0.013s sys 0m0.004s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue May 31 04:08:26 2005 Input: polgalois(x^6+3*x^3+4) Output: ? [36, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.038s user 0m0.027s sys 0m0.011s '85.164.' ************** PARI ***************** Host 85.164.101.199 (85.164.101.199) Time: Tue May 31 04:10:39 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.007s '158.109' ************** PARI ***************** Host 158.109.70.15 (158.109.70.15) Time: Tue May 31 04:55:13 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '203.144' ************** PARI ***************** Host 203.144.160.244 (203.144.160.244) Time: Tue May 31 08:18:50 2005 Input: polgalois(x^6 + 2*x^5 + 3*x^4 + 4*x^3 + 5*x^2 + 6*x + 7) Output: ? [120, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.376s user 0m0.019s sys 0m0.015s '203.144' ************** PARI ***************** Host 203.144.160.244 (203.144.160.244) Time: Tue May 31 08:25:54 2005 Input: polred(x^6 + 2*x^5 + 3*x^4 + 4*x^3 + 5*x^2 + 6*x + 7) Output: ? [x - 1, x^6 - 2*x^5 - 3*x^4 - 8*x^3 + 44*x^2 - 32*x + 8, x^6 - 2*x^5 + 3*x^4 - 4*x^3 + 5*x^2 - 6*x + 7, x^6 - 2*x^5 + 3*x^4 - 4*x^3 + 19*x^2 - 34*x + 49, x^6 - 2*x^5 + 9*x^4 - 8*x^3 + 24*x^2 + 32, x^6 + 6*x^4 - 16*x^3 + 32*x^2 - 32*x + 16] ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.019s sys 0m0.011s '203.144' ************** PARI ***************** Host 203.144.160.244 (203.144.160.244) Time: Tue May 31 08:27:40 2005 Input: polred(x^6 + 2*x^5 -7*x^4 -12*x^3 + 10*x^2 + 17*x + 4) Output: ? [x - 1, x^6 - 2*x^5 - 7*x^4 + 12*x^3 + 10*x^2 - 17*x + 4, x^6 - x^5 - 31*x^4 - x^3 + 222*x^2 + 289*x + 87, x^6 - x^5 - 17*x^4 + 4*x^3 + 80*x^2 + 32*x - 35, x^6 - 19*x^4 - 14*x^3 + 72*x^2 + 45*x - 58, x^6 - 18*x^4 - 20*x^3 + 29*x^2 + 19*x + 1] ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.014s sys 0m0.004s '195.13.' ************** PARI ***************** Host 195.13.11.226 (195.13.11.226) Time: Tue May 31 10:32:03 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.010s sys 0m0.008s '198.103' ************** PARI ***************** Host 198.103.172.9 (198.103.172.9) Time: Tue May 31 13:32:57 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.069s user 0m0.007s sys 0m0.012s '198.103' ************** PARI ***************** Host 198.103.172.9 (198.103.172.9) Time: Tue May 31 13:32:59 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '198.103' ************** PARI ***************** Host 198.103.172.9 (198.103.172.9) Time: Tue May 31 13:33:01 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed Jun 1 01:15:59 2005 Input: e=ellinit([0,0,0,11711,1681]*Mod(1,11903); e.disc Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...,11711,1681]*Mod(1,11903); ^- *** incorrect type in .disc: e.disc ^---- Timing: real 0m0.032s user 0m0.011s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed Jun 1 01:16:12 2005 Input: e=ellinit([0,0,0,11711,1681]*Mod(1,11903)); e.disc Output: ? ? Mod(11483, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.012s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed Jun 1 01:17:29 2005 Input: e=ellinit([0,0,0,11711,1681]*Mod(1,11903)); e.disc P1=[3,2330]; P2=[3,2330,1]; Q1=[2]P1 Output: ? ? Mod(11483, 11903) ? ? ? [2] ? Errors (if any) and Timing Info: *** Warning: unused characters: P1. Timing: real 0m0.018s user 0m0.008s sys 0m0.009s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed Jun 1 01:17:39 2005 Input: e=ellinit([0,0,0,11711,1681]*Mod(1,11903)); e.disc P1=[3,2330]; P2=[3,2330,1]; Q1=2*P1 Output: ? ? Mod(11483, 11903) ? ? ? [6, 4660] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.014s sys 0m0.003s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed Jun 1 01:17:51 2005 Input: e=ellinit([0,0,0,11711,1681]*Mod(1,11903)); e.disc P1=[3,2330]; P2=[3,2330,1]; Q1=[2]P1 Output: ? ? Mod(11483, 11903) ? ? ? [2] ? Errors (if any) and Timing Info: *** Warning: unused characters: P1. Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed Jun 1 01:19:07 2005 Input: e=ellinit([0,0,0,11711,1681]*Mod(1,11903)); e.disc P1=[3,2330]; P2=[3,2330,1]; Q1=elladd(e,P1,P1) Q2=elladd(e,P2,P2) R1=elladd(e,Q1,Q1) R2=elladd(e,Q2,Q2) Output: ? ? Mod(11483, 11903) ? ? ? [Mod(5155, 11903), Mod(1173, 11903)] ? [Mod(5155, 11903), Mod(1173, 11903)] ? [Mod(2848, 11903), Mod(8021, 11903)] ? [Mod(2848, 11903), Mod(8021, 11903)] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.013s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Wed Jun 1 01:21:01 2005 Input: e=ellinit([0,0,0,11711,1681]*Mod(1,11903)); e.disc P1=[3,2330]; P2=elladd(e,P1,P1) P4=elladd(e,P2,P2) P8=elladd(e,P4,P4) P16=elladd(e,P8,P8) P32=elladd(e,P16,P16) Output: ? ? Mod(11483, 11903) ? ? [Mod(5155, 11903), Mod(1173, 11903)] ? [Mod(2848, 11903), Mod(8021, 11903)] ? [Mod(6192, 11903), Mod(699, 11903)] ? [Mod(9517, 11903), Mod(4600, 11903)] ? [Mod(8972, 11903), Mod(3736, 11903)] ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.006s sys 0m0.012s '139.78.' ************** PARI ***************** Host 139.78.115.203 (139.78.115.203) Time: Wed Jun 1 12:20:37 2005 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Errors (if any) and Timing Info: Timing: real 0m0.225s user 0m0.005s sys 0m0.015s '139.78.' ************** PARI ***************** Host 139.78.115.203 (139.78.115.203) Time: Wed Jun 1 12:23:51 2005 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.010s sys 0m0.009s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Wed Jun 1 22:36:47 2005 Input: (1 + x)^20 Output: ? x^20 + 20*x^19 + 190*x^18 + 1140*x^17 + 4845*x^16 + 15504*x^15 + 38760*x^14 + 77520*x^13 + 125970*x^12 + 167960*x^11 + 184756*x^10 + 167960*x^9 + 125970*x^8 + 77520*x^7 + 38760*x^6 + 15504*x^5 + 4845*x^4 + 1140*x^3 + 190*x^2 + 20*x + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.061s user 0m0.012s sys 0m0.006s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Wed Jun 1 22:36:55 2005 Input: (1 + x)^100 Output: ? x^100 + 100*x^99 + 4950*x^98 + 161700*x^97 + 3921225*x^96 + 75287520*x^95 + 1192052400*x^94 + 16007560800*x^93 + 186087894300*x^92 + 1902231808400*x^91 + 17310309456440*x^90 + 141629804643600*x^89 + 1050421051106700*x^88 + 7110542499799200*x^87 + 44186942677323600*x^86 + 253338471349988640*x^85 + 1345860629046814650*x^84 + 6650134872937201800*x^83 + 30664510802988208300*x^82 + 132341572939212267400*x^81 + 535983370403809682970*x^80 + 2041841411062132125600*x^79 + 7332066885177656269200*x^78 + 24865270306254660391200*x^77 + 79776075565900368755100*x^76 + 242519269720337121015504*x^75 + 699574816500972464467800*x^74 + 1917353200780443050763600*x^73 + 4998813702034726525205100*x^72 + 12410847811948286545336800*x^71 + 29372339821610944823963760*x^70 + 66324638306863423796047200*x^69 + 143012501349174257560226775*x^68 + 294692427022540894366527900*x^67 + 580717429720889409486981450*x^66 + 1095067153187962886461165020*x^65 + 1977204582144932989443770175*x^64 + 3420029547493938143902737600*x^63 + 5670048986634686922786117600*x^62 + 9013924030034630492634340800*x^61 + 13746234145802811501267369720*x^60 + 20116440213369968050635175200*x^59 + 28258808871162574166368460400*x^58 + 38116532895986727945334202400*x^57 + 49378235797073715747364762200*x^56 + 61448471214136179596720592960*x^55 + 73470998190814997343905056800*x^54 + 84413487283064039501507937600*x^53 + 93206558875049876949581681100*x^52 + 98913082887808032681188722800*x^51 + 100891344545564193334812497256*x^50 + 98913082887808032681188722800*x^49 + 93206558875049876949581681100*x^48 + 84413487283064039501507937600*x^47 + 73470998190814997343905056800*x^46 + 61448471214136179596720592960*x^45 + 49378235797073715747364762200*x^44 + 38116532895986727945334202400*x^43 + 28258808871162574166368460400*x^42 + 20116440213369968050635175200*x^41 + 13746234145802811501267369720*x^40 + 9013924030034630492634340800*x^39 + 5670048986634686922786117600*x^38 + 3420029547493938143902737600*x^37 + 1977204582144932989443770175*x^36 + 1095067153187962886461165020*x^35 + 580717429720889409486981450*x^34 + 294692427022540894366527900*x^33 + 143012501349174257560226775*x^32 + 66324638306863423796047200*x^31 + 29372339821610944823963760*x^30 + 12410847811948286545336800*x^29 + 4998813702034726525205100*x^28 + 1917353200780443050763600*x^27 + 699574816500972464467800*x^26 + 242519269720337121015504*x^25 + 79776075565900368755100*x^24 + 24865270306254660391200*x^23 + 7332066885177656269200*x^22 + 2041841411062132125600*x^21 + 535983370403809682970*x^20 + 132341572939212267400*x^19 + 30664510802988208300*x^18 + 6650134872937201800*x^17 + 1345860629046814650*x^16 + 253338471349988640*x^15 + 44186942677323600*x^14 + 7110542499799200*x^13 + 1050421051106700*x^12 + 141629804643600*x^11 + 17310309456440*x^10 + 1902231808400*x^9 + 186087894300*x^8 + 16007560800*x^7 + 1192052400*x^6 + 75287520*x^5 + 3921225*x^4 + 161700*x^3 + 4950*x^2 + 100*x + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Wed Jun 1 22:37:09 2005 Input: (1 + x) = 0 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (1+x)=0 ^-- Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Wed Jun 1 22:37:27 2005 Input: x: 1 + x = 0 Output: ? 1 ? ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.010s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:09:54 2005 Input: Mod(-10730,11903) Output: ? Mod(1173, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.014s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:29:23 2005 Input: Mod(3*(5155^2),11903) Output: ? Mod(7684, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:30:01 2005 Input: Mod(27079,11903) Output: ? Mod(3273, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:32:45 2005 Input: Mod(2*10730,11903) Output: ? Mod(9557, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:33:28 2005 Input: Mod(9557^-1,11903) Output: ? Mod(7362, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.014s sys 0m0.004s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:35:18 2005 Input: Mod(3273*7362,11903) Output: ? Mod(4154, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:36:12 2005 Input: Mod(4154^2,11903) Output: ? Mod(8269, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:36:48 2005 Input: Mod(2*5155,11903) Output: ? Mod(10310, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:37:55 2005 Input: Mod(-2041,11903) Output: ? Mod(9862, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.010s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:38:45 2005 Input: Mod(3273*7362,11903) Output: ? Mod(4154, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:38:58 2005 Input: Mod(4154^2,11903) Output: ? Mod(8269, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:39:25 2005 Input: Mod(11711,11903) Output: ? Mod(11711, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:39:45 2005 Input: Mod(19395,11903) Output: ? Mod(7492, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:40:27 2005 Input: Mod(3*(5155^2) + 11711,11903) Output: ? Mod(7492, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:41:02 2005 Input: Mod(3*(5155^2) + 11711,11903) Mod(7492*7362,11903) Output: ? Mod(7492, 11903) ? Mod(9505, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:42:09 2005 Input: Mod(3*(5155^2) + 11711,11903) Mod(7492*7362,11903) Mod((9505^2) - 2*5155, 11903) Output: ? Mod(7492, 11903) ? @ 11903)Euler 11903)I 11903)List 11903)Mat 11903)Mod 11903)O 11903)Pi 11903)Pol 11903)Polrev 11903)Qfb 11903)Ser 11903)Set 11903)Str 11903)Vec 11903)abs 11903)acos 11903)acosh 11903)addhelp 11903)addprimes 11903)agm 11903)algdep 11903)alias 11903)allocatemem 11903)arg 11903)asin 11903)asinh 11903)atan 11903)atanh 11903)bernfrac 11903)bernreal 11903)bernvec 11903)besseljh 11903)besselk 11903)bestappr 11903)bezout 11903)bezoutres 11903)bigomega 11903)binary 11903)binomial 11903)bitand 11903)bitneg 11903)bitnegimply 11903)bitor 11903)bittest 11903)bitxor 11903)bnfcertify 11903)bnfclassunit 11903)bnfclgp 11903)bnfdecodemodule 11903)bnfinit 11903)bnfisintnorm 11903)bnfisnorm 11903)bnfisprincipal 11903)bnfissunit 11903)bnfisunit 11903)bnfmake 11903)bnfnarrow 11903)bnfreg 11903)bnfsignunit 11903)bnfsunit 11903)bnfunit 11903)bnrL1 11903)bnrclass 11903)bnrclassno 11903)bnrclassnolist 11903)bnrconductor 11903)bnrconductorofchar 11903)bnrdisc 11903)bnrdisclist 11903)bnrinit 11903)bnrisconductor 11903)bnrisprincipal 11903)bnrrootnumber 11903)bnrstark 11903)break 11903)ceil 11903)centerlift 11903)changevar 11903)charpoly 11903)chinese 11903)component 11903)concat 11903)conj 11903)conjvec 11903)content 11903)contfrac 11903)contfracpnqn 11903)core 11903)coredisc 11903)cos 11903)cosh 11903)cotan 11903)default 11903)denominator 11903)deriv 11903)dilog 11903)dirdiv 11903)direuler 11903)dirmul 11903)dirzetak 11903)divisors 11903)divrem 11903)eint1 11903)elladd 11903)ellak 11903)ellan 11903)ellap 11903)ellbil 11903)ellchangecurve 11903)ellchangepoint 11903)elleisnum 11903)elleta 11903)ellglobalred 11903)ellheight 11903)ellheightmatrix 11903)ellinit 11903)ellisoncurve 11903)ellj 11903)elllocalred 11903)elllseries 11903)ellorder 11903)ellordinate 11903)ellpointtoz 11903)ellpow 11903)ellrootno 11903)ellsigma 11903)ellsub 11903)elltaniyama 11903)elltors 11903)ellwp 11903)ellzeta 11903)ellztopoint 11903)erfc 11903)error 11903)eta 11903)eulerphi 11903)eval 11903)exp 11903)extern 11903)factor 11903)factorback 11903)factorcantor 11903)factorff 11903)factorial 11903)factorint 11903)factormod 11903)factornf 11903)factorpadic 11903)ffinit 11903)fibonacci 11903)floor 11903)for 11903)fordiv 11903)forprime 11903)forstep 11903)forsubgroup 11903)forvec 11903)frac 11903)galoisfixedfield 11903)galoisinit 11903)galoispermtopol 11903)galoissubcyclo 11903)gamma 11903)gammah 11903)gcd 11903)getheap 11903)getrand 11903)getstack 11903)gettime 11903)global 11903)hilbert 11903)hyperu 11903)idealadd 11903)idealaddtoone 11903)idealappr 11903)idealchinese 11903)idealcoprime 11903)idealdiv 11903)idealfactor 11903)idealhnf 11903)idealintersect 11903)idealinv 11903)ideallist 11903)ideallistarch 11903)ideallog 11903)idealmin 11903)idealmul 11903)idealnorm 11903)idealpow 11903)idealprimedec 11903)idealprincipal 11903)idealred 11903)idealstar 11903)idealtwoelt 11903)idealval 11903)ideleprincipal 11903)if 11903)imag 11903)incgam 11903)incgamc 11903)input 11903)install 11903)intformal 11903)intnum 11903)isfundamental 11903)isprime 11903)ispseudoprime 11903)issquare 11903)issquarefree 11903)kill 11903)kronecker 11903)lcm 11903)length 11903)lex 11903)lift 11903)lindep 11903)listcreate 11903)listinsert 11903)listkill 11903)listput 11903)listsort 11903)lngamma 11903)log 11903)matadjoint 11903)matalgtobasis 11903)matbasistoalg 11903)matcompanion 11903)matdet 11903)matdetint 11903)matdiagonal 11903)mateigen 11903)mathess 11903)mathilbert 11903)mathnf 11903)mathnfmod 11903)mathnfmodid 11903)matid 11903)matimage 11903)matimagecompl 11903)matindexrank 11903)matintersect 11903)matinverseimage 11903)matisdiagonal 11903)matker 11903)matkerint 11903)matmuldiagonal 11903)matmultodiagonal 11903)matpascal 11903)matrank 11903)matrix 11903)matrixqz 11903)matsize 11903)matsnf 11903)matsolve 11903)matsolvemod 11903)matsupplement 11903)mattranspose 11903)max 11903)min 11903)modreverse 11903)moebius 11903)newtonpoly 11903)next 11903)nextprime 11903)nfalgtobasis 11903)nfbasis 11903)nfbasistoalg 11903)nfdetint 11903)nfdisc 11903)nfeltdiv 11903)nfeltdiveuc 11903)nfeltdivmodpr 11903)nfeltdivrem 11903)nfeltmod 11903)nfeltmul 11903)nfeltmulmodpr 11903)nfeltpow 11903)nfeltpowmodpr 11903)nfeltreduce 11903)nfeltreducemodpr 11903)nfeltval 11903)nffactor 11903)nffactormod 11903)nfgaloisapply 11903)nfgaloisconj 11903)nfhilbert 11903)nfhnf 11903)nfhnfmod 11903)nfinit 11903)nfisideal 11903)nfisincl 11903)nfisisom 11903)nfkermodpr 11903)nfmodprinit 11903)nfnewprec 11903)nfroots 11903)nfrootsof1 11903)nfsnf 11903)nfsolvemodpr 11903)nfsubfields 11903)norm 11903)norml2 11903)numdiv 11903)numerator 11903)numtoperm 11903)omega 11903)padicappr 11903)padicprec 11903)permtonum 11903)plot 11903)plotbox 11903)plotclip 11903)plotcolor 11903)plotcopy 11903)plotcursor 11903)plotdraw 11903)plotfile 11903)ploth 11903)plothraw 11903)plothsizes 11903)plotinit 11903)plotkill 11903)plotlines 11903)plotlinetype 11903)plotmove 11903)plotpoints 11903)plotpointsize 11903)plotpointtype 11903)plotrbox 11903)plotrecth 11903)plotrecthraw 11903)plotrline 11903)plotrmove 11903)plotrpoint 11903)plotscale 11903)plotstring 11903)plotterm 11903)polcoeff 11903)polcompositum 11903)polcyclo 11903)poldegree 11903)poldisc 11903)poldiscreduced 11903)polgalois 11903)polhensellift 11903)polinterpolate 11903)polisirreducible 11903)pollead 11903)pollegendre 11903)polrecip 11903)polred 11903)polredabs 11903)polredord 11903)polresultant 11903)polroots 11903)polrootsmod 11903)polrootspadic 11903)polsturm 11903)polsubcyclo 11903)polsylvestermatrix 11903)polsym 11903)poltchebi 11903)poltschirnhaus 11903)polylog 11903)polzagier 11903)precision 11903)precprime 11903)prime 11903)primes 11903)print 11903)print1 11903)printp 11903)printp1 11903)printtex 11903)prod 11903)prodeuler 11903)prodinf 11903)psdraw 11903)psi 11903)psploth 11903)psplothraw 11903)qfbclassno 11903)qfbcompraw 11903)qfbhclassno 11903)qfbnucomp 11903)qfbnupow 11903)qfbpowraw 11903)qfbprimeform 11903)qfbred 11903)qfgaussred 11903)qfjacobi 11903)qflll 11903)qflllgram 11903)qfminim 11903)qfperfection 11903)qfsign 11903)quadclassunit 11903)quaddisc 11903)quadgen 11903)quadhilbert 11903)quadpoly 11903)quadray 11903)quadregulator 11903)quadunit 11903)quit 11903)random 11903)read 11903)real 11903)removeprimes 11903)reorder 11903)return 11903)rnfalgtobasis 11903)rnfbasis 11903)rnfbasistoalg 11903)rnfcharpoly 11903)rnfconductor 11903)rnfdedekind 11903)rnfdet 11903)rnfdisc 11903)rnfeltabstorel 11903)rnfeltdown 11903)rnfeltreltoabs 11903)rnfeltup 11903)rnfequation 11903)rnfhnfbasis 11903)rnfidealabstorel 11903)rnfidealdown 11903)rnfidealhnf 11903)rnfidealmul 11903)rnfidealnormabs 11903)rnfidealnormrel 11903)rnfidealreltoabs 11903)rnfidealtwoelt 11903)rnfidealup 11903)rnfinit 11903)rnfisfree 11903)rnfisnorm 11903)rnfkummer 11903)rnflllgram 11903)rnfnormgroup 11903)rnfpolred 11903)rnfpolredabs 11903)rnfpseudobasis 11903)rnfsteinitz 11903)round 11903)serconvol 11903)serlaplace 11903)serreverse 11903)setintersect 11903)setisset 11903)setminus 11903)setrand 11903)setsearch 11903)setunion 11903)shift 11903)shiftmul 11903)sigma ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** unexpected character: Mod(7492*7362,_ ^- Timing: real 0m0.020s user 0m0.011s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:42:22 2005 Input: Mod(3*(5155^2) + 11711,11903) Mod(7492*7362,11903) Mod((9505^2) - (2*5155), 11903) Output: ? Mod(7492, 11903) ? @ 11903)Euler 11903)I 11903)List 11903)Mat 11903)Mod 11903)O 11903)Pi 11903)Pol 11903)Polrev 11903)Qfb 11903)Ser 11903)Set 11903)Str 11903)Vec 11903)abs 11903)acos 11903)acosh 11903)addhelp 11903)addprimes 11903)agm 11903)algdep 11903)alias 11903)allocatemem 11903)arg 11903)asin 11903)asinh 11903)atan 11903)atanh 11903)bernfrac 11903)bernreal 11903)bernvec 11903)besseljh 11903)besselk 11903)bestappr 11903)bezout 11903)bezoutres 11903)bigomega 11903)binary 11903)binomial 11903)bitand 11903)bitneg 11903)bitnegimply 11903)bitor 11903)bittest 11903)bitxor 11903)bnfcertify 11903)bnfclassunit 11903)bnfclgp 11903)bnfdecodemodule 11903)bnfinit 11903)bnfisintnorm 11903)bnfisnorm 11903)bnfisprincipal 11903)bnfissunit 11903)bnfisunit 11903)bnfmake 11903)bnfnarrow 11903)bnfreg 11903)bnfsignunit 11903)bnfsunit 11903)bnfunit 11903)bnrL1 11903)bnrclass 11903)bnrclassno 11903)bnrclassnolist 11903)bnrconductor 11903)bnrconductorofchar 11903)bnrdisc 11903)bnrdisclist 11903)bnrinit 11903)bnrisconductor 11903)bnrisprincipal 11903)bnrrootnumber 11903)bnrstark 11903)break 11903)ceil 11903)centerlift 11903)changevar 11903)charpoly 11903)chinese 11903)component 11903)concat 11903)conj 11903)conjvec 11903)content 11903)contfrac 11903)contfracpnqn 11903)core 11903)coredisc 11903)cos 11903)cosh 11903)cotan 11903)default 11903)denominator 11903)deriv 11903)dilog 11903)dirdiv 11903)direuler 11903)dirmul 11903)dirzetak 11903)divisors 11903)divrem 11903)eint1 11903)elladd 11903)ellak 11903)ellan 11903)ellap 11903)ellbil 11903)ellchangecurve 11903)ellchangepoint 11903)elleisnum 11903)elleta 11903)ellglobalred 11903)ellheight 11903)ellheightmatrix 11903)ellinit 11903)ellisoncurve 11903)ellj 11903)elllocalred 11903)elllseries 11903)ellorder 11903)ellordinate 11903)ellpointtoz 11903)ellpow 11903)ellrootno 11903)ellsigma 11903)ellsub 11903)elltaniyama 11903)elltors 11903)ellwp 11903)ellzeta 11903)ellztopoint 11903)erfc 11903)error 11903)eta 11903)eulerphi 11903)eval 11903)exp 11903)extern 11903)factor 11903)factorback 11903)factorcantor 11903)factorff 11903)factorial 11903)factorint 11903)factormod 11903)factornf 11903)factorpadic 11903)ffinit 11903)fibonacci 11903)floor 11903)for 11903)fordiv 11903)forprime 11903)forstep 11903)forsubgroup 11903)forvec 11903)frac 11903)galoisfixedfield 11903)galoisinit 11903)galoispermtopol 11903)galoissubcyclo 11903)gamma 11903)gammah 11903)gcd 11903)getheap 11903)getrand 11903)getstack 11903)gettime 11903)global 11903)hilbert 11903)hyperu 11903)idealadd 11903)idealaddtoone 11903)idealappr 11903)idealchinese 11903)idealcoprime 11903)idealdiv 11903)idealfactor 11903)idealhnf 11903)idealintersect 11903)idealinv 11903)ideallist 11903)ideallistarch 11903)ideallog 11903)idealmin 11903)idealmul 11903)idealnorm 11903)idealpow 11903)idealprimedec 11903)idealprincipal 11903)idealred 11903)idealstar 11903)idealtwoelt 11903)idealval 11903)ideleprincipal 11903)if 11903)imag 11903)incgam 11903)incgamc 11903)input 11903)install 11903)intformal 11903)intnum 11903)isfundamental 11903)isprime 11903)ispseudoprime 11903)issquare 11903)issquarefree 11903)kill 11903)kronecker 11903)lcm 11903)length 11903)lex 11903)lift 11903)lindep 11903)listcreate 11903)listinsert 11903)listkill 11903)listput 11903)listsort 11903)lngamma 11903)log 11903)matadjoint 11903)matalgtobasis 11903)matbasistoalg 11903)matcompanion 11903)matdet 11903)matdetint 11903)matdiagonal 11903)mateigen 11903)mathess 11903)mathilbert 11903)mathnf 11903)mathnfmod 11903)mathnfmodid 11903)matid 11903)matimage 11903)matimagecompl 11903)matindexrank 11903)matintersect 11903)matinverseimage 11903)matisdiagonal 11903)matker 11903)matkerint 11903)matmuldiagonal 11903)matmultodiagonal 11903)matpascal 11903)matrank 11903)matrix 11903)matrixqz 11903)matsize 11903)matsnf 11903)matsolve 11903)matsolvemod 11903)matsupplement 11903)mattranspose 11903)max 11903)min 11903)modreverse 11903)moebius 11903)newtonpoly 11903)next 11903)nextprime 11903)nfalgtobasis 11903)nfbasis 11903)nfbasistoalg 11903)nfdetint 11903)nfdisc 11903)nfeltdiv 11903)nfeltdiveuc 11903)nfeltdivmodpr 11903)nfeltdivrem 11903)nfeltmod 11903)nfeltmul 11903)nfeltmulmodpr 11903)nfeltpow 11903)nfeltpowmodpr 11903)nfeltreduce 11903)nfeltreducemodpr 11903)nfeltval 11903)nffactor 11903)nffactormod 11903)nfgaloisapply 11903)nfgaloisconj 11903)nfhilbert 11903)nfhnf 11903)nfhnfmod 11903)nfinit 11903)nfisideal 11903)nfisincl 11903)nfisisom 11903)nfkermodpr 11903)nfmodprinit 11903)nfnewprec 11903)nfroots 11903)nfrootsof1 11903)nfsnf 11903)nfsolvemodpr 11903)nfsubfields 11903)norm 11903)norml2 11903)numdiv 11903)numerator 11903)numtoperm 11903)omega 11903)padicappr 11903)padicprec 11903)permtonum 11903)plot 11903)plotbox 11903)plotclip 11903)plotcolor 11903)plotcopy 11903)plotcursor 11903)plotdraw 11903)plotfile 11903)ploth 11903)plothraw 11903)plothsizes 11903)plotinit 11903)plotkill 11903)plotlines 11903)plotlinetype 11903)plotmove 11903)plotpoints 11903)plotpointsize 11903)plotpointtype 11903)plotrbox 11903)plotrecth 11903)plotrecthraw 11903)plotrline 11903)plotrmove 11903)plotrpoint 11903)plotscale 11903)plotstring 11903)plotterm 11903)polcoeff 11903)polcompositum 11903)polcyclo 11903)poldegree 11903)poldisc 11903)poldiscreduced 11903)polgalois 11903)polhensellift 11903)polinterpolate 11903)polisirreducible 11903)pollead 11903)pollegendre 11903)polrecip 11903)polred 11903)polredabs 11903)polredord 11903)polresultant 11903)polroots 11903)polrootsmod 11903)polrootspadic 11903)polsturm 11903)polsubcyclo 11903)polsylvestermatrix 11903)polsym 11903)poltchebi 11903)poltschirnhaus 11903)polylog 11903)polzagier 11903)precision 11903)precprime 11903)prime 11903)primes 11903)print 11903)print1 11903)printp 11903)printp1 11903)printtex 11903)prod 11903)prodeuler 11903)prodinf 11903)psdraw 11903)psi 11903)psploth 11903)psplothraw 11903)qfbclassno 11903)qfbcompraw 11903)qfbhclassno 11903)qfbnucomp 11903)qfbnupow 11903)qfbpowraw 11903)qfbprimeform 11903)qfbred 11903)qfgaussred 11903)qfjacobi 11903)qflll 11903)qflllgram 11903)qfminim 11903)qfperfection 11903)qfsign 11903)quadclassunit 11903)quaddisc 11903)quadgen 11903)quadhilbert 11903)quadpoly 11903)quadray 11903)quadregulator 11903)quadunit 11903)quit 11903)random 11903)read 11903)real 11903)removeprimes 11903)reorder 11903)return 11903)rnfalgtobasis 11903)rnfbasis 11903)rnfbasistoalg 11903)rnfcharpoly 11903)rnfconductor 11903)rnfdedekind 11903)rnfdet 11903)rnfdisc 11903)rnfeltabstorel 11903)rnfeltdown 11903)rnfeltreltoabs 11903)rnfeltup 11903)rnfequation 11903)rnfhnfbasis 11903)rnfidealabstorel 11903)rnfidealdown 11903)rnfidealhnf 11903)rnfidealmul 11903)rnfidealnormabs 11903)rnfidealnormrel 11903)rnfidealreltoabs 11903)rnfidealtwoelt 11903)rnfidealup 11903)rnfinit 11903)rnfisfree 11903)rnfisnorm 11903)rnfkummer 11903)rnflllgram 11903)rnfnormgroup 11903)rnfpolred 11903)rnfpolredabs 11903)rnfpseudobasis 11903)rnfsteinitz 11903)round 11903)serconvol 11903)serlaplace 11903)serreverse 11903)setintersect 11903)setisset 11903)setminus 11903)setrand 11903)setsearch 11903)setunion 11903)shift 11903)shiftmul 11903)sigma ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** unexpected character: Mod(7492*7362,_ ^- Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:42:42 2005 Input: Mod(3*(5155^2) + 11711,11903) Mod(7492*7362,11903) Mod(9505^2, 11903) Output: ? Mod(7492, 11903) ? @ 11903)Euler 11903)I 11903)List 11903)Mat 11903)Mod 11903)O 11903)Pi 11903)Pol 11903)Polrev 11903)Qfb 11903)Ser 11903)Set 11903)Str 11903)Vec 11903)abs 11903)acos 11903)acosh 11903)addhelp 11903)addprimes 11903)agm 11903)algdep 11903)alias 11903)allocatemem 11903)arg 11903)asin 11903)asinh 11903)atan 11903)atanh 11903)bernfrac 11903)bernreal 11903)bernvec 11903)besseljh 11903)besselk 11903)bestappr 11903)bezout 11903)bezoutres 11903)bigomega 11903)binary 11903)binomial 11903)bitand 11903)bitneg 11903)bitnegimply 11903)bitor 11903)bittest 11903)bitxor 11903)bnfcertify 11903)bnfclassunit 11903)bnfclgp 11903)bnfdecodemodule 11903)bnfinit 11903)bnfisintnorm 11903)bnfisnorm 11903)bnfisprincipal 11903)bnfissunit 11903)bnfisunit 11903)bnfmake 11903)bnfnarrow 11903)bnfreg 11903)bnfsignunit 11903)bnfsunit 11903)bnfunit 11903)bnrL1 11903)bnrclass 11903)bnrclassno 11903)bnrclassnolist 11903)bnrconductor 11903)bnrconductorofchar 11903)bnrdisc 11903)bnrdisclist 11903)bnrinit 11903)bnrisconductor 11903)bnrisprincipal 11903)bnrrootnumber 11903)bnrstark 11903)break 11903)ceil 11903)centerlift 11903)changevar 11903)charpoly 11903)chinese 11903)component 11903)concat 11903)conj 11903)conjvec 11903)content 11903)contfrac 11903)contfracpnqn 11903)core 11903)coredisc 11903)cos 11903)cosh 11903)cotan 11903)default 11903)denominator 11903)deriv 11903)dilog 11903)dirdiv 11903)direuler 11903)dirmul 11903)dirzetak 11903)divisors 11903)divrem 11903)eint1 11903)elladd 11903)ellak 11903)ellan 11903)ellap 11903)ellbil 11903)ellchangecurve 11903)ellchangepoint 11903)elleisnum 11903)elleta 11903)ellglobalred 11903)ellheight 11903)ellheightmatrix 11903)ellinit 11903)ellisoncurve 11903)ellj 11903)elllocalred 11903)elllseries 11903)ellorder 11903)ellordinate 11903)ellpointtoz 11903)ellpow 11903)ellrootno 11903)ellsigma 11903)ellsub 11903)elltaniyama 11903)elltors 11903)ellwp 11903)ellzeta 11903)ellztopoint 11903)erfc 11903)error 11903)eta 11903)eulerphi 11903)eval 11903)exp 11903)extern 11903)factor 11903)factorback 11903)factorcantor 11903)factorff 11903)factorial 11903)factorint 11903)factormod 11903)factornf 11903)factorpadic 11903)ffinit 11903)fibonacci 11903)floor 11903)for 11903)fordiv 11903)forprime 11903)forstep 11903)forsubgroup 11903)forvec 11903)frac 11903)galoisfixedfield 11903)galoisinit 11903)galoispermtopol 11903)galoissubcyclo 11903)gamma 11903)gammah 11903)gcd 11903)getheap 11903)getrand 11903)getstack 11903)gettime 11903)global 11903)hilbert 11903)hyperu 11903)idealadd 11903)idealaddtoone 11903)idealappr 11903)idealchinese 11903)idealcoprime 11903)idealdiv 11903)idealfactor 11903)idealhnf 11903)idealintersect 11903)idealinv 11903)ideallist 11903)ideallistarch 11903)ideallog 11903)idealmin 11903)idealmul 11903)idealnorm 11903)idealpow 11903)idealprimedec 11903)idealprincipal 11903)idealred 11903)idealstar 11903)idealtwoelt 11903)idealval 11903)ideleprincipal 11903)if 11903)imag 11903)incgam 11903)incgamc 11903)input 11903)install 11903)intformal 11903)intnum 11903)isfundamental 11903)isprime 11903)ispseudoprime 11903)issquare 11903)issquarefree 11903)kill 11903)kronecker 11903)lcm 11903)length 11903)lex 11903)lift 11903)lindep 11903)listcreate 11903)listinsert 11903)listkill 11903)listput 11903)listsort 11903)lngamma 11903)log 11903)matadjoint 11903)matalgtobasis 11903)matbasistoalg 11903)matcompanion 11903)matdet 11903)matdetint 11903)matdiagonal 11903)mateigen 11903)mathess 11903)mathilbert 11903)mathnf 11903)mathnfmod 11903)mathnfmodid 11903)matid 11903)matimage 11903)matimagecompl 11903)matindexrank 11903)matintersect 11903)matinverseimage 11903)matisdiagonal 11903)matker 11903)matkerint 11903)matmuldiagonal 11903)matmultodiagonal 11903)matpascal 11903)matrank 11903)matrix 11903)matrixqz 11903)matsize 11903)matsnf 11903)matsolve 11903)matsolvemod 11903)matsupplement 11903)mattranspose 11903)max 11903)min 11903)modreverse 11903)moebius 11903)newtonpoly 11903)next 11903)nextprime 11903)nfalgtobasis 11903)nfbasis 11903)nfbasistoalg 11903)nfdetint 11903)nfdisc 11903)nfeltdiv 11903)nfeltdiveuc 11903)nfeltdivmodpr 11903)nfeltdivrem 11903)nfeltmod 11903)nfeltmul 11903)nfeltmulmodpr 11903)nfeltpow 11903)nfeltpowmodpr 11903)nfeltreduce 11903)nfeltreducemodpr 11903)nfeltval 11903)nffactor 11903)nffactormod 11903)nfgaloisapply 11903)nfgaloisconj 11903)nfhilbert 11903)nfhnf 11903)nfhnfmod 11903)nfinit 11903)nfisideal 11903)nfisincl 11903)nfisisom 11903)nfkermodpr 11903)nfmodprinit 11903)nfnewprec 11903)nfroots 11903)nfrootsof1 11903)nfsnf 11903)nfsolvemodpr 11903)nfsubfields 11903)norm 11903)norml2 11903)numdiv 11903)numerator 11903)numtoperm 11903)omega 11903)padicappr 11903)padicprec 11903)permtonum 11903)plot 11903)plotbox 11903)plotclip 11903)plotcolor 11903)plotcopy 11903)plotcursor 11903)plotdraw 11903)plotfile 11903)ploth 11903)plothraw 11903)plothsizes 11903)plotinit 11903)plotkill 11903)plotlines 11903)plotlinetype 11903)plotmove 11903)plotpoints 11903)plotpointsize 11903)plotpointtype 11903)plotrbox 11903)plotrecth 11903)plotrecthraw 11903)plotrline 11903)plotrmove 11903)plotrpoint 11903)plotscale 11903)plotstring 11903)plotterm 11903)polcoeff 11903)polcompositum 11903)polcyclo 11903)poldegree 11903)poldisc 11903)poldiscreduced 11903)polgalois 11903)polhensellift 11903)polinterpolate 11903)polisirreducible 11903)pollead 11903)pollegendre 11903)polrecip 11903)polred 11903)polredabs 11903)polredord 11903)polresultant 11903)polroots 11903)polrootsmod 11903)polrootspadic 11903)polsturm 11903)polsubcyclo 11903)polsylvestermatrix 11903)polsym 11903)poltchebi 11903)poltschirnhaus 11903)polylog 11903)polzagier 11903)precision 11903)precprime 11903)prime 11903)primes 11903)print 11903)print1 11903)printp 11903)printp1 11903)printtex 11903)prod 11903)prodeuler 11903)prodinf 11903)psdraw 11903)psi 11903)psploth 11903)psplothraw 11903)qfbclassno 11903)qfbcompraw 11903)qfbhclassno 11903)qfbnucomp 11903)qfbnupow 11903)qfbpowraw 11903)qfbprimeform 11903)qfbred 11903)qfgaussred 11903)qfjacobi 11903)qflll 11903)qflllgram 11903)qfminim 11903)qfperfection 11903)qfsign 11903)quadclassunit 11903)quaddisc 11903)quadgen 11903)quadhilbert 11903)quadpoly 11903)quadray 11903)quadregulator 11903)quadunit 11903)quit 11903)random 11903)read 11903)real 11903)removeprimes 11903)reorder 11903)return 11903)rnfalgtobasis 11903)rnfbasis 11903)rnfbasistoalg 11903)rnfcharpoly 11903)rnfconductor 11903)rnfdedekind 11903)rnfdet 11903)rnfdisc 11903)rnfeltabstorel 11903)rnfeltdown 11903)rnfeltreltoabs 11903)rnfeltup 11903)rnfequation 11903)rnfhnfbasis 11903)rnfidealabstorel 11903)rnfidealdown 11903)rnfidealhnf 11903)rnfidealmul 11903)rnfidealnormabs 11903)rnfidealnormrel 11903)rnfidealreltoabs 11903)rnfidealtwoelt 11903)rnfidealup 11903)rnfinit 11903)rnfisfree 11903)rnfisnorm 11903)rnfkummer 11903)rnflllgram 11903)rnfnormgroup 11903)rnfpolred 11903)rnfpolredabs 11903)rnfpseudobasis 11903)rnfsteinitz 11903)round 11903)serconvol 11903)serlaplace 11903)serreverse 11903)setintersect 11903)setisset 11903)setminus 11903)setrand 11903)setsearch 11903)setunion 11903)shift 11903)shiftmul 11903)sigma ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** unexpected character: Mod(7492*7362,_ ^- Timing: real 0m0.019s user 0m0.013s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:42:46 2005 Input: Mod(3*(5155^2) + 11711,11903) Mod(7492*7362,11903) Mod(9505^2, 11903) Output: ? Mod(7492, 11903) ? @ 11903)Euler 11903)I 11903)List 11903)Mat 11903)Mod 11903)O 11903)Pi 11903)Pol 11903)Polrev 11903)Qfb 11903)Ser 11903)Set 11903)Str 11903)Vec 11903)abs 11903)acos 11903)acosh 11903)addhelp 11903)addprimes 11903)agm 11903)algdep 11903)alias 11903)allocatemem 11903)arg 11903)asin 11903)asinh 11903)atan 11903)atanh 11903)bernfrac 11903)bernreal 11903)bernvec 11903)besseljh 11903)besselk 11903)bestappr 11903)bezout 11903)bezoutres 11903)bigomega 11903)binary 11903)binomial 11903)bitand 11903)bitneg 11903)bitnegimply 11903)bitor 11903)bittest 11903)bitxor 11903)bnfcertify 11903)bnfclassunit 11903)bnfclgp 11903)bnfdecodemodule 11903)bnfinit 11903)bnfisintnorm 11903)bnfisnorm 11903)bnfisprincipal 11903)bnfissunit 11903)bnfisunit 11903)bnfmake 11903)bnfnarrow 11903)bnfreg 11903)bnfsignunit 11903)bnfsunit 11903)bnfunit 11903)bnrL1 11903)bnrclass 11903)bnrclassno 11903)bnrclassnolist 11903)bnrconductor 11903)bnrconductorofchar 11903)bnrdisc 11903)bnrdisclist 11903)bnrinit 11903)bnrisconductor 11903)bnrisprincipal 11903)bnrrootnumber 11903)bnrstark 11903)break 11903)ceil 11903)centerlift 11903)changevar 11903)charpoly 11903)chinese 11903)component 11903)concat 11903)conj 11903)conjvec 11903)content 11903)contfrac 11903)contfracpnqn 11903)core 11903)coredisc 11903)cos 11903)cosh 11903)cotan 11903)default 11903)denominator 11903)deriv 11903)dilog 11903)dirdiv 11903)direuler 11903)dirmul 11903)dirzetak 11903)divisors 11903)divrem 11903)eint1 11903)elladd 11903)ellak 11903)ellan 11903)ellap 11903)ellbil 11903)ellchangecurve 11903)ellchangepoint 11903)elleisnum 11903)elleta 11903)ellglobalred 11903)ellheight 11903)ellheightmatrix 11903)ellinit 11903)ellisoncurve 11903)ellj 11903)elllocalred 11903)elllseries 11903)ellorder 11903)ellordinate 11903)ellpointtoz 11903)ellpow 11903)ellrootno 11903)ellsigma 11903)ellsub 11903)elltaniyama 11903)elltors 11903)ellwp 11903)ellzeta 11903)ellztopoint 11903)erfc 11903)error 11903)eta 11903)eulerphi 11903)eval 11903)exp 11903)extern 11903)factor 11903)factorback 11903)factorcantor 11903)factorff 11903)factorial 11903)factorint 11903)factormod 11903)factornf 11903)factorpadic 11903)ffinit 11903)fibonacci 11903)floor 11903)for 11903)fordiv 11903)forprime 11903)forstep 11903)forsubgroup 11903)forvec 11903)frac 11903)galoisfixedfield 11903)galoisinit 11903)galoispermtopol 11903)galoissubcyclo 11903)gamma 11903)gammah 11903)gcd 11903)getheap 11903)getrand 11903)getstack 11903)gettime 11903)global 11903)hilbert 11903)hyperu 11903)idealadd 11903)idealaddtoone 11903)idealappr 11903)idealchinese 11903)idealcoprime 11903)idealdiv 11903)idealfactor 11903)idealhnf 11903)idealintersect 11903)idealinv 11903)ideallist 11903)ideallistarch 11903)ideallog 11903)idealmin 11903)idealmul 11903)idealnorm 11903)idealpow 11903)idealprimedec 11903)idealprincipal 11903)idealred 11903)idealstar 11903)idealtwoelt 11903)idealval 11903)ideleprincipal 11903)if 11903)imag 11903)incgam 11903)incgamc 11903)input 11903)install 11903)intformal 11903)intnum 11903)isfundamental 11903)isprime 11903)ispseudoprime 11903)issquare 11903)issquarefree 11903)kill 11903)kronecker 11903)lcm 11903)length 11903)lex 11903)lift 11903)lindep 11903)listcreate 11903)listinsert 11903)listkill 11903)listput 11903)listsort 11903)lngamma 11903)log 11903)matadjoint 11903)matalgtobasis 11903)matbasistoalg 11903)matcompanion 11903)matdet 11903)matdetint 11903)matdiagonal 11903)mateigen 11903)mathess 11903)mathilbert 11903)mathnf 11903)mathnfmod 11903)mathnfmodid 11903)matid 11903)matimage 11903)matimagecompl 11903)matindexrank 11903)matintersect 11903)matinverseimage 11903)matisdiagonal 11903)matker 11903)matkerint 11903)matmuldiagonal 11903)matmultodiagonal 11903)matpascal 11903)matrank 11903)matrix 11903)matrixqz 11903)matsize 11903)matsnf 11903)matsolve 11903)matsolvemod 11903)matsupplement 11903)mattranspose 11903)max 11903)min 11903)modreverse 11903)moebius 11903)newtonpoly 11903)next 11903)nextprime 11903)nfalgtobasis 11903)nfbasis 11903)nfbasistoalg 11903)nfdetint 11903)nfdisc 11903)nfeltdiv 11903)nfeltdiveuc 11903)nfeltdivmodpr 11903)nfeltdivrem 11903)nfeltmod 11903)nfeltmul 11903)nfeltmulmodpr 11903)nfeltpow 11903)nfeltpowmodpr 11903)nfeltreduce 11903)nfeltreducemodpr 11903)nfeltval 11903)nffactor 11903)nffactormod 11903)nfgaloisapply 11903)nfgaloisconj 11903)nfhilbert 11903)nfhnf 11903)nfhnfmod 11903)nfinit 11903)nfisideal 11903)nfisincl 11903)nfisisom 11903)nfkermodpr 11903)nfmodprinit 11903)nfnewprec 11903)nfroots 11903)nfrootsof1 11903)nfsnf 11903)nfsolvemodpr 11903)nfsubfields 11903)norm 11903)norml2 11903)numdiv 11903)numerator 11903)numtoperm 11903)omega 11903)padicappr 11903)padicprec 11903)permtonum 11903)plot 11903)plotbox 11903)plotclip 11903)plotcolor 11903)plotcopy 11903)plotcursor 11903)plotdraw 11903)plotfile 11903)ploth 11903)plothraw 11903)plothsizes 11903)plotinit 11903)plotkill 11903)plotlines 11903)plotlinetype 11903)plotmove 11903)plotpoints 11903)plotpointsize 11903)plotpointtype 11903)plotrbox 11903)plotrecth 11903)plotrecthraw 11903)plotrline 11903)plotrmove 11903)plotrpoint 11903)plotscale 11903)plotstring 11903)plotterm 11903)polcoeff 11903)polcompositum 11903)polcyclo 11903)poldegree 11903)poldisc 11903)poldiscreduced 11903)polgalois 11903)polhensellift 11903)polinterpolate 11903)polisirreducible 11903)pollead 11903)pollegendre 11903)polrecip 11903)polred 11903)polredabs 11903)polredord 11903)polresultant 11903)polroots 11903)polrootsmod 11903)polrootspadic 11903)polsturm 11903)polsubcyclo 11903)polsylvestermatrix 11903)polsym 11903)poltchebi 11903)poltschirnhaus 11903)polylog 11903)polzagier 11903)precision 11903)precprime 11903)prime 11903)primes 11903)print 11903)print1 11903)printp 11903)printp1 11903)printtex 11903)prod 11903)prodeuler 11903)prodinf 11903)psdraw 11903)psi 11903)psploth 11903)psplothraw 11903)qfbclassno 11903)qfbcompraw 11903)qfbhclassno 11903)qfbnucomp 11903)qfbnupow 11903)qfbpowraw 11903)qfbprimeform 11903)qfbred 11903)qfgaussred 11903)qfjacobi 11903)qflll 11903)qflllgram 11903)qfminim 11903)qfperfection 11903)qfsign 11903)quadclassunit 11903)quaddisc 11903)quadgen 11903)quadhilbert 11903)quadpoly 11903)quadray 11903)quadregulator 11903)quadunit 11903)quit 11903)random 11903)read 11903)real 11903)removeprimes 11903)reorder 11903)return 11903)rnfalgtobasis 11903)rnfbasis 11903)rnfbasistoalg 11903)rnfcharpoly 11903)rnfconductor 11903)rnfdedekind 11903)rnfdet 11903)rnfdisc 11903)rnfeltabstorel 11903)rnfeltdown 11903)rnfeltreltoabs 11903)rnfeltup 11903)rnfequation 11903)rnfhnfbasis 11903)rnfidealabstorel 11903)rnfidealdown 11903)rnfidealhnf 11903)rnfidealmul 11903)rnfidealnormabs 11903)rnfidealnormrel 11903)rnfidealreltoabs 11903)rnfidealtwoelt 11903)rnfidealup 11903)rnfinit 11903)rnfisfree 11903)rnfisnorm 11903)rnfkummer 11903)rnflllgram 11903)rnfnormgroup 11903)rnfpolred 11903)rnfpolredabs 11903)rnfpseudobasis 11903)rnfsteinitz 11903)round 11903)serconvol 11903)serlaplace 11903)serreverse 11903)setintersect 11903)setisset 11903)setminus 11903)setrand 11903)setsearch 11903)setunion 11903)shift 11903)shiftmul 11903)sigma ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: *** unexpected character: Mod(7492*7362,_ ^- Timing: real 0m0.019s user 0m0.012s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:43:05 2005 Input: Mod(9505^2, 11903) Output: ? Mod(1255, 11903) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Thu Jun 2 03:44:16 2005 Input: Mod(-9055, 11903) Output: ? Mod(2848, 11903) ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:09:25 2005 Input: x=4 x^4+2x+36 Output: ? 4 ? 258 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+36. Timing: real 0m0.272s user 0m0.010s sys 0m0.014s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:09:57 2005 Input: x=0 x^4+2x+36 Output: ? 0 ? 2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+36. Timing: real 0m0.019s user 0m0.012s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:10:01 2005 Input: x=3 x^4+2x+36 Output: ? 3 ? 83 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+36. Timing: real 0m0.020s user 0m0.010s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:10:07 2005 Input: x=1 x^4+2x+36 Output: ? 1 ? 3 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+36. Timing: real 0m0.017s user 0m0.008s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:10:21 2005 Input: x=1 x^4+2x+36 Output: ? 1 ? 3 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+36. Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:10:25 2005 Input: x=1 x^4+2x+36 Output: ? 1 ? 3 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+36. Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:10:29 2005 Input: x=0 x^4+2x+36 Output: ? 0 ? 2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+36. Timing: real 0m0.017s user 0m0.005s sys 0m0.012s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:10:35 2005 Input: x=0 (x^4+2x+36) Output: ? 0 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (x^4+2x+36) ^----- Timing: real 0m0.019s user 0m0.009s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:10:52 2005 Input: x=0 x^4+2*x+36 Output: ? 0 ? 36 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.012s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:10:58 2005 Input: x=4 x^4+2*x+36 Output: ? 4 ? 300 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:12:26 2005 Input: x=29 x^4+2*x+36 Output: ? 29 ? 707375 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:13:10 2005 Input: x=29 mod(x^4+2*x+36,7) Output: ? 29 ? ? Errors (if any) and Timing Info: *** obsolete function: mod(x^4+2*x+36,7) ^----------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.018s user 0m0.006s sys 0m0.013s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:13:26 2005 Input: x=29 Mod(x^4+2*x+36,7) Output: ? 29 ? Mod(4, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:13:33 2005 Input: x=0 Mod(x^4+2*x+36,7) Output: ? 0 ? Mod(1, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:13:41 2005 Input: x=1 Mod(x^4+2*x+36,7) Output: ? 1 ? Mod(4, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:13:46 2005 Input: x=2 Mod(x^4+2*x+36,7) Output: ? 2 ? Mod(0, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:13:55 2005 Input: x=3 Mod(x^4+2*x+36,7) Output: ? 3 ? Mod(4, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.011s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:14:03 2005 Input: x=4 Mod(x^4+2*x+36,7) Output: ? 4 ? Mod(6, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.010s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:14:07 2005 Input: x=5 Mod(x^4+2*x+36,7) Output: ? 5 ? Mod(6, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '132.230' ************** PARI ***************** Host 132.230.129.34 (132.230.129.34) Time: Thu Jun 2 10:14:13 2005 Input: x=6 Mod(x^4+2*x+36,7) Output: ? 6 ? Mod(0, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.013s sys 0m0.005s '194.214' ************** PARI ***************** Host 194.214.217.17 (194.214.217.17) Time: Thu Jun 2 11:36:14 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Fri Jun 3 02:26:03 2005 Input: e=ellinit([0,0,0,11711,1681]*Mod(1,11903)); P=[5155,10730] e.isoncurve(e,p) Output: ? ? [5155, 10730] ? ? Errors (if any) and Timing Info: *** Warning: unused characters: (e,p). *** unknown member function: e.isoncurve(e,p) ^-------------- Timing: real 0m0.065s user 0m0.012s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Fri Jun 3 02:26:30 2005 Input: e=ellinit([0,0,0,11711,1681]*Mod(1,11903)); P=[5155,10730] e.isOncurve(e,p) Output: ? ? [5155, 10730] ? ? Errors (if any) and Timing Info: *** Warning: unused characters: (e,p). *** unknown member function: e.isOncurve(e,p) ^-------------- Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Fri Jun 3 02:26:35 2005 Input: e=ellinit([0,0,0,11711,1681]*Mod(1,11903)); P=[5155,10730] e.isOncurve(e,P) Output: ? ? [5155, 10730] ? ? Errors (if any) and Timing Info: *** Warning: unused characters: (e,P). *** unknown member function: e.isOncurve(e,P) ^-------------- Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Fri Jun 3 02:27:12 2005 Input: e=ellinit([0,0,0,11711,1681]*Mod(1,11903)); P=[5155,10730] ellisoncurve(e,P) Output: ? ? [5155, 10730] ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 05:51:19 2005 Input: 25*(29^2)+0*(29)+7 Output: ? 21032 ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.010s sys 0m0.007s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 05:52:49 2005 Input: 11*(29^2)+4*(29)+13 Output: ? 9380 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 05:53:03 2005 Input: 25*(29^2)+0*(29)+7 Output: ? 21032 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.009s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 05:54:15 2005 Input: 19*(29^2)+7*(29)+4 Output: ? 16186 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 05:54:26 2005 Input: 14*(29^2)+17*(29)+8 Output: ? 12275 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 05:54:38 2005 Input: 4*(29^2)+26*(29)+26 Output: ? 4144 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 05:55:51 2005 Input: Mod(21032,22499)^1291 Output: ? Mod(18607, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.010s sys 0m0.009s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 05:56:51 2005 Input: Mod(9380,22499)^1291 Output: ? Mod(19484, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 05:57:06 2005 Input: Mod(16186,22499)^1291 Output: ? Mod(10802, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.011s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 05:57:25 2005 Input: Mod(12275,22499)^1291 Output: ? Mod(10771, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 05:57:41 2005 Input: MMod(4144,22499)^1291 Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: MMod(4144,22499)^129 ^-------------------- Timing: real 0m0.017s user 0m0.007s sys 0m0.011s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 05:58:08 2005 Input: MMod(4144,22499)^1291 Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: MMod(4144,22499)^129 ^-------------------- Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 05:58:15 2005 Input: Mod(4144,22499)^1291 Output: ? Mod(19841, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:02:07 2005 Input: base(10,29,18607) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: base(10,29,18607) ^----------------- Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:02:54 2005 Input: x=Mod(18607,29^2) Output: ? Mod(105, 841) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:03:10 2005 Input: x=Mod(18607,29^3) Output: ? Mod(18607, 24389) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:03:15 2005 Input: x=Mod(18607,29^2) Output: ? Mod(105, 841) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:03:29 2005 Input: x=Mod(18607,29^2) 18607/29 Output: ? Mod(105, 841) ? 18607/29 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.012s sys 0m0.006s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:03:36 2005 Input: x=Mod(18607,29^2^2) 18607/29^2 Output: ? Mod(18607, 707281) ? 18607/841 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.010s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:03:43 2005 Input: x=Mod(18607,29^2^2) Divide(18607/29^2) Output: ? Mod(18607, 707281) ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Divide(18607/29^2) ^------------------ Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:03:48 2005 Input: x=Mod(18607,29^2^2) divide(18607/29^2) Output: ? Mod(18607, 707281) ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: divide(18607/29^2) ^------------------ Timing: real 0m0.018s user 0m0.013s sys 0m0.004s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:03:53 2005 Input: x=Mod(18607,29^2^2) (18607/29^2) Output: ? Mod(18607, 707281) ? 18607/841 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:09:01 2005 Input: factor(22499) Output: ? [149 1] [151 1] ? Errors (if any) and Timing Info: Timing: real 0m0.049s user 0m0.009s sys 0m0.010s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:10:50 2005 Input: 167*169 Output: ? 28223 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:10:56 2005 Input: 167*169 168*168 Output: ? 28223 ? 28224 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.013s sys 0m0.005s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:11:37 2005 Input: Mod(1/1291,22200) Output: ? Mod(12811, 22200) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.006s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:12:15 2005 Input: Mod(12811*1291,22200) Output: ? Mod(1, 22200) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.012s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:14:30 2005 Input: 7*(29^2)+0*(29)+23 Output: ? 5910 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:14:44 2005 Input: 20*(29^2)+2*(29)+22 Output: ? 16900 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:15:00 2005 Input: 9*(29^2)+8*(29)+27 Output: ? 7828 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:15:13 2005 Input: 5*(29^2)+19*(29)+9 Output: ? 4765 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.008s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:15:53 2005 Input: Mod(5910,22499)^12811 Output: ? Mod(9695, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.009s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:16:43 2005 Input: Mod(16900,22499)^12811 Output: ? Mod(5642, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.007s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:16:53 2005 Input: Mod(7282,22499)^12811 Output: ? Mod(9858, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:17:02 2005 Input: Mod(4765,22499)^12811 Output: ? Mod(3144, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:25:52 2005 Input: Mod(4765,22499)^12811 Mod(18607,22499)^12811 Output: ? Mod(3144, 22499) ? Mod(21032, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:27:47 2005 Input: 8*(29^2)+1*(29)+24 Output: ? 6781 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.011s sys 0m0.006s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:28:03 2005 Input: 8*(29^2)+1*(29)+24 Mod(6781,22499)^12811 Output: ? 6781 ? Mod(15714, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.014s sys 0m0.006s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:30:57 2005 Input: 5*(30^2)+19*(30)+9 Mod(6781,22499)^12811 Output: ? 5079 ? Mod(15714, 22499) ? Errors (if any) and Timing Info: Timing: real 0m1.323s user 0m0.008s sys 0m0.012s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:31:01 2005 Input: 5*(30^2)+19*(30)+9 Mod(6781,22499)^12811 Output: ? 5079 ? Mod(15714, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.010s sys 0m0.011s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:31:08 2005 Input: 5*(30^2)+19*(30)+9 Mod(5079,22499)^12811 Output: ? 5079 ? Mod(13301, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.012s sys 0m0.009s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:37:42 2005 Input: 5*(30^2)+19*(30)+9 Mod(5079,22499)^12811 14,23,11=OXL=PYM (Mod(5910,22499)^1291)^12811 Output: ? 5079 ? Mod(13301, 22499) ? 14 ? ? Mod(5910, 22499) ? Errors (if any) and Timing Info: *** Warning: unused characters: ,23,11=OXL=PYM. Timing: real 0m0.076s user 0m0.006s sys 0m0.013s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:39:56 2005 Input: 3*(29^2)+21*(29)+12 Output: ? 3144 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.009s sys 0m0.011s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:40:29 2005 Input: 5*(29^2)+19*(29)+9 Output: ? 4765 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.011s sys 0m0.008s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:43:29 2005 Input: 7*(27^2)+0*(27)+23 Output: ? 5126 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.007s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:43:55 2005 Input: 7*(27^2)+0*(27)+23 Mod(5126,22499)^12811 Output: ? 5126 ? Mod(11015, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.011s sys 0m0.012s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:45:15 2005 Input: 20*(27^2)+2*(27)+22 Mod(5126,22499)^12811 15,2,26=PC Output: ? 14656 ? Mod(11015, 22499) ? 15 ? Errors (if any) and Timing Info: *** Warning: unused characters: ,2,26=PC. Timing: real 0m0.301s user 0m0.013s sys 0m0.012s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 06:45:24 2005 Input: 20*(27^2)+2*(27)+22 Mod(14656,22499)^12811 15,2,26=PC Output: ? 14656 ? Mod(16884, 22499) ? 15 ? Errors (if any) and Timing Info: *** Warning: unused characters: ,2,26=PC. Timing: real 0m0.021s user 0m0.009s sys 0m0.012s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Fri Jun 3 09:24:12 2005 Input: Mod(149,22499)^1291 Output: ? Mod(149, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.310s user 0m0.013s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Fri Jun 3 09:24:23 2005 Input: Mod(149,22499)^1290 Output: ? Mod(11175, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.009s sys 0m0.008s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Fri Jun 3 09:24:28 2005 Input: Mod(149,22499)^1291 Output: ? Mod(149, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.108s user 0m0.012s sys 0m0.004s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Fri Jun 3 09:24:56 2005 Input: Mod(149,22499)^101 Output: ? Mod(17582, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Fri Jun 3 09:25:12 2005 Input: Mod(149,22499)^101 Mod(1/101,22200) Output: ? Mod(17582, 22499) ? Mod(21101, 22200) ? Errors (if any) and Timing Info: Timing: real 0m0.140s user 0m0.009s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Fri Jun 3 09:25:25 2005 Input: Mod(149,22499)^101 Mod(1/101,22200) 148*150 Output: ? Mod(17582, 22499) ? Mod(21101, 22200) ? 22200 ? Errors (if any) and Timing Info: Timing: real 0m0.038s user 0m0.011s sys 0m0.007s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Fri Jun 3 09:30:44 2005 Input: (Mod(149,22499)^101)^21101 Mod(1/101,22200) Output: ? Mod(149, 22499) ? Mod(21101, 22200) ? Errors (if any) and Timing Info: Timing: real 0m0.505s user 0m0.009s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Fri Jun 3 09:30:44 2005 Input: (Mod(149,22499)^101) Mod(1/101,22200) Output: ? Mod(17582, 22499) ? Mod(21101, 22200) ? Errors (if any) and Timing Info: Timing: real 0m0.401s user 0m0.008s sys 0m0.008s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Fri Jun 3 09:30:55 2005 Input: Mod(149,22499)^101 Mod(1/101,22200) Output: ? Mod(17582, 22499) ? Mod(21101, 22200) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Fri Jun 3 09:31:16 2005 Input: Mod(149,22499)^101 Mod(17582,22499)^21101 Mod(1/101,22200) Output: ? Mod(17582, 22499) ? Mod(149, 22499) ? Mod(21101, 22200) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Fri Jun 3 09:31:45 2005 Input: Mod(149,22499)^(101*21101) Mod(17582,22499)^ Mod(1/101,22200) Output: ? Mod(149, 22499) ? ? Mod(21101, 22200) ? Errors (if any) and Timing Info: *** unexpected character: Mod(17582,22499)^ ^ Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 15:37:13 2005 Input: 6*27*27+4*27+7 Output: ? 4489 ? Errors (if any) and Timing Info: Timing: real 0m0.058s user 0m0.013s sys 0m0.004s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 15:37:38 2005 Input: 6*27*27+4*27+7 Mod(4489,22499)^1291 Output: ? 4489 ? Mod(7828, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.007s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 15:38:38 2005 Input: 9*(29^2)+8*(29)+27 Mod(4489,22499)^1291 Output: ? 7828 ? Mod(7828, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.011s sys 0m0.006s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 15:39:07 2005 Input: Mod(7828,22499)^12811 Output: ? Mod(4489, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 15:40:41 2005 Input: 25*(27^2)+0*(27)+7 11*(27^2)+4*(27)+13 19*(27^2)+7*(27)+4 14*(27^2)+17*(27)+8 4*(27^2)+26*(27)+26 Output: ? 18232 ? 8140 ? 14044 ? 10673 ? 3644 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '84.159.' ************** PARI ***************** Host 84.159.166.236 (84.159.166.236) Time: Fri Jun 3 15:42:10 2005 Input: Mod(18232,22499)^1291 Mod(8140,22499)^1291 Mod(14044,22499)^1291 Mod(10673,22499)^1291 Mod(3644,22499)^1291 Output: ? Mod(10232, 22499) ? Mod(22126, 22499) ? Mod(5286, 22499) ? Mod(6034, 22499) ? Mod(1633, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.014s sys 0m0.004s '200.119' ************** PARI ***************** Host 200.119.48.232 (200.119.48.232) Time: Sat Jun 4 10:17:42 2005 Input: 2+1 Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.498s user 0m0.010s sys 0m0.007s '80.58.3' ************** PARI ***************** Host 80.58.33.107 (80.58.33.107) Time: Sat Jun 4 14:07:28 2005 Input: P:=PolynomialRing(Integers()); G9:= ext< GF(3) | 2+2*x+x^2 >; P:=PolynomialRing(Integers()); MinimalPolynomial(a^2); (x-a)*(x-a^3); Output: ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: P:=PolynomialRing(Int ^-------------------- *** unexpected character: G9:=ext:=PolynomialRing(Int ^-------------------- *** expected character: ',' instead of: MinimalPolynomial(a^2); ^---- Timing: real 0m0.047s user 0m0.009s sys 0m0.008s '80.58.3' ************** PARI ***************** Host 80.58.33.107 (80.58.33.107) Time: Sat Jun 4 14:08:22 2005 Input: P:=PolynomialRing(Integers()) G9:= ext< GF(3) | 2+2*x+x^2 >; b:= (x-a)*(x-a^3) Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: P:=PolynomialRing(Int ^-------------------- *** unexpected character: G9:=ext Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.046s user 0m0.012s sys 0m0.006s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:34:41 2005 Input: Mod(32,13) Output: ? Mod(6, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.038s user 0m0.010s sys 0m0.008s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:35:09 2005 Input: Mod(128,13) Output: ? Mod(11, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:35:27 2005 Input: Mod(256,13) Output: ? Mod(9, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:35:34 2005 Input: Mod(512,13) Output: ? Mod(5, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.007s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:35:51 2005 Input: Mod(1024,13) Output: ? Mod(10, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.008s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:36:04 2005 Input: Mod(2048,13) Output: ? Mod(7, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:36:15 2005 Input: Mod(4096,13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:37:01 2005 Input: Mod(531441,13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.012s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:38:33 2005 Input: Mod(5^12,13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.047s user 0m0.010s sys 0m0.008s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:39:20 2005 Input: Mod(5^3,13) Output: ? Mod(8, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:39:25 2005 Input: Mod(5^4,13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:40:11 2005 Input: Mod(6^12,13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:40:16 2005 Input: Mod(6^12,13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.007s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:40:30 2005 Input: Mod(6^3,13) Output: ? Mod(8, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:40:36 2005 Input: Mod(6^4,13) Output: ? Mod(9, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:40:42 2005 Input: Mod(6^5,13) Output: ? Mod(2, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:40:48 2005 Input: Mod(6^6,13) Output: ? Mod(12, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:40:54 2005 Input: Mod(6^7,13) Output: ? Mod(7, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:41:00 2005 Input: Mod(6^8,13) Output: ? Mod(3, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:41:06 2005 Input: Mod(6^9,13) Output: ? Mod(5, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:41:12 2005 Input: Mod(6^10,13) Output: ? Mod(4, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:41:18 2005 Input: Mod(6^11,13) Output: ? Mod(11, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:41:23 2005 Input: Mod(6^12,13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:41:55 2005 Input: Mod(7^12,13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:42:04 2005 Input: Mod(7^2,13) Output: ? Mod(10, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:42:11 2005 Input: Mod(7^3,13) Output: ? Mod(5, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:42:16 2005 Input: Mod(7^4,13) Output: ? Mod(9, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:42:22 2005 Input: Mod(7^5,13) Output: ? Mod(11, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:42:27 2005 Input: Mod(7^6,13) Output: ? Mod(12, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.008s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:42:32 2005 Input: Mod(7^7,13) Output: ? Mod(6, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.011s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:42:38 2005 Input: Mod(7^8,13) Output: ? Mod(3, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:42:45 2005 Input: Mod(7^9,13) Output: ? Mod(8, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.007s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:42:52 2005 Input: Mod(7^10,13) Output: ? Mod(4, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.006s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:42:57 2005 Input: Mod(7^11,13) Output: ? Mod(2, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:43:02 2005 Input: Mod(7^12,13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:43:36 2005 Input: Mod(7^12,13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:43:42 2005 Input: Mod(10^12,13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:43:49 2005 Input: Mod(11^12,13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.116s user 0m0.010s sys 0m0.007s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:44:06 2005 Input: Mod(11^2,13) Output: ? Mod(4, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.005s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:44:13 2005 Input: Mod(11^3,13) Output: ? Mod(5, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:44:18 2005 Input: Mod(11^4,13) Output: ? Mod(3, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.008s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:44:24 2005 Input: Mod(11^5,13) Output: ? Mod(7, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:44:37 2005 Input: Mod(10^2,13) Output: ? Mod(9, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.007s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:44:43 2005 Input: Mod(10^3,13) Output: ? Mod(12, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:44:47 2005 Input: Mod(10^4,13) Output: ? Mod(3, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:44:53 2005 Input: Mod(10^5,13) Output: ? Mod(4, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:44:58 2005 Input: Mod(10^6,13) Output: ? Mod(1, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:45:57 2005 Input: Mod(11^7,13) Output: ? Mod(2, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.011s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:46:02 2005 Input: Mod(11^6,13) Output: ? Mod(12, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:46:08 2005 Input: Mod(11^8,13) Output: ? Mod(9, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:46:13 2005 Input: Mod(11^9,13) Output: ? Mod(8, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:46:21 2005 Input: Mod(11^10,13) Output: ? Mod(10, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '211.26.' ************** PARI ***************** Host 211.26.114.129 (211.26.114.129) Time: Sun Jun 5 21:46:26 2005 Input: Mod(11^11,13) Output: ? Mod(6, 13) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '129.72.' ************** PARI ***************** Host 129.72.70.115 (129.72.70.115) Time: Sun Jun 5 23:32:22 2005 Input: factor(4654678645435156486797464321546794543165467943513) Output: ? [5573389 1] [710191008343 1] [1412597223139 1] [832485790428921721 1] ? Errors (if any) and Timing Info: Timing: real 0m0.467s user 0m0.316s sys 0m0.028s '203.144' ************** PARI ***************** Host 203.144.160.247 (203.144.160.247) Time: Mon Jun 6 02:31:13 2005 Input: polgalois(x^5-2) Output: ? [20, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.015s sys 0m0.009s '203.144' ************** PARI ***************** Host 203.144.160.247 (203.144.160.247) Time: Mon Jun 6 02:33:46 2005 Input: polgalois(x^5+15*x+12) Output: ? [20, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.016s sys 0m0.010s '203.144' ************** PARI ***************** Host 203.144.160.247 (203.144.160.247) Time: Mon Jun 6 02:34:10 2005 Input: polgalois(x^5-5*x+12) Output: ? [10, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.027s sys 0m0.009s '203.144' ************** PARI ***************** Host 203.144.160.247 (203.144.160.247) Time: Mon Jun 6 02:35:00 2005 Input: polgalois(x^5-110*x^3-55*x^2+2310*x+979) Output: ? [5, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.016s sys 0m0.009s '203.144' ************** PARI ***************** Host 203.144.160.247 (203.144.160.247) Time: Mon Jun 6 02:38:54 2005 Input: polgalois(2*x^5-110*x^3-55*x^2+2310*x+979) Output: ? [120, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.017s sys 0m0.010s '203.144' ************** PARI ***************** Host 203.144.160.247 (203.144.160.247) Time: Mon Jun 6 02:49:19 2005 Input: polgalois(X^5 - X^4 - X^2 + X - 1) Output: ? [120, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.014s sys 0m0.009s '203.144' ************** PARI ***************** Host 203.144.160.246 (203.144.160.246) Time: Mon Jun 6 02:52:07 2005 Input: polgalois(x^4-x-10) Output: ? [24, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.017s sys 0m0.005s '67.185.' ************** PARI ***************** Host 67.185.98.19 (67.185.98.19) Time: Mon Jun 6 03:56:16 2005 Input: x = mod(3,1) x = mod(4,2) x = mod(5,3) x = mod(5,4) x = mod(0,7) Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** obsolete function: x=mod(3,1) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** obsolete function: x=mod(4,2) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** obsolete function: x=mod(5,3) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** obsolete function: x=mod(5,4) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** obsolete function: x=mod(0,7) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '67.185.' ************** PARI ***************** Host 67.185.98.19 (67.185.98.19) Time: Mon Jun 6 03:57:07 2005 Input: x = Mod(3,1) x = Mod(4,2) x = Mod(5,3) x = Mod(5,4) x = Mod(0,7) Output: ? Mod(0, 1) ? Mod(0, 2) ? Mod(2, 3) ? Mod(1, 4) ? Mod(0, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.009s '67.185.' ************** PARI ***************** Host 67.185.98.19 (67.185.98.19) Time: Mon Jun 6 03:58:01 2005 Input: x = Mod(1,3) x = Mod(2,4) x = Mod(3,5) x = Mod(4,6) x = Mod(0,7) Output: ? Mod(1, 3) ? Mod(2, 4) ? Mod(3, 5) ? Mod(4, 6) ? Mod(0, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.006s '67.185.' ************** PARI ***************** Host 67.185.98.19 (67.185.98.19) Time: Mon Jun 6 03:58:38 2005 Input: Mod(1,3) Mod(2,4) Mod(3,5) Mod(4,6) Mod(0,7) Output: ? Mod(1, 3) ? Mod(2, 4) ? Mod(3, 5) ? Mod(4, 6) ? Mod(0, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '193.205' ************** PARI ***************** Host 193.205.75.113 (193.205.75.113) Time: Mon Jun 6 05:25:43 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 12:52:19 2005 Input: x=1 y=2 z=3 x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? 1 ? 2 ? 3 ? 7 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.218s user 0m0.010s sys 0m0.015s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 12:53:19 2005 Input: x=1+2^(1/2) y=1+2^(1/2) z=4+2^(1/2)+2^(1/2) x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? 2.4142135623730950488016887242096980785 ? 2.4142135623730950488016887242096980785 ? 6.8284271247461900976033774484193961571 ? 27.313708498984760390413509793677584628 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.056s user 0m0.011s sys 0m0.007s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 12:54:02 2005 Input: x=1+2^(1/2) y=1+2^(1/2) z=-4+2^(1/2)+2^(1/2) x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? 2.4142135623730950488016887242096980785 ? 2.4142135623730950488016887242096980785 ? -1.1715728752538099023966225515806038428 ? 20.686291501015239609586490206322415371 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 12:54:08 2005 Input: x=1+2^(1/2) y=1+2^(1/2) z=-4-2^(1/2)+2^(1/2) x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? 2.4142135623730950488016887242096980785 ? 2.4142135623730950488016887242096980785 ? -4.0000000000000000000000000000000000000 ? 48.970562748477140585620264690516376942 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 12:54:14 2005 Input: x=1+2^(1/2) y=1+2^(1/2) z=-4-2^(1/2)-2^(1/2) x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? 2.4142135623730950488016887242096980785 ? 2.4142135623730950488016887242096980785 ? -6.8284271247461900976033774484193961571 ? 93.254833995939041561654039174710338514 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 12:57:53 2005 Input: x=-3+6^(1/2) y=-3+6^(1/2) z=-4-6^(1/2)-6^(1/2) x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? -0.55051025721682190180271592529410860804 ? -0.55051025721682190180271592529410860804 ? -8.8989794855663561963945681494117827839 ? 71.999999999999999999999999999999999999 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 12:58:14 2005 Input: x=-3+6^(1/2) y=-3+6^(1/2) z=-4+6^(1/2)+6^(1/2) x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? -0.55051025721682190180271592529410860804 ? -0.55051025721682190180271592529410860804 ? 0.89897948556635619639456814941178278391 ? 4.4040820577345752144217274023528688642 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 12:58:53 2005 Input: x=-3-6^(1/2) y=-3-6^(1/2) z=-4-6^(1/2)-6^(1/2) x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? -5.4494897427831780981972840747058913919 ? -5.4494897427831780981972840747058913919 ? -8.8989794855663561963945681494117827839 ? 43.595917942265424785578272597647131135 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.018s user 0m0.011s sys 0m0.008s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 12:58:55 2005 Input: x=-3-6^(1/2) y=-3-6^(1/2) z=-4-6^(1/2)-6^(1/2) x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? -5.4494897427831780981972840747058913919 ? -5.4494897427831780981972840747058913919 ? -8.8989794855663561963945681494117827839 ? 43.595917942265424785578272597647131135 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 12:59:19 2005 Input: z=-4-6^(1/2)-6^(1/2) x=z/2-1 x=y/2-1 x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? -8.8989794855663561963945681494117827839 ? -5.4494897427831780981972840747058913919 ? 1/2*y - 1 ? 5/4*y^2 + 12.348469228349534294591852224117674175*y + 73.292856398964493374761977045882479487 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.033s user 0m0.012s sys 0m0.006s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 12:59:43 2005 Input: z=-4-6^(1/2)-6^(1/2) x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? -8.8989794855663561963945681494117827839 ? -5.4494897427831780981972840747058913919 ? -5.4494897427831780981972840747058913919 ? 43.595917942265424785578272597647131135 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:00:31 2005 Input: z=0.89897948556635619639456814941178 x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? 0.89897948556635619639456814941177999999 ? -0.55051025721682190180271592529411000000 ? -0.55051025721682190180271592529411000000 ? 4.4040820577345752144217274023528663615 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:03:24 2005 Input: z=0 x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? 0 ? -1 ? -1 ? 4 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:03:30 2005 Input: z=1 x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? 1 ? -1/2 ? -1/2 ? 9/2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:03:34 2005 Input: z=2 x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? 2 ? 0 ? 0 ? 6 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.018s user 0m0.010s sys 0m0.007s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:03:39 2005 Input: z=3 x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? 3 ? 1/2 ? 1/2 ? 17/2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.018s user 0m0.009s sys 0m0.008s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:03:43 2005 Input: z=4 x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? 4 ? 1 ? 1 ? 12 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:05:37 2005 Input: z=10 x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? 10 ? 4 ? 4 ? 54 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:06:51 2005 Input: z=0 x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 Output: ? 0 ? -1 ? -1 ? 4 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:08:31 2005 Input: z=0 x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 x^2 y^2 z^2 -x*z -y*z 2x 2y 2z -2 Output: ? 0 ? -1 ? -1 ? 4 ? 1 ? 1 ? 0 ? 0 ? 0 ? 2 ? 2 ? 2 ? -2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. *** Warning: unused characters: x. *** Warning: unused characters: y. *** Warning: unused characters: z. Timing: real 0m0.018s user 0m0.005s sys 0m0.013s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:08:56 2005 Input: z=0 x=z/2-1 y=z/2-1 (x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2) x^2 y^2 z^2 -x*z -y*z 2x 2y 2z -2 Output: ? 0 ? -1 ? -1 ? ? 1 ? 1 ? 0 ? 0 ? 0 ? 2 ? 2 ? 2 ? -2 ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2) ^---------- *** Warning: unused characters: x. *** Warning: unused characters: y. *** Warning: unused characters: z. Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:09:10 2005 Input: z=0 x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+(2x+2y+2z-2) x^2 y^2 z^2 -x*z -y*z 2x 2y 2z -2 Output: ? 0 ? -1 ? -1 ? ? 1 ? 1 ? 0 ? 0 ? 0 ? 2 ? 2 ? 2 ? -2 ? Errors (if any) and Timing Info: *** expected character: ')' instead of: x^2+y^2+z^2-x*z-y*z+(2x+2y+2z-2) ^---------- *** Warning: unused characters: x. *** Warning: unused characters: y. *** Warning: unused characters: z. Timing: real 0m0.019s user 0m0.009s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:09:19 2005 Input: z=0 x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 x^2 y^2 z^2 -x*z -y*z 2x 2y 2z -2 Output: ? 0 ? -1 ? -1 ? 4 ? 1 ? 1 ? 0 ? 0 ? 0 ? 2 ? 2 ? 2 ? -2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. *** Warning: unused characters: x. *** Warning: unused characters: y. *** Warning: unused characters: z. Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:10:17 2005 Input: z=-3+2*(6^1/2) x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 x^2 y^2 z^2 -x*z -y*z 2x 2y 2z -2 Output: ? 3 ? 1/2 ? 1/2 ? 17/2 ? 1/4 ? 1/4 ? 9 ? -3/2 ? -3/2 ? 2 ? 2 ? 2 ? -2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. *** Warning: unused characters: x. *** Warning: unused characters: y. *** Warning: unused characters: z. Timing: real 0m0.018s user 0m0.009s sys 0m0.010s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:10:29 2005 Input: z=-3+2*(6^(1/2)) x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2x+2y+2z-2 x^2 y^2 z^2 -x*z -y*z 2x 2y 2z -2 Output: ? 1.8989794855663561963945681494117827839 ? -0.050510257216821901802715925294108608045 ? -0.050510257216821901802715925294108608045 ? 5.8030615433009314108162955517646516481 ? 0.0025512860841095090135796264705430401713 ? 0.0025512860841095090135796264705430401713 ? 3.6061230866018628216325911035293032963 ? 0.095917942265424785578272597647131135746 ? 0.095917942265424785578272597647131135746 ? 2 ? 2 ? 2 ? -2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. *** Warning: unused characters: x. *** Warning: unused characters: y. *** Warning: unused characters: z. Timing: real 0m0.018s user 0m0.014s sys 0m0.004s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:11:44 2005 Input: z=-3+2*(6^(1/2)) x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z 2x+2y+2z-2 x^2 y^2 z^2 -x*z -y*z 2x 2y 2z -2 Output: ? 1.8989794855663561963945681494117827839 ? -0.050510257216821901802715925294108608045 ? -0.050510257216821901802715925294108608045 ? 3.8030615433009314108162955517646516481 ? 2 ? 0.0025512860841095090135796264705430401713 ? 0.0025512860841095090135796264705430401713 ? 3.6061230866018628216325911035293032963 ? 0.095917942265424785578272597647131135746 ? 0.095917942265424785578272597647131135746 ? 2 ? 2 ? 2 ? -2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. *** Warning: unused characters: x. *** Warning: unused characters: y. *** Warning: unused characters: z. Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:11:52 2005 Input: z=-3+2*(6^(1/2)) x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z 2x+2y+2z-2 x^2 y^2 z^2 -x*z -y*z 2x 2y 2z -2 Output: ? 1.8989794855663561963945681494117827839 ? -0.050510257216821901802715925294108608045 ? -0.050510257216821901802715925294108608045 ? 3.8030615433009314108162955517646516481 ? 2 ? ? ? 0.0025512860841095090135796264705430401713 ? 0.0025512860841095090135796264705430401713 ? 3.6061230866018628216325911035293032963 ? 0.095917942265424785578272597647131135746 ? 0.095917942265424785578272597647131135746 ? 2 ? 2 ? 2 ? -2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x+2y+2z-2. *** Warning: unused characters: x. *** Warning: unused characters: y. *** Warning: unused characters: z. Timing: real 0m0.019s user 0m0.009s sys 0m0.010s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:12:11 2005 Input: z=-3+2*(6^(1/2)) x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2*x+2*y+2*z-2 x^2 y^2 z^2 -x*z -y*z 2x 2y 2z -2 Output: ? 1.8989794855663561963945681494117827839 ? -0.050510257216821901802715925294108608045 ? -0.050510257216821901802715925294108608045 ? 5.3989794855663561963945681494117827837 ? ? ? 0.0025512860841095090135796264705430401713 ? 0.0025512860841095090135796264705430401713 ? 3.6061230866018628216325911035293032963 ? 0.095917942265424785578272597647131135746 ? 0.095917942265424785578272597647131135746 ? 2 ? 2 ? 2 ? -2 ? Errors (if any) and Timing Info: *** Warning: unused characters: x. *** Warning: unused characters: y. *** Warning: unused characters: z. Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:15:27 2005 Input: z=-3+2*(6^(1/2)) x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2*x+2*y+2*z-2 Output: ? 1.8989794855663561963945681494117827839 ? -0.050510257216821901802715925294108608045 ? -0.050510257216821901802715925294108608045 ? 5.3989794855663561963945681494117827837 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:15:44 2005 Input: z=-3-2*(6^(1/2)) x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2*x+2*y+2*z-2 Output: ? -7.8989794855663561963945681494117827839 ? -4.9494897427831780981972840747058913919 ? -4.9494897427831780981972840747058913919 ? -4.3989794855663561963945681494117827837 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 13:15:52 2005 Input: z=-4-2*(6^(1/2)) x=z/2-1 y=z/2-1 x^2+y^2+z^2-x*z-y*z+2*x+2*y+2*z-2 Output: ? -8.8989794855663561963945681494117827838 ? -5.4494897427831780981972840747058913919 ? -5.4494897427831780981972840747058913919 ? 0.E-38 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.014s sys 0m0.004s '130.243' ************** PARI ***************** Host 130.243.79.252 (130.243.79.252) Time: Mon Jun 6 15:21:18 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.007s '130.243' ************** PARI ***************** Host 130.243.79.252 (130.243.79.252) Time: Mon Jun 6 15:21:45 2005 Input: sqrt(-1) Output: ? 1.0000000000000000000000000000000000000*I ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '130.243' ************** PARI ***************** Host 130.243.79.252 (130.243.79.252) Time: Mon Jun 6 15:22:01 2005 Input: sqrt(-1) Output: ? 1.0000000000000000000000000000000000000*I ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '217.75.' ************** PARI ***************** Host 217.75.158.216 (217.75.158.216) Time: Mon Jun 6 15:25:50 2005 Input: 55454+44444444444444444444444444444444444444 Output: ? 44444444444444444444444444444444499898 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.008s '217.75.' ************** PARI ***************** Host 217.75.158.216 (217.75.158.216) Time: Mon Jun 6 15:26:00 2005 Input: 554 Output: ? 554 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.008s '217.75.' ************** PARI ***************** Host 217.75.158.216 (217.75.158.216) Time: Mon Jun 6 15:26:17 2005 Input: 1000000000^1111 Output: ? 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.050s user 0m0.034s sys 0m0.016s '217.75.' ************** PARI ***************** Host 217.75.158.216 (217.75.158.216) Time: Mon Jun 6 15:26:39 2005 Input: 1000000000^11000000000000000000000000000000000000 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m7.236s user 0m7.199s sys 0m0.029s '217.75.' ************** PARI ***************** Host 217.75.158.216 (217.75.158.216) Time: Mon Jun 6 15:26:52 2005 Input: 1000000000^1100000000000000000000000 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m5.921s user 0m5.894s sys 0m0.024s '217.75.' ************** PARI ***************** Host 217.75.158.216 (217.75.158.216) Time: Mon Jun 6 15:27:01 2005 Input: 1000000000^110000000 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m5.027s user 0m5.001s sys 0m0.022s '217.75.' ************** PARI ***************** Host 217.75.158.216 (217.75.158.216) Time: Mon Jun 6 15:27:12 2005 Input: 1000000000^11000 Output: ? 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000[+++] ? Errors (if any) and Timing Info: Timing: real 0m2.916s user 0m2.902s sys 0m0.012s '217.75.' ************** PARI ***************** Host 217.75.158.216 (217.75.158.216) Time: Mon Jun 6 15:27:39 2005 Input: 1000000000^110000 Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 19181 Killed /usr/bin/gp -q -emacs Timing: real 0m21.522s user 0m20.973s sys 0m0.029s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 16:30:31 2005 Input: x=-2 4x^2-16*x-9 Output: ? -2 ? 4 ? Errors (if any) and Timing Info: *** Warning: unused characters: x^2-16*x-9. Timing: real 0m0.075s user 0m0.011s sys 0m0.006s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 16:32:20 2005 Input: x=9/2 4x^2-16*x-9 Output: ? 9/2 ? 4 ? Errors (if any) and Timing Info: *** Warning: unused characters: x^2-16*x-9. Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 16:32:22 2005 Input: x=9/2 4x^2-16*x-9 Output: ? 9/2 ? 4 ? Errors (if any) and Timing Info: *** Warning: unused characters: x^2-16*x-9. Timing: real 0m0.105s user 0m0.009s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 16:32:31 2005 Input: x=-1/2 4x^2-16*x-9 Output: ? -1/2 ? 4 ? Errors (if any) and Timing Info: *** Warning: unused characters: x^2-16*x-9. Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 16:32:33 2005 Input: x=-1/2 4x^2-16*x-9 Output: ? -1/2 ? 4 ? Errors (if any) and Timing Info: *** Warning: unused characters: x^2-16*x-9. Timing: real 0m0.017s user 0m0.009s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 16:32:36 2005 Input: x=-2/2 4x^2-16*x-9 Output: ? -1 ? 4 ? Errors (if any) and Timing Info: *** Warning: unused characters: x^2-16*x-9. Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 16:32:39 2005 Input: x=-3/2 4x^2-16*x-9 Output: ? -3/2 ? 4 ? Errors (if any) and Timing Info: *** Warning: unused characters: x^2-16*x-9. Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 16:32:49 2005 Input: x=-(9/2) 4x^2-16*x-9 Output: ? -9/2 ? 4 ? Errors (if any) and Timing Info: *** Warning: unused characters: x^2-16*x-9. Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 16:33:00 2005 Input: x=-(9/2) 4*(x^2)-16*x-9 Output: ? -9/2 ? 144 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 16:33:04 2005 Input: x=(9/2) 4*(x^2)-16*x-9 Output: ? 9/2 ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '129.143' ************** PARI ***************** Host 129.143.15.150 (129.143.15.150) Time: Mon Jun 6 16:33:09 2005 Input: x=(-1/2) 4*(x^2)-16*x-9 Output: ? -1/2 ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Mon Jun 6 19:57:33 2005 Input: e=ellint([0,0,0,11711,1681]*Mod(1,11903)); P=[3,2330] elladd(e,P,P) Output: ? ? [3, 2330] ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: e=ellint([0,0,0,11711, ^-------------------- *** bad argument for an elliptic curve related function Timing: real 0m0.042s user 0m0.012s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Mon Jun 6 19:57:40 2005 Input: e=ellinit([0,0,0,11711,1681]*Mod(1,11903)); P=[3,2330] elladd(e,P,P) Output: ? ? [3, 2330] ? [Mod(5155, 11903), Mod(1173, 11903)] ? Errors (if any) and Timing Info: Timing: real 0m0.049s user 0m0.005s sys 0m0.012s '137.111' ************** PARI ***************** Host 137.111.13.34 (137.111.13.34) Time: Mon Jun 6 20:03:17 2005 Input: e=ellinit([0,0,0,11711,1681]*Mod(1,11903)); P=[3,2330] elladd(e,P,P) Q=[5155,1173] elladd(e,Q,Q) Output: ? ? [3, 2330] ? [Mod(5155, 11903), Mod(1173, 11903)] ? [5155, 1173] ? [Mod(2848, 11903), Mod(8021, 11903)] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.009s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue Jun 7 01:15:42 2005 Input: polgalois(x^7+1) Output: ? ? Errors (if any) and Timing Info: *** sorry, galois of reducible polynomial is not yet implemented. Timing: real 0m0.094s user 0m0.008s sys 0m0.011s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue Jun 7 01:15:59 2005 Input: polgalois(x^7+2) Output: ? [42, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.072s user 0m0.032s sys 0m0.010s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue Jun 7 01:16:10 2005 Input: polgalois(x^7+3) Output: ? [42, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.033s sys 0m0.006s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue Jun 7 01:16:16 2005 Input: polgalois(x^7+4) Output: ? [42, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.033s sys 0m0.006s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue Jun 7 01:16:23 2005 Input: polgalois(x^7+5) Output: ? [42, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.041s user 0m0.034s sys 0m0.006s '203.144' ************** PARI ***************** Host 203.144.160.242 (203.144.160.242) Time: Tue Jun 7 01:16:31 2005 Input: polgalois(x^7-2) Output: ? [42, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.058s user 0m0.034s sys 0m0.004s '203.144' ************** PARI ***************** Host 203.144.160.242 (203.144.160.242) Time: Tue Jun 7 01:16:45 2005 Input: polgalois(x^7+x+1) Output: ? [5040, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.029s sys 0m0.010s '203.144' ************** PARI ***************** Host 203.144.160.242 (203.144.160.242) Time: Tue Jun 7 01:17:00 2005 Input: polgalois(x^7+x-1) Output: ? [5040, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.028s sys 0m0.011s '203.144' ************** PARI ***************** Host 203.144.160.242 (203.144.160.242) Time: Tue Jun 7 01:17:10 2005 Input: polgalois(x^7+x+1) Output: ? [5040, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.032s sys 0m0.008s '203.144' ************** PARI ***************** Host 203.144.160.242 (203.144.160.242) Time: Tue Jun 7 01:17:17 2005 Input: polgalois(x^7-x+1) Output: ? [5040, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.056s user 0m0.046s sys 0m0.010s '203.144' ************** PARI ***************** Host 203.144.160.242 (203.144.160.242) Time: Tue Jun 7 01:17:25 2005 Input: polgalois(x^7-x-1) Output: ? [5040, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.057s user 0m0.048s sys 0m0.009s '203.144' ************** PARI ***************** Host 203.144.160.242 (203.144.160.242) Time: Tue Jun 7 02:19:47 2005 Input: factor(x^4+4) Output: ? [x^2 - 2*x + 2 1] [x^2 + 2*x + 2 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.014s sys 0m0.005s '203.144' ************** PARI ***************** Host 203.144.160.242 (203.144.160.242) Time: Tue Jun 7 02:20:01 2005 Input: factor(x^2+1) Output: ? [x^2 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.013s sys 0m0.004s '203.144' ************** PARI ***************** Host 203.144.160.242 (203.144.160.242) Time: Tue Jun 7 02:39:54 2005 Input: polredabs(2^(1/2)) Output: ? ? Errors (if any) and Timing Info: *** not a number field in some number field-related function Timing: real 0m0.029s user 0m0.009s sys 0m0.008s '203.144' ************** PARI ***************** Host 203.144.160.242 (203.144.160.242) Time: Tue Jun 7 02:40:12 2005 Input: polredabs(sqrt(2)) Output: ? ? Errors (if any) and Timing Info: *** not a number field in some number field-related function Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue Jun 7 02:44:03 2005 Input: poltchebi(3) Output: ? 4*x^3 - 3*x ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Tue Jun 7 02:50:38 2005 Input: factornf(x^2+1, y^2+1) Output: ? [Mod(1, y^2 + 1)*x + Mod(-y, y^2 + 1) 1] [Mod(1, y^2 + 1)*x + Mod(y, y^2 + 1) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '84.56.2' ************** PARI ***************** Host 84.56.248.215 (84.56.248.215) Time: Tue Jun 7 12:00:59 2005 Input: Mod(3,8)^75 Output: ? Mod(3, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.276s user 0m0.007s sys 0m0.012s '84.56.2' ************** PARI ***************** Host 84.56.248.215 (84.56.248.215) Time: Tue Jun 7 12:02:57 2005 Input: Mod (1000,8) Output: ? Mod(0, 8) ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '84.56.2' ************** PARI ***************** Host 84.56.248.215 (84.56.248.215) Time: Tue Jun 7 12:03:26 2005 Input: Mod (9,8) Output: ? Mod(1, 8) ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '84.56.2' ************** PARI ***************** Host 84.56.248.215 (84.56.248.215) Time: Tue Jun 7 12:03:34 2005 Input: Mod(9,8) Output: ? Mod(1, 8) ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.005s sys 0m0.013s '84.56.2' ************** PARI ***************** Host 84.56.248.215 (84.56.248.215) Time: Tue Jun 7 12:03:52 2005 Input: Mod(9^75,8) Output: ? Mod(1, 8) ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.006s '84.56.2' ************** PARI ***************** Host 84.56.248.215 (84.56.248.215) Time: Tue Jun 7 12:04:00 2005 Input: Mod(3^75,8) Output: ? Mod(3, 8) ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '84.56.2' ************** PARI ***************** Host 84.56.248.215 (84.56.248.215) Time: Tue Jun 7 12:04:16 2005 Input: Mod(1001,8) Output: ? Mod(1, 8) ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '84.56.2' ************** PARI ***************** Host 84.56.248.215 (84.56.248.215) Time: Tue Jun 7 12:05:22 2005 Input: 12^27 Output: ? 137370551967459378662586974208 ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '84.56.2' ************** PARI ***************** Host 84.56.248.215 (84.56.248.215) Time: Tue Jun 7 12:05:59 2005 Input: 18232^1291 Output: ? 5458797883151334307458818723436640517448486180003885001048560084089228115112953594178619667002755546032481709965644117796592209583572210299415715399879912623638429270438522773958841136958812728433360310268823010794679578852656213950452775343769819236251937440389746136157760097726104270765740371758969231930470930325453400150115275055415346152155256154554616169264958785675739387108712408677824581643575304621741166514394828595803498398501229422869606316967597729486605530779589041283287457157794034597786918094232928824479744538801529694911259098287834555327739544401777766015351821286439535457691833121139586919773390534632453098413349663473001779128618987191313148801705524362745367359982704721086995471318817224424790043425563182731646713427067789025662961288643607038671113179203611098643878463544787422195128638501929501286466183085793050590862188236224617267034328362597746313541057617321680192177692354302334433031249915902821023827246940930813303093274952235674716505036512988887147665300869932253541884854273092464479146462316771022021014922708318839592969900335080398768451611353355090992716334369037330797739365698291073662752189717364659763990036394439696651899395990744804119819430391389399063800651724263360165707961899548217666979362173985563355236938275364866925515583260073185870137557856173253257973018767787039748558759643933550542520005627531227483364688057514167952826185847272054586809908555986123181314235600974747654613987967083860390337330504980767853680985363328475892170525925015955276210751009709164540056286462609251979212905034037651225462464180706275934197491569156255274261049283414198571725844295649896204886915085425358942925724448166055965626540688864501601550143878460353469078515289669528205914572586309385502006219819889902356997160051445688952569948176482216248286436221081847811919272105437707425119059009749292060681072265973289413530685753842799110217059113758394565820780464100916288670545461407546409428120379476094095042826880393896166003504297185230099267404423364221273179392638452150937124117822612678854275480952738621127051137453445678050778412542652900304113569338407087159907679205844937076347327051940584591030333437779224078750649999577493725841255947208812808581001107601732687011335155565733610875048209025633935601025919956020667410133441007591921882327323455754677469004861662786233073180304449743067340212954385019312342603261672487354026031723459959204762493146643904157288514655902858532568370638406743560488536768132506735616924752131616686444328410605637920902739659634611639251936149970007895228447261696461946858089536481929750733801945853003157383622093188720458609584642222819524195462575039188707139031215445724316205824635186470774787062211277916924506040155031178837858500514794686244636696457493194422441089261753285383945723527880226169607578922813628183605671740521900182674445439260532775705500242970518706564439031349196182024226607743371507432107807747770486473879645531089052094082604672395913832312734607979926107627313767032650510793950637517134799121265255468795140533441864112954501920531060348816644053067640666264335579568296983325113694211585848697587820043287692158631368896279634466458758006286030427070[+++] ? ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.020s sys 0m0.009s '84.56.2' ************** PARI ***************** Host 84.56.248.215 (84.56.248.215) Time: Tue Jun 7 12:06:16 2005 Input: 11^1003 Output: ? 3287480713865754850719161640548429786831655135752305388610882508886714128589701556414629801004195381517132539942607612596863486105066012927415488024519288180610622896328528192781428312036224847262710008270206126323256408436523683611929803172595437327408531888519494152143834313715470640347599099664938841562614486641758600750754941303769096148988276851135887543900722144426416100949796774002717079476737628947550912805427972151700291275204006702161592859586887356100059723703385422895542274970752419272357114791601508153783078099383310343891992901297400274397165480353897397707646554079283417388101429568992223810562255724965285357208075537385933606915842049142191149004787692374181252063328459685012270853210819469048795896864452509656641105915594478823075586687297663030078641513076142075171149148985131755609064604164974169026501059076215364182788000450575437441977829393141254449558044834740187813126640990810563327383560503528617208709825591174615682557311043544093105314335183408433825234758260927317836437429647834688753832331820816261331 ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '84.56.2' ************** PARI ***************** Host 84.56.248.215 (84.56.248.215) Time: Tue Jun 7 12:06:44 2005 Input: Mod(18232^1291,22499) Output: ? Mod(10232, 22499) ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.011s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Tue Jun 7 12:31:01 2005 Input: mod(18232,22499)^1291 Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(18232,22499)^129 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Tue Jun 7 12:31:38 2005 Input: Mod(18232,22499)^1291 Output: ? Mod(10232, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Tue Jun 7 12:32:38 2005 Input: Mod(8140,22499)^1291 Output: ? Mod(22126, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Tue Jun 7 12:33:04 2005 Input: Mod(14044,22499)^1291 Output: ? Mod(5286, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Tue Jun 7 12:33:21 2005 Input: Mod(10673,22499)^1291 Output: ? Mod(6034, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.011s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Tue Jun 7 12:33:38 2005 Input: Mod(3644,22499)^1291 Output: ? Mod(1633, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Tue Jun 7 12:34:35 2005 Input: Mod(3644,22499)^1291 Output: ? Mod(1633, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.009s '84.56.2' ************** PARI ***************** Host 84.56.248.215 (84.56.248.215) Time: Tue Jun 7 12:53:15 2005 Input: Mod(8140^1291,22499) Output: ? Mod(22126, 22499) ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '84.56.2' ************** PARI ***************** Host 84.56.248.215 (84.56.248.215) Time: Tue Jun 7 12:55:54 2005 Input: Mod(14044^1291,22499) Output: ? Mod(5286, 22499) ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.015s sys 0m0.003s '84.56.2' ************** PARI ***************** Host 84.56.248.215 (84.56.248.215) Time: Tue Jun 7 12:57:14 2005 Input: Mod(10673^1291,22499) Output: ? Mod(6034, 22499) ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '84.56.2' ************** PARI ***************** Host 84.56.248.215 (84.56.248.215) Time: Tue Jun 7 12:57:37 2005 Input: Mod(3644^1291,22499) Output: ? Mod(1633, 22499) ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:25:31 2005 Input: Mod(18232,22499)^1291 Output: ? Mod(10232, 22499) ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:25:33 2005 Input: Mod(18232,22499)^1291 Output: ? Mod(10232, 22499) ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:26:46 2005 Input: Mod(18232,22499)^1291 Output: ? Mod(10232, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:26:55 2005 Input: Mod(18232, 22499)^1291 Output: ? Mod(10232, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:27:35 2005 Input: Mod(8140,22499)^1291 Output: ? Mod(22126, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:28:13 2005 Input: Mod (8140,22499)^1291 Output: ? Mod(22126, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:28:29 2005 Input: Mod(8140, 22499)^1291 Output: ? Mod(22126, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:28:31 2005 Input: Mod(8140, 22499)^1291 Output: ? Mod(22126, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:31:46 2005 Input: Mod(8140,22499)*1291 Output: ? Mod(1707, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.010s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:32:55 2005 Input: Mod(20,7) Output: ? Mod(6, 7) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:33:22 2005 Input: Mod(20^2,7) Output: ? Mod(1, 7) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:33:31 2005 Input: Mod(3^2,7) Output: ? Mod(2, 7) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:33:46 2005 Input: Mod(3^3,7) Output: ? Mod(6, 7) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:34:30 2005 Input: Mod(18232^1291,22499) Output: ? Mod(10232, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.013s sys 0m0.005s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:35:35 2005 Input: Mod(18232^2,22499) Output: ? Mod(5598, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:35:56 2005 Input: Mod(5598^2, 22499) Output: ? Mod(18996, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:36:49 2005 Input: Mod(18232*5598, 22499) Output: ? Mod(7272, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:38:11 2005 Input: Mod(18996^2, 22499) Output: ? Mod(9054, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.012s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:39:15 2005 Input: Mod(7272*9054, 22499) Output: ? Mod(8614, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.012s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:40:01 2005 Input: Mod(9054^2, 22499) Output: ? Mod(11059, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:40:42 2005 Input: Mod(11059^8, 22499) Output: ? Mod(8946, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:41:36 2005 Input: Mod(8946^5, 22499) Output: ? Mod(18951, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.013s sys 0m0.005s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:42:17 2005 Input: Mod(18951^2, 22499) Output: ? Mod(11363, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:42:49 2005 Input: Mod(8614*11363, 22499) Output: ? Mod(10232, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:45:15 2005 Input: Mod(8140^1291, 22499) Output: ? Mod(22126, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.007s '147.83.' ************** PARI ***************** Host 147.83.104.38 (147.83.104.38) Time: Tue Jun 7 13:45:25 2005 Input: 1+1 Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.011s sys 0m0.006s '147.83.' ************** PARI ***************** Host 147.83.104.38 (147.83.104.38) Time: Tue Jun 7 13:45:39 2005 Input: 1 1 + Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 11+ ^ Timing: real 0m0.017s user 0m0.009s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:46:07 2005 Input: Mod(14044^1291, 22499) Output: ? Mod(5286, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.010s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:47:15 2005 Input: Mod(10673^1291, 22499) Output: ? Mod(6034, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:47:19 2005 Input: Mod(10673^1291, 22499) Output: ? Mod(6034, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:47:20 2005 Input: Mod(10673^1291, 22499) Output: ? Mod(6034, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.013s sys 0m0.005s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:48:06 2005 Input: Mod(3644^1291, 22499) Output: ? Mod(1633, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:48:12 2005 Input: Mod(3644^1291, 22499) Output: ? Mod(1633, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:48:15 2005 Input: Mod(3644^1291, 22499) Output: ? Mod(1633, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:48:20 2005 Input: Mod(3644^1291, 22499) Output: ? Mod(1633, 22499) ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 13:50:26 2005 Input: 10=2*x Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: 10=2*x ^---- Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:31:17 2005 Input: Mod(1291*8,22200) Output: ? Mod(10328, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:31:28 2005 Input: Mod(1291*9,22200) Output: ? Mod(11619, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:31:33 2005 Input: Mod(1291*10,22200) Output: ? Mod(12910, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:31:38 2005 Input: Mod(1291*11,22200) Output: ? Mod(14201, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:31:43 2005 Input: Mod(1291*12,22200) Output: ? Mod(15492, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:31:49 2005 Input: Mod(1291*13,22200) Output: ? Mod(16783, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:31:54 2005 Input: Mod(1291*14,22200) Output: ? Mod(18074, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:31:58 2005 Input: Mod(1291*15,22200) Output: ? Mod(19365, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:32:04 2005 Input: Mod(1291*16,22200) Output: ? Mod(20656, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:32:07 2005 Input: Mod(1291*17,22200) Output: ? Mod(21947, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:32:11 2005 Input: Mod(1291*18,22200) Output: ? Mod(1038, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:32:16 2005 Input: Mod(1291*19,22200) Output: ? Mod(2329, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:32:21 2005 Input: Mod(1291*20,22200) Output: ? Mod(3620, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:32:26 2005 Input: Mod(1291*21,22200) Output: ? Mod(4911, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:32:29 2005 Input: Mod(1291*22,22200) Output: ? Mod(6202, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:32:33 2005 Input: Mod(1291*23,22200) Output: ? Mod(7493, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:32:38 2005 Input: Mod(1291*24,22200) Output: ? Mod(8784, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:32:45 2005 Input: Mod(1291*25,22200) Output: ? Mod(10075, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:32:50 2005 Input: Mod(1291*26,22200) Output: ? Mod(11366, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:32:54 2005 Input: Mod(1291*27,22200) Output: ? Mod(12657, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:32:58 2005 Input: Mod(1291*28,22200) Output: ? Mod(13948, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:33:02 2005 Input: Mod(1291*29,22200) Output: ? Mod(15239, 22200) ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:33:52 2005 Input: x*1291+y*22200=1 Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: x*1291+y*22200=1 ^-- Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:34:04 2005 Input: x*1291 + y*22200 = 1 Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: x*1291+y*22200=1 ^-- Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:34:07 2005 Input: x*1291 + y*22200 = 1 Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: x*1291+y*22200=1 ^-- Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:34:37 2005 Input: X*1291 + Y*22200 = 1 Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: X*1291+Y*22200=1 ^-- Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:34:53 2005 Input: X*1291 + Y*22200 = 1 Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: X*1291+Y*22200=1 ^-- Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:47:34 2005 Input: Mod(-9389*1291,22200) Output: ? Mod(1, 22200) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:48:44 2005 Input: Mod(9389*1291,22200) Output: ? Mod(22199, 22200) ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:49:48 2005 Input: 22200-9389 Output: ? 12811 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:53:14 2005 Input: 29*29 Output: ? 841 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:53:47 2005 Input: 7*841+0*29+23 Output: ? 5910 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:54:39 2005 Input: 20*841+2*29+22 Output: ? 16900 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:54:56 2005 Input: 9*841+8*29+27 Output: ? 7828 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:55:33 2005 Input: 5*841+19*29+9 Output: ? 4765 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.013s sys 0m0.004s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 14:57:44 2005 Input: Mod(5910^12811,22499) Output: ? Mod(9695, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.018s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 15:01:16 2005 Input: Mod(16900^12811,22499) Output: ? Mod(5642, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.014s sys 0m0.010s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 15:01:30 2005 Input: Mod(7828^12811,22499) Output: ? Mod(4489, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.014s sys 0m0.010s '132.230' ************** PARI ***************** Host 132.230.1.131 (132.230.1.131) Time: Tue Jun 7 15:01:56 2005 Input: Mod(4765^12811,22499) Output: ? Mod(3144, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.015s sys 0m0.008s '84.159.' ************** PARI ***************** Host 84.159.77.239 (84.159.77.239) Time: Tue Jun 7 15:13:10 2005 Input: Mod(18232,22499)^1291 Output: ? Mod(10232, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '84.159.' ************** PARI ***************** Host 84.159.77.239 (84.159.77.239) Time: Tue Jun 7 15:13:38 2005 Input: Mod(18232)^1291,22499)^1291 Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Mod(18232)^1291,22499)^1291 ^------------------ Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '84.159.' ************** PARI ***************** Host 84.159.77.239 (84.159.77.239) Time: Tue Jun 7 15:13:49 2005 Input: Mod(18232)^1291,22499) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Mod(18232)^1291,22499) ^------------- Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '84.159.' ************** PARI ***************** Host 84.159.77.239 (84.159.77.239) Time: Tue Jun 7 15:14:06 2005 Input: Mod(18232)^1291,22499) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Mod(18232)^1291,22499) ^------------- Timing: real 0m0.020s user 0m0.008s sys 0m0.009s '84.159.' ************** PARI ***************** Host 84.159.77.239 (84.159.77.239) Time: Tue Jun 7 15:14:20 2005 Input: Mod(18232^1291.22499) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Mod(18232^1291.22499) ^- Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '84.159.' ************** PARI ***************** Host 84.159.77.239 (84.159.77.239) Time: Tue Jun 7 15:14:31 2005 Input: Mod(18232.22499)^1291 Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Mod(18232.22499)^1291 ^------ Timing: real 0m0.017s user 0m0.005s sys 0m0.013s '84.159.' ************** PARI ***************** Host 84.159.77.239 (84.159.77.239) Time: Tue Jun 7 15:14:41 2005 Input: mod(18232,22499)^1291 Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(18232,22499)^129 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.017s user 0m0.012s sys 0m0.006s '217.75.' ************** PARI ***************** Host 217.75.158.216 (217.75.158.216) Time: Tue Jun 7 15:36:55 2005 Input: 2^64 Output: ? 18446744073709551616 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '217.75.' ************** PARI ***************** Host 217.75.158.216 (217.75.158.216) Time: Tue Jun 7 15:37:58 2005 Input: 2^128 Output: ? 340282366920938463463374607431768211456 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.010s '217.75.' ************** PARI ***************** Host 217.75.158.216 (217.75.158.216) Time: Tue Jun 7 15:38:51 2005 Input: 2^1228 Output: ? 4622050384501541079063198370564118606036557611490203003743065735166521106191233191578966207005907034163181996235483687392512826552037215014641050195044389764708782979147558987242120731436393810330968987786310813708687240518612639513557072749900038873486151696084416697258142197059285474066136970301829657013867090765986365597716572168322172422029426139705149135001747456 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '217.75.' ************** PARI ***************** Host 217.75.158.216 (217.75.158.216) Time: Tue Jun 7 15:40:34 2005 Input: 2^12288866 Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 784 Killed /usr/bin/gp -q -emacs Timing: real 0m21.053s user 0m20.907s sys 0m0.096s '217.75.' ************** PARI ***************** Host 217.75.158.216 (217.75.158.216) Time: Tue Jun 7 15:57:11 2005 Input: Log(2.767777) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Log(2.767777) ^------------- Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '217.75.' ************** PARI ***************** Host 217.75.158.216 (217.75.158.216) Time: Tue Jun 7 15:57:27 2005 Input: Log[2.767777] Output: ? ? Errors (if any) and Timing Info: *** unexpected character: Log[2.767777] ^---------- Timing: real 0m0.025s user 0m0.009s sys 0m0.009s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Tue Jun 7 16:17:43 2005 Input: factor(12343901) Output: ? [19 1] [311 1] [2089 1] ? Errors (if any) and Timing Info: Timing: real 0m0.079s user 0m0.012s sys 0m0.008s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Tue Jun 7 16:18:13 2005 Input: prime(3) Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Tue Jun 7 16:18:22 2005 Input: prime(100) Output: ? 541 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.012s sys 0m0.005s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Tue Jun 7 16:18:34 2005 Input: isprime(100) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.009s sys 0m0.009s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Tue Jun 7 16:18:40 2005 Input: isprime(101) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.010s sys 0m0.006s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Tue Jun 7 16:35:56 2005 Input: isprime(29) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.007s '141.70.' ************** PARI ***************** Host 141.70.115.191 (141.70.115.191) Time: Tue Jun 7 16:38:26 2005 Input: mod(1234,22499)^1291 Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(1234,22499)^1291 ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.018s user 0m0.009s sys 0m0.008s '141.70.' ************** PARI ***************** Host 141.70.115.191 (141.70.115.191) Time: Tue Jun 7 16:39:02 2005 Input: mod(1234^1291,22499) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(1234^1291,22499) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Tue Jun 7 16:40:02 2005 Input: isprime(23) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.006s '141.70.' ************** PARI ***************** Host 141.70.115.191 (141.70.115.191) Time: Tue Jun 7 16:41:10 2005 Input: Mod(1234,22499)^1291 Output: ? Mod(14386, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '141.70.' ************** PARI ***************** Host 141.70.115.191 (141.70.115.191) Time: Tue Jun 7 16:45:27 2005 Input: 18232^1291Mod22499 Output: ? 5458797883151334307458818723436640517448486180003885001048560084089228115112953594178619667002755546032481709965644117796592209583572210299415715399879912623638429270438522773958841136958812728433360310268823010794679578852656213950452775343769819236251937440389746136157760097726104270765740371758969231930470930325453400150115275055415346152155256154554616169264958785675739387108712408677824581643575304621741166514394828595803498398501229422869606316967597729486605530779589041283287457157794034597786918094232928824479744538801529694911259098287834555327739544401777766015351821286439535457691833121139586919773390534632453098413349663473001779128618987191313148801705524362745367359982704721086995471318817224424790043425563182731646713427067789025662961288643607038671113179203611098643878463544787422195128638501929501286466183085793050590862188236224617267034328362597746313541057617321680192177692354302334433031249915902821023827246940930813303093274952235674716505036512988887147665300869932253541884854273092464479146462316771022021014922708318839592969900335080398768451611353355090992716334369037330797739365698291073662752189717364659763990036394439696651899395990744804119819430391389399063800651724263360165707961899548217666979362173985563355236938275364866925515583260073185870137557856173253257973018767787039748558759643933550542520005627531227483364688057514167952826185847272054586809908555986123181314235600974747654613987967083860390337330504980767853680985363328475892170525925015955276210751009709164540056286462609251979212905034037651225462464180706275934197491569156255274261049283414198571725844295649896204886915085425358942925724448166055965626540688864501601550143878460353469078515289669528205914572586309385502006219819889902356997160051445688952569948176482216248286436221081847811919272105437707425119059009749292060681072265973289413530685753842799110217059113758394565820780464100916288670545461407546409428120379476094095042826880393896166003504297185230099267404423364221273179392638452150937124117822612678854275480952738621127051137453445678050778412542652900304113569338407087159907679205844937076347327051940584591030333437779224078750649999577493725841255947208812808581001107601732687011335155565733610875048209025633935601025919956020667410133441007591921882327323455754677469004861662786233073180304449743067340212954385019312342603261672487354026031723459959204762493146643904157288514655902858532568370638406743560488536768132506735616924752131616686444328410605637920902739659634611639251936149970007895228447261696461946858089536481929750733801945853003157383622093188720458609584642222819524195462575039188707139031215445724316205824635186470774787062211277916924506040155031178837858500514794686244636696457493194422441089261753285383945723527880226169607578922813628183605671740521900182674445439260532775705500242970518706564439031349196182024226607743371507432107807747770486473879645531089052094082604672395913832312734607979926107627313767032650510793950637517134799121265255468795140533441864112954501920531060348816644053067640666264335579568296983325113694211585848697587820043287692158631368896279634466458758006286030427070[+++] ? Errors (if any) and Timing Info: *** Warning: unused characters: Mod22499. Timing: real 0m0.029s user 0m0.020s sys 0m0.009s '141.70.' ************** PARI ***************** Host 141.70.115.191 (141.70.115.191) Time: Tue Jun 7 16:45:59 2005 Input: 18232^1291Mod(22499) Output: ? 5458797883151334307458818723436640517448486180003885001048560084089228115112953594178619667002755546032481709965644117796592209583572210299415715399879912623638429270438522773958841136958812728433360310268823010794679578852656213950452775343769819236251937440389746136157760097726104270765740371758969231930470930325453400150115275055415346152155256154554616169264958785675739387108712408677824581643575304621741166514394828595803498398501229422869606316967597729486605530779589041283287457157794034597786918094232928824479744538801529694911259098287834555327739544401777766015351821286439535457691833121139586919773390534632453098413349663473001779128618987191313148801705524362745367359982704721086995471318817224424790043425563182731646713427067789025662961288643607038671113179203611098643878463544787422195128638501929501286466183085793050590862188236224617267034328362597746313541057617321680192177692354302334433031249915902821023827246940930813303093274952235674716505036512988887147665300869932253541884854273092464479146462316771022021014922708318839592969900335080398768451611353355090992716334369037330797739365698291073662752189717364659763990036394439696651899395990744804119819430391389399063800651724263360165707961899548217666979362173985563355236938275364866925515583260073185870137557856173253257973018767787039748558759643933550542520005627531227483364688057514167952826185847272054586809908555986123181314235600974747654613987967083860390337330504980767853680985363328475892170525925015955276210751009709164540056286462609251979212905034037651225462464180706275934197491569156255274261049283414198571725844295649896204886915085425358942925724448166055965626540688864501601550143878460353469078515289669528205914572586309385502006219819889902356997160051445688952569948176482216248286436221081847811919272105437707425119059009749292060681072265973289413530685753842799110217059113758394565820780464100916288670545461407546409428120379476094095042826880393896166003504297185230099267404423364221273179392638452150937124117822612678854275480952738621127051137453445678050778412542652900304113569338407087159907679205844937076347327051940584591030333437779224078750649999577493725841255947208812808581001107601732687011335155565733610875048209025633935601025919956020667410133441007591921882327323455754677469004861662786233073180304449743067340212954385019312342603261672487354026031723459959204762493146643904157288514655902858532568370638406743560488536768132506735616924752131616686444328410605637920902739659634611639251936149970007895228447261696461946858089536481929750733801945853003157383622093188720458609584642222819524195462575039188707139031215445724316205824635186470774787062211277916924506040155031178837858500514794686244636696457493194422441089261753285383945723527880226169607578922813628183605671740521900182674445439260532775705500242970518706564439031349196182024226607743371507432107807747770486473879645531089052094082604672395913832312734607979926107627313767032650510793950637517134799121265255468795140533441864112954501920531060348816644053067640666264335579568296983325113694211585848697587820043287692158631368896279634466458758006286030427070[+++] ? Errors (if any) and Timing Info: *** Warning: unused characters: Mod(22499). Timing: real 0m0.029s user 0m0.016s sys 0m0.012s '84.159.' ************** PARI ***************** Host 84.159.135.172 (84.159.135.172) Time: Tue Jun 7 16:58:47 2005 Input: mod(9,2) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(9,2) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '84.159.' ************** PARI ***************** Host 84.159.135.172 (84.159.135.172) Time: Tue Jun 7 16:59:00 2005 Input: modul(9,2) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: modul(9,2) ^---------- Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '193.248' ************** PARI ***************** Host 193.248.88.226 (193.248.88.226) Time: Tue Jun 7 17:18:22 2005 Input: 2*5 Output: ? 10 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.007s '203.144' ************** PARI ***************** Host 203.144.143.2 (203.144.143.2) Time: Tue Jun 7 19:13:29 2005 Input: factornf(x^2+1,y^2+1) Output: ? [Mod(1, y^2 + 1)*x + Mod(-y, y^2 + 1) 1] [Mod(1, y^2 + 1)*x + Mod(y, y^2 + 1) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.117s user 0m0.009s sys 0m0.009s '203.144' ************** PARI ***************** Host 203.144.143.2 (203.144.143.2) Time: Tue Jun 7 19:14:58 2005 Input: factornf(x^6+4*x^5+3*x^4-4*x^3-2*x^2+2*x+1,y^2+1) Output: ? [Mod(1, y^2 + 1)*x^3 + Mod(-y + 2, y^2 + 1)*x^2 + Mod(-y - 1, y^2 + 1)*x + Mod(-1, y^2 + 1) 1] [Mod(1, y^2 + 1)*x^3 + Mod(y + 2, y^2 + 1)*x^2 + Mod(y - 1, y^2 + 1)*x + Mod(-1, y^2 + 1) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.015s sys 0m0.008s '203.144' ************** PARI ***************** Host 203.144.143.2 (203.144.143.2) Time: Tue Jun 7 19:22:12 2005 Input: factornf(x^6-2*x^5-2*x^4+4*x^3-4*x+4,y^2+35) Output: ? [Mod(1, y^2 + 35)*x^6 + Mod(-2, y^2 + 35)*x^5 + Mod(-2, y^2 + 35)*x^4 + Mod(4, y^2 + 35)*x^3 + Mod(-4, y^2 + 35)*x + Mod(4, y^2 + 35) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.152s user 0m0.015s sys 0m0.007s '203.144' ************** PARI ***************** Host 203.144.143.2 (203.144.143.2) Time: Tue Jun 7 19:23:11 2005 Input: factornf(x^6-2*x^5-2*x^4+4*x^3-4*x+4,y^2+37) Output: ? [Mod(1, y^2 + 37)*x^6 + Mod(-2, y^2 + 37)*x^5 + Mod(-2, y^2 + 37)*x^4 + Mod(4, y^2 + 37)*x^3 + Mod(-4, y^2 + 37)*x + Mod(4, y^2 + 37) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.014s sys 0m0.009s '203.144' ************** PARI ***************** Host 203.144.143.2 (203.144.143.2) Time: Tue Jun 7 19:23:21 2005 Input: factornf(x^6-2*x^5-2*x^4+4*x^3-4*x+4,y^2-37) Output: ? [Mod(1, y^2 - 37)*x^6 + Mod(-2, y^2 - 37)*x^5 + Mod(-2, y^2 - 37)*x^4 + Mod(4, y^2 - 37)*x^3 + Mod(-4, y^2 - 37)*x + Mod(4, y^2 - 37) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.018s sys 0m0.004s '203.144' ************** PARI ***************** Host 203.144.143.2 (203.144.143.2) Time: Tue Jun 7 19:25:31 2005 Input: factornf(5,y^2+1) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in polfnf. Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '203.144' ************** PARI ***************** Host 203.144.143.2 (203.144.143.2) Time: Tue Jun 7 19:25:43 2005 Input: factornf(5*x,y^2+1) Output: ? [Mod(1, y^2 + 1)*x 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '203.144' ************** PARI ***************** Host 203.144.143.6 (203.144.143.6) Time: Tue Jun 7 20:04:16 2005 Input: polgalois(x^6-3*x^5+6*x^4-7*x^3+2*x^2+x-4) Output: ? [24, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.037s sys 0m0.005s '203.144' ************** PARI ***************** Host 203.144.143.6 (203.144.143.6) Time: Tue Jun 7 20:04:40 2005 Input: factornf(x^6-3*x^5+6*x^4-7*x^3+2*x^2+x-4,y^3+1) Output: ? ? Errors (if any) and Timing Info: *** non-invertible polynomial in polinvmod. Timing: real 0m0.026s user 0m0.015s sys 0m0.010s '203.144' ************** PARI ***************** Host 203.144.143.6 (203.144.143.6) Time: Tue Jun 7 20:04:54 2005 Input: factornf(x^6-3*x^5+6*x^4-7*x^3+2*x^2+x-4,y^3-1) Output: ? ? Errors (if any) and Timing Info: *** non-invertible polynomial in polinvmod. Timing: real 0m0.026s user 0m0.018s sys 0m0.008s '203.144' ************** PARI ***************** Host 203.144.143.6 (203.144.143.6) Time: Tue Jun 7 20:05:18 2005 Input: factor(x^6-3*x^5+6*x^4-7*x^3+2*x^2+x-4) Output: ? [x^6 - 3*x^5 + 6*x^4 - 7*x^3 + 2*x^2 + x - 4 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.009s '203.144' ************** PARI ***************** Host 203.144.143.7 (203.144.143.7) Time: Tue Jun 7 20:26:01 2005 Input: factornf(x^6-3*x^5+6*x^4-7*x^3+2*x^2+x-4, y^3+(9/4)*y^2-(37/16)*y-229/64) Output: ? [Mod(1, y^3 + 9/4*y^2 - 37/16*y - 229/64)*x^2 + Mod(-1, y^3 + 9/4*y^2 - 37/16*y - 229/64)*x + Mod(-y + 1/4, y^3 + 9/4*y^2 - 37/16*y - 229/64) 1] [Mod(1, y^3 + 9/4*y^2 - 37/16*y - 229/64)*x^4 + Mod(-2, y^3 + 9/4*y^2 - 37/16*y - 229/64)*x^3 + Mod(y + 15/4, y^3 + 9/4*y^2 - 37/16*y - 229/64)*x^2 + Mod(-y - 11/4, y^3 + 9/4*y^2 - 37/16*y - 229/64)*x + Mod(y^2 + 5/2*y - 27/16, y^3 + 9/4*y^2 - 37/16*y - 229/64) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.021s sys 0m0.008s '203.144' ************** PARI ***************** Host 203.144.143.6 (203.144.143.6) Time: Tue Jun 7 20:29:30 2005 Input: factornf(x^6-3*x^5+6*x^4-7*x^3+2*x^2+x-4, y^3-4*y-1) Output: ? [Mod(1, y^3 - 4*y - 1)*x^2 + Mod(-1, y^3 - 4*y - 1)*x + Mod(-y + 1, y^3 - 4*y - 1) 1] [Mod(1, y^3 - 4*y - 1)*x^4 + Mod(-2, y^3 - 4*y - 1)*x^3 + Mod(y + 3, y^3 - 4*y - 1)*x^2 + Mod(-y - 2, y^3 - 4*y - 1)*x + Mod(y^2 + y - 3, y^3 - 4*y - 1) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.018s sys 0m0.008s '203.144' ************** PARI ***************** Host 203.144.143.7 (203.144.143.7) Time: Wed Jun 8 01:11:41 2005 Input: factornf(x^4-x-10,y^3+40*y+1) Output: ? [Mod(1, y^3 + 40*y + 1)*x^4 + Mod(-1, y^3 + 40*y + 1)*x + Mod(-10, y^3 + 40*y + 1) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.013s sys 0m0.007s '203.144' ************** PARI ***************** Host 203.144.143.7 (203.144.143.7) Time: Wed Jun 8 01:11:58 2005 Input: factornf(x^4-x-10,y^3+40*y-1) Output: ? [Mod(1, y^3 + 40*y - 1)*x^4 + Mod(-1, y^3 + 40*y - 1)*x + Mod(-10, y^3 + 40*y - 1) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.013s sys 0m0.007s '203.144' ************** PARI ***************** Host 203.144.143.7 (203.144.143.7) Time: Wed Jun 8 01:12:41 2005 Input: factornf(x^4-x-10,y^6+40*y^2-1) Output: ? [Mod(1, y^6 + 40*y^2 - 1)*x^2 + Mod(-y, y^6 + 40*y^2 - 1)*x + Mod(-1/2*y^5 + 1/2*y^2 - 20*y, y^6 + 40*y^2 - 1) 1] [Mod(1, y^6 + 40*y^2 - 1)*x^2 + Mod(y, y^6 + 40*y^2 - 1)*x + Mod(1/2*y^5 + 1/2*y^2 + 20*y, y^6 + 40*y^2 - 1) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.026s sys 0m0.013s '62.214.' ************** PARI ***************** Host 62.214.193.101 (62.214.193.101) Time: Wed Jun 8 02:17:38 2005 Input: Mod(5910,12811)^(22499) Output: ? Mod(11361, 12811) ? Errors (if any) and Timing Info: Timing: real 0m0.041s user 0m0.011s sys 0m0.006s '62.214.' ************** PARI ***************** Host 62.214.193.101 (62.214.193.101) Time: Wed Jun 8 02:18:46 2005 Input: Mod(5910,22499)^(12811) Output: ? Mod(9695, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.007s '62.214.' ************** PARI ***************** Host 62.214.193.101 (62.214.193.101) Time: Wed Jun 8 02:19:26 2005 Input: Mod(16900,22499)^(12811) Output: ? Mod(5642, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '62.214.' ************** PARI ***************** Host 62.214.193.101 (62.214.193.101) Time: Wed Jun 8 02:20:23 2005 Input: Mod(7828,22499)^(12811) Output: ? Mod(4489, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.013s sys 0m0.005s '62.214.' ************** PARI ***************** Host 62.214.193.101 (62.214.193.101) Time: Wed Jun 8 02:20:48 2005 Input: Mod(4765,22499)^(12811) Output: ? Mod(3144, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '62.214.' ************** PARI ***************** Host 62.214.193.101 (62.214.193.101) Time: Wed Jun 8 02:21:30 2005 Input: Mod(5910,22499)^(12811) Output: ? Mod(9695, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '61.246.' ************** PARI ***************** Host 61.246.61.208 (61.246.61.208) Time: Wed Jun 8 04:48:17 2005 Input: 50c6 Output: ? 50 ? Errors (if any) and Timing Info: *** Warning: unused characters: c6. Timing: real 0m0.017s user 0m0.012s sys 0m0.006s '203.144' ************** PARI ***************** Host 203.144.143.6 (203.144.143.6) Time: Wed Jun 8 05:03:18 2005 Input: factornf(x^4+5*x^3+3*x^2-5*x-9,y^3+8*y+101) Output: ? [Mod(1, y^3 + 8*y + 101)*x^4 + Mod(5, y^3 + 8*y + 101)*x^3 + Mod(3, y^3 + 8*y + 101)*x^2 + Mod(-5, y^3 + 8*y + 101)*x + Mod(-9, y^3 + 8*y + 101) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.062s user 0m0.016s sys 0m0.007s '203.144' ************** PARI ***************** Host 203.144.143.6 (203.144.143.6) Time: Wed Jun 8 05:03:37 2005 Input: factornf(x^4+5*x^3+3*x^2-5*x-9,y^6+8*y^2+101) Output: ? [Mod(1, y^6 + 8*y^2 + 101)*x^4 + Mod(5, y^6 + 8*y^2 + 101)*x^3 + Mod(3, y^6 + 8*y^2 + 101)*x^2 + Mod(-5, y^6 + 8*y^2 + 101)*x + Mod(-9, y^6 + 8*y^2 + 101) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.038s user 0m0.030s sys 0m0.008s '203.144' ************** PARI ***************** Host 203.144.143.6 (203.144.143.6) Time: Wed Jun 8 05:05:28 2005 Input: factornf(x^4+5*x^3+3*x^2-5*x-9,y^6 - (51/4)*y^4 + (995/16)*y^2 - 625/64) Output: ? [Mod(1, y^6 - 51/4*y^4 + 995/16*y^2 - 625/64)*x^2 + Mod(-y + 5/2, y^6 - 51/4*y^4 + 995/16*y^2 - 625/64)*x + Mod(4/25*y^5 - 51/25*y^3 + 1/2*y^2 + 87/10*y - 13/8, y^6 - 51/4*y^4 + 995/16*y^2 - 625/64) 1] [Mod(1, y^6 - 51/4*y^4 + 995/16*y^2 - 625/64)*x^2 + Mod(y + 5/2, y^6 - 51/4*y^4 + 995/16*y^2 - 625/64)*x + Mod(-4/25*y^5 + 51/25*y^3 + 1/2*y^2 - 87/10*y - 13/8, y^6 - 51/4*y^4 + 995/16*y^2 - 625/64) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.046s user 0m0.040s sys 0m0.006s '62.203.' ************** PARI ***************** Host 62.203.167.134 (62.203.167.134) Time: Wed Jun 8 05:52:56 2005 Input: 5^x+2^x-(4/3)^x+7=0 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 5^x+2^x-(4/3)^x+7=0 ^-- Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '62.203.' ************** PARI ***************** Host 62.203.167.134 (62.203.167.134) Time: Wed Jun 8 05:53:18 2005 Input: 5^x+2^x-(4/3)^x+7=0 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 5^x+2^x-(4/3)^x+7=0 ^-- Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '62.203.' ************** PARI ***************** Host 62.203.167.134 (62.203.167.134) Time: Wed Jun 8 05:54:10 2005 Input: solve(5^x+2^x-(4/3)^x+7=0,x) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: solve(5^x+2^x-(4/3)^x+7=0, ^-------------------- Timing: real 0m0.017s user 0m0.012s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Wed Jun 8 09:18:44 2005 Input: Mod(149,22499)^(745*22200) Output: ? Mod(11175, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.305s user 0m0.012s sys 0m0.012s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Wed Jun 8 09:19:53 2005 Input: Mod(149^(745*22200),22499) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m6.396s user 0m6.362s sys 0m0.026s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Wed Jun 8 09:22:15 2005 Input: Mod(149,22499)^(745*22200) Output: ? Mod(11175, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Wed Jun 8 09:22:53 2005 Input: Mod(149,22499)^(12811*1291-1) Output: ? Mod(11175, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.009s sys 0m0.007s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Wed Jun 8 09:23:09 2005 Input: Mod(151,22499)^(12811*1291-1) Output: ? Mod(11325, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Wed Jun 8 09:25:53 2005 Input: Mod(151,22499)^(12811*1291) Output: ? Mod(151, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Wed Jun 8 09:26:19 2005 Input: Mod(149,22499)^(12811*1291) Output: ? Mod(149, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.009s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Wed Jun 8 09:27:16 2005 Input: Mod(1,22499)^(12811*1291) Output: ? Mod(1, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.008s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Wed Jun 8 09:27:23 2005 Input: Mod(1215,22499)^(12811*1291) Output: ? Mod(1215, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.012s sys 0m0.006s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Wed Jun 8 09:27:51 2005 Input: Mod(3129,22499)^(12811*1291) Output: ? Mod(3129, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.013s sys 0m0.005s '132.230' ************** PARI ***************** Host 132.230.73.1 (132.230.73.1) Time: Wed Jun 8 09:28:02 2005 Input: Mod(22499,22499)^(12811*1291) Output: ? Mod(0, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '84.56.2' ************** PARI ***************** Host 84.56.243.198 (84.56.243.198) Time: Wed Jun 8 09:42:09 2005 Input: Mod(10232^12811,22499) Output: ? Mod(18232, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.015s sys 0m0.009s '84.56.2' ************** PARI ***************** Host 84.56.243.198 (84.56.243.198) Time: Wed Jun 8 09:50:22 2005 Input: Mod(72^7,187) Output: ? Mod(30, 187) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '220.237' ************** PARI ***************** Host 220.237.99.72 (220.237.99.72) Time: Wed Jun 8 09:50:34 2005 Input: Factorisation(982390293028352998698533588612030840778202635041783163987203790462368667044579180217826253 ) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorisation(982390 ^-------------------- Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '220.237' ************** PARI ***************** Host 220.237.99.72 (220.237.99.72) Time: Wed Jun 8 09:51:05 2005 Input: Factorint(982390293028352998698533588612030840778202635041783163987203790462368667044579180217826253 ) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factorint(9823902930 ^-------------------- Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '220.237' ************** PARI ***************** Host 220.237.99.72 (220.237.99.72) Time: Wed Jun 8 09:51:16 2005 Input: Factor(982390293028352998698533588612030840778202635041783163987203790462368667044579180217826253 ) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Factor(9823902930283 ^-------------------- Timing: real 0m0.019s user 0m0.009s sys 0m0.010s '220.237' ************** PARI ***************** Host 220.237.99.72 (220.237.99.72) Time: Wed Jun 8 09:54:16 2005 Input: factor(982390293028352998698533588612030840778202635041783163987203790462368667044579180217826253 ) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 12256 Killed /usr/bin/gp -q -emacs Timing: real 0m21.031s user 0m20.992s sys 0m0.009s '84.56.2' ************** PARI ***************** Host 84.56.243.198 (84.56.243.198) Time: Wed Jun 8 09:56:03 2005 Input: Mod(8140^1291,22499) Output: ? Mod(22126, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.005s sys 0m0.012s '84.56.2' ************** PARI ***************** Host 84.56.243.198 (84.56.243.198) Time: Wed Jun 8 10:11:16 2005 Input: Mod(22126^12811,22499) Output: ? Mod(8140, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.017s sys 0m0.008s '84.56.2' ************** PARI ***************** Host 84.56.243.198 (84.56.243.198) Time: Wed Jun 8 10:11:27 2005 Input: Mod(22126^1291,22499) Output: ? Mod(16498, 22499) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.006s '84.56.2' ************** PARI ***************** Host 84.56.243.198 (84.56.243.198) Time: Wed Jun 8 10:21:10 2005 Input: Mod(3^75,8) Output: ? Mod(3, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '84.56.2' ************** PARI ***************** Host 84.56.243.198 (84.56.243.198) Time: Wed Jun 8 10:41:56 2005 Input: 11^1003 Output: ? 3287480713865754850719161640548429786831655135752305388610882508886714128589701556414629801004195381517132539942607612596863486105066012927415488024519288180610622896328528192781428312036224847262710008270206126323256408436523683611929803172595437327408531888519494152143834313715470640347599099664938841562614486641758600750754941303769096148988276851135887543900722144426416100949796774002717079476737628947550912805427972151700291275204006702161592859586887356100059723703385422895542274970752419272357114791601508153783078099383310343891992901297400274397165480353897397707646554079283417388101429568992223810562255724965285357208075537385933606915842049142191149004787692374181252063328459685012270853210819469048795896864452509656641105915594478823075586687297663030078641513076142075171149148985131755609064604164974169026501059076215364182788000450575437441977829393141254449558044834740187813126640990810563327383560503528617208709825591174615682557311043544093105314335183408433825234758260927317836437429647834688753832331820816261331 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.012s sys 0m0.006s '84.56.2' ************** PARI ***************** Host 84.56.243.198 (84.56.243.198) Time: Wed Jun 8 10:42:19 2005 Input: 11000^1003 Output: ? 3287480713865754850719161640548429786831655135752305388610882508886714128589701556414629801004195381517132539942607612596863486105066012927415488024519288180610622896328528192781428312036224847262710008270206126323256408436523683611929803172595437327408531888519494152143834313715470640347599099664938841562614486641758600750754941303769096148988276851135887543900722144426416100949796774002717079476737628947550912805427972151700291275204006702161592859586887356100059723703385422895542274970752419272357114791601508153783078099383310343891992901297400274397165480353897397707646554079283417388101429568992223810562255724965285357208075537385933606915842049142191149004787692374181252063328459685012270853210819469048795896864452509656641105915594478823075586687297663030078641513076142075171149148985131755609064604164974169026501059076215364182788000450575437441977829393141254449558044834740187813126640990810563327383560503528617208709825591174615682557311043544093105314335183408433825234758260927317836437429647834688753832331820816261331000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.015s sys 0m0.009s '84.56.2' ************** PARI ***************** Host 84.56.243.198 (84.56.243.198) Time: Wed Jun 8 10:42:41 2005 Input: 110001^1003 Output: ? 3317593502168536118039661283370631841258076817260867271720666068778913790064810786919058965095626742526263700193282427728212339618664819119481655685265457382860458893056185350934317110379055766255597084556772181524761988243341501841604704427241354139585718926277376080212200458114854653755534541391811177090548732208303080704552714970187298805920591561972231009156065084067960286418933951861753211143136023029224058314246027338893353640887200517504155678406440170883402427901123984441609216087937167741695094912133617687577533738931529682238011349162003109709096681235374155761961418554203944678182003631694732914939972672133904059845975702062708268844831400024315951839958940648074303417218325664446185866130458178030599922395171725854932970449650389078033645553978508299383012647051362273937928777357042541506362623352941596696623770559638816518437815172132610889064834659722658090402379704891098990784917368016070054308179781945343646163209387131059283085243770030708284428092974899005587891810147517591273833032451503304271763187226958308146392689717159496229911403561439646209827732798783913617688208953731336213662188095106867914144357447327397214479415262024551865349839681747017871765885971810348992634778672436368310564631701331181816537832587503660357150552487103929060142320203056936628873870262999847180041117127912299290468394766367806009277950160597669916274504213094588133709349265092311328168281384591044911504359452008664159922062431860308120954381973142801434550547453083135276481214878382529789546385525951755718667687383020395804543859002863152789386262713839495069768266586377773638587396058221677860060843912514045002173190251567304569158523288608311688891721614933487791658165199712943524738233085724386885658397535756650331022132500591436721941318935335870513212048734764528745087908628355598446633450988505365392447698220942867967203950688403841294734697847433394916864433662237144316083731173806507393855757462739754180075678257405166617477225621490574540549446612422353268615318605457133862363116470863007688718625081102659671282875686063044138774018145024841078773842439625461165866156840964719148799401690800432532437247346982326425718078248616449885370526506020327079681796681067168354156949667201095016678601607122497391279999655663350785718197006036319275163761043040733990088289144716338828525265428768941511978352247629034445956191903149558658087861811040139429497746006439317114914761539289041805943039011358562311488760072175015109515576842093616737727231823055634489715835814961915390477333770196534854154021473489240022205333020119157813903734116811021215012441496819688268595954967060808999302176862279109616973181414672143595092382954054978479122803108743112389098796614021928313602141359063225297332124394074499794670153035541245844382746686776371884764675115318378492302283836050311880935868999253066908617050323087526709683974580252417842488729564538254996188476344963996457013159290747447639759422428096843131297768020322708256542051924230548756927792675762063170857035190986318299855133463837401554179894322157402218873241266471440962663422297633082408496974147479951316132903774174128132477862368594872895916137757106000888064704575183800311461[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.019s sys 0m0.007s '84.56.2' ************** PARI ***************** Host 84.56.243.198 (84.56.243.198) Time: Wed Jun 8 10:48:00 2005 Input: (6924825^4+6924825*2+36)/875 Output: ? 2299509513060135140014240311/875 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '84.56.2' ************** PARI ***************** Host 84.56.243.198 (84.56.243.198) Time: Wed Jun 8 10:48:33 2005 Input: 2299509513060135140014240311/875 Output: ? 2299509513060135140014240311/875 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '204.107' ************** PARI ***************** Host 204.107.254.178 (204.107.254.178) Time: Wed Jun 8 10:54:39 2005 Input: (1/3)(9)³ = Output: ? 1/3 ? Errors (if any) and Timing Info: *** Warning: unused characters: (9)=. Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '204.107' ************** PARI ***************** Host 204.107.254.178 (204.107.254.178) Time: Wed Jun 8 10:55:18 2005 Input: 4(-2)² + 8(-2) + 3(-2) + 6 = Output: ? 4 ? Errors (if any) and Timing Info: *** Warning: unused characters: (-2)+8(-2)+3(-2)+6=. Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '24.86.1' ************** PARI ***************** Host 24.86.107.99 (24.86.107.99) Time: Wed Jun 8 15:08:42 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.004s sys 0m0.013s '24.86.1' ************** PARI ***************** Host 24.86.107.99 (24.86.107.99) Time: Wed Jun 8 15:09:04 2005 Input: (12^87)%34 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '24.86.1' ************** PARI ***************** Host 24.86.107.99 (24.86.107.99) Time: Wed Jun 8 15:09:16 2005 Input: gp>(12^87)%34 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '24.86.1' ************** PARI ***************** Host 24.86.107.99 (24.86.107.99) Time: Wed Jun 8 15:09:20 2005 Input: gp > (12^87)%34 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '24.86.1' ************** PARI ***************** Host 24.86.107.99 (24.86.107.99) Time: Wed Jun 8 15:09:25 2005 Input: gp > (12^87)mod34 Output: ? ? Errors (if any) and Timing Info: *** Warning: unused characters: mod34. *** incorrect type in comparison. Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '24.86.1' ************** PARI ***************** Host 24.86.107.99 (24.86.107.99) Time: Wed Jun 8 15:09:30 2005 Input: gp > (12^87) mod 34 Output: ? ? Errors (if any) and Timing Info: *** Warning: unused characters: mod34. *** incorrect type in comparison. Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '84.56.2' ************** PARI ***************** Host 84.56.237.207 (84.56.237.207) Time: Wed Jun 8 17:29:04 2005 Input: 123456789^987654321 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m6.578s user 0m6.547s sys 0m0.023s '84.56.2' ************** PARI ***************** Host 84.56.237.207 (84.56.237.207) Time: Wed Jun 8 17:29:18 2005 Input: 123456789^987654 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m6.820s user 0m6.756s sys 0m0.046s '84.56.2' ************** PARI ***************** Host 84.56.237.207 (84.56.237.207) Time: Wed Jun 8 17:29:31 2005 Input: 123456789^9876 Output: ? 6337449675659535991956088733304528283021629731138512320716598936901587953859470248143015385866515168106893154693466460522458132179682730970278124482526266031988434052289793830305410246701374237525529542317854752747988022620160564594022599388570438995275180675566248183374724068960693913099160950657957924259144419545600120154856065159540832341207666854059029747235755384969183095812913004420683584509860219493747460379411087858336159851811666670663047019797430489369295187309405312589228973072068381885819146805615226552842460843373448050817465564567227070437104156616912416700126389661883177081287698428351574665812482602122315808578901532199837765145020453054290635077257106825259402052805069563946558863308654368997472633052084960907034104005740514212517777745875970180305466324784637320159116695266571757717167485265539973816739132793292763691097150138936539563366711495560142867122172580345048123460452686380595667109602961402001404448866059850091177838661614368525120229142701565440670813081781306326619138386267318893358687118738843840494259323481973266214849776039392748590469757556996245654359212233900192573442563112698346616861503616946189856364289897685446618202564012547160718871638942809500100388173796378195267893368085399098459020555682960531267621674096839185356147125952216577068635702644604410369089703880475790301811858132360763359577531252811502814544408632439920616633641428651739532106067207040689585973869178491242711958177324255524209294735743100234081007765090687808579713792632252336615164353450068283666022809518162250668145087062077371473489806487522887225743484995621296350404401566760332679478213835185722231034159400186626875192890190206435935706800306285564774899832260716072453908305983971194154463045481955988702428687961047546542808757565038510643910633702508546224846340818175916444806714309414479745059410375754895269534471836557467342977610735583105282166458531668532904017877599191754878030012962313656457743754474247664594782674005327746215365805613427365125066109951213417364131869502402867808152944761630368517852784643199239396913117980043795679657758098397587026980324414856575766310286212954135180887711134416784311071580409384397003627230363918565792852080651345571283043227415114400010369111005902763763297010200650263897060690458100585056965348132741988441285178856838572875384185398854739699183435193225296954787088858625531354467762345794825080260570979238767944596196642661721345615706879108453293560928846448347622747613657156571458012547440549261548606728533833941269465259408660991821686589951764976715047410148313301361201189299313636007952773496651987602110616040036855999551693375257443688428233750608334847931287751650846936043602973288840816602657181313542162525768110400665617752561580531106344025617156885343819030563447792439652057918009747141122577011750959802075217135988487752291783664806455568072354185502027815962077054669105152700097206148684454905401855073267813091084978528012889444564040492380328531547648137269933468906056908293482032426136866049151188406460609507862589605053863584163441820882851546348021050719478293583868403945310821893700905513048711011062753439966425033699849513667132454302937301934325776298511[+++] ? Errors (if any) and Timing Info: Timing: real 0m2.216s user 0m2.203s sys 0m0.012s '84.56.2' ************** PARI ***************** Host 84.56.237.207 (84.56.237.207) Time: Wed Jun 8 19:04:36 2005 Input: Mod(1000,3) Output: ? Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '84.56.2' ************** PARI ***************** Host 84.56.237.207 (84.56.237.207) Time: Wed Jun 8 19:05:29 2005 Input: 3^332*4-2^500 Output: ? 1014650694236022471731092619673520677476262656279461774112948593231097473822941136412717639315901271084676311610379918552442374016519498829830446329592531841988 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.006s '84.56.2' ************** PARI ***************** Host 84.56.237.207 (84.56.237.207) Time: Wed Jun 8 19:05:40 2005 Input: 3^332 Output: ? 253662674377353269906808622421677593575965452124025955039003345678597210479768733204348048549792840852645117190316650670000611256434188843928959845730264857841 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '84.56.2' ************** PARI ***************** Host 84.56.237.207 (84.56.237.207) Time: Wed Jun 8 19:05:54 2005 Input: 3^332*4 Output: ? 1014650697509413079627234489686710374303861808496103820156013382714388841919074932817392194199171363410580468761266602680002445025736755375715839382921059431364 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '84.56.2' ************** PARI ***************** Host 84.56.237.207 (84.56.237.207) Time: Wed Jun 8 19:06:08 2005 Input: 2^500-(3^332)*4 Output: ? -1014650694236022471731092619673520677476262656279461774112948593231097473822941136412717639315901271084676311610379918552442374016519498829830446329592531841988 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.004s '84.56.2' ************** PARI ***************** Host 84.56.237.207 (84.56.237.207) Time: Wed Jun 8 19:06:24 2005 Input: (3^332)*4-2^500 Output: ? 1014650694236022471731092619673520677476262656279461774112948593231097473822941136412717639315901271084676311610379918552442374016519498829830446329592531841988 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '84.56.2' ************** PARI ***************** Host 84.56.237.207 (84.56.237.207) Time: Wed Jun 8 19:06:40 2005 Input: (3^332)*4-5^200 Output: ? 1014650697509413079565004336908098957232421167958302577750110861027177170588063766669495205858817528998741020530009466510432779130185530554468678948198159040739 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '84.56.2' ************** PARI ***************** Host 84.56.237.207 (84.56.237.207) Time: Wed Jun 8 19:08:29 2005 Input: 3^(5/3) Output: ? 6.2402514691557123435901704730736561589 ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.009s sys 0m0.008s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Thu Jun 9 17:11:11 2005 Input: isprime(31) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.048s user 0m0.010s sys 0m0.008s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Thu Jun 9 17:12:52 2005 Input: isprime(51) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.011s sys 0m0.006s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Thu Jun 9 17:13:03 2005 Input: isprime(61) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Thu Jun 9 17:13:54 2005 Input: isprime(111) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Thu Jun 9 17:14:01 2005 Input: isprime(101) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Thu Jun 9 17:14:59 2005 Input: isprime(141) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.010s sys 0m0.006s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Thu Jun 9 17:15:13 2005 Input: isprime(171) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Thu Jun 9 17:15:21 2005 Input: isprime(201) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Thu Jun 9 17:15:57 2005 Input: isprime(231) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Thu Jun 9 17:16:01 2005 Input: isprime(261) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.007s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Thu Jun 9 17:16:09 2005 Input: isprime(291) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.009s sys 0m0.007s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Thu Jun 9 17:16:18 2005 Input: isprime(221) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.005s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Thu Jun 9 17:16:22 2005 Input: isprime(251) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Thu Jun 9 17:16:40 2005 Input: isprime(23) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Fri Jun 10 01:37:43 2005 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: ? 366,378,582,594,846,1026,1374,1386, ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.011s sys 0m0.007s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Fri Jun 10 01:37:53 2005 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: ? 366,378,582,594,846,1026,1374,1386, ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '203.144' ************** PARI ***************** Host 203.144.143.6 (203.144.143.6) Time: Fri Jun 10 02:07:37 2005 Input: n=2^24*3^12*5^6 numdiv(n^2)/numdiv(n) Output: ? 139314069504000000 ? 7 ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.006s sys 0m0.010s '152.77.' ************** PARI ***************** Host 152.77.18.70 (152.77.18.70) Time: Fri Jun 10 10:08:58 2005 Input: ord (n) = d=mod(2,n); e=1; while(d-1,d*=2,e++); e forstep(m=1,LIM,10,forstep(n=m,m+9,2,print1([n,ord(n),eulerphi(n)/ord(n)]," "));print()) sort(M) = l=length(M); M1=vecsort(M); M2=matrix(l+3,2,a,b); s=0;t=1,;j1=1;for(j=1, l,if(M1[j]-s, M2[t,1]=s; M2[t,2]=j-j1;s=M1[j];t++;j1=j));M2[t,1]=s;M2[t,2]=l+1-j1; if(t>2,matrix(t-1,2,a,b,M2[a+1,b]),[M2[2,1],M2[2,2]]) test(n) = F=factor(polcyclo(n,x)*mod(1,2)); f=length(F~); M=vector(f);for(k=1,f,y=F[k,1]; z=mod(x,y); a=z+1/z+1; u=0,v=a,m=1;whole(v,m++;w=a*v+u;u=v;v=w);M[k]=m);print(n,ord(n),f]" "sort(M)) Output: ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...d(2,n);e=1;while(d-1,d*=2,e++);e ^------- *** incorrect type in comparison. *** Warning: unused characters: ,;j1=1;for(j=1,l,if(M1[j]-s,M2[t,1]=s;M2[t,2]=j-j1;s=M1[j];t++;j1=j));M2[t,1]=s;M2[t,2]=l+1-j1;if(t>2,matrix(t-1,2,a,b[+++]. *** expected character: ')' instead of: ...;z=mod(x,y);a=z+1/z+1;u=0 *** ,v=a,m=1;whole(v,m++ ^-------------------- Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '152.77.' ************** PARI ***************** Host 152.77.18.70 (152.77.18.70) Time: Fri Jun 10 10:11:53 2005 Input: ord (n) = d=mod(2,n); e=1; while(d-1,d*=2,e++); e forstep(m=1,LIM,10,forstep(n=m,m+9,2,print1([n,ord(n),eulerphi(n)/ord(n)]," "));print()) sort(M) = l=length(M); M1=vecsort(M); M2=matrix(l+3,2,a,b); s=0;t=1;j1=1;for(j=1, l,if(M1[j]-s, M2[t,1]=s; M2[t,2]=j-j1;s=M1[j];t++;j1=j));M2[t,1]=s;M2[t,2]=l+1-j1; if(t>2,matrix(t-1,2,a,b,M2[a+1,b]),[M2[2,1],M2[2,2]]) test(n) = F=factor(polcyclo(n,x)*mod(1,2)); f=length(F~); M=vector(f);for(k=1,f,y=F[k,1]; z=mod(x,y); a=z+1/z+1; u=0,v=a,m=1;whole(v,m++;w=a*v+u;u=v;v=w);M[k]=m);print(n,ord(n),f]" "sort(M)) Output: ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...d(2,n);e=1;while(d-1,d*=2,e++);e ^------- *** incorrect type in comparison. *** expected character: ')' instead of: ...;z=mod(x,y);a=z+1/z+1;u=0 *** ,v=a,m=1;whole(v,m++ ^-------------------- Timing: real 0m0.020s user 0m0.008s sys 0m0.011s '152.77.' ************** PARI ***************** Host 152.77.18.70 (152.77.18.70) Time: Fri Jun 10 10:17:41 2005 Input: ord (n) = d=mod(2,n); e=1; while(d-1,d*=2,e++); e forstep(m=1,LIM,10,forstep(n=m,m+9,2,print1([n,ord(n),eulerphi(n)/ord(n)]," "));print()) sort(M) = l=length(M); M1=vecsort(M); M2=matrix(l+3,2,a,b); s=0;t=1;j1=1;for(j=1,l,if(M1[j]-s, M2[t,1]=s; M2[t,2]=j-j1;s=M1[j];t++;j1=j));M2[t,1]=s;M2[t,2]=1+l-j1; if(t>2,matrix(t-1,2,a,b,M2[a+1,b]),[M2[2,1],M2[2,2]]) test(n) = F=factor(polcyclo(n,x)*mod(1,2)); f=length(F~); M=vector(f);for(k=1,f,y=F[k,1]; z=mod(x,y); a=z+1/z+1; u=0;v=a,m=1;while(v,m++;w=a*v+u;u=v;v=w);M[k]=m);print([n,ord(n),f]" "sort(M)) forstep(n=3,45,2,test(n)) Output: ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...d(2,n);e=1;while(d-1,d*=2,e++);e ^------- *** incorrect type in comparison. *** expected character: ')' instead of: ...od(x,y);a=z+1/z+1;u=0;v=a *** ,m=1;while(v,m++;w=a ^-------------------- *** expected character: '=' instead of: test(n)) ^- Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '152.77.' ************** PARI ***************** Host 152.77.18.70 (152.77.18.70) Time: Fri Jun 10 10:20:41 2005 Input: 2.3= Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 2.3= ^- Timing: real 0m0.017s user 0m0.011s sys 0m0.007s '152.77.' ************** PARI ***************** Host 152.77.18.70 (152.77.18.70) Time: Fri Jun 10 10:22:10 2005 Input: 2+3; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.012s sys 0m0.004s '200.181' ************** PARI ***************** Host 200.181.150.155 (200.181.150.155) Time: Fri Jun 10 12:52:25 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '200.181' ************** PARI ***************** Host 200.181.150.155 (200.181.150.155) Time: Fri Jun 10 12:53:25 2005 Input: exp(Pi*sqrt(163)) Output: ? 262537412640768743.99999999999925007253 ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.007s sys 0m0.010s '200.181' ************** PARI ***************** Host 200.181.150.155 (200.181.150.155) Time: Fri Jun 10 12:53:47 2005 Input: exp(Pi*sqrt(163)) Output: ? 262537412640768743.99999999999925007253 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '200.181' ************** PARI ***************** Host 200.181.150.155 (200.181.150.155) Time: Fri Jun 10 12:58:49 2005 Input: sqrt(163) Output: ? 12.767145334803704661710952009780892347 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.008s '200.181' ************** PARI ***************** Host 200.181.150.155 (200.181.150.155) Time: Fri Jun 10 12:59:00 2005 Input: sqrt(2) Output: ? 1.4142135623730950488016887242096980785 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '82.225.' ************** PARI ***************** Host 82.225.138.97 (82.225.138.97) Time: Fri Jun 10 18:13:43 2005 Input: 6+9 Output: ? 15 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '220.240' ************** PARI ***************** Host 220.240.172.150 (220.240.172.150) Time: Fri Jun 10 23:48:58 2005 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.011s sys 0m0.006s '220.240' ************** PARI ***************** Host 220.240.172.150 (220.240.172.150) Time: Fri Jun 10 23:49:05 2005 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '81.214.' ************** PARI ***************** Host 81.214.138.112 (81.214.138.112) Time: Sat Jun 11 05:38:05 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.129s user 0m0.013s sys 0m0.006s '68.46.1' ************** PARI ***************** Host 68.46.173.18 (68.46.173.18) Time: Sun Jun 12 01:08:09 2005 Input: 1/0 Output: ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.276s user 0m0.007s sys 0m0.014s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Sun Jun 12 17:35:43 2005 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Errors (if any) and Timing Info: Timing: real 0m0.294s user 0m0.010s sys 0m0.012s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Sun Jun 12 17:37:39 2005 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),sumdiv(x), ", ")) Output: ? ? ", " ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...x,")=",numdiv(x),sumdiv(x), ^-- *** Warning: unused characters: )). Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Sun Jun 12 17:38:32 2005 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),sigma(x), ", ")) Output: ? ? ", " ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...,")=",numdiv(x),sigma(x), ^ *** Warning: unused characters: )). Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Sun Jun 12 17:39:14 2005 Input: for(x=1,50,print1("d(",x,")=",sigma(x), ", ")) Output: ? ? ", " ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...nt1("d(",x,")=",sigma(x), ^ *** Warning: unused characters: )). Timing: real 0m0.018s user 0m0.010s sys 0m0.007s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Sun Jun 12 17:39:42 2005 Input: for(x=1,50,print1("d(",x,")=",sigma(x),", ")) Output: ? d(1)=1, d(2)=3, d(3)=4, d(4)=7, d(5)=6, d(6)=12, d(7)=8, d(8)=15, d(9)=13, d(10)=18, d(11)=12, d(12)=28, d(13)=14, d(14)=24, d(15)=24, d(16)=31, d(17)=18, d(18)=39, d(19)=20, d(20)=42, d(21)=32, d(22)=36, d(23)=24, d(24)=60, d(25)=31, d(26)=42, d(27)=40, d(28)=56, d(29)=30, d(30)=72, d(31)=32, d(32)=63, d(33)=48, d(34)=54, d(35)=48, d(36)=91, d(37)=38, d(38)=60, d(39)=56, d(40)=90, d(41)=42, d(42)=96, d(43)=44, d(44)=84, d(45)=78, d(46)=72, d(47)=48, d(48)=124, d(49)=57, d(50)=93, ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Sun Jun 12 17:40:06 2005 Input: for(x=1,50,print1("sigma(",x,")=",sigma(x),", ")) Output: ? sigma(1)=1, sigma(2)=3, sigma(3)=4, sigma(4)=7, sigma(5)=6, sigma(6)=12, sigma(7)=8, sigma(8)=15, sigma(9)=13, sigma(10)=18, sigma(11)=12, sigma(12)=28, sigma(13)=14, sigma(14)=24, sigma(15)=24, sigma(16)=31, sigma(17)=18, sigma(18)=39, sigma(19)=20, sigma(20)=42, sigma(21)=32, sigma(22)=36, sigma(23)=24, sigma(24)=60, sigma(25)=31, sigma(26)=42, sigma(27)=40, sigma(28)=56, sigma(29)=30, sigma(30)=72, sigma(31)=32, sigma(32)=63, sigma(33)=48, sigma(34)=54, sigma(35)=48, sigma(36)=91, sigma(37)=38, sigma(38)=60, sigma(39)=56, sigma(40)=90, sigma(41)=42, sigma(42)=96, sigma(43)=44, sigma(44)=84, sigma(45)=78, sigma(46)=72, sigma(47)=48, sigma(48)=124, sigma(49)=57, sigma(50)=93, ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Sun Jun 12 17:41:17 2005 Input: for(x=1,500,print1("sigma(",x,")=",sigma(x),", ")) Output: ? sigma(1)=1, sigma(2)=3, sigma(3)=4, sigma(4)=7, sigma(5)=6, sigma(6)=12, sigma(7)=8, sigma(8)=15, sigma(9)=13, sigma(10)=18, sigma(11)=12, sigma(12)=28, sigma(13)=14, sigma(14)=24, sigma(15)=24, sigma(16)=31, sigma(17)=18, sigma(18)=39, sigma(19)=20, sigma(20)=42, sigma(21)=32, sigma(22)=36, sigma(23)=24, sigma(24)=60, sigma(25)=31, sigma(26)=42, sigma(27)=40, sigma(28)=56, sigma(29)=30, sigma(30)=72, sigma(31)=32, sigma(32)=63, sigma(33)=48, sigma(34)=54, sigma(35)=48, sigma(36)=91, sigma(37)=38, sigma(38)=60, sigma(39)=56, sigma(40)=90, sigma(41)=42, sigma(42)=96, sigma(43)=44, sigma(44)=84, sigma(45)=78, sigma(46)=72, sigma(47)=48, sigma(48)=124, sigma(49)=57, sigma(50)=93, sigma(51)=72, sigma(52)=98, sigma(53)=54, sigma(54)=120, sigma(55)=72, sigma(56)=120, sigma(57)=80, sigma(58)=90, sigma(59)=60, sigma(60)=168, sigma(61)=62, sigma(62)=96, sigma(63)=104, sigma(64)=127, sigma(65)=84, sigma(66)=144, sigma(67)=68, sigma(68)=126, sigma(69)=96, sigma(70)=144, sigma(71)=72, sigma(72)=195, sigma(73)=74, sigma(74)=114, sigma(75)=124, sigma(76)=140, sigma(77)=96, sigma(78)=168, sigma(79)=80, sigma(80)=186, sigma(81)=121, sigma(82)=126, sigma(83)=84, sigma(84)=224, sigma(85)=108, sigma(86)=132, sigma(87)=120, sigma(88)=180, sigma(89)=90, sigma(90)=234, sigma(91)=112, sigma(92)=168, sigma(93)=128, sigma(94)=144, sigma(95)=120, sigma(96)=252, sigma(97)=98, sigma(98)=171, sigma(99)=156, sigma(100)=217, sigma(101)=102, sigma(102)=216, sigma(103)=104, sigma(104)=210, sigma(105)=192, sigma(106)=162, sigma(107)=108, sigma(108)=280, sigma(109)=110, sigma(110)=216, sigma(111)=152, sigma(112)=248, sigma(113)=114, sigma(114)=240, sigma(115)=144, sigma(116)=210, sigma(117)=182, sigma(118)=180, sigma(119)=144, sigma(120)=360, sigma(121)=133, sigma(122)=186, sigma(123)=168, sigma(124)=224, sigma(125)=156, sigma(126)=312, sigma(127)=128, sigma(128)=255, sigma(129)=176, sigma(130)=252, sigma(131)=132, sigma(132)=336, sigma(133)=160, sigma(134)=204, sigma(135)=240, sigma(136)=270, sigma(137)=138, sigma(138)=288, sigma(139)=140, sigma(140)=336, sigma(141)=192, sigma(142)=216, sigma(143)=168, sigma(144)=403, sigma(145)=180, sigma(146)=222, sigma(147)=228, sigma(148)=266, sigma(149)=150, sigma(150)=372, sigma(151)=152, sigma(152)=300, sigma(153)=234, sigma(154)=288, sigma(155)=192, sigma(156)=392, sigma(157)=158, sigma(158)=240, sigma(159)=216, sigma(160)=378, sigma(161)=192, sigma(162)=363, sigma(163)=164, sigma(164)=294, sigma(165)=288, sigma(166)=252, sigma(167)=168, sigma(168)=480, sigma(169)=183, sigma(170)=324, sigma(171)=260, sigma(172)=308, sigma(173)=174, sigma(174)=360, sigma(175)=248, sigma(176)=372, sigma(177)=240, sigma(178)=270, sigma(179)=180, sigma(180)=546, sigma(181)=182, sigma(182)=336, sigma(183)=248, sigma(184)=360, sigma(185)=228, sigma(186)=384, sigma(187)=216, sigma(188)=336, sigma(189)=320, sigma(190)=360, sigma(191)=192, sigma(192)=508, sigma(193)=194, sigma(194)=294, sigma(195)=336, sigma(196)=399, sigma(197)=198, sigma(198)=468, sigma(199)=200, sigma(200)=465, sigma(201)=272, sigma(202)=306, sigma(203)=240, sigma(204)=504, sigma(205)=252, sigma(206)=312, sigma(207)=312, sigma(208)=434, sigma(209)=240, sigma(210)=576, sigma(211)=212, sigma(212)=378, sigma(213)=288, sigma(214)=324, sigma(215)=264, sigma(216)=600, sigma(217)=256, sigma(218)=330, sigma(219)=296, sigma(220)=504, sigma(221)=252, sigma(222)=456, sigma(223)=224, sigma(224)=504, sigma(225)=403, sigma(226)=342, sigma(227)=228, sigma(228)=560, sigma(229)=230, sigma(230)=432, sigma(231)=384, sigma(232)=450, sigma(233)=234, sigma(234)=546, sigma(235)=288, sigma(236)=420, sigma(237)=320, sigma(238)=432, sigma(239)=240, sigma(240)=744, sigma(241)=242, sigma(242)=399, sigma(243)=364, sigma(244)=434, sigma(245)=342, sigma(246)=504, sigma(247)=280, sigma(248)=480, sigma(249)=336, sigma(250)=468, sigma(251)=252, sigma(252)=728, sigma(253)=288, sigma(254)=384, sigma(255)=432, sigma(256)=511, sigma(257)=258, sigma(258)=528, sigma(259)=304, sigma(260)=588, sigma(261)=390, sigma(262)=396, sigma(263)=264, sigma(264)=720, sigma(265)=324, sigma(266)=480, sigma(267)=360, sigma(268)=476, sigma(269)=270, sigma(270)=720, sigma(271)=272, sigma(272)=558, sigma(273)=448, sigma(274)=414, sigma(275)=372, sigma(276)=672, sigma(277)=278, sigma(278)=420, sigma(279)=416, sigma(280)=720, sigma(281)=282, sigma(282)=576, sigma(283)=284, sigma(284)=504, sigma(285)=480, sigma(286)=504, sigma(287)=336, sigma(288)=819, sigma(289)=307, sigma(290)=540, sigma(291)=392, sigma(292)=518, sigma(293)=294, sigma(294)=684, sigma(295)=360, sigma(296)=570, sigma(297)=480, sigma(298)=450, sigma(299)=336, sigma(300)=868, sigma(301)=352, sigma(302)=456, sigma(303)=408, sigma(304)=620, sigma(305)=372, sigma(306)=702, sigma(307)=308, sigma(308)=672, sigma(309)=416, sigma(310)=576, sigma(311)=312, sigma(312)=840, sigma(313)=314, sigma(314)=474, sigma(315)=624, sigma(316)=560, sigma(317)=318, sigma(318)=648, sigma(319)=360, sigma(320)=762, sigma(321)=432, sigma(322)=576, sigma(323)=360, sigma(324)=847, sigma(325)=434, sigma(326)=492, sigma(327)=440, sigma(328)=630, sigma(329)=384, sigma(330)=864, sigma(331)=332, sigma(332)=588, sigma(333)=494, sigma(334)=504, sigma(335)=408, sigma(336)=992, sigma(337)=338, sigma(338)=549, sigma(339)=456, sigma(340)=756, sigma(341)=384, sigma(342)=780, sigma(343)=400, sigma(344)=660, sigma(345)=576, sigma(346)=522, sigma(347)=348, sigma(348)=840, sigma(349)=350, sigma(350)=744, sigma(351)=560, sigma(352)=756, sigma(353)=354, sigma(354)=720, sigma(355)=432, sigma(356)=630, sigma(357)=576, sigma(358)=540, sigma(359)=360, sigma(360)=1170, sigma(361)=381, sigma(362)=546, sigma(363)=532, sigma(364)=784, sigma(365)=444, sigma(366)=744, sigma(367)=368, sigma(368)=744, sigma(369)=546, sigma(370)=684, sigma(371)=432, sigma(372)=896, sigma(373)=374, sigma(374)=648, sigma(375)=624, sigma(376)=720, sigma(377)=420, sigma(378)=960, sigma(379)=380, sigma(380)=840, sigma(381)=512, sigma(382)=576, sigma(383)=384, sigma(384)=1020, sigma(385)=576, sigma(386)=582, sigma(387)=572, sigma(388)=686, sigma(389)=390, sigma(390)=1008, sigma(391)=432, sigma(392)=855, sigma(393)=528, sigma(394)=594, sigma(395)=480, sigma(396)=1092, sigma(397)=398, sigma(398)=600, sigma(399)=640, sigma(400)=961, sigma(401)=402, sigma(402)=816, sigma(403)=448, sigma(404)=714, sigma(405)=726, sigma(406)=720, sigma(407)=456, sigma(408)=1080, sigma(409)=410, sigma(410)=756, sigma(411)=552, sigma(412)=728, sigma(413)=480, sigma(414)=936, sigma(415)=504, sigma(416)=882, sigma(417)=560, sigma(418)=720, sigma(419)=420, sigma(420)=1344, sigma(421)=422, sigma(422)=636, sigma(423)=624, sigma(424)=810, sigma(425)=558, sigma(426)=864, sigma(427)=496, sigma(428)=756, sigma(429)=672, sigma(430)=792, sigma(431)=432, sigma(432)=1240, sigma(433)=434, sigma(434)=768, sigma(435)=720, sigma(436)=770, sigma(437)=480, sigma(438)=888, sigma(439)=440, sigma(440)=1080, sigma(441)=741, sigma(442)=756, sigma(443)=444, sigma(444)=1064, sigma(445)=540, sigma(446)=672, sigma(447)=600, sigma(448)=1016, sigma(449)=450, sigma(450)=1209, sigma(451)=504, sigma(452)=798, sigma(453)=608, sigma(454)=684, sigma(455)=672, sigma(456)=1200, sigma(457)=458, sigma(458)=690, sigma(459)=720, sigma(460)=1008, sigma(461)=462, sigma(462)=1152, sigma(463)=464, sigma(464)=930, sigma(465)=768, sigma(466)=702, sigma(467)=468, sigma(468)=1274, sigma(469)=544, sigma(470)=864, sigma(471)=632, sigma(472)=900, sigma(473)=528, sigma(474)=960, sigma(475)=620, sigma(476)=1008, sigma(477)=702, sigma(478)=720, sigma(479)=480, sigma(480)=1512, sigma(481)=532, sigma(482)=726, sigma(483)=768, sigma(484)=931, sigma(485)=588, sigma(486)=1092, sigma(487)=488, sigma(488)=930, sigma(489)=656, sigma(490)=1026, sigma(491)=492, sigma(492)=1176, sigma(493)=540, sigma(494)=840, sigma(495)=936, sigma(496)=992, sigma(497)=576, sigma(498)=1008, sigma(499)=500, sigma(500)=1092, ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.017s sys 0m0.006s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Sun Jun 12 17:42:46 2005 Input: for(x=1,500,if sigma(x) = x*x, print1("sigma(",x,")=",sigma(x),", ")) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...or(x=1,500,ifsigma(x)=x*x *** ,print1("sigma(",x," ^-------------------- Timing: real 0m0.017s user 0m0.009s sys 0m0.009s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Sun Jun 12 17:43:16 2005 Input: for(x=1,500,if (sigma(x) = x*x, print1("sigma(",x,")=",sigma(x),", "))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: for(x=1,500,if(sigma(x)=x*x,print1("sigma(" ^-------------------- Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Sun Jun 12 17:45:46 2005 Input: for(x=1,500,if ((sigma(x) == x*x), print1("sigma(",x,")=",sigma(x),", "))) Output: ? sigma(1)=1, ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.014s sys 0m0.007s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Sun Jun 12 17:46:14 2005 Input: for(x=1,500,if ((sigma(x) = x*x), print1("sigma(",x,")=",sigma(x),", "))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: for(x=1,500,if((sigma(x)=x*x),print1("sigma( ^-------------------- Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Sun Jun 12 17:47:07 2005 Input: print1(sigma(6)) Output: ? 12 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Sun Jun 12 17:47:25 2005 Input: print1(sigma(36)) Output: ? 91 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Sun Jun 12 17:47:37 2005 Input: print1(sigma(144)) Output: ? 403 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '151.197' ************** PARI ***************** Host 151.197.25.169 (151.197.25.169) Time: Sun Jun 12 19:12:51 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.011s sys 0m0.007s '172.161' ************** PARI ***************** Host 172.161.248.234 (172.161.248.234) Time: Sun Jun 12 21:32:40 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:52:01 2005 Input: (1 + sqrt(5))^2 Output: ? 10.472135954999579392818347337462552470 ? Errors (if any) and Timing Info: Timing: real 0m0.063s user 0m0.007s sys 0m0.011s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:53:25 2005 Input: (((1 + sqrt(5)/2))^2 + ((1 - sqrt(5)/2))^2)/sqrt(5) Output: ? 2.0124611797498107267682563018581486118 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.010s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:53:41 2005 Input: (((1 + sqrt(5)/2))^2 - ((1 - sqrt(5)/2))^2)/sqrt(5) Output: ? 2.0000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:53:49 2005 Input: (((1 + sqrt(5)/2))^789 - ((1 - sqrt(5)/2))^789)/sqrt(5) Output: ? 6.4802668598495048236379673154258459153 E256 ? Errors (if any) and Timing Info: Timing: real 0m0.078s user 0m0.011s sys 0m0.007s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:54:35 2005 Input: (((1 + sqrt(5)/2))^789 - ((1 - sqrt(5)/2))^789)/sqrt(5) Output: ? 6.4802668598495048236379673154258459153 E256 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.011s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:55:12 2005 Input: (((1 + sqrt(5)/2))^7 - ((1 - sqrt(5)/2))^7)/sqrt(5) Output: ? 85.515624999999999999999999999999999997 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:55:38 2005 Input: (((1 + sqrt(5)/2))^7 - ((1 - sqrt(5)/2))^7)/sqrt(5) Output: ? 85.515624999999999999999999999999999997 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:56:06 2005 Input: (((1 + sqrt(5)/2))^1 - ((1 - sqrt(5)/2))^1)/sqrt(5) Output: ? 1.0000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.010s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:56:13 2005 Input: (((1 + sqrt(5)/2))^2 - ((1 - sqrt(5)/2))^2)/sqrt(5) Output: ? 2.0000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.007s sys 0m0.012s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:56:20 2005 Input: (((1 + sqrt(5)/2))^3 - ((1 - sqrt(5)/2))^3)/sqrt(5) Output: ? 4.2499999999999999999999999999999999999 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:56:43 2005 Input: ((((1 + sqrt(5))/2))^3 - (((1 - sqrt(5))/2))^3)/sqrt(5) Output: ? 1.9999999999999999999999999999999999999 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:56:58 2005 Input: ((((1 + sqrt(5))/2))^789 - (((1 - sqrt(5))/2))^789)/sqrt(5) Output: ? 3.4814739911549047329849104541489456156 E164 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:57:43 2005 Input: ((((1 + sqrt(5))/2))^789 - (((1 - sqrt(5))/2))^789)/sqrt(5) Output: ? 3.4814739911549047329849104541489456156 E164 ? Errors (if any) and Timing Info: Timing: real 0m0.111s user 0m0.010s sys 0m0.007s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:58:18 2005 Input: ((((1 + sqrt(5))/2))^789)/sqrt(5) Output: ? 3.4814739911549047329849104541489456156 E164 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:58:32 2005 Input: (((1 + sqrt(5))/2)^789)/sqrt(5) Output: ? 3.4814739911549047329849104541489456156 E164 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:58:55 2005 Input: (((1 + sqrt(5))/2)^7)/sqrt(5) Output: ? 12.984597134749390119586603639320701082 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:59:00 2005 Input: (((1 + sqrt(5))/2)^12)/sqrt(5) Output: ? 144.00138887549322822437539213314709477 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:59:09 2005 Input: (((1 + sqrt(5))/2)^30)/sqrt(5) Output: ? 832040.00000024037305898747923272019728 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Sun Jun 12 23:59:19 2005 Input: (((1 + sqrt(5))/2)^50)/sqrt(5) Output: ? 12586269025.000000000015890332520522297 ? Errors (if any) and Timing Info: Timing: real 0m0.085s user 0m0.012s sys 0m0.005s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Mon Jun 13 00:00:27 2005 Input: (((1 + sqrt(5))/2)^3)/sqrt(5) Output: ? 1.8944271909999158785636694674925104941 ? Errors (if any) and Timing Info: Timing: real 0m0.158s user 0m0.008s sys 0m0.010s '158.109' ************** PARI ***************** Host 158.109.70.15 (158.109.70.15) Time: Tue Jun 14 05:20:41 2005 Input: Binom(20,3); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Binom(20,3); ^------------ Timing: real 0m0.103s user 0m0.006s sys 0m0.011s '84.56.2' ************** PARI ***************** Host 84.56.225.125 (84.56.225.125) Time: Tue Jun 14 11:17:02 2005 Input: 2206^2 Output: ? 4866436 ? Errors (if any) and Timing Info: Timing: real 0m0.297s user 0m0.013s sys 0m0.010s '24.221.' ************** PARI ***************** Host 24.221.169.26 (24.221.169.26) Time: Tue Jun 14 11:32:53 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '24.221.' ************** PARI ***************** Host 24.221.169.26 (24.221.169.26) Time: Tue Jun 14 11:33:23 2005 Input: 2^64 Output: ? 18446744073709551616 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '24.221.' ************** PARI ***************** Host 24.221.169.26 (24.221.169.26) Time: Tue Jun 14 11:33:43 2005 Input: (2^64) / 150000 Output: ? 1152921504606846976/9375 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.010s sys 0m0.007s '24.221.' ************** PARI ***************** Host 24.221.169.26 (24.221.169.26) Time: Tue Jun 14 11:33:58 2005 Input: 1152921504606846976/9375 Output: ? 1152921504606846976/9375 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '24.221.' ************** PARI ***************** Host 24.221.169.26 (24.221.169.26) Time: Tue Jun 14 11:37:00 2005 Input: 2^64 Output: ? 18446744073709551616 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Jun 14 17:30:20 2005 Input: 3^2-2^2 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.339s user 0m0.008s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Jun 14 17:30:26 2005 Input: 5^2-3^2-2^2 Output: ? 12 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Tue Jun 14 17:30:35 2005 Input: 4^2-3^2-2^2 Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '67.85.2' ************** PARI ***************** Host 67.85.24.98 (67.85.24.98) Time: Wed Jun 15 07:48:25 2005 Input: 3/17+O(5^20) Output: ? 4 + 5 + 2*5^2 + 5^3 + 2*5^5 + 4*5^6 + 5^8 + 3*5^9 + 2*5^10 + 3*5^11 + 4*5^12 + 2*5^13 + 4*5^15 + 3*5^16 + 5^17 + 2*5^18 + 5^19 + O(5^20) ? Errors (if any) and Timing Info: Timing: real 0m0.318s user 0m0.009s sys 0m0.009s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Wed Jun 15 10:31:10 2005 Input: isprime(73) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.203s user 0m0.010s sys 0m0.009s '162.95.' ************** PARI ***************** Host 162.95.80.197 (162.95.80.197) Time: Wed Jun 15 10:31:38 2005 Input: isprime(91) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.043s user 0m0.009s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Wed Jun 15 16:29:30 2005 Input: mod(2,3) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(2,3) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.038s user 0m0.011s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Wed Jun 15 16:30:22 2005 Input: mod(2,3) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(2,3) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Wed Jun 15 16:30:23 2005 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '155.207' ************** PARI ***************** Host 155.207.209.243 (155.207.209.243) Time: Wed Jun 15 20:58:41 2005 Input: G := CyclicGroup(4); RG := InvariantRing(G, RationaField()); P:=PrimaryInvariants(R) Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: G:=CyclicGroup(4); ^---------------- *** unexpected character: RG:=InvariantRing(G,Rat ^-------------------- *** unexpected character: P:=PrimaryInvariants(R ^-------------------- Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '150.214' ************** PARI ***************** Host 150.214.50.121 (150.214.50.121) Time: Thu Jun 16 06:07:17 2005 Input: HilbertClassPolynomial(-3); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: HilbertClassPolynomi ^-------------------- Timing: real 0m0.109s user 0m0.011s sys 0m0.007s '24.11.1' ************** PARI ***************** Host 24.11.159.218 (24.11.159.218) Time: Thu Jun 16 12:52:00 2005 Input: read("computel"); read the ComputeL package and set the default values default(realprecision,28); set working precision; used throughout P = 37; May change this to to any other odd prime Chi = Legendre character modulo this P initialize L-function parameters conductor = P; exponential factor gammaV = [P%4==3]; [0] if P=1 mod 4 (even), [1] if 3 mod 4 (odd) weight = 1; L(s)=sgn*L(weight-s) sgn = 1; sign in the functional equation a(n) = if(n%P,(-1)^((P-1)/znorder(Mod(n,P))),0); coefficients: 1 for n square mod P, -1 for non-square, 0 for n=0 mod P initLdata("a(k)"); initialize L-function parameters zinit = zetakinit(nfinit(quadpoly(quaddisc(if(P%4==3,-P,P))))); LPari(x) = zetak(zinit,x)/zeta(x); alternatively the same L-function is the Dedekind zeta function of the maximal order of Q(sqrt(P)) (p=1 mod 4) or Q(sqrt(-P)) (p=3 mod 4) divided by the Riemann zeta function print("EXAMPLE: L(s)=L(Chi(P),s), Chi(P)=(Legendre) quadratic character modulo P"); print(" with ",default(realprecision,,1)," digits precision"); print(" take P=",P); print("Verifying functional equation. Error: ",errprint(checkfeq())); print("L(Chi(P),2) = ",L(2)); print(" (pari) = ",LPari(2)); print("L(Chi(P),I) = ",L(I)); print(" (pari) = ",LPari(I)); Output: WARNING: PARI command contains unsafe command 'read', so it will not be executed. '24.11.1' ************** PARI ***************** Host 24.11.159.218 (24.11.159.218) Time: Thu Jun 16 12:52:10 2005 Input: read the ComputeL package and set the default values default(realprecision,28); set working precision; used throughout P = 37; May change this to to any other odd prime Chi = Legendre character modulo this P initialize L-function parameters conductor = P; exponential factor gammaV = [P%4==3]; [0] if P=1 mod 4 (even), [1] if 3 mod 4 (odd) weight = 1; L(s)=sgn*L(weight-s) sgn = 1; sign in the functional equation a(n) = if(n%P,(-1)^((P-1)/znorder(Mod(n,P))),0); coefficients: 1 for n square mod P, -1 for non-square, 0 for n=0 mod P initLdata("a(k)"); initialize L-function parameters zinit = zetakinit(nfinit(quadpoly(quaddisc(if(P%4==3,-P,P))))); LPari(x) = zetak(zinit,x)/zeta(x); alternatively the same L-function is the Dedekind zeta function of the maximal order of Q(sqrt(P)) (p=1 mod 4) or Q(sqrt(-P)) (p=3 mod 4) divided by the Riemann zeta function print("EXAMPLE: L(s)=L(Chi(P),s), Chi(P)=(Legendre) quadratic character modulo P"); print(" with ",default(realprecision,,1)," digits precision"); print(" take P=",P); print("Verifying functional equation. Error: ",errprint(checkfeq())); print("L(Chi(P),2) = ",L(2)); print(" (pari) = ",LPari(2)); print("L(Chi(P),I) = ",L(I)); print(" (pari) = ",LPari(I)); Output: WARNING: PARI command contains unsafe command 'read', so it will not be executed. '24.11.1' ************** PARI ***************** Host 24.11.159.218 (24.11.159.218) Time: Thu Jun 16 12:52:17 2005 Input: read("computel"); read the ComputeL package and set the default values default(realprecision,28); set working precision; used throughout P = 37; May change this to to any other odd prime Chi = Legendre character modulo this P initialize L-function parameters conductor = P; exponential factor gammaV = [P%4==3]; [0] if P=1 mod 4 (even), [1] if 3 mod 4 (odd) weight = 1; L(s)=sgn*L(weight-s) sgn = 1; sign in the functional equation a(n) = if(n%P,(-1)^((P-1)/znorder(Mod(n,P))),0); coefficients: 1 for n square mod P, -1 for non-square, 0 for n=0 mod P initLdata("a(k)"); initialize L-function parameters zinit = zetakinit(nfinit(quadpoly(quaddisc(if(P%4==3,-P,P))))); LPari(x) = zetak(zinit,x)/zeta(x); alternatively the same L-function is the Dedekind zeta function of the maximal order of Q(sqrt(P)) (p=1 mod 4) or Q(sqrt(-P)) (p=3 mod 4) divided by the Riemann zeta function print("EXAMPLE: L(s)=L(Chi(P),s), Chi(P)=(Legendre) quadratic character modulo P"); print(" with ",default(realprecision,,1)," digits precision"); print(" take P=",P); print("Verifying functional equation. Error: ",errprint(checkfeq())); print("L(Chi(P),2) = ",L(2)); print(" (pari) = ",LPari(2)); print("L(Chi(P),I) = ",L(I)); print(" (pari) = ",LPari(I)); Output: WARNING: PARI command contains unsafe command 'read', so it will not be executed. '130.91.' ************** PARI ***************** Host 130.91.119.32 (130.91.119.32) Time: Thu Jun 16 19:04:01 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.224s user 0m0.011s sys 0m0.015s '130.91.' ************** PARI ***************** Host 130.91.119.32 (130.91.119.32) Time: Thu Jun 16 19:04:50 2005 Input: divisors(15) Output: ? [1, 3, 5, 15] ? Errors (if any) and Timing Info: Timing: real 0m0.075s user 0m0.011s sys 0m0.006s '130.91.' ************** PARI ***************** Host 130.91.119.32 (130.91.119.32) Time: Thu Jun 16 19:05:16 2005 Input: divisors(2000) Output: ? [1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '84.0.20' ************** PARI ***************** Host 84.0.206.199 (84.0.206.199) Time: Fri Jun 17 12:34:14 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.299s user 0m0.009s sys 0m0.014s '68.57.2' ************** PARI ***************** Host 68.57.240.104 (68.57.240.104) Time: Fri Jun 17 19:43:04 2005 Input: gcd(5,20) Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.164s user 0m0.016s sys 0m0.005s '68.57.2' ************** PARI ***************** Host 68.57.240.104 (68.57.240.104) Time: Fri Jun 17 19:43:16 2005 Input: gcd(9,12) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.043s user 0m0.010s sys 0m0.008s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Sat Jun 18 20:50:16 2005 Input: ec=[0,-1,1,-10,-20]]; ellinit(ec); ellan(ec,10) Output: ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ];. *** bad argument for an elliptic curve related function Timing: real 0m0.320s user 0m0.013s sys 0m0.014s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Sat Jun 18 20:50:24 2005 Input: ec=[0,-1,1,-10,-20]; ellinit(ec); ellan(ec,10) Output: ? ? ? ? Errors (if any) and Timing Info: *** bad argument for an elliptic curve related function Timing: real 0m0.021s user 0m0.016s sys 0m0.005s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Sat Jun 18 20:50:38 2005 Input: ec=[0,-1,1,-10,-20]; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Sat Jun 18 20:52:50 2005 Input: ec=[0,-1,1,-10,-20] Output: ? [0, -1, 1, -10, -20] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Sat Jun 18 20:53:23 2005 Input: ellinit([0,-1,1,-10,-20]) Output: ? [0, -1, 1, -10, -20, -4, -20, -79, -21, 496, 20008, -161051, -122023936/161051, [4.3463081582053944219694907905834258736, -1.6731540791026972109847453952917129368 + 1.3208489222690756656025159770879936319*I, -1.6731540791026972109847453952917129368 - 1.3208489222690756656025159770879936319*I]~, 1.2692093042795534216887946167545473052, 0.63460465213977671084439730837727365261 + 1.4588166169384952293308896129036752571*I, -1.3187017138260129139402174138729968787 + 1.153306698273828119 E-38*I, -0.65935085691300645697010870693649843937 - 3.9909387753659048872536198729891868906*I, 1.8515436234559593177080067118252488887] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.010s sys 0m0.010s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Sat Jun 18 20:53:32 2005 Input: s=[0,-1,1,-10,-20] Output: ? [0, -1, 1, -10, -20] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.009s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Sat Jun 18 20:53:43 2005 Input: s=[0,-1,1,-10,-20];ellinit(s) Output: ? [0, -1, 1, -10, -20, -4, -20, -79, -21, 496, 20008, -161051, -122023936/161051, [4.3463081582053944219694907905834258736, -1.6731540791026972109847453952917129368 + 1.3208489222690756656025159770879936319*I, -1.6731540791026972109847453952917129368 - 1.3208489222690756656025159770879936319*I]~, 1.2692093042795534216887946167545473052, 0.63460465213977671084439730837727365261 + 1.4588166169384952293308896129036752571*I, -1.3187017138260129139402174138729968787 + 1.153306698273828119 E-38*I, -0.65935085691300645697010870693649843937 - 3.9909387753659048872536198729891868906*I, 1.8515436234559593177080067118252488887] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.017s sys 0m0.003s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Sat Jun 18 20:53:51 2005 Input: s=[0,-1,1,-10,-20];ellinit(s); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.015s sys 0m0.006s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Sat Jun 18 20:54:13 2005 Input: s=[0,-1,1,-10,-20];ellinit(s); ellan(s,10) Output: ? ? ? Errors (if any) and Timing Info: *** bad argument for an elliptic curve related function Timing: real 0m0.020s user 0m0.011s sys 0m0.009s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Sat Jun 18 20:54:20 2005 Input: s=[0,-1,1,-10,-20];ellinit(s);ellan(s,10) Output: ? ? Errors (if any) and Timing Info: *** bad argument for an elliptic curve related function Timing: real 0m0.020s user 0m0.012s sys 0m0.009s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Sat Jun 18 20:54:39 2005 Input: s=[0,-1,1,-10,-20];ellinit(s);ellap(s,3) Output: ? ? Errors (if any) and Timing Info: *** bad argument for an elliptic curve related function Timing: real 0m0.020s user 0m0.012s sys 0m0.008s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Sat Jun 18 20:55:03 2005 Input: s=[0,-1,1,-10,-20];ellinit(s);ellap(s,3) Output: ? ? Errors (if any) and Timing Info: *** bad argument for an elliptic curve related function Timing: real 0m0.020s user 0m0.011s sys 0m0.009s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Sat Jun 18 20:55:10 2005 Input: s=[0,-1,1,-10,-20];ellinit(s) Output: ? [0, -1, 1, -10, -20, -4, -20, -79, -21, 496, 20008, -161051, -122023936/161051, [4.3463081582053944219694907905834258736, -1.6731540791026972109847453952917129368 + 1.3208489222690756656025159770879936319*I, -1.6731540791026972109847453952917129368 - 1.3208489222690756656025159770879936319*I]~, 1.2692093042795534216887946167545473052, 0.63460465213977671084439730837727365261 + 1.4588166169384952293308896129036752571*I, -1.3187017138260129139402174138729968787 + 1.153306698273828119 E-38*I, -0.65935085691300645697010870693649843937 - 3.9909387753659048872536198729891868906*I, 1.8515436234559593177080067118252488887] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.009s sys 0m0.011s '221.186' ************** PARI ***************** Host 221.186.0.23 (221.186.0.23) Time: Sun Jun 19 05:43:53 2005 Input: 256128064032016008004002001/999999999999999999999999999 Output: ? 256128064032016008004002001/999999999999999999999999999 ? Errors (if any) and Timing Info: Timing: real 0m0.313s user 0m0.010s sys 0m0.008s '221.186' ************** PARI ***************** Host 221.186.0.23 (221.186.0.23) Time: Sun Jun 19 05:44:04 2005 Input: 256128064032016008004002001/999999999999999999999999999= Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...9999999999999999999999999= ^- Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '84.188.' ************** PARI ***************** Host 84.188.171.110 (84.188.171.110) Time: Sun Jun 19 11:11:09 2005 Input: 6+7 Output: ? 13 ? Errors (if any) and Timing Info: Timing: real 0m0.281s user 0m0.012s sys 0m0.012s '221.186' ************** PARI ***************** Host 221.186.0.23 (221.186.0.23) Time: Mon Jun 20 13:26:12 2005 Input: FindGroupOrder2 := function (p, s) K := GF(p); v := K ! (4*s); u := K ! (s^2-5); x := u^3; b := 4*x*v; a := (v-u)^3*(3*u+v); A := a/b-2; x := x/v^3; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); return FactoredOrder(E); end function; p := 140853945410621700611366248656986006762214430713643; s := 941728572; FindGroupOrder2(p, s); Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: FindGroupOrder2:=function(p,s) ^-------------- *** unexpected character: K:=GF(p); ^------- *** unexpected character: v:=K!(4*s); ^--------- *** unexpected character: u:=K!(s^2-5); ^----------- *** unexpected character: x:=u^3; ^----- *** unexpected character: b:=4*x*v; ^------- *** unexpected character: a:=(v-u)^3*(3*u+v); ^----------------- *** unexpected character: A:=a/b-2; ^------- *** unexpected character: x:=x/v^3; ^------- *** unexpected character: b:=x^3+A*x^2+x; ^------------- *** unexpected character: E:=EllipticCurve([0,b* ^-------------------- *** expected character: '=' instead of: returnFactoredOrder(E); ^- *** unexpected character: p:=1408539454106217006 ^-------------------- *** unexpected character: s:=941728572; ^----------- *** expected character: '=' instead of: FindGroupOrder2(p,s); ^- Timing: real 0m0.266s user 0m0.009s sys 0m0.012s '84.98.2' ************** PARI ***************** Host 84.98.227.208 (84.98.227.208) Time: Mon Jun 20 16:25:12 2005 Input: 909 Output: ? 909 ? Errors (if any) and Timing Info: Timing: real 0m0.091s user 0m0.010s sys 0m0.006s '218.47.' ************** PARI ***************** Host 218.47.18.98 (218.47.18.98) Time: Mon Jun 20 19:21:31 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.012s sys 0m0.007s '195.250' ************** PARI ***************** Host 195.250.185.98 (195.250.185.98) Time: Tue Jun 21 07:33:19 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.291s user 0m0.012s sys 0m0.011s '12.3.62' ************** PARI ***************** Host 12.3.62.1 (12.3.62.1) Time: Tue Jun 21 10:25:12 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.007s sys 0m0.012s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Tue Jun 21 19:37:32 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.229s user 0m0.010s sys 0m0.014s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Tue Jun 21 19:37:50 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Tue Jun 21 19:38:06 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Tue Jun 21 19:44:28 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Tue Jun 21 19:44:52 2005 Input: for(n=1,100, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, 8: 761/280, 9: 7129/2520, 10: 7381/2520, 11: 83711/27720, 12: 86021/27720, 13: 1145993/360360, 14: 1171733/360360, 15: 1195757/360360, 16: 2436559/720720, 17: 42142223/12252240, 18: 14274301/4084080, 19: 275295799/77597520, 20: 55835135/15519504, 21: 18858053/5173168, 22: 19093197/5173168, 23: 444316699/118982864, 24: 1347822955/356948592, 25: 34052522467/8923714800, 26: 34395742267/8923714800, 27: 312536252003/80313433200, 28: 315404588903/80313433200, 29: 9227046511387/2329089562800, 30: 9304682830147/2329089562800, 31: 290774257297357/72201776446800, 32: 586061125622639/144403552893600, 33: 53676090078349/13127595717600, 34: 54062195834749/13127595717600, 35: 54437269998109/13127595717600, 36: 54801925434709/13127595717600, 37: 2040798836801833/485721041551200, 38: 2053580969474233/485721041551200, 39: 2066035355155033/485721041551200, 40: 2078178381193813/485721041551200, 41: 85691034670497533/19914562703599200, 42: 12309312989335019/2844937529085600, 43: 532145396070491417/122332313750680800, 44: 5884182435213075787/1345655451257488800, 45: 5914085889685464427/1345655451257488800, 46: 5943339269060627227/1345655451257488800, 47: 280682601097106968469/63245806209101973600, 48: 282000222059796592919/63245806209101973600, 49: 13881256687139135026631/3099044504245996706400, 50: 13943237577224054960759/3099044504245996706400, 51: 14004003155738682347159/3099044504245996706400, 52: 14063600165435720745359/3099044504245996706400, 53: 748469853272339196210427/164249358725037825439200, 54: 250503836021181200128409/54749786241679275146400, 55: 251499286680120823312889/54749786241679275146400, 56: 252476961434436524654789/54749786241679275146400, 57: 253437484000080020709989/54749786241679275146400, 58: 254381445831833111660789/54749786241679275146400, 59: 15063255090319832863132951/3230237388259077233637600, 60: 15117092380124150817026911/3230237388259077233637600, 61: 925372872575832277072279171/197044480683803711251893600, 62: 928551009361054917576341971/197044480683803711251893600, 63: 310559566510213034489743057/65681493561267903750631200, 64: 623171679694215690971693339/131362987122535807501262400, 65: 625192648726870088010174299/131362987122535807501262400, 66: 209060999005535159677640233/43787662374178602500420800, 67: 14050874595745034300902316411/2933773379069966367528193600, 68: 14094018321907827923954201611/2933773379069966367528193600, 69: 42409610330030873613929048033/8801320137209899102584580800, 70: 42535343474848157886823113473/8801320137209899102584580800, 71: 3028810706851429109067025637383/624893729741902836283505236800, 72: 9112469359293533278712889630349/1874681189225708508850515710400, 73: 667084944417653637854891458725877/136851726813476721146087646859200, 74: 668934292077295215167676426926677/136851726813476721146087646859200, 75: 670758981768141571449624262218133/136851726813476721146087646859200, 76: 672559662384108370412072783887333/136851726813476721146087646859200, 77: 61303359776139104182852056677903/12441066073952429195098876987200, 78: 61462860623241058403302042280303/12441066073952429195098876987200, 79: 4868007055309996043055960217131137/982844219842241906412811281988800, 80: 4880292608058024066886120358155997/982844219842241906412811281988800, 81: 44031838385838021258243173365847173/8845597978580177157715301537899200, 82: 44139711531918267321142140457772773/8845597978580177157715301537899200, 83: 3672441655127796364812512959533039359/734184632222154704090370027645633600, 84: 3681181948368536301765969745576439759/734184632222154704090370027645633600, 85: 3689819414629973415931738804725211919/734184632222154704090370027645633600, 86: 3698356445237207772956045432953649519/734184632222154704090370027645633600, 87: 3706795349055853229324900260857622319/734184632222154704090370027645633600, 88: 40866521918642154860585199122889549709/8076030954443701744994070304101969600, 89: 3645196481713595484337076792241271893701/718766754945489455304472257065075294400, 90: 3653182778990767589396015372875328285861/718766754945489455304472257065075294400, 91: 3661081314759399341652108474601318124261/718766754945489455304472257065075294400, 92: 3668893996878372053122809260004199377461/718766754945489455304472257065075294400, 93: 3676622671662732154792749821908124918261/718766754945489455304472257065075294400, 94: 3684269126502577787295988888472646995861/718766754945489455304472257065075294400, 95: 3691835092344109255246562280652279367381/718766754945489455304472257065075294400, 96: 3699322246041458103739317199996707235031/718766754945489455304472257065075294400, 97: 359553024620966925518018240656745677092407/69720375229712477164533808935312303556800, 98: 360264457021270114060513483605065190394007/69720375229712477164533808935312303556800, 99: 360968703235711654233892612988250163157207/69720375229712477164533808935312303556800, 100: 14466636279520351160221518043104131447711/2788815009188499086581352357412492142272, ? Errors (if any) and Timing Info: Timing: real 0m0.061s user 0m0.019s sys 0m0.008s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Tue Jun 21 19:51:57 2005 Input: for(n=1,105, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, 8: 761/280, 9: 7129/2520, 10: 7381/2520, 11: 83711/27720, 12: 86021/27720, 13: 1145993/360360, 14: 1171733/360360, 15: 1195757/360360, 16: 2436559/720720, 17: 42142223/12252240, 18: 14274301/4084080, 19: 275295799/77597520, 20: 55835135/15519504, 21: 18858053/5173168, 22: 19093197/5173168, 23: 444316699/118982864, 24: 1347822955/356948592, 25: 34052522467/8923714800, 26: 34395742267/8923714800, 27: 312536252003/80313433200, 28: 315404588903/80313433200, 29: 9227046511387/2329089562800, 30: 9304682830147/2329089562800, 31: 290774257297357/72201776446800, 32: 586061125622639/144403552893600, 33: 53676090078349/13127595717600, 34: 54062195834749/13127595717600, 35: 54437269998109/13127595717600, 36: 54801925434709/13127595717600, 37: 2040798836801833/485721041551200, 38: 2053580969474233/485721041551200, 39: 2066035355155033/485721041551200, 40: 2078178381193813/485721041551200, 41: 85691034670497533/19914562703599200, 42: 12309312989335019/2844937529085600, 43: 532145396070491417/122332313750680800, 44: 5884182435213075787/1345655451257488800, 45: 5914085889685464427/1345655451257488800, 46: 5943339269060627227/1345655451257488800, 47: 280682601097106968469/63245806209101973600, 48: 282000222059796592919/63245806209101973600, 49: 13881256687139135026631/3099044504245996706400, 50: 13943237577224054960759/3099044504245996706400, 51: 14004003155738682347159/3099044504245996706400, 52: 14063600165435720745359/3099044504245996706400, 53: 748469853272339196210427/164249358725037825439200, 54: 250503836021181200128409/54749786241679275146400, 55: 251499286680120823312889/54749786241679275146400, 56: 252476961434436524654789/54749786241679275146400, 57: 253437484000080020709989/54749786241679275146400, 58: 254381445831833111660789/54749786241679275146400, 59: 15063255090319832863132951/3230237388259077233637600, 60: 15117092380124150817026911/3230237388259077233637600, 61: 925372872575832277072279171/197044480683803711251893600, 62: 928551009361054917576341971/197044480683803711251893600, 63: 310559566510213034489743057/65681493561267903750631200, 64: 623171679694215690971693339/131362987122535807501262400, 65: 625192648726870088010174299/131362987122535807501262400, 66: 209060999005535159677640233/43787662374178602500420800, 67: 14050874595745034300902316411/2933773379069966367528193600, 68: 14094018321907827923954201611/2933773379069966367528193600, 69: 42409610330030873613929048033/8801320137209899102584580800, 70: 42535343474848157886823113473/8801320137209899102584580800, 71: 3028810706851429109067025637383/624893729741902836283505236800, 72: 9112469359293533278712889630349/1874681189225708508850515710400, 73: 667084944417653637854891458725877/136851726813476721146087646859200, 74: 668934292077295215167676426926677/136851726813476721146087646859200, 75: 670758981768141571449624262218133/136851726813476721146087646859200, 76: 672559662384108370412072783887333/136851726813476721146087646859200, 77: 61303359776139104182852056677903/12441066073952429195098876987200, 78: 61462860623241058403302042280303/12441066073952429195098876987200, 79: 4868007055309996043055960217131137/982844219842241906412811281988800, 80: 4880292608058024066886120358155997/982844219842241906412811281988800, 81: 44031838385838021258243173365847173/8845597978580177157715301537899200, 82: 44139711531918267321142140457772773/8845597978580177157715301537899200, 83: 3672441655127796364812512959533039359/734184632222154704090370027645633600, 84: 3681181948368536301765969745576439759/734184632222154704090370027645633600, 85: 3689819414629973415931738804725211919/734184632222154704090370027645633600, 86: 3698356445237207772956045432953649519/734184632222154704090370027645633600, 87: 3706795349055853229324900260857622319/734184632222154704090370027645633600, 88: 40866521918642154860585199122889549709/8076030954443701744994070304101969600, 89: 3645196481713595484337076792241271893701/718766754945489455304472257065075294400, 90: 3653182778990767589396015372875328285861/718766754945489455304472257065075294400, 91: 3661081314759399341652108474601318124261/718766754945489455304472257065075294400, 92: 3668893996878372053122809260004199377461/718766754945489455304472257065075294400, 93: 3676622671662732154792749821908124918261/718766754945489455304472257065075294400, 94: 3684269126502577787295988888472646995861/718766754945489455304472257065075294400, 95: 3691835092344109255246562280652279367381/718766754945489455304472257065075294400, 96: 3699322246041458103739317199996707235031/718766754945489455304472257065075294400, 97: 359553024620966925518018240656745677092407/69720375229712477164533808935312303556800, 98: 360264457021270114060513483605065190394007/69720375229712477164533808935312303556800, 99: 360968703235711654233892612988250163157207/69720375229712477164533808935312303556800, 100: 14466636279520351160221518043104131447711/2788815009188499086581352357412492142272, 101: 1463919079240743966268954674710929768361083/281670315928038407744716588098661706369472, 102: 1466680552926312970266451896162877432149019/281670315928038407744716588098661706369472, 103: 151349767267338274345189261892875037217718429/29012042540587955997705808574162155756055616, 104: 151628729214843927768244125436857365638449733/29012042540587955997705808574162155756055616, 105: 759525171909485731983968522830675502275870361/145060212702939779988529042870810778780278080, ? Errors (if any) and Timing Info: Timing: real 0m0.130s user 0m0.015s sys 0m0.011s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Tue Jun 21 20:00:26 2005 Input: for(n=100,105, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 100: 14466636279520351160221518043104131447711/2788815009188499086581352357412492142272, 101: 1463919079240743966268954674710929768361083/281670315928038407744716588098661706369472, 102: 1466680552926312970266451896162877432149019/281670315928038407744716588098661706369472, 103: 151349767267338274345189261892875037217718429/29012042540587955997705808574162155756055616, 104: 151628729214843927768244125436857365638449733/29012042540587955997705808574162155756055616, 105: 759525171909485731983968522830675502275870361/145060212702939779988529042870810778780278080, ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.010s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Tue Jun 21 20:00:55 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.096s user 0m0.013s sys 0m0.004s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Tue Jun 21 20:06:30 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.011s '24.21.5' ************** PARI ***************** Host 24.21.50.230 (24.21.50.230) Time: Tue Jun 21 22:02:57 2005 Input: 1000! Output: ? 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.058s user 0m0.011s sys 0m0.011s '24.21.5' ************** PARI ***************** Host 24.21.50.230 (24.21.50.230) Time: Tue Jun 21 22:03:17 2005 Input: 25000! Output: ? 5447918548062263258561368239285288935878604361829680079137844171152518995254265927539650140698539532595021970422908846016533816908712644620984486590262302767015316608104811655362187507337693273469492352336557534726714074620194594802660892105328791442483462520139532964812705322302518223875907642656191997837700601216431500486653991103870225210234637477747279576629303653567945701617901390491108597115301739078220049404650088937786573871051782509061721691238094993486051834198972577928952217624899853700287091046013489032083580064733782406946026092196826927424088403481062744493715409593897361185668859776489190273071180613480001638659250287867246024550935401773238573122253887387462131684236484307324892141862046262796593956442063169761616054952125007427088828964394812409060510606296509581527339623918477966598847562543851178160453558473102183560280015593076560040025152551417264504606530287168623999306636516118811366428126240637225552973181882982303180533308928816159035401923834835649359838257644723553225375480508220907568622074293259519569663894347007211145945791998434646270258557071455883403738352031859497390928965419926807696735434206073645012543580923626716772135597607576802119652090916493740645487660069513883569310672117376362908024529980889668761144280277481555411666235995337186271291072616814670370153942308185744813822447586215483268249004953609555515920567999521047624267487351200565113442474846363814771471484806921561781277946487625927517870447877269381536430592099111903219456388122600512358287564636370190204929092024604573861456865857113924907730959038682843277446097991311698956173979349501317613701913499186030309375127843969621882851807432871104607642201592147469265147848966547271971834502829291379176481980013366392682643174965593711970343534495972871802995246726227949756688504126391963149081020345557879810500351358752541374439697189881393655657603937431433113744363436099353996723233614586273303349482743291547780170189440320117712542800437376221291534722756094467983820770976535456737783869250432233909739105763745670290172362767311219631061018722681188252808188495705458463643121509739184594545066497521060154569275377097861200313463493074932061866245992031283919774385955940496634722500845648133971273432636825043900298010070315014065194983193428980837495865299570597078514010382516921948749969574501131108944443754526254212630795436830197425166781308467906714454073774094855693647806527698880991273949082503709508634683472590914120056928199634918250357505956267457726639359966857765216887578683756576929775249913724363048660111748168845686036549448001527018851734061632333169700306628597120191553639491039911065943087251307190847201401768416043441032263578698443921396738734993554306061380751306841153040056262845710177467833187887484796767221642485667472067608260407249857691454721484298153471523226764039193778215399148727383814212723112393821039036703999057507003187945378367835695674781550892864401115579711047043077083018999847719533144321259138614771551863112635811062630934060850714475340407771356763018994720077799703137161373357954745961285821589418172006467560123485362336052796894561040054318959597690697877544972147510604947436411103650151249[+++] ? Errors (if any) and Timing Info: Timing: real 0m4.219s user 0m3.424s sys 0m0.012s '133.5.1' ************** PARI ***************** Host 133.5.165.4 (133.5.165.4) Time: Wed Jun 22 00:16:06 2005 Input: factor(100) Output: ? [2 2] [5 2] ? Errors (if any) and Timing Info: Timing: real 0m0.045s user 0m0.008s sys 0m0.009s '80.58.4' ************** PARI ***************** Host 80.58.42.235 (80.58.42.235) Time: Wed Jun 22 04:20:02 2005 Input: 3*2 Output: ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.014s sys 0m0.004s '80.58.4' ************** PARI ***************** Host 80.58.42.235 (80.58.42.235) Time: Wed Jun 22 04:20:15 2005 Input: 3*22222222222222222222222222222222222 Output: ? 66666666666666666666666666666666666 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.007s '80.58.4' ************** PARI ***************** Host 80.58.42.235 (80.58.42.235) Time: Wed Jun 22 04:20:53 2005 Input: 3*1/0 Output: ? ? Errors (if any) and Timing Info: *** division by zero in dvmdii Timing: real 0m0.017s user 0m0.007s sys 0m0.011s '137.195' ************** PARI ***************** Host 137.195.27.150 (137.195.27.150) Time: Wed Jun 22 05:48:21 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.011s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Wed Jun 22 20:15:28 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.180s user 0m0.012s sys 0m0.008s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Wed Jun 22 20:16:03 2005 Input: for(n=1,20 print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: for(n=1,20print1(n,": ",sum(x= ^-------------------- Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Wed Jun 22 20:16:06 2005 Input: for(n=1,20 print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: for(n=1,20print1(n,": ",sum(x= ^-------------------- Timing: real 0m0.018s user 0m0.006s sys 0m0.011s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Wed Jun 22 20:16:24 2005 Input: for(n=1,20 print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: for(n=1,20print1(n,": ",sum(x= ^-------------------- Timing: real 0m0.017s user 0m0.011s sys 0m0.007s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Wed Jun 22 20:16:49 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Wed Jun 22 20:17:03 2005 Input: for(n=1,20, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, 8: 761/280, 9: 7129/2520, 10: 7381/2520, 11: 83711/27720, 12: 86021/27720, 13: 1145993/360360, 14: 1171733/360360, 15: 1195757/360360, 16: 2436559/720720, 17: 42142223/12252240, 18: 14274301/4084080, 19: 275295799/77597520, 20: 55835135/15519504, ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.010s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Wed Jun 22 20:27:01 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.011s sys 0m0.007s '130.91.' ************** PARI ***************** Host 130.91.119.79 (130.91.119.79) Time: Wed Jun 22 20:27:44 2005 Input: for(n=1,30, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, 8: 761/280, 9: 7129/2520, 10: 7381/2520, 11: 83711/27720, 12: 86021/27720, 13: 1145993/360360, 14: 1171733/360360, 15: 1195757/360360, 16: 2436559/720720, 17: 42142223/12252240, 18: 14274301/4084080, 19: 275295799/77597520, 20: 55835135/15519504, 21: 18858053/5173168, 22: 19093197/5173168, 23: 444316699/118982864, 24: 1347822955/356948592, 25: 34052522467/8923714800, 26: 34395742267/8923714800, 27: 312536252003/80313433200, 28: 315404588903/80313433200, 29: 9227046511387/2329089562800, 30: 9304682830147/2329089562800, ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.010s sys 0m0.008s '216.195' ************** PARI ***************** Host 216.195.16.222 (216.195.16.222) Time: Wed Jun 22 23:11:58 2005 Input: FindGroupOrder2 := function (p, s) K := GF(p); v := K ! (4*s); u := K ! (s^2-5); x := u^3; b := 4*x*v; a := (v-u)^3*(3*u+v); A := a/b-2; x := x/v^3; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); return FactoredOrder(E); end function; p := 111993188756365886853577743582861876119213; s := 2227459121; FindGroupOrder2(p, s); Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: FindGroupOrder2:=function(p,s) ^-------------- *** unexpected character: K:=GF(p); ^------- *** unexpected character: v:=K!(4*s); ^--------- *** unexpected character: u:=K!(s^2-5); ^----------- *** unexpected character: x:=u^3; ^----- *** unexpected character: b:=4*x*v; ^------- *** unexpected character: a:=(v-u)^3*(3*u+v); ^----------------- *** unexpected character: A:=a/b-2; ^------- *** unexpected character: x:=x/v^3; ^------- *** unexpected character: b:=x^3+A*x^2+x; ^------------- *** unexpected character: E:=EllipticCurve([0,b* ^-------------------- *** expected character: '=' instead of: returnFactoredOrder(E); ^- *** unexpected character: p:=1119931887563658868 ^-------------------- *** unexpected character: s:=2227459121; ^------------ *** expected character: '=' instead of: FindGroupOrder2(p,s); ^- Timing: real 0m0.051s user 0m0.012s sys 0m0.007s '130.91.' ************** PARI ***************** Host 130.91.119.168 (130.91.119.168) Time: Thu Jun 23 16:44:55 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.215s user 0m0.010s sys 0m0.011s '130.91.' ************** PARI ***************** Host 130.91.119.168 (130.91.119.168) Time: Thu Jun 23 16:45:06 2005 Input: for(n=1,10, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, 8: 761/280, 9: 7129/2520, 10: 7381/2520, ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.011s '130.91.' ************** PARI ***************** Host 130.91.119.168 (130.91.119.168) Time: Thu Jun 23 16:46:34 2005 Input: for(n=10,20, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 10: 7381/2520, 11: 83711/27720, 12: 86021/27720, 13: 1145993/360360, 14: 1171733/360360, 15: 1195757/360360, 16: 2436559/720720, 17: 42142223/12252240, 18: 14274301/4084080, 19: 275295799/77597520, 20: 55835135/15519504, ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.008s sys 0m0.010s '130.91.' ************** PARI ***************** Host 130.91.119.168 (130.91.119.168) Time: Thu Jun 23 16:58:20 2005 Input: for(n=20,30, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 20: 55835135/15519504, 21: 18858053/5173168, 22: 19093197/5173168, 23: 444316699/118982864, 24: 1347822955/356948592, 25: 34052522467/8923714800, 26: 34395742267/8923714800, 27: 312536252003/80313433200, 28: 315404588903/80313433200, 29: 9227046511387/2329089562800, 30: 9304682830147/2329089562800, ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.009s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Thu Jun 23 19:29:41 2005 Input: factor(2^(2^5)+1) Output: ? [641 1] [6700417 1] ? Errors (if any) and Timing Info: Timing: real 0m0.645s user 0m0.008s sys 0m0.011s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Thu Jun 23 19:33:04 2005 Input: factor(2^(2^5)+1) Output: ? [641 1] [6700417 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Thu Jun 23 19:34:31 2005 Input: factor(2^(2^5)+1) Output: ? [641 1] [6700417 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.007s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Thu Jun 23 19:34:36 2005 Input: factor(2^(2^5)+1) Output: ? [641 1] [6700417 1] ? Errors (if any) and Timing Info: Timing: real 0m0.166s user 0m0.013s sys 0m0.006s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Thu Jun 23 19:51:11 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Thu Jun 23 19:51:44 2005 Input: for(n=1,100, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, 8: 761/280, 9: 7129/2520, 10: 7381/2520, 11: 83711/27720, 12: 86021/27720, 13: 1145993/360360, 14: 1171733/360360, 15: 1195757/360360, 16: 2436559/720720, 17: 42142223/12252240, 18: 14274301/4084080, 19: 275295799/77597520, 20: 55835135/15519504, 21: 18858053/5173168, 22: 19093197/5173168, 23: 444316699/118982864, 24: 1347822955/356948592, 25: 34052522467/8923714800, 26: 34395742267/8923714800, 27: 312536252003/80313433200, 28: 315404588903/80313433200, 29: 9227046511387/2329089562800, 30: 9304682830147/2329089562800, 31: 290774257297357/72201776446800, 32: 586061125622639/144403552893600, 33: 53676090078349/13127595717600, 34: 54062195834749/13127595717600, 35: 54437269998109/13127595717600, 36: 54801925434709/13127595717600, 37: 2040798836801833/485721041551200, 38: 2053580969474233/485721041551200, 39: 2066035355155033/485721041551200, 40: 2078178381193813/485721041551200, 41: 85691034670497533/19914562703599200, 42: 12309312989335019/2844937529085600, 43: 532145396070491417/122332313750680800, 44: 5884182435213075787/1345655451257488800, 45: 5914085889685464427/1345655451257488800, 46: 5943339269060627227/1345655451257488800, 47: 280682601097106968469/63245806209101973600, 48: 282000222059796592919/63245806209101973600, 49: 13881256687139135026631/3099044504245996706400, 50: 13943237577224054960759/3099044504245996706400, 51: 14004003155738682347159/3099044504245996706400, 52: 14063600165435720745359/3099044504245996706400, 53: 748469853272339196210427/164249358725037825439200, 54: 250503836021181200128409/54749786241679275146400, 55: 251499286680120823312889/54749786241679275146400, 56: 252476961434436524654789/54749786241679275146400, 57: 253437484000080020709989/54749786241679275146400, 58: 254381445831833111660789/54749786241679275146400, 59: 15063255090319832863132951/3230237388259077233637600, 60: 15117092380124150817026911/3230237388259077233637600, 61: 925372872575832277072279171/197044480683803711251893600, 62: 928551009361054917576341971/197044480683803711251893600, 63: 310559566510213034489743057/65681493561267903750631200, 64: 623171679694215690971693339/131362987122535807501262400, 65: 625192648726870088010174299/131362987122535807501262400, 66: 209060999005535159677640233/43787662374178602500420800, 67: 14050874595745034300902316411/2933773379069966367528193600, 68: 14094018321907827923954201611/2933773379069966367528193600, 69: 42409610330030873613929048033/8801320137209899102584580800, 70: 42535343474848157886823113473/8801320137209899102584580800, 71: 3028810706851429109067025637383/624893729741902836283505236800, 72: 9112469359293533278712889630349/1874681189225708508850515710400, 73: 667084944417653637854891458725877/136851726813476721146087646859200, 74: 668934292077295215167676426926677/136851726813476721146087646859200, 75: 670758981768141571449624262218133/136851726813476721146087646859200, 76: 672559662384108370412072783887333/136851726813476721146087646859200, 77: 61303359776139104182852056677903/12441066073952429195098876987200, 78: 61462860623241058403302042280303/12441066073952429195098876987200, 79: 4868007055309996043055960217131137/982844219842241906412811281988800, 80: 4880292608058024066886120358155997/982844219842241906412811281988800, 81: 44031838385838021258243173365847173/8845597978580177157715301537899200, 82: 44139711531918267321142140457772773/8845597978580177157715301537899200, 83: 3672441655127796364812512959533039359/734184632222154704090370027645633600, 84: 3681181948368536301765969745576439759/734184632222154704090370027645633600, 85: 3689819414629973415931738804725211919/734184632222154704090370027645633600, 86: 3698356445237207772956045432953649519/734184632222154704090370027645633600, 87: 3706795349055853229324900260857622319/734184632222154704090370027645633600, 88: 40866521918642154860585199122889549709/8076030954443701744994070304101969600, 89: 3645196481713595484337076792241271893701/718766754945489455304472257065075294400, 90: 3653182778990767589396015372875328285861/718766754945489455304472257065075294400, 91: 3661081314759399341652108474601318124261/718766754945489455304472257065075294400, 92: 3668893996878372053122809260004199377461/718766754945489455304472257065075294400, 93: 3676622671662732154792749821908124918261/718766754945489455304472257065075294400, 94: 3684269126502577787295988888472646995861/718766754945489455304472257065075294400, 95: 3691835092344109255246562280652279367381/718766754945489455304472257065075294400, 96: 3699322246041458103739317199996707235031/718766754945489455304472257065075294400, 97: 359553024620966925518018240656745677092407/69720375229712477164533808935312303556800, 98: 360264457021270114060513483605065190394007/69720375229712477164533808935312303556800, 99: 360968703235711654233892612988250163157207/69720375229712477164533808935312303556800, 100: 14466636279520351160221518043104131447711/2788815009188499086581352357412492142272, ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.016s sys 0m0.010s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Thu Jun 23 19:54:38 2005 Input: for(n=1,200print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: for(n=1,200print1(n,": ",sum(x= ^-------------------- Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Thu Jun 23 19:54:51 2005 Input: for(n=1,200,print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, 8: 761/280, 9: 7129/2520, 10: 7381/2520, 11: 83711/27720, 12: 86021/27720, 13: 1145993/360360, 14: 1171733/360360, 15: 1195757/360360, 16: 2436559/720720, 17: 42142223/12252240, 18: 14274301/4084080, 19: 275295799/77597520, 20: 55835135/15519504, 21: 18858053/5173168, 22: 19093197/5173168, 23: 444316699/118982864, 24: 1347822955/356948592, 25: 34052522467/8923714800, 26: 34395742267/8923714800, 27: 312536252003/80313433200, 28: 315404588903/80313433200, 29: 9227046511387/2329089562800, 30: 9304682830147/2329089562800, 31: 290774257297357/72201776446800, 32: 586061125622639/144403552893600, 33: 53676090078349/13127595717600, 34: 54062195834749/13127595717600, 35: 54437269998109/13127595717600, 36: 54801925434709/13127595717600, 37: 2040798836801833/485721041551200, 38: 2053580969474233/485721041551200, 39: 2066035355155033/485721041551200, 40: 2078178381193813/485721041551200, 41: 85691034670497533/19914562703599200, 42: 12309312989335019/2844937529085600, 43: 532145396070491417/122332313750680800, 44: 5884182435213075787/1345655451257488800, 45: 5914085889685464427/1345655451257488800, 46: 5943339269060627227/1345655451257488800, 47: 280682601097106968469/63245806209101973600, 48: 282000222059796592919/63245806209101973600, 49: 13881256687139135026631/3099044504245996706400, 50: 13943237577224054960759/3099044504245996706400, 51: 14004003155738682347159/3099044504245996706400, 52: 14063600165435720745359/3099044504245996706400, 53: 748469853272339196210427/164249358725037825439200, 54: 250503836021181200128409/54749786241679275146400, 55: 251499286680120823312889/54749786241679275146400, 56: 252476961434436524654789/54749786241679275146400, 57: 253437484000080020709989/54749786241679275146400, 58: 254381445831833111660789/54749786241679275146400, 59: 15063255090319832863132951/3230237388259077233637600, 60: 15117092380124150817026911/3230237388259077233637600, 61: 925372872575832277072279171/197044480683803711251893600, 62: 928551009361054917576341971/197044480683803711251893600, 63: 310559566510213034489743057/65681493561267903750631200, 64: 623171679694215690971693339/131362987122535807501262400, 65: 625192648726870088010174299/131362987122535807501262400, 66: 209060999005535159677640233/43787662374178602500420800, 67: 14050874595745034300902316411/2933773379069966367528193600, 68: 14094018321907827923954201611/2933773379069966367528193600, 69: 42409610330030873613929048033/8801320137209899102584580800, 70: 42535343474848157886823113473/8801320137209899102584580800, 71: 3028810706851429109067025637383/624893729741902836283505236800, 72: 9112469359293533278712889630349/1874681189225708508850515710400, 73: 667084944417653637854891458725877/136851726813476721146087646859200, 74: 668934292077295215167676426926677/136851726813476721146087646859200, 75: 670758981768141571449624262218133/136851726813476721146087646859200, 76: 672559662384108370412072783887333/136851726813476721146087646859200, 77: 61303359776139104182852056677903/12441066073952429195098876987200, 78: 61462860623241058403302042280303/12441066073952429195098876987200, 79: 4868007055309996043055960217131137/982844219842241906412811281988800, 80: 4880292608058024066886120358155997/982844219842241906412811281988800, 81: 44031838385838021258243173365847173/8845597978580177157715301537899200, 82: 44139711531918267321142140457772773/8845597978580177157715301537899200, 83: 3672441655127796364812512959533039359/734184632222154704090370027645633600, 84: 3681181948368536301765969745576439759/734184632222154704090370027645633600, 85: 3689819414629973415931738804725211919/734184632222154704090370027645633600, 86: 3698356445237207772956045432953649519/734184632222154704090370027645633600, 87: 3706795349055853229324900260857622319/734184632222154704090370027645633600, 88: 40866521918642154860585199122889549709/8076030954443701744994070304101969600, 89: 3645196481713595484337076792241271893701/718766754945489455304472257065075294400, 90: 3653182778990767589396015372875328285861/718766754945489455304472257065075294400, 91: 3661081314759399341652108474601318124261/718766754945489455304472257065075294400, 92: 3668893996878372053122809260004199377461/718766754945489455304472257065075294400, 93: 3676622671662732154792749821908124918261/718766754945489455304472257065075294400, 94: 3684269126502577787295988888472646995861/718766754945489455304472257065075294400, 95: 3691835092344109255246562280652279367381/718766754945489455304472257065075294400, 96: 3699322246041458103739317199996707235031/718766754945489455304472257065075294400, 97: 359553024620966925518018240656745677092407/69720375229712477164533808935312303556800, 98: 360264457021270114060513483605065190394007/69720375229712477164533808935312303556800, 99: 360968703235711654233892612988250163157207/69720375229712477164533808935312303556800, 100: 14466636279520351160221518043104131447711/2788815009188499086581352357412492142272, 101: 1463919079240743966268954674710929768361083/281670315928038407744716588098661706369472, 102: 1466680552926312970266451896162877432149019/281670315928038407744716588098661706369472, 103: 151349767267338274345189261892875037217718429/29012042540587955997705808574162155756055616, 104: 151628729214843927768244125436857365638449733/29012042540587955997705808574162155756055616, 105: 759525171909485731983968522830675502275870361/145060212702939779988529042870810778780278080, 106: 760893664482154975191407476065305792641722041/145060212702939779988529042870810778780278080, 107: 81560682312293522125469128981858530591444536467/15521442759214556458772607587176753329489754560, 108: 81704399374878842092679986459517574603754626787/15521442759214556458772607587176753329489754560, 109: 8921300974621008344560891131674592385138744074343/1691837260754386654006214227002266112914383247040, 110: 812425573941376284756780362571245808659649778037/153803387341307877636928566091115101174034840640, 111: 813811190043550229600356295599093692454010452277/153803387341307877636928566091115101174034840640, 112: 815184434573383335650686014939192934428778620497/153803387341307877636928566091115101174034840640, 113: 92269644494133624806164448254219916691626018956801/17379782769567790172972927968296006432665936992320, 114: 92422098728954394895401052885520758853316071035681/17379782769567790172972927968296006432665936992320, 115: 92573227274776723505600817476549419778817513966049/17379782769567790172972927968296006432665936992320, 116: 92723052988307480317436790993517488799788772043569/17379782769567790172972927968296006432665936992320, 117: 92871598140184128096692969865041386290666258684529/17379782769567790172972927968296006432665936992320, 118: 93018884434841482250701215017315081260434614082769/17379782769567790172972927968296006432665936992320, 119: 93164933029543732588289222815367988877515840444049/17379782769567790172972927968296006432665936992320, 120: 18661952910524692834612799443020757786224277983797/3475956553913558034594585593659201286533187398464, 121: 2261572258727401391022743318199170893419670823437901/420590743023540522185944856832763355670515675214144, 122: 2265019723834151723171808439976488625843199640447853/420590743023540522185944856832763355670515675214144, 123: 2268439160769302459124539698975128978328325784148781/420590743023540522185944856832763355670515675214144, 124: 2271831021600137463335716673627006102164378329916637/420590743023540522185944856832763355670515675214144, 125: 284399468443040723439150529060208526126217806914793769/52573842877942565273243107104095419458814459401768000, 126: 284816721164294235861954045783256902471129032783061769/52573842877942565273243107104095419458814459401768000, 127: 36224297430743310519741406921577722033292201622850612663/6676878045498705789701874602220118271269436344024536000, 128: 72552921080947538317446905633815133414572988188576608701/13353756090997411579403749204440236542538872688049072000, 129: 72656438570025037632015926945477460829631429062127376701/13353756090997411579403749204440236542538872688049072000, 130: 72759159770725017721088263477819308803035574236650831101/13353756090997411579403749204440236542538872688049072000, 131: 9544803686055974733041966264798769689740199097689307946231/1749342047920660916901891145781670987072592322134428432000, 132: 9558056277328100952109404834084994469945294494069114222231/1749342047920660916901891145781670987072592322134428432000, 133: 9571209225056827725920697248714931845787945564160350526231/1749342047920660916901891145781670987072592322134428432000, 134: 9584264016459220717837875540847630883004905208355383574231/1749342047920660916901891145781670987072592322134428432000, 135: 9597222105703077465370482141927495112538776262593416377431/1749342047920660916901891145781670987072592322134428432000, 136: 9610084914878964677994760753293536810973133559079698939431/1749342047920660916901891145781670987072592322134428432000, 137: 1318330975386338821802184114346996214090391889916053183134047/239659860565130545615559086972088925228945148132416695184000, 138: 1320067641042607883726934542513460626592050912728606927302047/239659860565130545615559086972088925228945148132416695184000, 139: 183729061965487626383659460496343116021524022017408779590168533/33312720618553145840562713089120360606823375590405920630576000, 140: 183967009969905863139663479875551118597287046128768821880386933/33312720618553145840562713089120360606823375590405920630576000, 141: 184203270399824679776830591315899489949108488508842622735922933/33312720618553145840562713089120360606823375590405920630576000, 142: 184437867023898997705285258309484844601269216505958157388250933/33312720618553145840562713089120360606823375590405920630576000, 143: 184670823112140628095778703855562609360757491859737219770282933/333127206185531458405627130891203606068233755904059206305760 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.058s user 0m0.044s sys 0m0.011s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Thu Jun 23 20:02:57 2005 Input: for(n=1,200,print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, 8: 761/280, 9: 7129/2520, 10: 7381/2520, 11: 83711/27720, 12: 86021/27720, 13: 1145993/360360, 14: 1171733/360360, 15: 1195757/360360, 16: 2436559/720720, 17: 42142223/12252240, 18: 14274301/4084080, 19: 275295799/77597520, 20: 55835135/15519504, 21: 18858053/5173168, 22: 19093197/5173168, 23: 444316699/118982864, 24: 1347822955/356948592, 25: 34052522467/8923714800, 26: 34395742267/8923714800, 27: 312536252003/80313433200, 28: 315404588903/80313433200, 29: 9227046511387/2329089562800, 30: 9304682830147/2329089562800, 31: 290774257297357/72201776446800, 32: 586061125622639/144403552893600, 33: 53676090078349/13127595717600, 34: 54062195834749/13127595717600, 35: 54437269998109/13127595717600, 36: 54801925434709/13127595717600, 37: 2040798836801833/485721041551200, 38: 2053580969474233/485721041551200, 39: 2066035355155033/485721041551200, 40: 2078178381193813/485721041551200, 41: 85691034670497533/19914562703599200, 42: 12309312989335019/2844937529085600, 43: 532145396070491417/122332313750680800, 44: 5884182435213075787/1345655451257488800, 45: 5914085889685464427/1345655451257488800, 46: 5943339269060627227/1345655451257488800, 47: 280682601097106968469/63245806209101973600, 48: 282000222059796592919/63245806209101973600, 49: 13881256687139135026631/3099044504245996706400, 50: 13943237577224054960759/3099044504245996706400, 51: 14004003155738682347159/3099044504245996706400, 52: 14063600165435720745359/3099044504245996706400, 53: 748469853272339196210427/164249358725037825439200, 54: 250503836021181200128409/54749786241679275146400, 55: 251499286680120823312889/54749786241679275146400, 56: 252476961434436524654789/54749786241679275146400, 57: 253437484000080020709989/54749786241679275146400, 58: 254381445831833111660789/54749786241679275146400, 59: 15063255090319832863132951/3230237388259077233637600, 60: 15117092380124150817026911/3230237388259077233637600, 61: 925372872575832277072279171/197044480683803711251893600, 62: 928551009361054917576341971/197044480683803711251893600, 63: 310559566510213034489743057/65681493561267903750631200, 64: 623171679694215690971693339/131362987122535807501262400, 65: 625192648726870088010174299/131362987122535807501262400, 66: 209060999005535159677640233/43787662374178602500420800, 67: 14050874595745034300902316411/2933773379069966367528193600, 68: 14094018321907827923954201611/2933773379069966367528193600, 69: 42409610330030873613929048033/8801320137209899102584580800, 70: 42535343474848157886823113473/8801320137209899102584580800, 71: 3028810706851429109067025637383/624893729741902836283505236800, 72: 9112469359293533278712889630349/1874681189225708508850515710400, 73: 667084944417653637854891458725877/136851726813476721146087646859200, 74: 668934292077295215167676426926677/136851726813476721146087646859200, 75: 670758981768141571449624262218133/136851726813476721146087646859200, 76: 672559662384108370412072783887333/136851726813476721146087646859200, 77: 61303359776139104182852056677903/12441066073952429195098876987200, 78: 61462860623241058403302042280303/12441066073952429195098876987200, 79: 4868007055309996043055960217131137/982844219842241906412811281988800, 80: 4880292608058024066886120358155997/982844219842241906412811281988800, 81: 44031838385838021258243173365847173/8845597978580177157715301537899200, 82: 44139711531918267321142140457772773/8845597978580177157715301537899200, 83: 3672441655127796364812512959533039359/734184632222154704090370027645633600, 84: 3681181948368536301765969745576439759/734184632222154704090370027645633600, 85: 3689819414629973415931738804725211919/734184632222154704090370027645633600, 86: 3698356445237207772956045432953649519/734184632222154704090370027645633600, 87: 3706795349055853229324900260857622319/734184632222154704090370027645633600, 88: 40866521918642154860585199122889549709/8076030954443701744994070304101969600, 89: 3645196481713595484337076792241271893701/718766754945489455304472257065075294400, 90: 3653182778990767589396015372875328285861/718766754945489455304472257065075294400, 91: 3661081314759399341652108474601318124261/718766754945489455304472257065075294400, 92: 3668893996878372053122809260004199377461/718766754945489455304472257065075294400, 93: 3676622671662732154792749821908124918261/718766754945489455304472257065075294400, 94: 3684269126502577787295988888472646995861/718766754945489455304472257065075294400, 95: 3691835092344109255246562280652279367381/718766754945489455304472257065075294400, 96: 3699322246041458103739317199996707235031/718766754945489455304472257065075294400, 97: 359553024620966925518018240656745677092407/69720375229712477164533808935312303556800, 98: 360264457021270114060513483605065190394007/69720375229712477164533808935312303556800, 99: 360968703235711654233892612988250163157207/69720375229712477164533808935312303556800, 100: 14466636279520351160221518043104131447711/2788815009188499086581352357412492142272, 101: 1463919079240743966268954674710929768361083/281670315928038407744716588098661706369472, 102: 1466680552926312970266451896162877432149019/281670315928038407744716588098661706369472, 103: 151349767267338274345189261892875037217718429/29012042540587955997705808574162155756055616, 104: 151628729214843927768244125436857365638449733/29012042540587955997705808574162155756055616, 105: 759525171909485731983968522830675502275870361/145060212702939779988529042870810778780278080, 106: 760893664482154975191407476065305792641722041/145060212702939779988529042870810778780278080, 107: 81560682312293522125469128981858530591444536467/15521442759214556458772607587176753329489754560, 108: 81704399374878842092679986459517574603754626787/15521442759214556458772607587176753329489754560, 109: 8921300974621008344560891131674592385138744074343/1691837260754386654006214227002266112914383247040, 110: 812425573941376284756780362571245808659649778037/153803387341307877636928566091115101174034840640, 111: 813811190043550229600356295599093692454010452277/153803387341307877636928566091115101174034840640, 112: 815184434573383335650686014939192934428778620497/153803387341307877636928566091115101174034840640, 113: 92269644494133624806164448254219916691626018956801/17379782769567790172972927968296006432665936992320, 114: 92422098728954394895401052885520758853316071035681/17379782769567790172972927968296006432665936992320, 115: 92573227274776723505600817476549419778817513966049/17379782769567790172972927968296006432665936992320, 116: 92723052988307480317436790993517488799788772043569/17379782769567790172972927968296006432665936992320, 117: 92871598140184128096692969865041386290666258684529/17379782769567790172972927968296006432665936992320, 118: 93018884434841482250701215017315081260434614082769/17379782769567790172972927968296006432665936992320, 119: 93164933029543732588289222815367988877515840444049/17379782769567790172972927968296006432665936992320, 120: 18661952910524692834612799443020757786224277983797/3475956553913558034594585593659201286533187398464, 121: 2261572258727401391022743318199170893419670823437901/420590743023540522185944856832763355670515675214144, 122: 2265019723834151723171808439976488625843199640447853/420590743023540522185944856832763355670515675214144, 123: 2268439160769302459124539698975128978328325784148781/420590743023540522185944856832763355670515675214144, 124: 2271831021600137463335716673627006102164378329916637/420590743023540522185944856832763355670515675214144, 125: 284399468443040723439150529060208526126217806914793769/52573842877942565273243107104095419458814459401768000, 126: 284816721164294235861954045783256902471129032783061769/52573842877942565273243107104095419458814459401768000, 127: 36224297430743310519741406921577722033292201622850612663/6676878045498705789701874602220118271269436344024536000, 128: 72552921080947538317446905633815133414572988188576608701/13353756090997411579403749204440236542538872688049072000, 129: 72656438570025037632015926945477460829631429062127376701/13353756090997411579403749204440236542538872688049072000, 130: 72759159770725017721088263477819308803035574236650831101/13353756090997411579403749204440236542538872688049072000, 131: 9544803686055974733041966264798769689740199097689307946231/1749342047920660916901891145781670987072592322134428432000, 132: 9558056277328100952109404834084994469945294494069114222231/1749342047920660916901891145781670987072592322134428432000, 133: 9571209225056827725920697248714931845787945564160350526231/1749342047920660916901891145781670987072592322134428432000, 134: 9584264016459220717837875540847630883004905208355383574231/1749342047920660916901891145781670987072592322134428432000, 135: 9597222105703077465370482141927495112538776262593416377431/1749342047920660916901891145781670987072592322134428432000, 136: 9610084914878964677994760753293536810973133559079698939431/1749342047920660916901891145781670987072592322134428432000, 137: 1318330975386338821802184114346996214090391889916053183134047/239659860565130545615559086972088925228945148132416695184000, 138: 1320067641042607883726934542513460626592050912728606927302047/239659860565130545615559086972088925228945148132416695184000, 139: 183729061965487626383659460496343116021524022017408779590168533/33312720618553145840562713089120360606823375590405920630576000, 140: 183967009969905863139663479875551118597287046128768821880386933/33312720618553145840562713089120360606823375590405920630576000, 141: 184203270399824679776830591315899489949108488508842622735922933/33312720618553145840562713089120360606823375590405920630576000, 142: 184437867023898997705285258309484844601269216505958157388250933/33312720618553145840562713089120360606823375590405920630576000, 143: 184670823112140628095778703855562609360757491859737219770282933/333127206185531458405627130891203606068233755904059206305760 ** WARNING: Output too long, hence truncated. Errors (if any) and Timing Info: Timing: real 0m0.058s user 0m0.051s sys 0m0.007s '84.159.' ************** PARI ***************** Host 84.159.147.108 (84.159.147.108) Time: Fri Jun 24 05:04:11 2005 Input: 1+2^.5 Output: ? 2.4142135623730950488016887242096980785 ? Errors (if any) and Timing Info: Timing: real 0m0.184s user 0m0.010s sys 0m0.008s '84.159.' ************** PARI ***************** Host 84.159.147.108 (84.159.147.108) Time: Fri Jun 24 05:04:46 2005 Input: (1+2^.5)^0 (1+2^.5)^1 (1+2^.5)^2 (1+2^.5)^3 (1+2^.5)^4 (1+2^.5)^5 (1+2^.5)^6 (1+2^.5)^7 (1+2^.5)^8 (1+2^.5)^9 (1+2^.5)^10 Output: ? 1 ? 2.4142135623730950488016887242096980785 ? 5.8284271247461900976033774484193961571 ? 14.071067811865475244008443621048490392 ? 33.970562748477140585620264690516376942 ? 82.012193308819756415248973002081244278 ? 197.99494936611665341611821069467886549 ? 478.00209204105306324748539439143897527 ? 1153.9991334482227799110889994775568160 ? 2786.0003589374986230696633933465526073 ? 6725.9998513232200260504157861706620308 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.014s sys 0m0.004s '84.159.' ************** PARI ***************** Host 84.159.147.108 (84.159.147.108) Time: Fri Jun 24 05:06:21 2005 Input: (1+2^.5)^0 (1+2^.5)^1 (1+2^.5)^2 (1+2^.5)^3 (1+2^.5)^4 (1+2^.5)^5 (1+2^.5)^6 (1+2^.5)^7 (1+2^.5)^8 (1+2^.5)^9 (1+2^.5)^10 (-1+2^.5)^0 (-1+2^.5)^1 (-1+2^.5)^2 (-1+2^.5)^3 (-1+2^.5)^4 (-1+2^.5)^5 (-1+2^.5)^6 (-1+2^.5)^7 (-1+2^.5)^8 (-1+2^.5)^9 (-1+2^.5)^10 Output: ? 1 ? 2.4142135623730950488016887242096980785 ? 5.8284271247461900976033774484193961571 ? 14.071067811865475244008443621048490392 ? 33.970562748477140585620264690516376942 ? 82.012193308819756415248973002081244278 ? 197.99494936611665341611821069467886549 ? 478.00209204105306324748539439143897527 ? 1153.9991334482227799110889994775568160 ? 2786.0003589374986230696633933465526073 ? 6725.9998513232200260504157861706620308 ? 1 ? 0.41421356237309504880168872420969807856 ? 0.17157287525380990239662255158060384286 ? 0.071067811865475244008443621048490392848 ? 0.029437251522859414379735309483623057163 ? 0.012193308819756415248973002081244278520 ? 0.0050506338833465838817893053211345001229 ? 0.0020920410530632474853943914389752782745 ? 0.00086655177722008891100052244318394357386 ? 0.00035893749862306966339334655260739112679 ? 0.00014867677997394958421382933796916132027 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.010s sys 0m0.011s '84.159.' ************** PARI ***************** Host 84.159.147.108 (84.159.147.108) Time: Fri Jun 24 05:08:20 2005 Input: (1+2^.5)^0 (1+2^.5)^1 (1+2^.5)^2 (1+2^.5)^3 (1+2^.5)^4 (1+2^.5)^5 (1+2^.5)^6 (1+2^.5)^7 (1+2^.5)^8 (1+2^.5)^9 (1+2^.5)^10 (-1+2^.5)^0 (-1+2^.5)^1 (-1+2^.5)^2 (-1+2^.5)^3 (-1+2^.5)^4 (-1+2^.5)^5 (-1+2^.5)^6 (-1+2^.5)^7 (-1+2^.5)^8 (-1+2^.5)^9 (-1+2^.5)^10 (-1+2^.5)^0+(1+2^.5)^0 (-1+2^.5)^1+(1+2^.5)^1 (-1+2^.5)^2+(1+2^.5)^2 (-1+2^.5)^3+(1+2^.5)^3 Output: ? 1 ? 2.4142135623730950488016887242096980785 ? 5.8284271247461900976033774484193961571 ? 14.071067811865475244008443621048490392 ? 33.970562748477140585620264690516376942 ? 82.012193308819756415248973002081244278 ? 197.99494936611665341611821069467886549 ? 478.00209204105306324748539439143897527 ? 1153.9991334482227799110889994775568160 ? 2786.0003589374986230696633933465526073 ? 6725.9998513232200260504157861706620308 ? 1 ? 0.41421356237309504880168872420969807856 ? 0.17157287525380990239662255158060384286 ? 0.071067811865475244008443621048490392848 ? 0.029437251522859414379735309483623057163 ? 0.012193308819756415248973002081244278520 ? 0.0050506338833465838817893053211345001229 ? 0.0020920410530632474853943914389752782745 ? 0.00086655177722008891100052244318394357386 ? 0.00035893749862306966339334655260739112679 ? 0.00014867677997394958421382933796916132027 ? ? ? 2 ? 2.8284271247461900976033774484193961571 ? 6.0000000000000000000000000000000000000 ? 14.142135623730950488016887242096980785 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.012s sys 0m0.008s '84.159.' ************** PARI ***************** Host 84.159.147.108 (84.159.147.108) Time: Fri Jun 24 05:08:53 2005 Input: (1+2^.5)^0 (1+2^.5)^1 (1+2^.5)^2 (1+2^.5)^3 (1+2^.5)^4 (1+2^.5)^5 (1+2^.5)^6 (1+2^.5)^7 (1+2^.5)^8 (1+2^.5)^9 (1+2^.5)^10 (-1+2^.5)^0 (-1+2^.5)^1 (-1+2^.5)^2 (-1+2^.5)^3 (-1+2^.5)^4 (-1+2^.5)^5 (-1+2^.5)^6 (-1+2^.5)^7 (-1+2^.5)^8 (-1+2^.5)^9 (-1+2^.5)^10 (-1+2^.5)^0+(1+2^.5)^0 (-1+2^.5)^1+(1+2^.5)^1 (-1+2^.5)^2+(1+2^.5)^2 (-1+2^.5)^3+(1+2^.5)^3 (-1+2^.5)^4+(1+2^.5)^4 (-1+2^.5)^5+(1+2^.5)^5 Output: ? 1 ? 2.4142135623730950488016887242096980785 ? 5.8284271247461900976033774484193961571 ? 14.071067811865475244008443621048490392 ? 33.970562748477140585620264690516376942 ? 82.012193308819756415248973002081244278 ? 197.99494936611665341611821069467886549 ? 478.00209204105306324748539439143897527 ? 1153.9991334482227799110889994775568160 ? 2786.0003589374986230696633933465526073 ? 6725.9998513232200260504157861706620308 ? 1 ? 0.41421356237309504880168872420969807856 ? 0.17157287525380990239662255158060384286 ? 0.071067811865475244008443621048490392848 ? 0.029437251522859414379735309483623057163 ? 0.012193308819756415248973002081244278520 ? 0.0050506338833465838817893053211345001229 ? 0.0020920410530632474853943914389752782745 ? 0.00086655177722008891100052244318394357386 ? 0.00035893749862306966339334655260739112679 ? 0.00014867677997394958421382933796916132027 ? ? ? 2 ? 2.8284271247461900976033774484193961571 ? 6.0000000000000000000000000000000000000 ? 14.142135623730950488016887242096980785 ? 34.000000000000000000000000000000000000 ? 82.024386617639512830497946004162488557 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.015s sys 0m0.005s '84.159.' ************** PARI ***************** Host 84.159.147.108 (84.159.147.108) Time: Fri Jun 24 05:16:44 2005 Input: (1+2^.5)^0 (1+2^.5)^1 (1+2^.5)^2 (1+2^.5)^3 (1+2^.5)^4 (1+2^.5)^5 (1+2^.5)^6 (1+2^.5)^7 (1+2^.5)^8 (1+2^.5)^9 (1+2^.5)^10 (-1+2^.5)^0 (-1+2^.5)^1 (-1+2^.5)^2 (-1+2^.5)^3 (-1+2^.5)^4 (-1+2^.5)^5 (-1+2^.5)^6 (-1+2^.5)^7 (-1+2^.5)^8 (-1+2^.5)^9 (-1+2^.5)^10 (-1+2^.5)^0+(1+2^.5)^0 (-1+2^.5)^1-(1+2^.5)^1 (-1+2^.5)^2+(1+2^.5)^2 (-1+2^.5)^3-(1+2^.5)^3 (-1+2^.5)^4+(1+2^.5)^4 (-1+2^.5)^5-(1+2^.5)^5 Output: ? 1 ? 2.4142135623730950488016887242096980785 ? 5.8284271247461900976033774484193961571 ? 14.071067811865475244008443621048490392 ? 33.970562748477140585620264690516376942 ? 82.012193308819756415248973002081244278 ? 197.99494936611665341611821069467886549 ? 478.00209204105306324748539439143897527 ? 1153.9991334482227799110889994775568160 ? 2786.0003589374986230696633933465526073 ? 6725.9998513232200260504157861706620308 ? 1 ? 0.41421356237309504880168872420969807856 ? 0.17157287525380990239662255158060384286 ? 0.071067811865475244008443621048490392848 ? 0.029437251522859414379735309483623057163 ? 0.012193308819756415248973002081244278520 ? 0.0050506338833465838817893053211345001229 ? 0.0020920410530632474853943914389752782745 ? 0.00086655177722008891100052244318394357386 ? 0.00035893749862306966339334655260739112679 ? 0.00014867677997394958421382933796916132027 ? ? ? 2 ? -2.0000000000000000000000000000000000000 ? 6.0000000000000000000000000000000000000 ? -14.000000000000000000000000000000000000 ? 34.000000000000000000000000000000000000 ? -82.000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.009s sys 0m0.012s '84.159.' ************** PARI ***************** Host 84.159.147.108 (84.159.147.108) Time: Fri Jun 24 05:18:23 2005 Input: (-1+2^.5)^0+(1+2^.5)^0 -(-1+2^.5)^1+(1+2^.5)^1 (-1+2^.5)^2+(1+2^.5)^2 -(-1+2^.5)^3+(1+2^.5)^3 (-1+2^.5)^4+(1+2^.5)^4 -(-1+2^.5)^5+(1+2^.5)^5 Output: ? ? 2 ? 2.0000000000000000000000000000000000000 ? 6.0000000000000000000000000000000000000 ? 14.000000000000000000000000000000000000 ? 34.000000000000000000000000000000000000 ? 82.000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '84.159.' ************** PARI ***************** Host 84.159.147.108 (84.159.147.108) Time: Fri Jun 24 05:37:47 2005 Input: (-1+2^.5)^0+(1+2^.5)^0 -(-1+2^.5)^1+(1+2^.5)^1 (-1+2^.5)^2+(1+2^.5)^2 -(-1+2^.5)^3+(1+2^.5)^3 (-1+2^.5)^4+(1+2^.5)^4 -(-1+2^.5)^5+(1+2^.5)^5 1+2^4+3^4 Output: ? 2 ? 2.0000000000000000000000000000000000000 ? 6.0000000000000000000000000000000000000 ? 14.000000000000000000000000000000000000 ? 34.000000000000000000000000000000000000 ? 82.000000000000000000000000000000000000 ? ? 98 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '84.159.' ************** PARI ***************** Host 84.159.147.108 (84.159.147.108) Time: Fri Jun 24 05:38:02 2005 Input: (-1+2^.5)^0+(1+2^.5)^0 -(-1+2^.5)^1+(1+2^.5)^1 (-1+2^.5)^2+(1+2^.5)^2 -(-1+2^.5)^3+(1+2^.5)^3 (-1+2^.5)^4+(1+2^.5)^4 -(-1+2^.5)^5+(1+2^.5)^5 1+2^3+3^3 Output: ? 2 ? 2.0000000000000000000000000000000000000 ? 6.0000000000000000000000000000000000000 ? 14.000000000000000000000000000000000000 ? 34.000000000000000000000000000000000000 ? 82.000000000000000000000000000000000000 ? ? 36 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '84.159.' ************** PARI ***************** Host 84.159.147.108 (84.159.147.108) Time: Fri Jun 24 05:38:09 2005 Input: (-1+2^.5)^0+(1+2^.5)^0 -(-1+2^.5)^1+(1+2^.5)^1 (-1+2^.5)^2+(1+2^.5)^2 -(-1+2^.5)^3+(1+2^.5)^3 (-1+2^.5)^4+(1+2^.5)^4 -(-1+2^.5)^5+(1+2^.5)^5 1+2^3+3^3+4^3 Output: ? 2 ? 2.0000000000000000000000000000000000000 ? 6.0000000000000000000000000000000000000 ? 14.000000000000000000000000000000000000 ? 34.000000000000000000000000000000000000 ? 82.000000000000000000000000000000000000 ? ? 100 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '84.159.' ************** PARI ***************** Host 84.159.147.108 (84.159.147.108) Time: Fri Jun 24 05:40:23 2005 Input: (-1+2^.5)^0+(1+2^.5)^0 -(-1+2^.5)^1+(1+2^.5)^1 (-1+2^.5)^2+(1+2^.5)^2 -(-1+2^.5)^3+(1+2^.5)^3 (-1+2^.5)^4+(1+2^.5)^4 -(-1+2^.5)^5+(1+2^.5)^5 1+2^3+2^3+3^3+3^3+4^3 Output: ? 2 ? 2.0000000000000000000000000000000000000 ? 6.0000000000000000000000000000000000000 ? 14.000000000000000000000000000000000000 ? 34.000000000000000000000000000000000000 ? 82.000000000000000000000000000000000000 ? ? 135 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.011s sys 0m0.007s '84.159.' ************** PARI ***************** Host 84.159.147.108 (84.159.147.108) Time: Fri Jun 24 05:45:33 2005 Input: (-1+2^.5)^0+(1+2^.5)^0 -(-1+2^.5)^1+(1+2^.5)^1 (-1+2^.5)^2+(1+2^.5)^2 -(-1+2^.5)^3+(1+2^.5)^3 (-1+2^.5)^4+(1+2^.5)^4 -(-1+2^.5)^5+(1+2^.5)^5 1+2^3+2^3+3^3+4^3+4^3 1+8+8+ Output: ? 2 ? 2.0000000000000000000000000000000000000 ? 6.0000000000000000000000000000000000000 ? 14.000000000000000000000000000000000000 ? 34.000000000000000000000000000000000000 ? 82.000000000000000000000000000000000000 ? ? 172 ? ? Errors (if any) and Timing Info: *** unexpected character: 1+8+8+ ^ Timing: real 0m0.019s user 0m0.011s sys 0m0.008s '84.159.' ************** PARI ***************** Host 84.159.147.108 (84.159.147.108) Time: Fri Jun 24 05:46:31 2005 Input: (-1+2^.5)^0+(1+2^.5)^0 -(-1+2^.5)^1+(1+2^.5)^1 (-1+2^.5)^2+(1+2^.5)^2 -(-1+2^.5)^3+(1+2^.5)^3 (-1+2^.5)^4+(1+2^.5)^4 -(-1+2^.5)^5+(1+2^.5)^5 1+2^3+2^3+3^3+4^3+6^3 Output: ? 2 ? 2.0000000000000000000000000000000000000 ? 6.0000000000000000000000000000000000000 ? 14.000000000000000000000000000000000000 ? 34.000000000000000000000000000000000000 ? 82.000000000000000000000000000000000000 ? ? 324 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.010s sys 0m0.009s '84.159.' ************** PARI ***************** Host 84.159.147.108 (84.159.147.108) Time: Fri Jun 24 05:46:41 2005 Input: (-1+2^.5)^0+(1+2^.5)^0 -(-1+2^.5)^1+(1+2^.5)^1 (-1+2^.5)^2+(1+2^.5)^2 -(-1+2^.5)^3+(1+2^.5)^3 (-1+2^.5)^4+(1+2^.5)^4 -(-1+2^.5)^5+(1+2^.5)^5 1+2^3+2^3+3^3+4^3+6^3 18^2 Output: ? 2 ? 2.0000000000000000000000000000000000000 ? 6.0000000000000000000000000000000000000 ? 14.000000000000000000000000000000000000 ? 34.000000000000000000000000000000000000 ? 82.000000000000000000000000000000000000 ? ? 324 ? 324 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.011s sys 0m0.006s '83.192.' ************** PARI ***************** Host 83.192.142.137 (83.192.142.137) Time: Sat Jun 25 02:59:04 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.011s sys 0m0.006s '164.107' ************** PARI ***************** Host 164.107.211.82 (164.107.211.82) Time: Sat Jun 25 17:01:37 2005 Input: 573/3232 Output: ? 573/3232 ? Errors (if any) and Timing Info: Timing: real 0m0.268s user 0m0.008s sys 0m0.012s '219.107' ************** PARI ***************** Host 219.107.212.208 (219.107.212.208) Time: Sun Jun 26 03:51:05 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.154s user 0m0.007s sys 0m0.014s '84.169.' ************** PARI ***************** Host 84.169.138.244 (84.169.138.244) Time: Mon Jun 27 11:46:05 2005 Input: 1 1 Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.278s user 0m0.008s sys 0m0.012s '84.169.' ************** PARI ***************** Host 84.169.138.244 (84.169.138.244) Time: Mon Jun 27 11:46:15 2005 Input: 1 1 Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '85.64.1' ************** PARI ***************** Host 85.64.167.59 (85.64.167.59) Time: Mon Jun 27 14:41:13 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Mon Jun 27 16:14:43 2005 Input: prime(2^10000) Output: ? ? Errors (if any) and Timing Info: *** impossible assignment I-->S Timing: real 0m0.026s user 0m0.007s sys 0m0.010s '203.144' ************** PARI ***************** Host 203.144.160.247 (203.144.160.247) Time: Mon Jun 27 18:03:15 2005 Input: polgalois(X^3 + X^2 - 2*X - 1) Output: ? [3, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.105s user 0m0.011s sys 0m0.010s '84.165.' ************** PARI ***************** Host 84.165.155.48 (84.165.155.48) Time: Tue Jun 28 12:43:55 2005 Input: factor(2^128+1) Output: ? [59649589127497217 1] [5704689200685129054721 1] ? Errors (if any) and Timing Info: Timing: real 0m0.802s user 0m0.415s sys 0m0.040s '84.165.' ************** PARI ***************** Host 84.165.155.48 (84.165.155.48) Time: Tue Jun 28 12:44:10 2005 Input: factor(2^190+1) Output: ? [5 2] [41 1] [229 1] [457 1] [761 1] [54721 1] [525313 1] [276696631250953741 1] [2416923620660807201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.317s user 0m0.286s sys 0m0.031s '84.165.' ************** PARI ***************** Host 84.165.155.48 (84.165.155.48) Time: Tue Jun 28 12:44:19 2005 Input: factor(2^220+1) Output: ? [17 1] [353 1] [61681 1] [109121 1] [148721 1] [2931542417 1] [3404676001 1] [11035465708081 1] [2546717317681681 1] ? Errors (if any) and Timing Info: Timing: real 0m0.511s user 0m0.472s sys 0m0.038s '84.165.' ************** PARI ***************** Host 84.165.155.48 (84.165.155.48) Time: Tue Jun 28 12:44:30 2005 Input: factor(2^300+1) Output: ? [17 1] [241 1] [401 1] [61681 1] [340801 1] [2787601 1] [3173389601 1] [4562284561 1] [1461503031127477825099979369543473122548042956801 1] ? Errors (if any) and Timing Info: Timing: real 0m0.854s user 0m0.846s sys 0m0.007s '84.165.' ************** PARI ***************** Host 84.165.155.48 (84.165.155.48) Time: Tue Jun 28 12:44:49 2005 Input: factor(2^256+1) Output: ? [1238926361552897 1] [93461639715357977769163558199606896584051237541638188580280321 1] ? Errors (if any) and Timing Info: Timing: real 0m9.695s user 0m9.669s sys 0m0.023s '24.209.' ************** PARI ***************** Host 24.209.46.54 (24.209.46.54) Time: Tue Jun 28 16:09:43 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.014s sys 0m0.004s '24.217.' ************** PARI ***************** Host 24.217.221.253 (24.217.221.253) Time: Wed Jun 29 02:07:42 2005 Input: 123*2^431368+1 Output: ? 6267216414663594357109181917688001735407164030406205413505303064715711950295651163978743593984870174443170732388810463414613135345591818071752723758712766161427847620685775524650509170180564331947827887963151724738314208259751805153736261286741824921052704826042378150090622276119004097647277892919661384051120185058504827561291464627067470190949499012379007400155991127544884362385748465223118687100399724220636948438362886453569784480422529466324635467326942685549133624077098528714247700707794943163167101256982576305381998256895351719856699419709182131293351282454733577837006026321808539231407042172082799596500047801781709823027517556494992141036412146000565372305196629673193207882926405554885637716917198756750203604048983136889985802383167044282321733124871500653066003239203729741654570869281830214968863172004630045189806977452890495390297790172949092873946742705361318924571279070760172172605647772360897703032275154528879760375730422715860730195814440980970266315765091923310536274117666756741333754371146083967274992092257801268855553169674622446119510221846490089881625951783514578800400390179235016775684029547890143648737661136535266412248572349434748473312508189351098810994959700625705467739507040538539022524180747148631611798047715073246112465290863607943451069146611053514005353596973688165780631716249450131896943179034410130762676405840523138139756827344805615956873969387709629233835748693281356651537808308802671376912411928178047623603649817683073944273135149285467479083201094085409864224961452365145654909611914386892738738568841704879011568053791830839948896869971953294901318386908300011349078274960710963451791671033875525661197246367082144094065162752795467699828764776181690108416708763022265669665815595549923866175180338809534404532680989554126423016377304358076008791293967748663075609816009637217259867189479552481150342404492646321912159828177624751658563376847654606942340059761735210459191638345341907677955756245837458833166473839511339144044020781252710499241580400777325228863822950640123691716682143280693338043117214401651831879476731000366281368393503060327147845189961136086513887910834221335633720207807103358214008498003694607743975817896634000993101355655916827094897518528839048337412253700422539511007188580485499113207395586268374147721354974694478560741010121558848347498033507675364153301015807696312721857498928467119233989092156914010925043314394616799906488939247618886687811803482760141722710284018162658184686136807344861649025112259340294432852815353095760138322972130313474404186495407983574655066390885986295311034764506970111425701747020590591338744694108048108105423036776404209374187872339576310084209518840758088602682290554722737751628894056256011674512601092189061884024067716721093199968407373162122240451379519144374523556990136474372551085249595085877682208914926362458084893765410894668099172690012504975009962498682418312457509273979476596346787260381899125853927484604247901681760704033643202647542226834697033599498885471348879952885037769779055164354778523929942358311254058262570529314364833514365877357855189352449922721453014032023960412162977650907993130571202890552810160947410466808892348548609133481164863[+++] ? Errors (if any) and Timing Info: Timing: real 0m5.804s user 0m5.763s sys 0m0.016s '24.217.' ************** PARI ***************** Host 24.217.221.253 (24.217.221.253) Time: Wed Jun 29 02:08:46 2005 Input: nfs(n)= { l=log(n); d=(3*l/log(l))^(1/3)1; k=3*llog(2); m=n^(1/d)1; t=d; s=n; H=vector(d+1,i,1); (p(i)=prime(i)); for(i=1,d, s-=H[i]*m^t; H[i+1]=sm^t-- ); (f(x)=eval(Pol(H))); (F(x,y)=y^d*f(x/y)); (G(x,y)=x-m*y;); (h(x)=eval(deriv(Pol(H)))); t=B=precprime( 2*exp( (l*log(l)^2)^(1/3) ) ); (z(i)=primepi(i)); P=z(B); R=vector(P,i, lift(polrootsmod(f(x),p(i))) ); q=vector(k,i, while( !r=polrootsmod(f(x),t=nextprime(t+2)), ); [t,lift(r[1])] ); K=exp(log(n)/200); (L(B)=log(B)/log(K)/1); w=vectorsmall(P,i, L(p(i)) ); b=r=0; A=vector(P); for(i=2,P, A[i]=A[i-1]+#R[i] ); o=A[P]+#R[P]; s=o+P+k+1; M=matrix(s,s); N=vector(s); while(1, b++; e=vectorsmall(8*B+1,a, L(abs(F(a-4*B,b)*G(a-4*B,b))+1) ); for(i=1,P, t=p(i); for(j=1,#R[i], forstep(k=-4*B+1+b*R[i][j]%t,4*B,t, e[k+4*B]-=w[i] ) ); for(j=1,if(t1 , (u(y,x=0)=eval( lift(U[1,1]) )); g=gcd(u(m)-h(m)*v,n); if(g>1&&g:= FunctionField(Rationals()); R:= PolynomialRing(k); f:= x^15 + (-1875*t^2 - 125)*x^3 + (4500*t^2 + 300)*x^2 + (-3600*t^2 - 240)*x + 960*t^2+ 64; G, r, p:= GaloisGroup(f); G; Output: ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: k:=FunctionField(Rationals());. *** unexpected character: R:=PolynomialRing(k); ^-------------------- *** unexpected character: f:=x^15+(-1875*t^2-125 ^-------------------- *** Warning: unused characters: ,r,p:=GaloisGroup(f);. Timing: real 0m0.030s user 0m0.010s sys 0m0.009s '200.231' ************** PARI ***************** Host 200.231.0.66 (200.231.0.66) Time: Wed Jun 29 09:27:47 2005 Input: x^2+x%(x) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '200.231' ************** PARI ***************** Host 200.231.0.66 (200.231.0.66) Time: Wed Jun 29 09:27:59 2005 Input: Mod(x^2+x,x) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.013s sys 0m0.006s '200.231' ************** PARI ***************** Host 200.231.0.66 (200.231.0.66) Time: Wed Jun 29 09:28:07 2005 Input: Mod(x^2+x,x+1) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.007s '200.231' ************** PARI ***************** Host 200.231.0.66 (200.231.0.66) Time: Wed Jun 29 09:28:12 2005 Input: Mod(x^2+x,x+1) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '129.194' ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Wed Jun 29 09:30:29 2005 Input: k:=Rationals(); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: k:=Rationals(); ^------------- Timing: real 0m0.018s user 0m0.013s sys 0m0.006s '201.6.2' ************** PARI ***************** Host 201.6.227.191 (201.6.227.191) Time: Wed Jun 29 12:28:41 2005 Input: factorint(1372) Output: ? [2 2] [7 3] ? Errors (if any) and Timing Info: Timing: real 0m0.064s user 0m0.007s sys 0m0.011s '62.134.' ************** PARI ***************** Host 62.134.108.39 (62.134.108.39) Time: Wed Jun 29 17:31:12 2005 Input: F:=pAdicField(2 : Precision:=100); P:=PolynomialRing(F); f:=y^6+y^5+y^4+y^3+y^2+y^+1; I:=ideal

; PI:=quo

; e0:=PI ! (x^4+x^2+x); e0^2-e0; Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: F:=pAdicField(2:Precis ^-------------------- *** unexpected character: P:=PolynomialRing(F); ^-------------------- *** unexpected character: f:=y^6+y^5+y^4+y^3+y^2 ^-------------------- *** unexpected character: I:=ideal; ^-------------- *** unexpected character: PI:=quo; ^----------- *** unexpected character: e0:=PI!(x^4+x^2+x); ^---------------- Timing: real 0m0.018s user 0m0.007s sys 0m0.011s '203.144' ************** PARI ***************** Host 203.144.143.7 (203.144.143.7) Time: Wed Jun 29 17:53:00 2005 Input: polgalois(16*x^5-20*x^3+5*x+1) Output: ? ? Errors (if any) and Timing Info: *** sorry, galois of reducible polynomial is not yet implemented. Timing: real 0m0.045s user 0m0.011s sys 0m0.009s '203.144' ************** PARI ***************** Host 203.144.143.7 (203.144.143.7) Time: Wed Jun 29 17:53:13 2005 Input: polgalois(16*x^5-20*x^3+5*x+2) Output: ? [20, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.079s user 0m0.015s sys 0m0.012s '203.144' ************** PARI ***************** Host 203.144.143.7 (203.144.143.7) Time: Wed Jun 29 17:53:33 2005 Input: polgalois(16*x^5-20*x^3+5*x+3) Output: ? [20, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.020s sys 0m0.006s '203.144' ************** PARI ***************** Host 203.144.143.7 (203.144.143.7) Time: Wed Jun 29 17:54:14 2005 Input: polgalois(3*x^3-3*x+1) Output: ? [3, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '203.144' ************** PARI ***************** Host 203.144.143.7 (203.144.143.7) Time: Wed Jun 29 17:54:27 2005 Input: polgalois(x^3-x+1) Output: ? [6, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '203.144' ************** PARI ***************** Host 203.144.143.7 (203.144.143.7) Time: Wed Jun 29 17:54:50 2005 Input: polgalois(x^3-x+1/9) Output: ? [6, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '203.144' ************** PARI ***************** Host 203.144.160.243 (203.144.160.243) Time: Wed Jun 29 21:09:47 2005 Input: polgalois(X^3 - 20*X^2 - 348*X + 1898) Output: ? [6, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.010s sys 0m0.009s '195.220' ************** PARI ***************** Host 195.220.151.50 (195.220.151.50) Time: Thu Jun 30 01:19:00 2005 Input: 2+2; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '195.66.' ************** PARI ***************** Host 195.66.187.42 (195.66.187.42) Time: Thu Jun 30 11:53:37 2005 Input: 12231231313123123123231231231232312312323 Output: ? 12231231313123123123231231231232312312323 ? Errors (if any) and Timing Info: Timing: real 0m0.296s user 0m0.010s sys 0m0.012s '81.244.' ************** PARI ***************** Host 81.244.39.24 (81.244.39.24) Time: Thu Jun 30 14:23:46 2005 Input: F := pAdicField (5 :Precision := 100); P := PolynomialRing(F); f:=y^3-2; I:=ideal; PI:=quo; e0:=PI ! (x^3+3*x^2+4*x e0^2-e0; //(5^2 + O(5^100))*x^2 + (6*5 + O(5^100))*x + 2*5^2 + O(5^100) e1:=3*e0^2-2*e0^3; e1^2-e1; // (69192*5^2 + O(5^100))*x^2 + (17418*5^3 + O(5^100))*x + 21996*5^3 + O(5^100) e2:=3*e1^2-2*e1^3; e2^2-e2; // (150298369603494948*5^5 + O(5^100))*x^2 + (946820397191405616*5^4 + O(5^100))*x + 238583789949331728*5^5 + O(5^100) e3:=3*e2^2-2*e2^3; e3^2-e3; // (24061830692357808087818345172775438927866121025097527260032*5^8 + O(5^100))*x^2 + (6063201397661626486221561530994298640082354387391483932192*5^9 + O(5^100))*x + 7639155070665898812912888171341748707306644877963100570624*5^9 + O(5^100) e4:=3*e3^2-2*e3^3; e4^2-e4; // -(19360341222580688530174881987034285512511095265572450893*5^17 + O(5^100))*x^2 - (9822711558526250332664384053537621910704386860991072173594*5^16 + O(5^100))*x + 736745668056309464652703520494463208527135208779232538882*5^17 + O(5^100) e5:=3*e4^2-2*e4^3; e5^2-e5; // (122212544784603243547342467439155665198590379017*5^32 + O(5^100))*x^2 - (1733183443408412697947330830201464722137363272*5^33 + O(5^100))*x + 5826111006229778003238918505621691599288189711*5^33 + O(5^100) e6:=3*e5^2-2*e5^3; e6^2-e6; // (25399353898222195208218*5^65 + O(5^100))*x^2 - (4554952300349100846737059*5^64 + O(5^100))*x - 930687728343010931258077*5^65 + O(5^100) e7:=3*e6^2-2*e6^3; e7^2-e7; // O(5^100)*x^2 + O(5^100)*x + O(5^100) e7; // (598400185620818811438305832010583989770316503596270341483026286925363 + O(5^100))*x^2 + (3638174303960455584490182526202564335210900186187636879262099459371864 + O(5^100))*x - 2629536350736706018039095217609287432244021450363410015900929768880208 + O(5^100) e := P ! 598400185620818811438305832010583989770316503596270341483026286925363*y^2 + 3638174303960455584490182526202564335210900186187636879262099459371864*y – 2629536350736706018039095217609287432244021450363410015900929768880208; g:=GCD(e,f); g; // (1 + O(5^100))*y^2 + (3590401113724912868629834992063503938621899021577622048898157721552178 + O(5^100))*y - 1836781332867620655410761801268200878930791936144868867535771163690691 + O(5^100) => g = y^2 + 3590401113724912868629834992063503938621899021577622048898157721552178 *y -1836781332867620655410761801268200878930791936144868867535771163690691 h:=GCD(1-e,f); h; // (1 + O(5^100))*y - 3590401113724912868629834992063503938621899021577622048898157721552178 + O(5^100) => h = y - 3590401113724912868629834992063503938621899021577622048898157721552178 g*h; // (1 + O(5^100))*y^3 + O(5^100)*y^2 + O(5^100)*y - 2 + O(5^100) => f = g*h Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 3*5^5 + 4*5^7 + 3*5^8 + 5^10 + 2*5^11 + 5^12 + 4*5^14 + 3*5^16 + 3*5^17 + 3*5^19 + 3*5^20 + 2*5^21 + 5^22 + 3*5^23 + 3*5^24 + 5^25 + 4*5^29 + O(5^100) ? ? ? ? ? ? ? O(5^100) ? ? ? ? ? ? ? O(5^100) ? ? ? ? ? ? ? 5^33 + 2*5^34 + 3*5^35 + 2*5^36 + 3*5^37 + 4*5^39 + 3*5^40 + 2*5^41 + 2*5^43 + 3*5^44 + 3*5^46 + 5^47 + 3*5^49 + 3*5^50 + 2*5^51 + 3*5^52 + 2*5^53 + 5^54 + 5^56 + 3*5^60 + 5^61 + 5^62 + 4*5^63 + 5^64 + 3*5^65 + 2*5^66 + 4*5^69 + 2*5^70 + 2*5^71 + 4*5^72 + 3*5^73 + 4*5^74 + 4*5^75 + 2*5^76 + 4*5^77 + 2*5^78 + 5^80 + 2*5^81 + 3*5^82 + 5^83 + 3*5^84 + 2*5^86 + 2*5^88 + 5^90 + 5^91 + 2*5^93 + 3*5^94 + 3*5^95 + 3*5^96 + 2*5^98 + O(5^100) ? ? ? ? ? ? O(5^100) ? ? ? ? ? ? ? ? ? ? O(5^100) ? ? ? ? ? ? ? ? ? ? ? -1836781332867620655410761801268200878930791936144868867535771163690691 ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: F:=pAdicField(5:Precis ^-------------------- *** unexpected character: P:=PolynomialRing(F); ^-------------------- *** unexpected character: f:=y^3-2; ^------- *** unexpected character: I:=ideal; ^-------------- *** unexpected character: PI:=quo; ^----------- *** unexpected character: e0:=PI!(x^3+3*x^2+4*x ^------------------ *** unexpected character: //(5^2+O(5^100))*x^2 ^-------------------- *** unexpected character: e1:=3*e0^2-2*e0^3; ^--------------- *** unexpected character: //(69192*5^2+O(5^100 ^-------------------- *** unexpected character: e2:=3*e1^2-2*e1^3; ^--------------- *** unexpected character: //(15029836960349494 ^-------------------- *** unexpected character: e3:=3*e2^2-2*e2^3; ^--------------- *** unexpected character: //(24061830692357808 ^-------------------- *** unexpected character: ...82354387391483932192*5^9+ ^ *** Warning: unused characters: )*x+7639155070665898812912888171341748707306644877963100570624*5^9+O(5^100). *** unexpected character: e4:=3*e3^2-2*e3^3; ^--------------- *** unexpected character: //-(1936034122258068 ^-------------------- *** unexpected character: ...4386860991072173594*5^16+ ^ *** Warning: unused characters: )*x+736745668056309464652703520494463208527135208779232538882*5^17+O(5^100). *** unexpected character: e5:=3*e4^2-2*e4^3; ^--------------- *** unexpected character: //(12221254478460324 ^-------------------- *** unexpected character: ...7363272*5^33+O(5^100))*x+ ^ *** unexpected character: e6:=3*e5^2-2*e5^3; ^--------------- *** unexpected character: //(25399353898222195 ^-------------------- *** Warning: unused characters: )*x-930687728343010931258077*5^65+O(5^100). *** unexpected character: e7:=3*e6^2-2*e6^3; ^--------------- *** unexpected character: //O(5^100)*x^2+O(5^1 ^-------------------- *** unexpected character: //(59840018562081881 ^-------------------- *** Warning: unused characters: )*x^2+(3638174303960455584490182526202564335210900186187636879262099459371864+O(5^100))*x-2629536350736706018039095217[+++]. *** unexpected character: e:=P!59840018562081881 ^-------------------- *** unexpected character: g:=GCD(e,f); ^---------- *** unexpected character: //(1+O(5^100))*y^2+( ^-------------------- *** unexpected character: =>g=y^2+359040111372 ^-------------------- *** unexpected character: h:=GCD(1-e,f); ^------------ *** unexpected character: //(1+O(5^100))*y-359 ^-------------------- *** unexpected character: =>h=y-35904011137249 ^-------------------- *** unexpected character: //(1+O(5^100))*y^3+O ^-------------------- *** unexpected character: =>f=g*h ^------- Timing: real 0m0.059s user 0m0.013s sys 0m0.012s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 18:20:47 2005 Input: factor(1400) Output: ? [2 3] [5 2] [7 1] ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.008s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 18:21:26 2005 Input: factor(130) Output: ? [2 1] [5 1] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 18:21:38 2005 Input: factor(2600) Output: ? [2 3] [5 2] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 18:22:07 2005 Input: factor(1090) Output: ? [2 1] [5 1] [109 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.014s sys 0m0.003s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 18:22:33 2005 Input: factor(210) Output: ? [2 1] [3 1] [5 1] [7 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 18:23:40 2005 Input: factor(130) Output: ? [2 1] [5 1] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:11:52 2005 Input: factor(241) Output: ? [241 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:12:12 2005 Input: factor(2161) Output: ? [2161 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:12:32 2005 Input: factor(23761) Output: ? [23761 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:12:39 2005 Input: factor(23759) Output: ? [23 1] [1033 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.012s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:12:48 2005 Input: factor(23761) Output: ? [23761 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:13:09 2005 Input: factor(332641) Output: ? [332641 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:13:29 2005 Input: factor(4989601) Output: ? [277 1] [18013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.012s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:15:25 2005 Input: factor(4989600-1) Output: ? [4989599 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.011s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:15:39 2005 Input: factor(4989601) Output: ? [277 1] [18013 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.011s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:16:48 2005 Input: factor(89812800+1) Output: ? [13 1] [37 1] [61 1] [3061 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:16:52 2005 Input: factor(89812800-1) Output: ? [71 1] [1264969 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:17:29 2005 Input: factor(2*3*5*8*9*11*13*15-1) Output: ? [4633199 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:17:39 2005 Input: factor(2*3*5*8*9*11*13*15*16+1) Output: ? [83 1] [893147 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:17:44 2005 Input: factor(2*3*5*8*9*11*13*15*16-1) Output: ? [31 1] [59 1] [40531 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.011s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:17:51 2005 Input: factor(2*3*5*8*9*11*13*15*17-1) Output: ? [7 1] [199 1] [56543 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:17:57 2005 Input: factor(2*3*5*8*9*11*13*15*17+1) Output: ? [211 1] [373291 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:18:03 2005 Input: factor(2*3*5*8*9*11*13*15*18+1) Output: ? [7 1] [2389 1] [4987 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.011s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:18:07 2005 Input: factor(2*3*5*8*9*11*13*15*18-1) Output: ? [47 1] [677 1] [2621 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:18:13 2005 Input: factor(2*3*5*8*9*11*13*15*19-1) Output: ? [2521 1] [34919 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:18:19 2005 Input: factor(2*3*5*8*9*11*13*15*19+1) Output: ? [88030801 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:19:01 2005 Input: factor(2*3*5*8*9*11*13*15*19*21+1) Output: ? [1848646801 1] ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.011s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:19:07 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23+1) Output: ? [42518876401 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:19:13 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25+1) Output: ? [1062971910001 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:19:19 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*27+1) Output: ? [707437 1] [1622773 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.008s sys 0m0.011s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:19:26 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27+1) Output: ? [317 1] [92143 1] [982571 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:19:31 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27-1) Output: ? [28700241569999 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:20:08 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27-1) 66666666666666666666666666666 factor(2*4+1) Output: ? [28700241569999 1] ? 66666666666666666666666666666 ? [3 2] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:20:13 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27-1) 66666666666666666666666666666 factor(2*4-1) Output: ? [28700241569999 1] ? 66666666666666666666666666666 ? [7 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:20:22 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27-1) 66666666666666666666666666666 factor(2*4*5-1) Output: ? [28700241569999 1] ? 66666666666666666666666666666 ? [3 1] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.011s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:20:27 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27-1) 66666666666666666666666666666 factor(2*4*5+1) Output: ? [28700241569999 1] ? 66666666666666666666666666666 ? [41 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:20:40 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27-1) 66666666666666666666666666666 factor(2*4*5*6+1) Output: ? [28700241569999 1] ? 66666666666666666666666666666 ? [241 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:20:48 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27-1) 66666666666666666666666666666 factor(2*4*5*6*7+1) Output: ? [28700241569999 1] ? 66666666666666666666666666666 ? [41 2] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:20:53 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27-1) 66666666666666666666666666666 factor(2*4*5*6*7-1) Output: ? [28700241569999 1] ? 66666666666666666666666666666 ? [23 1] [73 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:21:21 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27-1) 66666666666666666666666666666 factor(2*4*5*6*8+1) Output: ? [28700241569999 1] ? 66666666666666666666666666666 ? [17 1] [113 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.010s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:21:25 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27-1) 66666666666666666666666666666 factor(2*4*5*6*8-1) Output: ? [28700241569999 1] ? 66666666666666666666666666666 ? [19 1] [101 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.011s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:21:29 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27-1) 66666666666666666666666666666 factor(2*4*5*6*9-1) Output: ? [28700241569999 1] ? 66666666666666666666666666666 ? [17 1] [127 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:21:34 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27-1) 66666666666666666666666666666 factor(2*4*5*6*9+1) Output: ? [28700241569999 1] ? 66666666666666666666666666666 ? [2161 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:21:54 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27-1) 66666666666666666666666666666 factor(2*4*5*6*9*10+1) Output: ? [28700241569999 1] ? 66666666666666666666666666666 ? [21601 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.013s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:21:59 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27-1) 66666666666666666666666666666 factor(2*4*5*6*9*100+1) Output: ? [28700241569999 1] ? 66666666666666666666666666666 ? [61 1] [3541 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:22:02 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27-1) 66666666666666666666666666666 factor(2*4*5*6*9*10+1) Output: ? [28700241569999 1] ? 66666666666666666666666666666 ? [21601 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:22:07 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27-1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [28700241569999 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:22:49 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*29-1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [19891 1] [41843396789 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.011s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:22:55 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*29+1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [53 1] [87961 1] [178532597 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.008s sys 0m0.012s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:22:59 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*28+1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [173 2] [26850438169 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:23:02 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*28-1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [79 1] [10172237518481 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:23:10 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*30-1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [1597601 1] [538937599 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.012s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:23:14 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*30+1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [113 1] [397 1] [19192778741 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:23:17 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31+1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [889707488670001 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.006s sys 0m0.014s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:23:55 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34+1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [67 1] [25073 1] [40531 1] [444281 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.013s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:24:05 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*33+1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [17 1] [89 1] [557 1] [2633 1] [13231717 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:24:11 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*33-1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [67 1] [438214136210597 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:24:19 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*35+1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [3041 1] [10239974384561 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.010s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:24:23 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*35-1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [17 1] [2153 1] [850789926599 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.013s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:24:28 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34-1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [30250054614779999 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.014s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:24:54 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36-1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [774427 1] [1406203510637 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.012s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:24:58 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36+1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [1089001966132080001 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.011s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:25:34 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37+1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [40293072746886960001 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.012s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:25:39 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36+1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [1089001966132080001 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.010s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:25:43 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37+1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [40293072746886960001 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.011s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:25:59 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*40+1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [269 1] [8311 1] [13440529 1] [53637491 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.012s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:26:03 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*40-1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [6759377 1] [238442523604687 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.112s user 0m0.026s sys 0m0.017s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:26:11 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*41+1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [163 1] [353 1] [28711239031306859 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:26:16 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39+1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [317 1] [41203 1] [241393 1] [498404807 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:26:22 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39-1) 66666666666666666666666666666 factor(2*4*5*6*9*10*7+1) Output: ? [1571429837128591439999 1] ? 66666666666666666666666666666 ? [151201 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.013s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:26:42 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39-1) 66666666666666666666666666666 factor(2*3*5*7*9+1) Output: ? [1571429837128591439999 1] ? 66666666666666666666666666666 ? [31 1] [61 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.012s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:26:47 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39-1) 66666666666666666666666666666 factor(2*3*5*7*9*10+1) Output: ? [1571429837128591439999 1] ? 66666666666666666666666666666 ? [41 1] [461 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.015s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:26:51 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39-1) 66666666666666666666666666666 factor(2*3*5*7*9*10-1) Output: ? [1571429837128591439999 1] ? 66666666666666666666666666666 ? [18899 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.013s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:26:56 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39-1) 66666666666666666666666666666 factor(2*3*5*7*9*10*11-1) Output: ? [1571429837128591439999 1] ? 66666666666666666666666666666 ? [127 1] [1637 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.013s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:27:00 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39-1) 66666666666666666666666666666 factor(2*3*5*7*9*10*11+1) Output: ? [1571429837128591439999 1] ? 66666666666666666666666666666 ? [29 1] [67 1] [107 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:27:07 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39-1) 66666666666666666666666666666 factor(2*3*5*7*9*11+1) Output: ? [1571429837128591439999 1] ? 66666666666666666666666666666 ? [17 1] [1223 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.013s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:27:11 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39-1) 66666666666666666666666666666 factor(2*3*5*7*9*11-1) Output: ? [1571429837128591439999 1] ? 66666666666666666666666666666 ? [20789 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.012s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:27:16 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13-1) Output: ? [1571429837128591439999 1] ? 66666666666666666666666666666 ? [270269 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.010s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:27:21 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15-1) Output: ? [1571429837128591439999 1] ? 66666666666666666666666666666 ? [19 1] [23 1] [9277 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.013s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:27:26 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15+1) Output: ? [1571429837128591439999 1] ? 66666666666666666666666666666 ? [1801 1] [2251 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:28:07 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17+1) Output: ? [1571429837128591439999 1] ? 66666666666666666666666666666 ? [68918851 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.007s sys 0m0.013s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:28:13 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19+1) Output: ? [1571429837128591439999 1] ? 66666666666666666666666666666 ? [5393 1] [242807 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.010s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:28:17 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21+1) Output: ? [1571429837128591439999 1] ? 66666666666666666666666666666 ? [2543 1] [10813457 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.015s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:28:22 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23+1) Output: ? [1571429837128591439999 1] ? 66666666666666666666666666666 ? [1063 1] [21613 1] [27529 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.012s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:28:26 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [1571429837128591439999 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.013s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:30:28 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*40-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [691 1] [10613 1] [64340917 1] [133214509 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.011s sys 0m0.011s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:30:34 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*40+1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [1696517 1] [37050730104763853 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.023s sys 0m0.014s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:30:38 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*41+1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [73 1] [127 1] [523 1] [29437 1] [346217 1] [1303793 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.015s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:30:43 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*41-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [859049 1] [74999939843096551 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.012s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:30:51 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*42-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [6571 1] [10044141403043804669 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.010s sys 0m0.009s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:30:56 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*42+1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [4057 1] [16268191560118521193 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.016s sys 0m0.004s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:31:01 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*43+1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [109 1] [132589 1] [141719 1] [32991448079 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.016s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:31:05 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*43-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [181 1] [1069 1] [349226483141312591 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.009s sys 0m0.011s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:31:17 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*44-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [593 1] [1163 1] [100256667184301261 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.008s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:31:21 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*44+1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [69142912833658023360001 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.010s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:31:30 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*44*45+1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [47387 1] [1649993 1] [39794116626811 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.054s user 0m0.024s sys 0m0.018s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:31:37 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*44*45-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [29 2] [59 1] [349 1] [7307 1] [24589383677147 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.010s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:31:44 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*44*45*46-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [53 1] [2053 1] [30271 1] [522211 1] [83210937331 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.016s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:31:48 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*44*45*46+1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [71 1] [307 1] [6566308646404189033133 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.013s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:31:52 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*44*45*47+1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [146237260643186719406400001 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.011s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:32:06 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*44*45*47-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [1773795449353 1] [82443136662983 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.088s user 0m0.061s sys 0m0.026s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:32:16 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*44*45*48+1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [97 1] [3631 1] [3727 1] [19622639 1] [5798112431 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.014s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:32:20 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*44*45*48-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [233 1] [276277 1] [83375993 1] [27826574723 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.022s sys 0m0.015s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:32:24 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*44*45*49-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [97 1] [5237 1] [300124850731444857091 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.015s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:32:29 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*44*45*49+1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [687600109171 1] [221727892076731 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.034s sys 0m0.019s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:32:35 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*44*45*50+1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [113 1] [1376739414829473916460177 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.012s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:32:38 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*44*45*50-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [2239 1] [147062819 1] [472468881288139 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.038s user 0m0.028s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Thu Jun 30 20:32:44 2005 Input: factor(2*3*5*8*9*11*13*15*19*21*23*25*27*31*34*36*37*39*44*45*51-1) 66666666666666666666666666666 factor(2*3*5*7*9*11*13*15*17*19*21*23-1) Output: ? [158682984953245163611199999 1] ? 66666666666666666666666666666 ? [89 1] [269 1] [1181 1] [22369 1] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.013s sys 0m0.008s '69.143.' ************** PARI ***************** Host 69.143.117.110 (69.143.117.110) Time: Thu Jun 30 21:50:28 2005 Input: NextPrime(4294967311); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: NextPrime(4294967311 ^-------------------- Timing: real 0m0.036s user 0m0.010s sys 0m0.009s '212.154' ************** PARI ***************** Host 212.154.104.10 (212.154.104.10) Time: Fri Jul 1 01:29:20 2005 Input: nextprime(10^7) Output: ? 10000019 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.011s sys 0m0.007s '137.226' ************** PARI ***************** Host 137.226.152.140 (137.226.152.140) Time: Fri Jul 1 05:48:57 2005 Input: F:=pAdicField(5: Precision:=100); P:=PolynomialRing(F); F:=x^3-2; I:=idal

; PI:=quo

; e0:=PI ! (x^2+3*x+4); e0^2-e0; Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: F:=pAdicField(5:Precis ^-------------------- *** unexpected character: P:=PolynomialRing(F); ^-------------------- *** unexpected character: F:=x^3-2; ^------- *** unexpected character: I:=idal; ^------------- *** unexpected character: PI:=quo; ^----------- *** unexpected character: e0:=PI!(x^2+3*x+4); ^---------------- Timing: real 0m0.018s user 0m0.015s sys 0m0.003s '137.226' ************** PARI ***************** Host 137.226.152.140 (137.226.152.140) Time: Fri Jul 1 05:53:32 2005 Input: F:=pAdicField(5: Precision:=4); P:=PolynomialRing(F); f:=y^3-2; I:=ideal

; PI:=quo

; e0:=PI ! (-3/2*x-1-1/2*x^2); e0^2-e0; Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: F:=pAdicField(5:Precis ^-------------------- *** unexpected character: P:=PolynomialRing(F); ^-------------------- *** unexpected character: f:=y^3-2; ^------- *** unexpected character: I:=ideal; ^-------------- *** unexpected character: PI:=quo; ^----------- *** unexpected character: e0:=PI!(-3/2*x-1-1/2*x^ ^-------------------- Timing: real 0m0.018s user 0m0.009s sys 0m0.008s '83.130.' ************** PARI ***************** Host 83.130.14.183 (83.130.14.183) Time: Fri Jul 1 13:08:38 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.236s user 0m0.010s sys 0m0.014s '83.130.' ************** PARI ***************** Host 83.130.14.183 (83.130.14.183) Time: Fri Jul 1 13:10:32 2005 Input: factor(1234567890^20+1) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 9303 Killed /usr/bin/gp -q -emacs Timing: real 0m41.504s user 0m20.988s sys 0m0.013s '83.130.' ************** PARI ***************** Host 83.130.14.183 (83.130.14.183) Time: Fri Jul 1 13:10:33 2005 Input: factor(1234567890^20+1) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 9307 Killed /usr/bin/gp -q -emacs Timing: real 0m41.444s user 0m20.993s sys 0m0.009s '132.248' ************** PARI ***************** Host 132.248.51.128 (132.248.51.128) Time: Fri Jul 1 18:43:38 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.082s user 0m0.007s sys 0m0.011s '143.89.' ************** PARI ***************** Host 143.89.90.190 (143.89.90.190) Time: Sat Jul 2 07:01:23 2005 Input: p := 3; m := 5; q:=p^m; n := (q - 1) div 2; K := GF(q); F := GF(p); N := m*n; Vlong := VectorSpace(F, N); v := Vlong ! [0: i in [1..N]]; //for x^2; v2 := Vlong ! [0: i in [1..N]]; //for x^10+x^6-x^2; beta:=w^2; for i in [1..m] do for j in [1..n] do x := beta^(j-1); v[(i-1)*n+j] := Trace(w^(i-1) * (w*x-1)); v2[(i-1)*n+j] := Trace(w^(i-1) * (x^5+x^3-x)); end for; end for; M := KMatrixSpace(F, m, n); //C is from x^2; u := Eltseq(v); genmat := M ! u; C := LinearCode(genmat); //C2 is from x^10+x^6-x^2; u2 := Eltseq(v2); genmat2 := M ! u2; C2 := LinearCode(genmat2); print "weight distrib. of C:",WeightDistribution(C); print "weight distrib. of C2:",WeightDistribution(C2); print "size of permutation group of C:",#PermutationGroup(C); print "size of permutation group of C2:",#PermutationGroup(C2); Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: p:=3; ^--- *** unexpected character: m:=5; ^--- *** unexpected character: q:=p^m; ^----- *** unexpected character: n:=(q-1)div2; ^----------- *** unexpected character: K:=GF(q); ^-------- *** unexpected character: F:=GF(p); ^------- *** unexpected character: N:=m*n; ^----- *** unexpected character: Vlong:=VectorSpace(F,N); ^------------------ *** unexpected character: v:=Vlong![0:iin[1..N]] ^-------------------- *** unexpected character: v2:=Vlong![0:iin[1..N]] ^-------------------- *** unexpected character: beta:=w^2; ^----- *** Warning: unused characters: do. *** unexpected character: foriin[1..m]do ^-------- *** Warning: unused characters: do. *** unexpected character: forjin[1..n]do ^-------- *** unexpected character: x:=beta^(j-1); ^------------ *** unexpected character: v[(i-1)*n+j]:=Trace(w^(i-1)*(w*x- ^-------------------- *** unexpected character: v2[(i-1)*n+j]:=Trace(w^(i-1)*(x^5+ ^-------------------- *** unexpected character: M:=KMatrixSpace(F,m,n) ^-------------------- *** unexpected character: //Cisfromx^2; ^------------- *** unexpected character: u:=Eltseq(v); ^----------- *** unexpected character: genmat:=M!u; ^----- *** unexpected character: C:=LinearCode(genmat); ^-------------------- *** unexpected character: //C2isfromx^10+x^6-x ^-------------------- *** unexpected character: u2:=Eltseq(v2); ^------------ *** unexpected character: genmat2:=M!u2; ^------ *** unexpected character: C2:=LinearCode(genmat2) ^-------------------- *** Warning: unused characters: "weight distrib. of C:",WeightDistribution(C);. *** expected character: '=' instead of: ...C:",WeightDistribution(C); ^- *** Warning: unused characters: "weight distrib. of C2:",WeightDistribution(C2);. *** expected character: '=' instead of: ...:",WeightDistribution(C2); ^- *** Warning: unused characters: "size of permutation group of C:",#PermutationGroup(C);. *** unexpected character: ...permutation group of C:",#PermutationGroup(C) ^-------------------- *** Warning: unused characters: "size of permutation group of C2:",#PermutationGroup(C2);. *** unexpected character: ...ermutation group of C2:",#PermutationGroup(C2 ^-------------------- Timing: real 0m0.472s user 0m0.011s sys 0m0.023s '193.248' ************** PARI ***************** Host 193.248.28.201 (193.248.28.201) Time: Sun Jul 3 12:06:36 2005 Input: mod(2833,840) mod(840,2833) Output: ? ? ? ? ? Errors (if any) and Timing Info: *** obsolete function: mod(2833,840) ^------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** obsolete function: mod(840,2833) ^------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.255s user 0m0.012s sys 0m0.006s '193.253' ************** PARI ***************** Host 193.253.27.164 (193.253.27.164) Time: Sun Jul 3 14:23:54 2005 Input: Mod(7541,325) Output: ? Mod(66, 325) ? Errors (if any) and Timing Info: Timing: real 0m0.042s user 0m0.011s sys 0m0.007s '193.253' ************** PARI ***************** Host 193.253.27.164 (193.253.27.164) Time: Sun Jul 3 14:24:07 2005 Input: Mod(7541,325) Output: ? Mod(66, 325) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '193.253' ************** PARI ***************** Host 193.253.27.164 (193.253.27.164) Time: Sun Jul 3 14:24:08 2005 Input: Mod(7541,325) Output: ? Mod(66, 325) ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '67.10.2' ************** PARI ***************** Host 67.10.229.100 (67.10.229.100) Time: Mon Jul 4 02:36:17 2005 Input: 12^1000 Output: ? 151791008917230196677247156866538521959544559582693695271473033403921064048921603364399500904620475395050503171731001136320009293256130358778327926043116312387122983708799660440956982321378813558667920006534432363672481308846689138864193052799326359127652518020579426714467173077598247127067844595877050639138903109466566927220183839574730419500585318517030222965035497770637709842792291839452561853063601489330288576265113029418340377321749228403929685072857859299265384962468406429488841710177135198202464470288179691559158038375716987501700781189361714888857960330986071687967560154797319303186034952727828396525113400343723663935527822341843570958699722952068094081056227323884130825294614422724551591268271259202391398770616420322544804721099678240930588156578566335064269943879024542896570648335555764510955533106742100977254361036226168195530315814192656420186359083932203335535864049655999109307925787659355811941329081508204306895426902090570277222355892718991046129529960704106358716208000305166229340929343627905607311714631743441688247527228733794417499122906091749376 ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.012s sys 0m0.005s '67.10.2' ************** PARI ***************** Host 67.10.229.100 (67.10.229.100) Time: Mon Jul 4 02:36:28 2005 Input: 12^1000 Output: ? 151791008917230196677247156866538521959544559582693695271473033403921064048921603364399500904620475395050503171731001136320009293256130358778327926043116312387122983708799660440956982321378813558667920006534432363672481308846689138864193052799326359127652518020579426714467173077598247127067844595877050639138903109466566927220183839574730419500585318517030222965035497770637709842792291839452561853063601489330288576265113029418340377321749228403929685072857859299265384962468406429488841710177135198202464470288179691559158038375716987501700781189361714888857960330986071687967560154797319303186034952727828396525113400343723663935527822341843570958699722952068094081056227323884130825294614422724551591268271259202391398770616420322544804721099678240930588156578566335064269943879024542896570648335555764510955533106742100977254361036226168195530315814192656420186359083932203335535864049655999109307925787659355811941329081508204306895426902090570277222355892718991046129529960704106358716208000305166229340929343627905607311714631743441688247527228733794417499122906091749376 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '82.161.' ************** PARI ***************** Host 82.161.111.3 (82.161.111.3) Time: Mon Jul 4 14:21:16 2005 Input: 2^20 Output: ? 1048576 ? Errors (if any) and Timing Info: Timing: real 0m0.268s user 0m0.007s sys 0m0.012s '64.91.9' ************** PARI ***************** Host 64.91.98.137 (64.91.98.137) Time: Mon Jul 4 16:36:54 2005 Input: 480 ncr 99 Output: ? 480 ? Errors (if any) and Timing Info: *** Warning: unused characters: ncr99. Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '64.91.9' ************** PARI ***************** Host 64.91.98.137 (64.91.98.137) Time: Mon Jul 4 16:37:11 2005 Input: Ncr(480,99) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Ncr(480,99) ^----------- Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:37:18 2005 Input: 3456789*987654321 Output: ? 3414112592635269 ? Errors (if any) and Timing Info: Timing: real 0m0.232s user 0m0.010s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:37:41 2005 Input: 3456789999999*9876543219999999 Output: ? 34141135837453919999990000001 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.010s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:38:09 2005 Input: 1111111111111111*11111111111111111111111111111111111 Output: ? 12345679012345677777777777777777777654320987654321 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:38:26 2005 Input: 11111111111111111111111111111*11111111111111111111111111111111111 Output: ? 123456790123456790123456790122222220987654320987654320987654321 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:38:47 2005 Input: 11111111111111111111111111111111111*1111111111111111111111111111111111111111 Output: ? 12345679012345679012345679012345678888887654320987654320987654320987654321 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:39:06 2005 Input: 11111*11111 Output: ? 123454321 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:39:14 2005 Input: 11111111*11111111 Output: ? 123456787654321 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.011s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:39:21 2005 Input: 111111111*111111111 Output: ? 12345678987654321 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:39:29 2005 Input: 1111111111*1111111111 Output: ? 1234567900987654321 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:39:36 2005 Input: 11111111111*11111111111 Output: ? 123456790120987654321 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:39:46 2005 Input: 1111111111111*1111111111111 Output: ? 1234567901234320987654321 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.011s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:40:21 2005 Input: 11111111111*11111111111 Output: ? 123456790120987654321 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:40:45 2005 Input: 1111111111111111*1111111111111111 Output: ? 1234567901234567654320987654321 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:42:05 2005 Input: 111111111111111111111*111111111111111111111 Output: ? 12345679012345679012320987654320987654321 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:42:20 2005 Input: 11111111111111111111111111*11111111111111111111111111 Output: ? 123456790123456790123456787654320987654320987654321 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.008s sys 0m0.010s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:42:44 2005 Input: 11111111111111111111111111*1111111111111111 Output: ? 12345679012345677777777777654320987654321 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.109 (165.95.7.109) Time: Tue Jul 5 17:43:00 2005 Input: 11111111111111111111111111*1111111 Output: ? 12345677777777777777777777654321 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.007s '151.25.' ************** PARI ***************** Host 151.25.38.109 (151.25.38.109) Time: Wed Jul 6 09:11:52 2005 Input: 2344444 Output: ? 2344444 ? Errors (if any) and Timing Info: Timing: real 0m0.305s user 0m0.009s sys 0m0.013s '80.184.' ************** PARI ***************** Host 80.184.144.204 (80.184.144.204) Time: Wed Jul 6 09:17:48 2005 Input: K:=GF(4); D:=PolynomialRing(K); F:=FieldOfFractions(D); D2:=PolynomialRing(D); f:=T^2+T- (x^2/(x+1)); Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: K:=GF(4); ^------- *** unexpected character: D:=PolynomialRing(K); ^-------------------- *** unexpected character: F:=FieldOfFractions(D) ^-------------------- *** unexpected character: D2:=PolynomialRing(D); ^-------------------- *** unexpected character: f:=T^2+T-(x^2/(x+1)); ^------------------- Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Wed Jul 6 18:16:54 2005 Input: 45*(1122.55/11.2) 45*(800.4/8) Output: ? 4510.2455357142857142857142857142857142 ? 4502.2499999999999999999999999999999999 ? Errors (if any) and Timing Info: Timing: real 0m0.062s user 0m0.011s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Wed Jul 6 18:17:16 2005 Input: 45/(1122.55/11.2) 45/(800.4/8) Output: ? 0.44897777381853814974834083114337891408 ? 0.44977511244377811094452773613193403298 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.013s sys 0m0.005s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Wed Jul 6 18:17:43 2005 Input: 45/(1122.55/11.2) 45/(800.4*8) Output: ? 0.44897777381853814974834083114337891408 ? 0.0070277361319340329835082458770614692653 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.013s sys 0m0.006s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Wed Jul 6 18:17:58 2005 Input: 45/(1122.55/11.2) 45/800.4*8 Output: ? 0.44897777381853814974834083114337891408 ? 0.44977511244377811094452773613193403298 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Wed Jul 6 19:23:14 2005 Input: 45/(1122.55/11.2) 45/800.4*8 (800.4*11.2)/1122.55 Output: ? 0.44897777381853814974834083114337891408 ? 0.44977511244377811094452773613193403298 ? ? 7.9858180036523985568571555832702329517 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Wed Jul 6 19:23:22 2005 Input: 45/(1122.55/11.2) 45/800.4*8 (300*11.2)/1122.55 Output: ? 0.44897777381853814974834083114337891408 ? 0.44977511244377811094452773613193403298 ? ? 2.9931851587902543316556055409558594271 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.007s '140.159' ************** PARI ***************** Host 140.159.4.5 (140.159.4.5) Time: Thu Jul 7 04:02:05 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.007s sys 0m0.012s '140.159' ************** PARI ***************** Host 140.159.4.5 (140.159.4.5) Time: Thu Jul 7 04:02:12 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '203.196' ************** PARI ***************** Host 203.196.131.130 (203.196.131.130) Time: Thu Jul 7 06:18:24 2005 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: ? ? 75 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.011s '212.98.' ************** PARI ***************** Host 212.98.201.1 (212.98.201.1) Time: Thu Jul 7 09:21:47 2005 Input: S:= [GF(11)| 3,4,9,7,6,1,5,0,10,8,2]; > C, L := BerlekampMassey(S); C; Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: S:=[GF(11)|3,4,9,7,6,1 ^-------------------- *** unexpected character: >C,L:=BerlekampMa ^-------------------- Timing: real 0m0.274s user 0m0.008s sys 0m0.015s '193.144' ************** PARI ***************** Host 193.144.197.190 (193.144.197.190) Time: Thu Jul 7 10:08:47 2005 Input: factor(6366223796340423057152171586); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.051s user 0m0.013s sys 0m0.007s '193.144' ************** PARI ***************** Host 193.144.197.190 (193.144.197.190) Time: Thu Jul 7 10:09:04 2005 Input: factor(6366223796340423057152171586); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.012s sys 0m0.008s '199.46.' ************** PARI ***************** Host 199.46.199.230 (199.46.199.230) Time: Thu Jul 7 11:53:01 2005 Input: 5076819464927872633 Output: ? 5076819464927872633 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.006s '199.46.' ************** PARI ***************** Host 199.46.199.230 (199.46.199.230) Time: Thu Jul 7 11:54:09 2005 Input: x=5076819464927872633 Output: ? 5076819464927872633 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.013s sys 0m0.005s '199.46.' ************** PARI ***************** Host 199.46.199.230 (199.46.199.230) Time: Thu Jul 7 12:04:23 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.008s sys 0m0.010s '80.103.' ************** PARI ***************** Host 80.103.90.125 (80.103.90.125) Time: Thu Jul 7 12:07:17 2005 Input: 1728/16 Output: ? 108 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.010s sys 0m0.008s '80.103.' ************** PARI ***************** Host 80.103.90.125 (80.103.90.125) Time: Thu Jul 7 12:07:32 2005 Input: factor(108) Output: ? [2 2] [3 3] ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.012s sys 0m0.005s '199.46.' ************** PARI ***************** Host 199.46.199.230 (199.46.199.230) Time: Thu Jul 7 12:08:15 2005 Input: -6399904559872356325 - 1 Output: ? -6399904559872356326 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '199.46.' ************** PARI ***************** Host 199.46.199.230 (199.46.199.230) Time: Thu Jul 7 12:08:41 2005 Input: 1 - 6399904559872356325 Output: ? -6399904559872356324 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '209.82.' ************** PARI ***************** Host 209.82.57.219 (209.82.57.219) Time: Thu Jul 7 12:34:18 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '209.82.' ************** PARI ***************** Host 209.82.57.219 (209.82.57.219) Time: Thu Jul 7 12:34:51 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" int(X) Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: int(X) ^ Timing: real 0m0.029s user 0m0.012s sys 0m0.005s '209.82.' ************** PARI ***************** Host 209.82.57.219 (209.82.57.219) Time: Thu Jul 7 12:35:14 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" int(X)=X Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.009s '80.103.' ************** PARI ***************** Host 80.103.90.125 (80.103.90.125) Time: Thu Jul 7 13:03:03 2005 Input: 24*72 Output: ? 1728 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.010s '80.103.' ************** PARI ***************** Host 80.103.90.125 (80.103.90.125) Time: Thu Jul 7 13:03:53 2005 Input: 36*72 Output: ? 2592 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.005s sys 0m0.013s '80.103.' ************** PARI ***************** Host 80.103.90.125 (80.103.90.125) Time: Thu Jul 7 13:04:23 2005 Input: 216*4 Output: ? 864 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '80.103.' ************** PARI ***************** Host 80.103.90.125 (80.103.90.125) Time: Thu Jul 7 13:04:41 2005 Input: 2592-864 Output: ? 1728 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '83.92.1' ************** PARI ***************** Host 83.92.160.68 (83.92.160.68) Time: Fri Jul 8 05:10:15 2005 Input: 855559101891907529647258156689893817970499226519708650933953538190306906288330985801116411632637054452072432818359762169765646811466434868755501234277981 div 6; Output: ? ? Errors (if any) and Timing Info: *** Warning: unused characters: div6;. Timing: real 0m0.244s user 0m0.009s sys 0m0.011s '62.131.' ************** PARI ***************** Host 62.131.166.92 (62.131.166.92) Time: Fri Jul 8 07:24:57 2005 Input: 123456 Output: ? 123456 ? Errors (if any) and Timing Info: Timing: real 0m0.797s user 0m0.013s sys 0m0.011s '62.131.' ************** PARI ***************** Host 62.131.166.92 (62.131.166.92) Time: Fri Jul 8 07:25:20 2005 Input: x³-1 Output: ? x - 2 ? Errors (if any) and Timing Info: Timing: real 0m0.584s user 0m0.009s sys 0m0.007s '62.131.' ************** PARI ***************** Host 62.131.166.92 (62.131.166.92) Time: Fri Jul 8 07:27:28 2005 Input: x³-1 Output: ? x - 2 ? ? Errors (if any) and Timing Info: Timing: real 0m0.464s user 0m0.013s sys 0m0.014s '62.131.' ************** PARI ***************** Host 62.131.166.92 (62.131.166.92) Time: Fri Jul 8 07:27:52 2005 Input: 3+2 Output: ? 5 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.302s user 0m0.012s sys 0m0.008s '62.131.' ************** PARI ***************** Host 62.131.166.92 (62.131.166.92) Time: Fri Jul 8 07:28:16 2005 Input: log(exp(1)) Output: ? 0.99999999999999999999999999999999999999 ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.376s user 0m0.010s sys 0m0.009s '62.131.' ************** PARI ***************** Host 62.131.166.92 (62.131.166.92) Time: Fri Jul 8 07:29:03 2005 Input: 1/3 Output: ? 1/3 ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.149s user 0m0.011s sys 0m0.009s '62.131.' ************** PARI ***************** Host 62.131.166.92 (62.131.166.92) Time: Fri Jul 8 07:29:12 2005 Input: 1./3 Output: ? 0.33333333333333333333333333333333333333 ? ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.011s sys 0m0.009s '62.131.' ************** PARI ***************** Host 62.131.166.92 (62.131.166.92) Time: Fri Jul 8 07:29:19 2005 Input: 1./7 Output: ? 0.14285714285714285714285714285714285714 ? ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.008s sys 0m0.013s '62.131.' ************** PARI ***************** Host 62.131.166.92 (62.131.166.92) Time: Fri Jul 8 07:29:26 2005 Input: pi Output: ? pi ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.038s user 0m0.007s sys 0m0.014s '62.131.' ************** PARI ***************** Host 62.131.166.92 (62.131.166.92) Time: Fri Jul 8 07:29:37 2005 Input: pi. Output: ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unknown member function: pi. ^ Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '66.69.9' ************** PARI ***************** Host 66.69.97.5 (66.69.97.5) Time: Fri Jul 8 13:03:28 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.291s user 0m0.011s sys 0m0.008s '66.69.9' ************** PARI ***************** Host 66.69.97.5 (66.69.97.5) Time: Fri Jul 8 13:04:28 2005 Input: gcd(4814439,5157437) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.013s sys 0m0.006s '66.69.9' ************** PARI ***************** Host 66.69.97.5 (66.69.97.5) Time: Fri Jul 8 13:07:01 2005 Input: n=4814439 m=5157437 gcd(n,m) Output: ? 4814439 ? 5157437 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '218.253' ************** PARI ***************** Host 218.253.173.169 (218.253.173.169) Time: Sun Jul 10 10:40:24 2005 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Errors (if any) and Timing Info: Timing: real 0m0.319s user 0m0.009s sys 0m0.016s '130.60.' ************** PARI ***************** Host 130.60.188.8 (130.60.188.8) Time: Mon Jul 11 04:39:08 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.109s user 0m0.018s sys 0m0.003s '80.136.' ************** PARI ***************** Host 80.136.90.72 (80.136.90.72) Time: Mon Jul 11 06:37:43 2005 Input: 3*Pi Output: ? 9.4247779607693797153879301498385086525 ? Errors (if any) and Timing Info: Timing: real 0m0.247s user 0m0.009s sys 0m0.014s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Mon Jul 11 12:17:30 2005 Input: factor(414.25) Output: ? ? Errors (if any) and Timing Info: *** can't factor 414.25000000000000000000000000000000000. Timing: real 0m0.309s user 0m0.008s sys 0m0.016s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Mon Jul 11 12:17:35 2005 Input: factor(414) Output: ? [2 1] [3 2] [23 1] ? Errors (if any) and Timing Info: Timing: real 0m0.047s user 0m0.009s sys 0m0.007s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Mon Jul 11 12:20:50 2005 Input: factor(414) factor(14) Output: ? [2 1] [3 2] [23 1] ? [2 1] [7 1] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '68.47.1' ************** PARI ***************** Host 68.47.153.89 (68.47.153.89) Time: Mon Jul 11 17:22:58 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.007s sys 0m0.012s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 04:16:00 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.199s user 0m0.011s sys 0m0.010s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:11:50 2005 Input: ? ?? Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.022s user 0m0.014s sys 0m0.006s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:12:38 2005 Input: ? ?? ?1 Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? ? divrem lex max min shift shiftmul sign vecmax vecmin ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.020s user 0m0.009s sys 0m0.012s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:13:05 2005 Input: ? ?? ?1 ?2 Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? ? divrem lex max min shift shiftmul sign vecmax vecmin ? List Mat Mod Pol Polrev Qfb Ser Set Str Vec binary bitand bitneg bitnegimply bitor bittest bitxor ceil centerlift changevar component conj conjvec denominator floor frac imag length lift norm norml2 numerator numtoperm padicprec permtonum precision random real round simplify sizebyte sizedigit truncate valuation variable ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.021s user 0m0.011s sys 0m0.010s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:14:56 2005 Input: ? ?? ?1 ?2 factor((3+2i)*(5+7i)) Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? ? divrem lex max min shift shiftmul sign vecmax vecmin ? List Mat Mod Pol Polrev Qfb Ser Set Str Vec binary bitand bitneg bitnegimply bitor bittest bitxor ceil centerlift changevar component conj conjvec denominator floor frac imag length lift norm norml2 numerator numtoperm padicprec permtonum precision random real round simplify sizebyte sizedigit truncate valuation variable ? ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory *** expected character: ')' instead of: factor((3+2i)*(5+7i)) ^---------- Timing: real 0m0.022s user 0m0.016s sys 0m0.005s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:15:53 2005 Input: ? ?? ?1 ?2 factor(384736222883) Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? ? divrem lex max min shift shiftmul sign vecmax vecmin ? List Mat Mod Pol Polrev Qfb Ser Set Str Vec binary bitand bitneg bitnegimply bitor bittest bitxor ceil centerlift changevar component conj conjvec denominator floor frac imag length lift norm norml2 numerator numtoperm padicprec permtonum precision random real round simplify sizebyte sizedigit truncate valuation variable ? [683 1] [863 1] [652727 1] ? ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.053s user 0m0.010s sys 0m0.012s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:16:31 2005 Input: ? ?? ?1 ?2 factor(384736222883) sqrt(-4) Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? ? divrem lex max min shift shiftmul sign vecmax vecmin ? List Mat Mod Pol Polrev Qfb Ser Set Str Vec binary bitand bitneg bitnegimply bitor bittest bitxor ceil centerlift changevar component conj conjvec denominator floor frac imag length lift norm norml2 numerator numtoperm padicprec permtonum precision random real round simplify sizebyte sizedigit truncate valuation variable ? [683 1] [863 1] [652727 1] ? 2.0000000000000000000000000000000000000*I ? ? ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.044s user 0m0.011s sys 0m0.011s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:17:44 2005 Input: ? ?? ?1 ?2 factor(384736222883) sqrt(-4) version() Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? ? divrem lex max min shift shiftmul sign vecmax vecmin ? List Mat Mod Pol Polrev Qfb Ser Set Str Vec binary bitand bitneg bitnegimply bitor bittest bitxor ceil centerlift changevar component conj conjvec denominator floor frac imag length lift norm norml2 numerator numtoperm padicprec permtonum precision random real round simplify sizebyte sizedigit truncate valuation variable ? [683 1] [863 1] [652727 1] ? 2.0000000000000000000000000000000000000*I ? ? ? ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory *** expected character: '=' instead of: version() ^ Timing: real 0m0.022s user 0m0.008s sys 0m0.014s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:18:16 2005 Input: ? ?? ?1 ?2 factor(384736222883) sqrt(-4) version() ?11 Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? ? divrem lex max min shift shiftmul sign vecmax vecmin ? List Mat Mod Pol Polrev Qfb Ser Set Str Vec binary bitand bitneg bitnegimply bitor bittest bitxor ceil centerlift changevar component conj conjvec denominator floor frac imag length lift norm norml2 numerator numtoperm padicprec permtonum precision random real round simplify sizebyte sizedigit truncate valuation variable ? [683 1] [863 1] [652727 1] ? 2.0000000000000000000000000000000000000*I ? ? addhelp alias allocatemem break default error extern for fordiv forprime forstep forsubgroup forvec getheap getrand getstack gettime global if input install kill next print print1 printp printp1 printtex quit read reorder return setrand system trap type until whatnow while write write1 writetex ? ? ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory *** expected character: '=' instead of: version() ^ Timing: real 0m0.022s user 0m0.011s sys 0m0.010s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:19:04 2005 Input: ? ?? ?1 ?2 factor(384736222883) sqrt(-4) version() ?11 system() Output: WARNING: PARI command contains unsafe command 'system', so it will not be executed. '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:19:52 2005 Input: ? ?? ?1 ?2 factor(384736222883) sqrt(-4) version() ?11 system() ? Output: WARNING: PARI command contains unsafe command 'system', so it will not be executed. '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:19:57 2005 Input: ? ?? ?1 ?2 factor(384736222883) sqrt(-4) version() ?11 system() ? Output: WARNING: PARI command contains unsafe command 'system', so it will not be executed. '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:20:03 2005 Input: ? ?? ?1 ?2 factor(384736222883) sqrt(-4) version() ?11 system() ? Output: WARNING: PARI command contains unsafe command 'system', so it will not be executed. '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:20:19 2005 Input: ? ?? ?1 ?2 factor(384736222883) sqrt(-4) version() ?11 system() ?? Output: WARNING: PARI command contains unsafe command 'system', so it will not be executed. '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:20:35 2005 Input: ? ?? ?1 ?2 factor(384736222883) sqrt(-4) version() ?11 system() ?? Output: WARNING: PARI command contains unsafe command 'system', so it will not be executed. '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:20:37 2005 Input: ? ?? ?1 ?2 factor(384736222883) sqrt(-4) version() ?11 system() ?? Output: WARNING: PARI command contains unsafe command 'system', so it will not be executed. '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:20:40 2005 Input: ? ?? ?1 ?2 factor(384736222883) sqrt(-4) version() ?11 system() ?? Output: WARNING: PARI command contains unsafe command 'system', so it will not be executed. '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:39:07 2005 Input: ?4 Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.013s sys 0m0.004s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:39:56 2005 Input: ?4 ?prime(10000) Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? prime(n): returns the n-th prime (n C-integer). ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.009s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:40:16 2005 Input: ?4 prime(10000) Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? ? 104729 ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:40:31 2005 Input: ?4 prime(100000) Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? ? ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.018s user 0m0.013s sys 0m0.004s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:41:03 2005 Input: ?4 prime(20000) Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? ? 224737 ? ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.014s sys 0m0.004s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:41:21 2005 Input: ?4 prime(20000) ??prime Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? ? 224737 ? ? ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.022s user 0m0.012s sys 0m0.010s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:41:39 2005 Input: ?4 prime(20000) ??prime Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? ? 224737 ? ? ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.022s user 0m0.012s sys 0m0.010s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:42:14 2005 Input: ?4 prime(20000) ??prime ?factorback Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? ? 224737 ? ? ? factorback(fa,{nf}): given a factorisation fa, gives the factored object back. If this is a prime ideal factorisation you must supply the corresponding number field as second argument. ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.022s user 0m0.015s sys 0m0.006s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:42:44 2005 Input: ?4 prime(20000) ??prime ?factormod Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? ? 224737 ? ? ? factormod(x,p,{flag=0}): factorization mod p of the polynomial x using Berlekamp. flag is optional, and can be 0: default or 1: simple factormod, same except that only the degrees of the irreducible factors are given. ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.021s user 0m0.011s sys 0m0.010s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:43:38 2005 Input: ?4 prime(20000) ??prime ?factormod 2^6666 Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? ? 224737 ? ? ? factormod(x,p,{flag=0}): factorization mod p of the polynomial x using Berlekamp. flag is optional, and can be 0: default or 1: simple factormod, same except that only the degrees of the irreducible factors are given. ? ? 463394736051317298602497107458753279906949728561046280539269868945489593645010610413475485621093424172944326852638820383727586019558042815214421966942761367485789790213652385391335448705618678511094799298045786451859627321562289140703826169952508951272601293948908921831215213522520867807169015269668857765701531312569268703994121129315526264450677108976906227321143852321494967744247208541593234427271034189977229300067325653787436348178067226252090651357926129372287405946531776163762686040876321245004552994366985835834158567447862932517990390986022400831048477916562493844121223892234635145929187051170972862181729833063233818169034498998798221214210411445692536792362142307598845802898112033680882643309399213804768301113115453160711282946465404511413165917910282279311680680073573866597524164127972930165991345542118226242599956046438216831588518623272598915601260178927019021050620558666165636353180431633904887138357298318965584900079578136278581113780614035055971624395052765695059169929930357939008141315223985437641063475746992103634340244366387082433448098091402985594339016271377726002591931543259313477315171285511548447641347767922749769426205714169888435436487073717111529910410648527165279482103375594205882358509436609909746182776365339695889037374677737621680121282928541717599320727162563127636070959774685091397704321579798855530185649133151636675942702158490229731018773476342629393836474200375741924277440207133080577802525357886440163209463315272785346141727061590479139345913640225310767259645532331097871288622989224251907430539943543403305643794518018501618407393103214534698616839183694527416522027574540647964060106425761449640545177256729798292183951829791523225560870501899110019415483215870681183804389466261741450719957329733909971079467895765117097966612279658042541204558369984106303854631768081599741241637708606284376374730537791311349519437507100117839104369597862070141492044082661284954629306628533604546118756254913079683608266780287028320177737998767161115058110464 ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.023s user 0m0.008s sys 0m0.014s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:44:31 2005 Input: ?4 prime(20000) ??prime ?factormod 2^6666 ?bezoutres Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? ? 224737 ? ? ? factormod(x,p,{flag=0}): factorization mod p of the polynomial x using Berlekamp. flag is optional, and can be 0: default or 1: simple factormod, same except that only the degrees of the irreducible factors are given. ? ? 463394736051317298602497107458753279906949728561046280539269868945489593645010610413475485621093424172944326852638820383727586019558042815214421966942761367485789790213652385391335448705618678511094799298045786451859627321562289140703826169952508951272601293948908921831215213522520867807169015269668857765701531312569268703994121129315526264450677108976906227321143852321494967744247208541593234427271034189977229300067325653787436348178067226252090651357926129372287405946531776163762686040876321245004552994366985835834158567447862932517990390986022400831048477916562493844121223892234635145929187051170972862181729833063233818169034498998798221214210411445692536792362142307598845802898112033680882643309399213804768301113115453160711282946465404511413165917910282279311680680073573866597524164127972930165991345542118226242599956046438216831588518623272598915601260178927019021050620558666165636353180431633904887138357298318965584900079578136278581113780614035055971624395052765695059169929930357939008141315223985437641063475746992103634340244366387082433448098091402985594339016271377726002591931543259313477315171285511548447641347767922749769426205714169888435436487073717111529910410648527165279482103375594205882358509436609909746182776365339695889037374677737621680121282928541717599320727162563127636070959774685091397704321579798855530185649133151636675942702158490229731018773476342629393836474200375741924277440207133080577802525357886440163209463315272785346141727061590479139345913640225310767259645532331097871288622989224251907430539943543403305643794518018501618407393103214534698616839183694527416522027574540647964060106425761449640545177256729798292183951829791523225560870501899110019415483215870681183804389466261741450719957329733909971079467895765117097966612279658042541204558369984106303854631768081599741241637708606284376374730537791311349519437507100117839104369597862070141492044082661284954629306628533604546118756254913079683608266780287028320177737998767161115058110464 ? bezoutres(x,y): gives a 3-dimensional row vector [u,v,d] such that d=resultant(x,y) and u*x+v*y=d, where x and y are polynomials. ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.024s user 0m0.014s sys 0m0.010s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:46:00 2005 Input: ?4 prime(20000) ??prime ?factormod 2^6666 ?bezoutres ?7 Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? ? 224737 ? ? ? factormod(x,p,{flag=0}): factorization mod p of the polynomial x using Berlekamp. flag is optional, and can be 0: default or 1: simple factormod, same except that only the degrees of the irreducible factors are given. ? ? 463394736051317298602497107458753279906949728561046280539269868945489593645010610413475485621093424172944326852638820383727586019558042815214421966942761367485789790213652385391335448705618678511094799298045786451859627321562289140703826169952508951272601293948908921831215213522520867807169015269668857765701531312569268703994121129315526264450677108976906227321143852321494967744247208541593234427271034189977229300067325653787436348178067226252090651357926129372287405946531776163762686040876321245004552994366985835834158567447862932517990390986022400831048477916562493844121223892234635145929187051170972862181729833063233818169034498998798221214210411445692536792362142307598845802898112033680882643309399213804768301113115453160711282946465404511413165917910282279311680680073573866597524164127972930165991345542118226242599956046438216831588518623272598915601260178927019021050620558666165636353180431633904887138357298318965584900079578136278581113780614035055971624395052765695059169929930357939008141315223985437641063475746992103634340244366387082433448098091402985594339016271377726002591931543259313477315171285511548447641347767922749769426205714169888435436487073717111529910410648527165279482103375594205882358509436609909746182776365339695889037374677737621680121282928541717599320727162563127636070959774685091397704321579798855530185649133151636675942702158490229731018773476342629393836474200375741924277440207133080577802525357886440163209463315272785346141727061590479139345913640225310767259645532331097871288622989224251907430539943543403305643794518018501618407393103214534698616839183694527416522027574540647964060106425761449640545177256729798292183951829791523225560870501899110019415483215870681183804389466261741450719957329733909971079467895765117097966612279658042541204558369984106303854631768081599741241637708606284376374730537791311349519437507100117839104369597862070141492044082661284954629306628533604546118756254913079683608266780287028320177737998767161115058110464 ? bezoutres(x,y): gives a 3-dimensional row vector [u,v,d] such that d=resultant(x,y) and u*x+v*y=d, where x and y are polynomials. ? O deriv eval factorpadic intformal padicappr polcoeff polcyclo poldegree poldisc poldiscreduced polhensellift polinterpolate polisirreducible pollead pollegendre polrecip polresultant polroots polrootsmod polrootspadic polsturm polsubcyclo polsylvestermatrix polsym poltchebi polzagier serconvol serlaplace serreverse subst taylor thue thueinit ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.024s user 0m0.010s sys 0m0.013s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:46:37 2005 Input: ?4 prime(20000) ??prime ?factormod 2^6666 ?bezoutres ?7 ?polinterpolate Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? ? 224737 ? ? ? factormod(x,p,{flag=0}): factorization mod p of the polynomial x using Berlekamp. flag is optional, and can be 0: default or 1: simple factormod, same except that only the degrees of the irreducible factors are given. ? ? 463394736051317298602497107458753279906949728561046280539269868945489593645010610413475485621093424172944326852638820383727586019558042815214421966942761367485789790213652385391335448705618678511094799298045786451859627321562289140703826169952508951272601293948908921831215213522520867807169015269668857765701531312569268703994121129315526264450677108976906227321143852321494967744247208541593234427271034189977229300067325653787436348178067226252090651357926129372287405946531776163762686040876321245004552994366985835834158567447862932517990390986022400831048477916562493844121223892234635145929187051170972862181729833063233818169034498998798221214210411445692536792362142307598845802898112033680882643309399213804768301113115453160711282946465404511413165917910282279311680680073573866597524164127972930165991345542118226242599956046438216831588518623272598915601260178927019021050620558666165636353180431633904887138357298318965584900079578136278581113780614035055971624395052765695059169929930357939008141315223985437641063475746992103634340244366387082433448098091402985594339016271377726002591931543259313477315171285511548447641347767922749769426205714169888435436487073717111529910410648527165279482103375594205882358509436609909746182776365339695889037374677737621680121282928541717599320727162563127636070959774685091397704321579798855530185649133151636675942702158490229731018773476342629393836474200375741924277440207133080577802525357886440163209463315272785346141727061590479139345913640225310767259645532331097871288622989224251907430539943543403305643794518018501618407393103214534698616839183694527416522027574540647964060106425761449640545177256729798292183951829791523225560870501899110019415483215870681183804389466261741450719957329733909971079467895765117097966612279658042541204558369984106303854631768081599741241637708606284376374730537791311349519437507100117839104369597862070141492044082661284954629306628533604546118756254913079683608266780287028320177737998767161115058110464 ? bezoutres(x,y): gives a 3-dimensional row vector [u,v,d] such that d=resultant(x,y) and u*x+v*y=d, where x and y are polynomials. ? O deriv eval factorpadic intformal padicappr polcoeff polcyclo poldegree poldisc poldiscreduced polhensellift polinterpolate polisirreducible pollead pollegendre polrecip polresultant polroots polrootsmod polrootspadic polsturm polsubcyclo polsylvestermatrix polsym poltchebi polzagier serconvol serlaplace serreverse subst taylor thue thueinit ? polinterpolate(xa,{ya},{x},{&e}): polynomial interpolation at x according to data vectors xa, ya (ie return P such that P(xa[i]) = ya[i] for all i). If ya is omitter, return P such that P(i) = xa[i]. If present, e will contain an error estimate on the returned value. ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.022s user 0m0.013s sys 0m0.009s '81.208.' ************** PARI ***************** Host 81.208.74.187 (81.208.74.187) Time: Wed Jul 13 05:47:49 2005 Input: ?4 prime(20000) ??prime ?factormod 2^6666 ?bezoutres ?7 ?polinterpolate ?polresultant Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? ? 224737 ? ? ? factormod(x,p,{flag=0}): factorization mod p of the polynomial x using Berlekamp. flag is optional, and can be 0: default or 1: simple factormod, same except that only the degrees of the irreducible factors are given. ? ? 463394736051317298602497107458753279906949728561046280539269868945489593645010610413475485621093424172944326852638820383727586019558042815214421966942761367485789790213652385391335448705618678511094799298045786451859627321562289140703826169952508951272601293948908921831215213522520867807169015269668857765701531312569268703994121129315526264450677108976906227321143852321494967744247208541593234427271034189977229300067325653787436348178067226252090651357926129372287405946531776163762686040876321245004552994366985835834158567447862932517990390986022400831048477916562493844121223892234635145929187051170972862181729833063233818169034498998798221214210411445692536792362142307598845802898112033680882643309399213804768301113115453160711282946465404511413165917910282279311680680073573866597524164127972930165991345542118226242599956046438216831588518623272598915601260178927019021050620558666165636353180431633904887138357298318965584900079578136278581113780614035055971624395052765695059169929930357939008141315223985437641063475746992103634340244366387082433448098091402985594339016271377726002591931543259313477315171285511548447641347767922749769426205714169888435436487073717111529910410648527165279482103375594205882358509436609909746182776365339695889037374677737621680121282928541717599320727162563127636070959774685091397704321579798855530185649133151636675942702158490229731018773476342629393836474200375741924277440207133080577802525357886440163209463315272785346141727061590479139345913640225310767259645532331097871288622989224251907430539943543403305643794518018501618407393103214534698616839183694527416522027574540647964060106425761449640545177256729798292183951829791523225560870501899110019415483215870681183804389466261741450719957329733909971079467895765117097966612279658042541204558369984106303854631768081599741241637708606284376374730537791311349519437507100117839104369597862070141492044082661284954629306628533604546118756254913079683608266780287028320177737998767161115058110464 ? bezoutres(x,y): gives a 3-dimensional row vector [u,v,d] such that d=resultant(x,y) and u*x+v*y=d, where x and y are polynomials. ? O deriv eval factorpadic intformal padicappr polcoeff polcyclo poldegree poldisc poldiscreduced polhensellift polinterpolate polisirreducible pollead pollegendre polrecip polresultant polroots polrootsmod polrootspadic polsturm polsubcyclo polsylvestermatrix polsym poltchebi polzagier serconvol serlaplace serreverse subst taylor thue thueinit ? polinterpolate(xa,{ya},{x},{&e}): polynomial interpolation at x according to data vectors xa, ya (ie return P such that P(xa[i]) = ya[i] for all i). If ya is omitter, return P such that P(i) = xa[i]. If present, e will contain an error estimate on the returned value. ? polresultant(x,y,{v},{flag=0}): resultant of the polynomials x and y, with respect to the main variables of x and y if v is omitted, with respect to the variable v otherwise. flag is optional, and can be 0: default, assumes that the polynomials have exact entries (uses the subresultant algorithm), 1 for arbitrary polynomials, using Sylvester's matrix, or 2: using a Ducos's modified subresultant algorithm. ? Errors (if any) and Timing Info:sh: /usr/bin/gphelp: No such file or directory Timing: real 0m0.022s user 0m0.013s sys 0m0.010s '130.237' ************** PARI ***************** Host 130.237.152.168 (130.237.152.168) Time: Wed Jul 13 10:38:29 2005 Input: rho(4) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: rho(4) ^------ Timing: real 0m0.164s user 0m0.007s sys 0m0.013s '70.112.' ************** PARI ***************** Host 70.112.73.15 (70.112.73.15) Time: Wed Jul 13 12:23:26 2005 Input: K := GF(3); C:= D^5 + 2*D + 1; C; IsPrimitive(C); C := C * Coefficient(C,0)^-1; C; S := LFSRSequence (C, [K| 1,1,1,1,1], 48); S; Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: K:=GF(3); ^------- *** unexpected character: C:=D^5+2*D+1; ^------------ *** expected character: '=' instead of: IsPrimitive(C); ^- *** unexpected character: C:=C*Coefficient(C,0)^ ^-------------------- *** unexpected character: S:=LFSRSequence(C,[K|1 ^-------------------- Timing: real 0m0.042s user 0m0.013s sys 0m0.005s '86.128.' ************** PARI ***************** Host 86.128.69.29 (86.128.69.29) Time: Wed Jul 13 12:35:17 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '86.128.' ************** PARI ***************** Host 86.128.69.29 (86.128.69.29) Time: Wed Jul 13 12:35:48 2005 Input: "@i0908 '~@ ;'lk';l;[8-8890 -*9-;=-9-89-@p'o; Output: ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: '"' instead of: "@i0908 ^ *** variable name expected: '~@ ^-- *** ; or ] expected: ;'lk';l;[8-8890 ^ *** unexpected character: -*9-;=-9-89-@p'o; ^---------------- Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '86.128.' ************** PARI ***************** Host 86.128.69.29 (86.128.69.29) Time: Wed Jul 13 12:36:07 2005 Input: A23=-59695985768y98756979575967945h9745y98h7979578694769457694758hg9rt7yh94769547-5486#[;#8;#907#[0#[l9[67o8[7o8[67o8[o895-895-985-698-5698-59786745638945693845 Output: ? -59695985768 ? Errors (if any) and Timing Info: *** Warning: unused characters: y98756979575967945h9745y98h7979578694769457694758hg9rt7yh94769547-5486#[;#8;#907#[0#[l9[67o8[7o8[67o8[o895-895-985-698[+++]. Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '192.154' ************** PARI ***************** Host 192.154.129.194 (192.154.129.194) Time: Wed Jul 13 13:14:13 2005 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: ? [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.010s sys 0m0.008s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:02:38 2005 Input: gp 2+3 Output: ? gp ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:02:56 2005 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.006s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:03:19 2005 Input: sgr(9) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: sgr(9) ^------ Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:03:38 2005 Input: sqr(9) Output: ? 81 ? ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.010s sys 0m0.007s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:04:17 2005 Input: binomial(5,7) Output: ? 0 ? ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.012s sys 0m0.005s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:04:29 2005 Input: binomial(5,7) Output: ? 0 ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:18:47 2005 Input: divisors(18) Output: ? [1, 2, 3, 6, 9, 18] ? Errors (if any) and Timing Info: Timing: real 0m0.049s user 0m0.010s sys 0m0.008s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:26:15 2005 Input: gsumdiv(5,3) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: gsumdiv(5,3) ^------------ Timing: real 0m0.018s user 0m0.006s sys 0m0.011s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:27:44 2005 Input: sigma(5,{k=2}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: sigma(5,{k=2}) ^------ Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:27:55 2005 Input: sigma(5,{k=1}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: sigma(5,{k=1}) ^------ Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:31:30 2005 Input: sumdiv(5) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: sumdiv(5) ^- Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:32:02 2005 Input: sumdiv(5,{k=1}) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: sumdiv(5,{k=1}) ^------ Timing: real 0m0.017s user 0m0.006s sys 0m0.011s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:32:44 2005 Input: divisor(4) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: divisor(4) ^---------- Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:32:57 2005 Input: divisors(4) Output: ? [1, 2, 4] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:42:58 2005 Input: numdiv(7) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.007s sys 0m0.011s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:45:05 2005 Input: Kronecker(3,7) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Kronecker(3,7) ^-------------- Timing: real 0m0.019s user 0m0.007s sys 0m0.011s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:49:44 2005 Input: signa(5,{2}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: signa(5,{2}) ^---- Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:49:55 2005 Input: sigma(5,{2}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: sigma(5,{2}) ^---- Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:50:07 2005 Input: sigma(5,{k=2}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: sigma(5,{k=2}) ^------ Timing: real 0m0.018s user 0m0.013s sys 0m0.005s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:52:56 2005 Input: sigma(5,2) Output: ? 26 ? Errors (if any) and Timing Info: Timing: real 0m0.043s user 0m0.012s sys 0m0.006s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:53:40 2005 Input: sigma(100,3) Output: ? 1149823 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.007s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:54:01 2005 Input: sigma(100,5) Output: ? 10325569807 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:55:09 2005 Input: sigma(91,5) Output: ? 6240709552 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.009s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:55:29 2005 Input: sigma(1000,5) Output: ? 1032587508080700 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:55:37 2005 Input: sigma(100000,5) Output: ? 10325884918721628860677458 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:55:49 2005 Input: sigma(10000000000,5) Output: ? 103258849283383583107309114077391112449465678620007 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.010s sys 0m0.008s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:56:03 2005 Input: sigma(1000000007000007,5) Output: ? 1004117965855856314133143527690156103502158123677104602370967398273962200000 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.007s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:56:42 2005 Input: sigma(1000000007000007090908908888888,5) Output: ? 1032324944498289831660265168716860555789894505420992634658742640387713134019185075009784189562384451369748466765058597707982035820560415399176278400000 ? Errors (if any) and Timing Info: Timing: real 0m0.139s user 0m0.052s sys 0m0.019s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:56:57 2005 Input: sigma(10000000070000070909089088888880000087777777777,5) Output: ? 100000003500003594465495955006974528321431429759700637223523119687906566644866556798665368818818951979504304863940829835872652091697496590330349898576544658379145041510191691405585616308339949703362597929520021590769431685806720116 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.017s sys 0m0.007s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Wed Jul 13 18:57:12 2005 Input: sigma(10000000070000070909089088888880000087766666666666666666666666666999999999999999999999999977777777,5) Output: ? 100000003574716118816922307692668162546767201995758904540820587878867426284889260475014444970949063641653020608493553269192663626975357667351705421959770464759137443433948457836335546602986112247747583959077790196358888300902334380350219275863024150842499690999748644679768422634629379605026102474805265669671253497978019587969831077056545256434615335039293709653402506075057897856109607990314406436539066395018244842754928453092363554354803956740656333461104416963193082276928917729600 ? Errors (if any) and Timing Info: Timing: real 0m0.176s user 0m0.169s sys 0m0.008s '158.109' ************** PARI ***************** Host 158.109.70.130 (158.109.70.130) Time: Thu Jul 14 08:22:15 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.292s user 0m0.006s sys 0m0.013s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 03:51:57 2005 Input: vector(20,j,sigmas(j,3)) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: sigmas(j,3)) ^------------ Timing: real 0m0.125s user 0m0.005s sys 0m0.014s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 03:52:11 2005 Input: vector(20,j,sigma(j,3)) Output: ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134, 1332, 2044, 2198, 3096, 3528, 4681, 4914, 6813, 6860, 9198] ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.010s sys 0m0.008s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 03:52:54 2005 Input: vector(20,j,sigma(j,3)) vector(20,j,sigma(j,5)) Output: ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134, 1332, 2044, 2198, 3096, 3528, 4681, 4914, 6813, 6860, 9198] ? [1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158, 161052, 257908, 371294, 554664, 762744, 1082401, 1419858, 1956669, 2476100, 3304182] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 03:53:51 2005 Input: vector(20,j,sigma(j,3)) vector(20,j,sigma(j,5)) vector(100,j,sigma(j,3)) Output: ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134, 1332, 2044, 2198, 3096, 3528, 4681, 4914, 6813, 6860, 9198] ? [1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158, 161052, 257908, 371294, 554664, 762744, 1082401, 1419858, 1956669, 2476100, 3304182] ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134, 1332, 2044, 2198, 3096, 3528, 4681, 4914, 6813, 6860, 9198, 9632, 11988, 12168, 16380, 15751, 19782, 20440, 25112, 24390, 31752, 29792, 37449, 37296, 44226, 43344, 55261, 50654, 61740, 61544, 73710, 68922, 86688, 79508, 97236, 95382, 109512, 103824, 131068, 117993, 141759, 137592, 160454, 148878, 183960, 167832, 201240, 192080, 219510, 205380, 257544, 226982, 268128, 260408, 299593, 276948, 335664, 300764, 358722, 340704, 390096, 357912, 442845, 389018, 455886, 441028, 500780, 458208, 553896, 493040, 589806, 551881, 620298, 571788, 703136, 619164, 715572, 682920, 779220, 704970, 858438, 756112, 888264, 834176, 934416, 864360, 1048572, 912674, 1061937, 1008324, 1149823] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 03:54:10 2005 Input: vector(20,j,sigma(j,3)) vector(20,j,sigma(j,5)) vector(1000,j,sigma(j,3)) Output: ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134, 1332, 2044, 2198, 3096, 3528, 4681, 4914, 6813, 6860, 9198] ? [1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158, 161052, 257908, 371294, 554664, 762744, 1082401, 1419858, 1956669, 2476100, 3304182] ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134, 1332, 2044, 2198, 3096, 3528, 4681, 4914, 6813, 6860, 9198, 9632, 11988, 12168, 16380, 15751, 19782, 20440, 25112, 24390, 31752, 29792, 37449, 37296, 44226, 43344, 55261, 50654, 61740, 61544, 73710, 68922, 86688, 79508, 97236, 95382, 109512, 103824, 131068, 117993, 141759, 137592, 160454, 148878, 183960, 167832, 201240, 192080, 219510, 205380, 257544, 226982, 268128, 260408, 299593, 276948, 335664, 300764, 358722, 340704, 390096, 357912, 442845, 389018, 455886, 441028, 500780, 458208, 553896, 493040, 589806, 551881, 620298, 571788, 703136, 619164, 715572, 682920, 779220, 704970, 858438, 756112, 888264, 834176, 934416, 864360, 1048572, 912674, 1061937, 1008324, 1149823, 1030302, 1238328, 1092728, 1285830, 1213632, 1339902, 1225044, 1492120, 1295030, 1510488, 1418312, 1610264, 1442898, 1728720, 1533168, 1780470, 1663886, 1848420, 1690416, 2063880, 1772893, 2042838, 1929816, 2174816, 1968876, 2343672, 2048384, 2396745, 2226224, 2492532, 2248092, 2722608, 2359840, 2706876, 2575440, 2874690, 2571354, 3066336, 2685620, 3164112, 2907072, 3221208, 2927736, 3543517, 3073140, 3501162, 3303804, 3697742, 3307950, 3969252, 3442952, 4013100, 3719898, 4123872, 3753792, 4492712, 3869894, 4437360, 4168584, 4718574, 4185792, 4966929, 4330748, 5031306, 4699296, 5146092, 4657464, 5634720, 4829007, 5572476, 5193020, 5804084, 5177718, 6146280, 5418344, 6235092, 5750640, 6344730, 5735340, 6962886, 5929742, 6805008, 6355496, 7118280, 6382404, 7507584, 6545448, 7579152, 7031360, 7779240, 6967872, 8388604, 7189058, 8214066, 7754544, 8613489, 7645374, 9074916, 7880600, 9214335, 8421392, 9272718, 8390160, 10044216, 8684172, 9834552, 9211176, 10288838, 9137520, 10922688, 9393932, 10868094, 10021536, 11025396, 10018008, 11957400, 10248448, 11655270, 10892504, 12251736, 10800972, 12764808, 11089568, 12882456, 11923507, 12986082, 11697084, 14021840, 12008990, 13798512, 12829824, 14268150, 12649338, 14974974, 13081824, 14992740, 13805120, 15213744, 13651920, 16514568, 13997522, 15956037, 14900788, 16569686, 14867118, 17368344, 15078280, 17428320, 16010064, 17719884, 15813252, 19009784, 16207776, 18435456, 17336592, 19173961, 16974594, 20036016, 17424976, 20217204, 18463230, 20232828, 18191448, 21818160, 18758628, 21238560, 19739160, 21955772, 19465110, 23178960, 19902512, 23002434, 21171136, 23142186, 20980332, 24871392, 21253934, 24170580, 22552544, 25356240, 22188042, 26163648, 22665188, 26127576, 24202080, 26349624, 23709168, 28348893, 24142483, 27658260, 25554872, 28398314, 25153758, 29734236, 25877880, 29632590, 27226080, 29771550, 26745264, 32195044, 27350752, 30986568, 28848456, 32111660, 28599732, 33479082, 28934444, 33449184, 30596384, 33784128, 30080232, 36003240, 30664298, 34829046, 32811408, 35991920, 31855014, 37517256, 32487480, 37748718, 34301232, 37672128, 33710040, 40287313, 34620698, 38976732, 36260840, 40319370, 35715456, 42293664, 36264692, 41740524, 38345078, 41917176, 37896264, 45087392, 38272754, 43461063, 40401144, 45198972, 39682944, 46737180, 40471600, 46512180, 42928704, 46599462, 41781924, 49853160, 42508550, 48765096, 44927120, 49882068, 43986978, 51755760, 45096912, 51462810, 47331648, 5161[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.019s sys 0m0.005s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 03:54:45 2005 Input: vector(20,j,sigma(j,3)) vector(20,j,sigma(j,5)) vector(100000,j,sigma(j,3)) Output: ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134, 1332, 2044, 2198, 3096, 3528, 4681, 4914, 6813, 6860, 9198] ? [1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158, 161052, 257908, 371294, 554664, 762744, 1082401, 1419858, 1956669, 2476100, 3304182] ? 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Errors (if any) and Timing Info: Timing: real 0m6.759s user 0m6.740s sys 0m0.018s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 03:55:40 2005 Input: vector(20,j,sigma(j,3)) vector(20,j,sigma(j,5)) vector(100000,j,sigma(j,3)) vector(100000,j,sigma(j,5)) Output: ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134, 1332, 2044, 2198, 3096, 3528, 4681, 4914, 6813, 6860, 9198] ? [1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158, 161052, 257908, 371294, 554664, 762744, 1082401, 1419858, 1956669, 2476100, 3304182] ? 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Errors (if any) and Timing Info: Timing: real 0m13.539s user 0m13.509s sys 0m0.028s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 03:56:46 2005 Input: vector(20,j,sigma(j,3)) vector(20,j,sigma(j,5)) vector(100000,j,sigma(j,3)) vector(1000000,j,sigma(j,5)) Output: ** WARNING: Computation used more memory than allowed. ** ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134, 1332, 2044, 2198, 3096, 3528, 4681, 4914, 6813, 6860, 9198] ? [1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158, 161052, 257908, 371294, 554664, 762744, 1082401, 1419858, 1956669, 2476100, 3304182] ? 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Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m6.762s user 0m6.735s sys 0m0.023s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 03:57:53 2005 Input: vector(100000,j,sigma(j,3)) vector(100000,j,sigma(j,5)) Output: ? 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Errors (if any) and Timing Info: Timing: real 0m13.535s user 0m13.503s sys 0m0.026s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 04:17:13 2005 Input: vector(100000,j,sigma(j,3)) vector(10,j,sigma(j,5)) Output: ? 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[1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158] ? Errors (if any) and Timing Info: Timing: real 0m8.762s user 0m6.728s sys 0m0.023s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 04:17:18 2005 Input: vector(100000,j,sigma(j,3)) vector(10,j,sigma(j,5)) Output: ? 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[1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158] ? Errors (if any) and Timing Info: Timing: real 0m8.640s user 0m6.737s sys 0m0.019s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 04:17:57 2005 Input: vector(100000,j,sigma(j,3)) a=vector(10,j,sigma(j,5)) Output: ? 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[1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158] ? Errors (if any) and Timing Info: Timing: real 0m6.752s user 0m6.730s sys 0m0.021s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 04:18:32 2005 Input: vector(100000,j,sigma(j,3)) a=vector(10,j,sigma(j,5)) a[4] Output: ? 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[1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158] ? 1057 ? Errors (if any) and Timing Info: Timing: real 0m6.752s user 0m6.727s sys 0m0.024s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 04:20:04 2005 Input: vector(100000,j,sigma(j,3)) a=vector(10,j,sigma(j,5)) a[4] c=a[2]-a[1] Output: ? 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[1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158] ? 1057 ? 32 ? Errors (if any) and Timing Info: Timing: real 0m6.758s user 0m6.728s sys 0m0.019s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 04:20:49 2005 Input: vector(100000,j,sigma(j,3)) a=vector(10,j,sigma(j,5)) a[4] c=a[2]-a[1] d=a[5] Output: ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134, 1332, 2044, 2198, 3096, 3528, 4681, 4914, 6813, 6860, 9198, 9632, 11988, 12168, 16380, 15751, 19782, 20440, 25112, 24390, 31752, 29792, 37449, 37296, 44226, 43344, 55261, 50654, 61740, 61544, 73710, 68922, 86688, 79508, 97236, 95382, 109512, 103824, 131068, 117993, 141759, 137592, 160454, 148878, 183960, 167832, 201240, 192080, 219510, 205380, 257544, 226982, 268128, 260408, 299593, 276948, 335664, 300764, 358722, 340704, 390096, 357912, 442845, 389018, 455886, 441028, 500780, 458208, 553896, 493040, 589806, 551881, 620298, 571788, 703136, 619164, 715572, 682920, 779220, 704970, 858438, 756112, 888264, 834176, 934416, 864360, 1048572, 912674, 1061937, 1008324, 1149823, 1030302, 1238328, 1092728, 1285830, 1213632, 1339902, 1225044, 1492120, 1295030, 1510488, 1418312, 1610264, 1442898, 1728720, 1533168, 1780470, 1663886, 1848420, 1690416, 2063880, 1772893, 2042838, 1929816, 2174816, 1968876, 2343672, 2048384, 2396745, 2226224, 2492532, 2248092, 2722608, 2359840, 2706876, 2575440, 2874690, 2571354, 3066336, 2685620, 3164112, 2907072, 3221208, 2927736, 3543517, 3073140, 3501162, 3303804, 3697742, 3307950, 3969252, 3442952, 4013100, 3719898, 4123872, 3753792, 4492712, 3869894, 4437360, 4168584, 4718574, 4185792, 4966929, 4330748, 5031306, 4699296, 5146092, 4657464, 5634720, 4829007, 5572476, 5193020, 5804084, 5177718, 6146280, 5418344, 6235092, 5750640, 6344730, 5735340, 6962886, 5929742, 6805008, 6355496, 7118280, 6382404, 7507584, 6545448, 7579152, 7031360, 7779240, 6967872, 8388604, 7189058, 8214066, 7754544, 8613489, 7645374, 9074916, 7880600, 9214335, 8421392, 9272718, 8390160, 10044216, 8684172, 9834552, 9211176, 10288838, 9137520, 10922688, 9393932, 10868094, 10021536, 11025396, 10018008, 11957400, 10248448, 11655270, 10892504, 12251736, 10800972, 12764808, 11089568, 12882456, 11923507, 12986082, 11697084, 14021840, 12008990, 13798512, 12829824, 14268150, 12649338, 14974974, 13081824, 14992740, 13805120, 15213744, 13651920, 16514568, 13997522, 15956037, 14900788, 16569686, 14867118, 17368344, 15078280, 17428320, 16010064, 17719884, 15813252, 19009784, 16207776, 18435456, 17336592, 19173961, 16974594, 20036016, 17424976, 20217204, 18463230, 20232828, 18191448, 21818160, 18758628, 21238560, 19739160, 21955772, 19465110, 23178960, 19902512, 23002434, 21171136, 23142186, 20980332, 24871392, 21253934, 24170580, 22552544, 25356240, 22188042, 26163648, 22665188, 26127576, 24202080, 26349624, 23709168, 28348893, 24142483, 27658260, 25554872, 28398314, 25153758, 29734236, 25877880, 29632590, 27226080, 29771550, 26745264, 32195044, 27350752, 30986568, 28848456, 32111660, 28599732, 33479082, 28934444, 33449184, 30596384, 33784128, 30080232, 36003240, 30664298, 34829046, 32811408, 35991920, 31855014, 37517256, 32487480, 37748718, 34301232, 37672128, 33710040, 40287313, 34620698, 38976732, 36260840, 40319370, 35715456, 42293664, 36264692, 41740524, 38345078, 41917176, 37896264, 45087392, 38272754, 43461063, 40401144, 45198972, 39682944, 46737180, 40471600, 46512180, 42928704, 46599462, 41781924, 49853160, 42508550, 48765096, 44927120, 49882068, 43986978, 51755760, 45096912, 51462810, 47331648, 5161[+++] ? [1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158] ? 1057 ? 32 ? 3126 ? Errors (if any) and Timing Info: Timing: real 0m6.751s user 0m6.734s sys 0m0.013s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 04:20:57 2005 Input: vector(100,j,sigma(j,3)) a=vector(10,j,sigma(j,5)) a[4] c=a[2]-a[1] d=a[5] Output: ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134, 1332, 2044, 2198, 3096, 3528, 4681, 4914, 6813, 6860, 9198, 9632, 11988, 12168, 16380, 15751, 19782, 20440, 25112, 24390, 31752, 29792, 37449, 37296, 44226, 43344, 55261, 50654, 61740, 61544, 73710, 68922, 86688, 79508, 97236, 95382, 109512, 103824, 131068, 117993, 141759, 137592, 160454, 148878, 183960, 167832, 201240, 192080, 219510, 205380, 257544, 226982, 268128, 260408, 299593, 276948, 335664, 300764, 358722, 340704, 390096, 357912, 442845, 389018, 455886, 441028, 500780, 458208, 553896, 493040, 589806, 551881, 620298, 571788, 703136, 619164, 715572, 682920, 779220, 704970, 858438, 756112, 888264, 834176, 934416, 864360, 1048572, 912674, 1061937, 1008324, 1149823] ? [1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158] ? 1057 ? 32 ? 3126 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 04:21:15 2005 Input: vector(100,j,sigma(j,3)) a=vector(10,j,sigma(j,5)) a[4] c=a[2]-a[1] d=a[5] c Output: ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134, 1332, 2044, 2198, 3096, 3528, 4681, 4914, 6813, 6860, 9198, 9632, 11988, 12168, 16380, 15751, 19782, 20440, 25112, 24390, 31752, 29792, 37449, 37296, 44226, 43344, 55261, 50654, 61740, 61544, 73710, 68922, 86688, 79508, 97236, 95382, 109512, 103824, 131068, 117993, 141759, 137592, 160454, 148878, 183960, 167832, 201240, 192080, 219510, 205380, 257544, 226982, 268128, 260408, 299593, 276948, 335664, 300764, 358722, 340704, 390096, 357912, 442845, 389018, 455886, 441028, 500780, 458208, 553896, 493040, 589806, 551881, 620298, 571788, 703136, 619164, 715572, 682920, 779220, 704970, 858438, 756112, 888264, 834176, 934416, 864360, 1048572, 912674, 1061937, 1008324, 1149823] ? [1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158] ? 1057 ? 32 ? 3126 ? 32 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 04:21:25 2005 Input: vector(10,j,sigma(j,3)) a=vector(10,j,sigma(j,5)) a[4] c=a[2]-a[1] d=a[5] c Output: ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134] ? [1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158] ? 1057 ? 32 ? 3126 ? 32 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 04:44:23 2005 Input: vector(10,j,sigma(j,3)) a=vector(10,j,sigma(j,5)) a[4] c=a[2]-a[1] d=a[5] c f=(1-rt+nt^2)^(-k+1) Output: ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134] ? [1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158] ? 1057 ? 32 ? 3126 ? 32 ? (1 + (-k + 1)*nt^2 + (1/2*k^2 - 1/2*k)*nt^4 + (-1/6*k^3 + 1/6*k)*nt^6 + (1/24*k^4 + 1/12*k^3 - 1/24*k^2 - 1/12*k)*nt^8 + (-1/120*k^5 - 1/24*k^4 - 1/24*k^3 + 1/24*k^2 + 1/20*k)*nt^10 + (1/720*k^6 + 1/80*k^5 + 5/144*k^4 + 1/48*k^3 - 13/360*k^2 - 1/30*k)*nt^12 + (-1/5040*k^7 - 1/360*k^6 - 1/72*k^5 - 1/36*k^4 - 7/720*k^3 + 11/360*k^2 + 1/42*k)*nt^14 + O(nt^16)) + ((k - 1) + (-k^2 + k)*nt^2 + (1/2*k^3 - 1/2*k)*nt^4 + (-1/6*k^4 - 1/3*k^3 + 1/6*k^2 + 1/3*k)*nt^6 + (1/24*k^5 + 5/24*k^4 + 5/24*k^3 - 5/24*k^2 - 1/4*k)*nt^8 + (-1/120*k^6 - 3/40*k^5 - 5/24*k^4 - 1/8*k^3 + 13/60*k^2 + 1/5*k)*nt^10 + (1/720*k^7 + 7/360*k^6 + 7/72*k^5 + 7/36*k^4 + 49/720*k^3 - 77/360*k^2 - 1/6*k)*nt^12 + (-1/5040*k^8 - 1/252*k^7 - 11/360*k^6 - 1/9*k^5 - 127/720*k^4 - 1/36*k^3 + 29/140*k^2 + 1/7*k)*nt^14 + O(nt^16))*rt + ((1/2*k^2 - 1/2*k) + (-1/2*k^3 + 1/2*k)*nt^2 + (1/4*k^4 + 1/2*k^3 - 1/4*k^2 - 1/2*k)*nt^4 + (-1/12*k^5 - 5/12*k^4 - 5/12*k^3 + 5/12*k^2 + 1/2*k)*nt^6 + (1/48*k^6 + 3/16*k^5 + 25/48*k^4 + 5/16*k^3 - 13/24*k^2 - 1/2*k)*nt^8 + (-1/240*k^7 - 7/120*k^6 - 7/24*k^5 - 7/12*k^4 - 49/240*k^3 + 77/120*k^2 + 1/2*k)*nt^10 + (1/1440*k^8 + 1/72*k^7 + 77/720*k^6 + 7/18*k^5 + 889/1440*k^4 + 7/72*k^3 - 29/40*k^2 - 1/2*k)*nt^12 + (-1/10080*k^9 - 3/1120*k^8 - 7/240*k^7 - 13/80*k^6 - 229/480*k^5 - 101/160*k^4 + 2/315*k^3 + 223/280*k^2 + 1/2*k)*nt^14 + O(nt^16))*rt^2 + ((1/6*k^3 - 1/6*k) + (-1/6*k^4 - 1/3*k^3 + 1/6*k^2 + 1/3*k)*nt^2 + (1/12*k^5 + 5/12*k^4 + 5/12*k^3 - 5/12*k^2 - 1/2*k)*nt^4 + (-1/36*k^6 - 1/4*k^5 - 25/36*k^4 - 5/12*k^3 + 13/18*k^2 + 2/3*k)*nt^6 + (1/144*k^7 + 7/72*k^6 + 35/72*k^5 + 35/36*k^4 + 49/144*k^3 - 77/72*k^2 - 5/6*k)*nt^8 + (-1/720*k^8 - 1/36*k^7 - 77/360*k^6 - 7/9*k^5 - 889/720*k^4 - 7/36*k^3 + 29/20*k^2 + k)*nt^10 + (1/4320*k^9 + 1/160*k^8 + 49/720*k^7 + 91/240*k^6 + 1603/1440*k^5 + 707/480*k^4 - 2/135*k^3 - 223/120*k^2 - 7/6*k)*nt^12 + (-1/30240*k^10 - 1/864*k^9 - 17/1008*k^8 - 19/144*k^7 - 853/1440*k^6 - 427/288*k^5 - 1271/756*k^4 + 61/216*k^3 + 481/210*k^2 + 4/3*k)*nt^14 + O(nt^16))*rt^3 + ((1/24*k^4 + 1/12*k^3 - 1/24*k^2 - 1/12*k) + (-1/24*k^5 - 5/24*k^4 - 5/24*k^3 + 5/24*k^2 + 1/4*k)*nt^2 + (1/48*k^6 + 3/16*k^5 + 25/48*k^4 + 5/16*k^3 - 13/24*k^2 - 1/2*k)*nt^4 + (-1/144*k^7 - 7/72*k^6 - 35/72*k^5 - 35/36*k^4 - 49/144*k^3 + 77/72*k^2 + 5/6*k)*nt^6 + (1/576*k^8 + 5/144*k^7 + 77/288*k^6 + 35/36*k^5 + 889/576*k^4 + 35/144*k^3 - 29/16*k^2 - 5/4*k)*nt^8 + (-1/2880*k^9 - 3/320*k^8 - 49/480*k^7 - 91/160*k^6 - 1603/960*k^5 - 707/320*k^4 + 1/45*k^3 + 223/80*k^2 + 7/4*k)*nt^10 + (1/17280*k^10 + 7/3456*k^9 + 17/576*k^8 + 133/576*k^7 + 5971/5760*k^6 + 2989/1152*k^5 + 1271/432*k^4 - 427/864*k^3 - 481/120*k^2 - 7/3*k)*nt^12 + (-1/120960*k^11 - 11/30240*k^10 - 55/8064*k^9 - 143/2016*k^8 - 2563/5760*k^7 - 2453/1440*k^6 - 90871/24192*k^5 - 22451/6048*k^4 + 1353/1120*k^3 + 4609/840*k^2 + 3*k)*nt^14 + O(nt^16))*rt^4 + ((1/120*k^5 + 1/24*k^4 + 1/24*k^3 - 1/24*k^2 - 1/20*k) + (-1/120*k^6 - 3/40*k^5 - 5/24*k^4 - 1/8*k^3 + 13/60*k^2 + 1/5*k)*nt^2 + (1/240*k^7 + 7/120*k^6 + 7/24*k^5 + 7/12*k^4 + 49/240*k^3 - 77/120*k^2 - 1/2*k)*nt^4 + (-1/720*k^8 - 1/36*k^7 - 77/360*k^6 - 7/9*k^5 - 889/720*k^4 - 7/36*k^3 + 29/20*k^2 + k)*nt^6 + (1/2880*k^9 + 3/320*k^8 + 49/480*k^7[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.079s user 0m0.044s sys 0m0.008s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 04:47:27 2005 Input: vector(10,j,sigma(j,3)) a=vector(10,j,sigma(j,5)) a[4] c=a[2]-a[1] d=a[5] c g=taylor(=(1-rt+nt^2)^(-k+1),t) Output: ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134] ? [1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158] ? 1057 ? 32 ? 3126 ? 32 ? ? Errors (if any) and Timing Info: *** unexpected character: g=taylor(=(1-rt+nt^2)^(-k+1), ^-------------------- Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 04:47:38 2005 Input: vector(10,j,sigma(j,3)) a=vector(10,j,sigma(j,5)) a[4] c=a[2]-a[1] d=a[5] c g=taylor((1-rt+nt^2)^(-k+1),t) Output: ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134] ? [1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158] ? 1057 ? 32 ? 3126 ? 32 ? ((1 + O(t^16)) + (-k + 1)*nt^2 + (1/2*k^2 - 1/2*k)*nt^4 + (-1/6*k^3 + 1/6*k)*nt^6 + (1/24*k^4 + 1/12*k^3 - 1/24*k^2 - 1/12*k)*nt^8 + (-1/120*k^5 - 1/24*k^4 - 1/24*k^3 + 1/24*k^2 + 1/20*k)*nt^10 + (1/720*k^6 + 1/80*k^5 + 5/144*k^4 + 1/48*k^3 - 13/360*k^2 - 1/30*k)*nt^12 + (-1/5040*k^7 - 1/360*k^6 - 1/72*k^5 - 1/36*k^4 - 7/720*k^3 + 11/360*k^2 + 1/42*k)*nt^14 + O(nt^16)) + ((-1/5040*k^8 - 1/252*k^7 - 11/360*k^6 - 1/9*k^5 - 127/720*k^4 - 1/36*k^3 + 29/140*k^2 + 1/7*k)*nt^14 + (1/720*k^7 + 7/360*k^6 + 7/72*k^5 + 7/36*k^4 + 49/720*k^3 - 77/360*k^2 - 1/6*k)*nt^12 + (-1/120*k^6 - 3/40*k^5 - 5/24*k^4 - 1/8*k^3 + 13/60*k^2 + 1/5*k)*nt^10 + (1/24*k^5 + 5/24*k^4 + 5/24*k^3 - 5/24*k^2 - 1/4*k)*nt^8 + (-1/6*k^4 - 1/3*k^3 + 1/6*k^2 + 1/3*k)*nt^6 + (1/2*k^3 - 1/2*k)*nt^4 + (-k^2 + k)*nt^2 + (k - 1))*rt + ((-1/10080*k^9 - 3/1120*k^8 - 7/240*k^7 - 13/80*k^6 - 229/480*k^5 - 101/160*k^4 + 2/315*k^3 + 223/280*k^2 + 1/2*k)*nt^14 + (1/1440*k^8 + 1/72*k^7 + 77/720*k^6 + 7/18*k^5 + 889/1440*k^4 + 7/72*k^3 - 29/40*k^2 - 1/2*k)*nt^12 + (-1/240*k^7 - 7/120*k^6 - 7/24*k^5 - 7/12*k^4 - 49/240*k^3 + 77/120*k^2 + 1/2*k)*nt^10 + (1/48*k^6 + 3/16*k^5 + 25/48*k^4 + 5/16*k^3 - 13/24*k^2 - 1/2*k)*nt^8 + (-1/12*k^5 - 5/12*k^4 - 5/12*k^3 + 5/12*k^2 + 1/2*k)*nt^6 + (1/4*k^4 + 1/2*k^3 - 1/4*k^2 - 1/2*k)*nt^4 + (-1/2*k^3 + 1/2*k)*nt^2 + (1/2*k^2 - 1/2*k))*rt^2 + ((-1/30240*k^10 - 1/864*k^9 - 17/1008*k^8 - 19/144*k^7 - 853/1440*k^6 - 427/288*k^5 - 1271/756*k^4 + 61/216*k^3 + 481/210*k^2 + 4/3*k)*nt^14 + (1/4320*k^9 + 1/160*k^8 + 49/720*k^7 + 91/240*k^6 + 1603/1440*k^5 + 707/480*k^4 - 2/135*k^3 - 223/120*k^2 - 7/6*k)*nt^12 + (-1/720*k^8 - 1/36*k^7 - 77/360*k^6 - 7/9*k^5 - 889/720*k^4 - 7/36*k^3 + 29/20*k^2 + k)*nt^10 + (1/144*k^7 + 7/72*k^6 + 35/72*k^5 + 35/36*k^4 + 49/144*k^3 - 77/72*k^2 - 5/6*k)*nt^8 + (-1/36*k^6 - 1/4*k^5 - 25/36*k^4 - 5/12*k^3 + 13/18*k^2 + 2/3*k)*nt^6 + (1/12*k^5 + 5/12*k^4 + 5/12*k^3 - 5/12*k^2 - 1/2*k)*nt^4 + (-1/6*k^4 - 1/3*k^3 + 1/6*k^2 + 1/3*k)*nt^2 + (1/6*k^3 - 1/6*k))*rt^3 + ((-1/120960*k^11 - 11/30240*k^10 - 55/8064*k^9 - 143/2016*k^8 - 2563/5760*k^7 - 2453/1440*k^6 - 90871/24192*k^5 - 22451/6048*k^4 + 1353/1120*k^3 + 4609/840*k^2 + 3*k)*nt^14 + (1/17280*k^10 + 7/3456*k^9 + 17/576*k^8 + 133/576*k^7 + 5971/5760*k^6 + 2989/1152*k^5 + 1271/432*k^4 - 427/864*k^3 - 481/120*k^2 - 7/3*k)*nt^12 + (-1/2880*k^9 - 3/320*k^8 - 49/480*k^7 - 91/160*k^6 - 1603/960*k^5 - 707/320*k^4 + 1/45*k^3 + 223/80*k^2 + 7/4*k)*nt^10 + (1/576*k^8 + 5/144*k^7 + 77/288*k^6 + 35/36*k^5 + 889/576*k^4 + 35/144*k^3 - 29/16*k^2 - 5/4*k)*nt^8 + (-1/144*k^7 - 7/72*k^6 - 35/72*k^5 - 35/36*k^4 - 49/144*k^3 + 77/72*k^2 + 5/6*k)*nt^6 + (1/48*k^6 + 3/16*k^5 + 25/48*k^4 + 5/16*k^3 - 13/24*k^2 - 1/2*k)*nt^4 + (-1/24*k^5 - 5/24*k^4 - 5/24*k^3 + 5/24*k^2 + 1/4*k)*nt^2 + (1/24*k^4 + 1/12*k^3 - 1/24*k^2 - 1/12*k))*rt^4 + ((-1/604800*k^12 - 1/11200*k^11 - 253/120960*k^10 - 187/6720*k^9 - 46541/201600*k^8 - 1969/1600*k^7 - 100595/24192*k^6 - 18491/2240*k^5 - 1086019/151200*k^4 + 29513/8400*k^3 + 4861/420*k^2 + 6*k)*nt^14 + (1/86400*k^11 + 11/21600*k^10 + 11/1152*k^9 + 143/1440*k^8 + 17941/28800*k^7 + 17171/7200*k^6 + 90871/17280*k^5 + 22451/4320*k^4 - 1353/800*k^3 - 4609/600*k^2 - 21/5*k)*nt^12 [+++] ? Errors (if any) and Timing Info: Timing: real 0m0.086s user 0m0.072s sys 0m0.012s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 05:01:04 2005 Input: vector(10,j,sigma(j,3)) a=vector(10,j,sigma(j,5)) a[4] c=a[2]-a[1] d=a[5] c g=taylor((1-rt+nt^2)^(-k+1),t) kronecker(-3,1) Output: ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134] ? [1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158] ? 1057 ? 32 ? 3126 ? 32 ? ((1 + O(t^16)) + (-k + 1)*nt^2 + (1/2*k^2 - 1/2*k)*nt^4 + (-1/6*k^3 + 1/6*k)*nt^6 + (1/24*k^4 + 1/12*k^3 - 1/24*k^2 - 1/12*k)*nt^8 + (-1/120*k^5 - 1/24*k^4 - 1/24*k^3 + 1/24*k^2 + 1/20*k)*nt^10 + (1/720*k^6 + 1/80*k^5 + 5/144*k^4 + 1/48*k^3 - 13/360*k^2 - 1/30*k)*nt^12 + (-1/5040*k^7 - 1/360*k^6 - 1/72*k^5 - 1/36*k^4 - 7/720*k^3 + 11/360*k^2 + 1/42*k)*nt^14 + O(nt^16)) + ((-1/5040*k^8 - 1/252*k^7 - 11/360*k^6 - 1/9*k^5 - 127/720*k^4 - 1/36*k^3 + 29/140*k^2 + 1/7*k)*nt^14 + (1/720*k^7 + 7/360*k^6 + 7/72*k^5 + 7/36*k^4 + 49/720*k^3 - 77/360*k^2 - 1/6*k)*nt^12 + (-1/120*k^6 - 3/40*k^5 - 5/24*k^4 - 1/8*k^3 + 13/60*k^2 + 1/5*k)*nt^10 + (1/24*k^5 + 5/24*k^4 + 5/24*k^3 - 5/24*k^2 - 1/4*k)*nt^8 + (-1/6*k^4 - 1/3*k^3 + 1/6*k^2 + 1/3*k)*nt^6 + (1/2*k^3 - 1/2*k)*nt^4 + (-k^2 + k)*nt^2 + (k - 1))*rt + ((-1/10080*k^9 - 3/1120*k^8 - 7/240*k^7 - 13/80*k^6 - 229/480*k^5 - 101/160*k^4 + 2/315*k^3 + 223/280*k^2 + 1/2*k)*nt^14 + (1/1440*k^8 + 1/72*k^7 + 77/720*k^6 + 7/18*k^5 + 889/1440*k^4 + 7/72*k^3 - 29/40*k^2 - 1/2*k)*nt^12 + (-1/240*k^7 - 7/120*k^6 - 7/24*k^5 - 7/12*k^4 - 49/240*k^3 + 77/120*k^2 + 1/2*k)*nt^10 + (1/48*k^6 + 3/16*k^5 + 25/48*k^4 + 5/16*k^3 - 13/24*k^2 - 1/2*k)*nt^8 + (-1/12*k^5 - 5/12*k^4 - 5/12*k^3 + 5/12*k^2 + 1/2*k)*nt^6 + (1/4*k^4 + 1/2*k^3 - 1/4*k^2 - 1/2*k)*nt^4 + (-1/2*k^3 + 1/2*k)*nt^2 + (1/2*k^2 - 1/2*k))*rt^2 + ((-1/30240*k^10 - 1/864*k^9 - 17/1008*k^8 - 19/144*k^7 - 853/1440*k^6 - 427/288*k^5 - 1271/756*k^4 + 61/216*k^3 + 481/210*k^2 + 4/3*k)*nt^14 + (1/4320*k^9 + 1/160*k^8 + 49/720*k^7 + 91/240*k^6 + 1603/1440*k^5 + 707/480*k^4 - 2/135*k^3 - 223/120*k^2 - 7/6*k)*nt^12 + (-1/720*k^8 - 1/36*k^7 - 77/360*k^6 - 7/9*k^5 - 889/720*k^4 - 7/36*k^3 + 29/20*k^2 + k)*nt^10 + (1/144*k^7 + 7/72*k^6 + 35/72*k^5 + 35/36*k^4 + 49/144*k^3 - 77/72*k^2 - 5/6*k)*nt^8 + (-1/36*k^6 - 1/4*k^5 - 25/36*k^4 - 5/12*k^3 + 13/18*k^2 + 2/3*k)*nt^6 + (1/12*k^5 + 5/12*k^4 + 5/12*k^3 - 5/12*k^2 - 1/2*k)*nt^4 + (-1/6*k^4 - 1/3*k^3 + 1/6*k^2 + 1/3*k)*nt^2 + (1/6*k^3 - 1/6*k))*rt^3 + ((-1/120960*k^11 - 11/30240*k^10 - 55/8064*k^9 - 143/2016*k^8 - 2563/5760*k^7 - 2453/1440*k^6 - 90871/24192*k^5 - 22451/6048*k^4 + 1353/1120*k^3 + 4609/840*k^2 + 3*k)*nt^14 + (1/17280*k^10 + 7/3456*k^9 + 17/576*k^8 + 133/576*k^7 + 5971/5760*k^6 + 2989/1152*k^5 + 1271/432*k^4 - 427/864*k^3 - 481/120*k^2 - 7/3*k)*nt^12 + (-1/2880*k^9 - 3/320*k^8 - 49/480*k^7 - 91/160*k^6 - 1603/960*k^5 - 707/320*k^4 + 1/45*k^3 + 223/80*k^2 + 7/4*k)*nt^10 + (1/576*k^8 + 5/144*k^7 + 77/288*k^6 + 35/36*k^5 + 889/576*k^4 + 35/144*k^3 - 29/16*k^2 - 5/4*k)*nt^8 + (-1/144*k^7 - 7/72*k^6 - 35/72*k^5 - 35/36*k^4 - 49/144*k^3 + 77/72*k^2 + 5/6*k)*nt^6 + (1/48*k^6 + 3/16*k^5 + 25/48*k^4 + 5/16*k^3 - 13/24*k^2 - 1/2*k)*nt^4 + (-1/24*k^5 - 5/24*k^4 - 5/24*k^3 + 5/24*k^2 + 1/4*k)*nt^2 + (1/24*k^4 + 1/12*k^3 - 1/24*k^2 - 1/12*k))*rt^4 + ((-1/604800*k^12 - 1/11200*k^11 - 253/120960*k^10 - 187/6720*k^9 - 46541/201600*k^8 - 1969/1600*k^7 - 100595/24192*k^6 - 18491/2240*k^5 - 1086019/151200*k^4 + 29513/8400*k^3 + 4861/420*k^2 + 6*k)*nt^14 + (1/86400*k^11 + 11/21600*k^10 + 11/1152*k^9 + 143/1440*k^8 + 17941/28800*k^7 + 17171/7200*k^6 + 90871/17280*k^5 + 22451/4320*k^4 - 1353/800*k^3 - 4609/600*k^2 - 21/5*k)*nt^12 [+++] ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.084s user 0m0.068s sys 0m0.015s '195.93.' ************** PARI ***************** Host 195.93.60.105 (195.93.60.105) Time: Fri Jul 15 05:02:04 2005 Input: vector(10,j,sigma(j,3)) a=vector(10,j,sigma(j,5)) a[4] c=a[2]-a[1] d=a[5] c g=taylor((1-rt+nt^2)^(-k+1),t) kronecker(-3,1) h=vector(100,j,kronecker(-3,j)) Output: ? [1, 9, 28, 73, 126, 252, 344, 585, 757, 1134] ? [1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158] ? 1057 ? 32 ? 3126 ? 32 ? ((1 + O(t^16)) + (-k + 1)*nt^2 + (1/2*k^2 - 1/2*k)*nt^4 + (-1/6*k^3 + 1/6*k)*nt^6 + (1/24*k^4 + 1/12*k^3 - 1/24*k^2 - 1/12*k)*nt^8 + (-1/120*k^5 - 1/24*k^4 - 1/24*k^3 + 1/24*k^2 + 1/20*k)*nt^10 + (1/720*k^6 + 1/80*k^5 + 5/144*k^4 + 1/48*k^3 - 13/360*k^2 - 1/30*k)*nt^12 + (-1/5040*k^7 - 1/360*k^6 - 1/72*k^5 - 1/36*k^4 - 7/720*k^3 + 11/360*k^2 + 1/42*k)*nt^14 + O(nt^16)) + ((-1/5040*k^8 - 1/252*k^7 - 11/360*k^6 - 1/9*k^5 - 127/720*k^4 - 1/36*k^3 + 29/140*k^2 + 1/7*k)*nt^14 + (1/720*k^7 + 7/360*k^6 + 7/72*k^5 + 7/36*k^4 + 49/720*k^3 - 77/360*k^2 - 1/6*k)*nt^12 + (-1/120*k^6 - 3/40*k^5 - 5/24*k^4 - 1/8*k^3 + 13/60*k^2 + 1/5*k)*nt^10 + (1/24*k^5 + 5/24*k^4 + 5/24*k^3 - 5/24*k^2 - 1/4*k)*nt^8 + (-1/6*k^4 - 1/3*k^3 + 1/6*k^2 + 1/3*k)*nt^6 + (1/2*k^3 - 1/2*k)*nt^4 + (-k^2 + k)*nt^2 + (k - 1))*rt + ((-1/10080*k^9 - 3/1120*k^8 - 7/240*k^7 - 13/80*k^6 - 229/480*k^5 - 101/160*k^4 + 2/315*k^3 + 223/280*k^2 + 1/2*k)*nt^14 + (1/1440*k^8 + 1/72*k^7 + 77/720*k^6 + 7/18*k^5 + 889/1440*k^4 + 7/72*k^3 - 29/40*k^2 - 1/2*k)*nt^12 + (-1/240*k^7 - 7/120*k^6 - 7/24*k^5 - 7/12*k^4 - 49/240*k^3 + 77/120*k^2 + 1/2*k)*nt^10 + (1/48*k^6 + 3/16*k^5 + 25/48*k^4 + 5/16*k^3 - 13/24*k^2 - 1/2*k)*nt^8 + (-1/12*k^5 - 5/12*k^4 - 5/12*k^3 + 5/12*k^2 + 1/2*k)*nt^6 + (1/4*k^4 + 1/2*k^3 - 1/4*k^2 - 1/2*k)*nt^4 + (-1/2*k^3 + 1/2*k)*nt^2 + (1/2*k^2 - 1/2*k))*rt^2 + ((-1/30240*k^10 - 1/864*k^9 - 17/1008*k^8 - 19/144*k^7 - 853/1440*k^6 - 427/288*k^5 - 1271/756*k^4 + 61/216*k^3 + 481/210*k^2 + 4/3*k)*nt^14 + (1/4320*k^9 + 1/160*k^8 + 49/720*k^7 + 91/240*k^6 + 1603/1440*k^5 + 707/480*k^4 - 2/135*k^3 - 223/120*k^2 - 7/6*k)*nt^12 + (-1/720*k^8 - 1/36*k^7 - 77/360*k^6 - 7/9*k^5 - 889/720*k^4 - 7/36*k^3 + 29/20*k^2 + k)*nt^10 + (1/144*k^7 + 7/72*k^6 + 35/72*k^5 + 35/36*k^4 + 49/144*k^3 - 77/72*k^2 - 5/6*k)*nt^8 + (-1/36*k^6 - 1/4*k^5 - 25/36*k^4 - 5/12*k^3 + 13/18*k^2 + 2/3*k)*nt^6 + (1/12*k^5 + 5/12*k^4 + 5/12*k^3 - 5/12*k^2 - 1/2*k)*nt^4 + (-1/6*k^4 - 1/3*k^3 + 1/6*k^2 + 1/3*k)*nt^2 + (1/6*k^3 - 1/6*k))*rt^3 + ((-1/120960*k^11 - 11/30240*k^10 - 55/8064*k^9 - 143/2016*k^8 - 2563/5760*k^7 - 2453/1440*k^6 - 90871/24192*k^5 - 22451/6048*k^4 + 1353/1120*k^3 + 4609/840*k^2 + 3*k)*nt^14 + (1/17280*k^10 + 7/3456*k^9 + 17/576*k^8 + 133/576*k^7 + 5971/5760*k^6 + 2989/1152*k^5 + 1271/432*k^4 - 427/864*k^3 - 481/120*k^2 - 7/3*k)*nt^12 + (-1/2880*k^9 - 3/320*k^8 - 49/480*k^7 - 91/160*k^6 - 1603/960*k^5 - 707/320*k^4 + 1/45*k^3 + 223/80*k^2 + 7/4*k)*nt^10 + (1/576*k^8 + 5/144*k^7 + 77/288*k^6 + 35/36*k^5 + 889/576*k^4 + 35/144*k^3 - 29/16*k^2 - 5/4*k)*nt^8 + (-1/144*k^7 - 7/72*k^6 - 35/72*k^5 - 35/36*k^4 - 49/144*k^3 + 77/72*k^2 + 5/6*k)*nt^6 + (1/48*k^6 + 3/16*k^5 + 25/48*k^4 + 5/16*k^3 - 13/24*k^2 - 1/2*k)*nt^4 + (-1/24*k^5 - 5/24*k^4 - 5/24*k^3 + 5/24*k^2 + 1/4*k)*nt^2 + (1/24*k^4 + 1/12*k^3 - 1/24*k^2 - 1/12*k))*rt^4 + ((-1/604800*k^12 - 1/11200*k^11 - 253/120960*k^10 - 187/6720*k^9 - 46541/201600*k^8 - 1969/1600*k^7 - 100595/24192*k^6 - 18491/2240*k^5 - 1086019/151200*k^4 + 29513/8400*k^3 + 4861/420*k^2 + 6*k)*nt^14 + (1/86400*k^11 + 11/21600*k^10 + 11/1152*k^9 + 143/1440*k^8 + 17941/28800*k^7 + 17171/7200*k^6 + 90871/17280*k^5 + 22451/4320*k^4 - 1353/800*k^3 - 4609/600*k^2 - 21/5*k)*nt^12 [+++] ? 1 ? [1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.085s user 0m0.077s sys 0m0.007s '161.116' ************** PARI ***************** Host 161.116.84.25 (161.116.84.25) Time: Fri Jul 15 11:09:44 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.189s user 0m0.006s sys 0m0.013s '69.196.' ************** PARI ***************** Host 69.196.245.161 (69.196.245.161) Time: Fri Jul 15 22:43:44 2005 Input: 1/133 * 60 Output: ? 60/133 ? Errors (if any) and Timing Info: Timing: real 0m0.133s user 0m0.009s sys 0m0.011s '69.196.' ************** PARI ***************** Host 69.196.245.161 (69.196.245.161) Time: Fri Jul 15 22:43:55 2005 Input: (1/133) * 60 Output: ? 60/133 ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.011s sys 0m0.007s '69.196.' ************** PARI ***************** Host 69.196.245.161 (69.196.245.161) Time: Fri Jul 15 22:44:41 2005 Input: (1/133) * 60 Output: ? 60/133 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.009s sys 0m0.008s '69.196.' ************** PARI ***************** Host 69.196.245.161 (69.196.245.161) Time: Fri Jul 15 22:44:54 2005 Input: x = 1/133 Output: ? 1/133 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.010s '69.196.' ************** PARI ***************** Host 69.196.245.161 (69.196.245.161) Time: Fri Jul 15 22:45:22 2005 Input: 1/133 Output: ? 1/133 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '69.196.' ************** PARI ***************** Host 69.196.245.161 (69.196.245.161) Time: Fri Jul 15 22:45:31 2005 Input: =1/133 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: =1/133 ^------ Timing: real 0m0.031s user 0m0.008s sys 0m0.009s '69.196.' ************** PARI ***************** Host 69.196.245.161 (69.196.245.161) Time: Fri Jul 15 22:45:38 2005 Input: x=1/133 Output: ? 1/133 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.008s sys 0m0.009s '71.105.' ************** PARI ***************** Host 71.105.92.89 (71.105.92.89) Time: Sat Jul 16 12:24:22 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.299s user 0m0.011s sys 0m0.009s '209.208' ************** PARI ***************** Host 209.208.77.157 (209.208.77.157) Time: Mon Jul 18 16:21:53 2005 Input: 7^.5 Output: ? 2.6457513110645905905016157536392604257 ? Errors (if any) and Timing Info: Timing: real 0m0.197s user 0m0.009s sys 0m0.008s '203.197' ************** PARI ***************** Host 203.197.75.5 (203.197.75.5) Time: Tue Jul 19 04:03:42 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.095s user 0m0.041s sys 0m0.010s '20.133.' ************** PARI ***************** Host 20.133.32.18 (20.133.32.18) Time: Tue Jul 19 04:29:51 2005 Input: 3*7 Output: ? 21 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '20.133.' ************** PARI ***************** Host 20.133.32.18 (20.133.32.18) Time: Tue Jul 19 04:30:19 2005 Input: 2^9 Output: ? 512 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.007s sys 0m0.011s '20.133.' ************** PARI ***************** Host 20.133.32.18 (20.133.32.18) Time: Tue Jul 19 04:30:34 2005 Input: 2^19 Output: ? 524288 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.009s sys 0m0.007s '20.133.' ************** PARI ***************** Host 20.133.32.18 (20.133.32.18) Time: Tue Jul 19 04:30:50 2005 Input: 2^32763 Output: ? 4423315722015483715629853211702973754212908473351213022607455463351145732002641417487579238989526297110862103005175395288718151811077305777756057175783978724199774354827853159531758285243615718271750661822634167253773579417140530802662034816526609885004634360590797179564444058236484385481028825870571673951300820539916587978992232332750979287464414467129636132619309152996461805781475619738046378912361221864600058265917627658761498844438647504324515208723279014804744571291009635746991386495126315303562261807121727407225996182278140295459579653367490110612553605009906407410318796132637102190973061107763467870819709011800032735463879667501537323372003974977875610412447077906581764772629496690242766139559214546519286378513981173832005102344219145798031190691542406456382204632768877759892612071361651990768932351261737767955285123355930912497143676078761577062397366960123549489084792677840047644000434986154565850019692469915483846058263722306300204200409785023763325168429502590327068897447607429835710274037317942299832846509346576493322454605620401212688929902899823856012277727131023443842415509783877671417937303365253236394310572048385730862660631367545077340321778181747457874409536079274897199272446311591048371934786510341658741795025616686973522622002237212850665922271158492518754027809029283471550777694879699591266295427838306865380517478329141852613537945607534795635860966768837955282207345630810297691550822909433382113492399217295534558663236148998615375752465965845378918709784472699694665733576147990414093600590088985507222863891513214501529443153949182573846660134452858087074775420997456575514564391737504974883683269932173167686783695771810113403320676382556473659497757972779215150857884040811130368313106358432005640273535234619092511366126549711187485520061363803215398666848970564990057893981956546919922466995560050223992314894017517512831634489592710733367885852111138934348972713794065003223293492927081085265489609012610333191520203699370918289374385389437078693300763818997605272795339176276628398183980964056883470615876482750780683931285909157870352230621261340942620988370558981703795090706832114382153164014146343989522990089890244774145999426339621575649826427794978706197157334516177771038519543475930154763874626261566970521129313624767370383494381107148492460522648471180246670826476714524334525957283658944906298518306267124238973435085140316071267968029888077353787397572581915513017746426890288803077859679446751669132292043365566497636143019974363473766091320713525797915817324617268268841889084777781416217007898577078567229909800584771484108130217969976519064086151381396349314471976689293993575857669462773872630427557828636749719891037470727960821853764328806632599976012075765460607470120801113825117099789013913082955287820323372095624855697391231909436552376797701333758900946974388455417288212656813393856797402871335814456382089557172314709109522465779664309364532793768382303347343765215488104395603702620730293963780699698241076304300122419484409541340146410700681109915321620784386284325338758284154248113455107228272152265978247115037312781593298682143555716138167426915069407337367956085409523382891708132945791177811903996275[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.073s user 0m0.041s sys 0m0.012s '20.133.' ************** PARI ***************** Host 20.133.32.18 (20.133.32.18) Time: Tue Jul 19 04:31:17 2005 Input: 2^3276 Output: ? 149370830337841678774793254944774600474505906961104735699619819249098622325986666303602673898790490959910132780474072897961746713346961988345510477260152941284374385545573534557679916003167004767851346913436591920041548533215161008440520873693549019392890303756398685460712455388349734977307444747912712507014852496930732988474389790449613081878962606553572550870582651207868273821611978529487464179237369406207210488204721467487527041444447269549695112151851030797970366540336467610048178739205460343774170930040401172505611639981778979361193894983750770022584011096496667220621426117911945860606298990766445090674690774044778832658006610401620758994230439785122918583643459506949453295811133636451768551666148756716442887255707592002880474325282212596671514504515121298021972548301394100251715560647618172237293960228154118751125266079788970143254083991380292395412252871360365126530275638485587159742867822421864927186224822395170137600895591201230023793898178570408106640350837211136 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.010s sys 0m0.008s '20.133.' ************** PARI ***************** Host 20.133.32.18 (20.133.32.18) Time: Tue Jul 19 04:37:03 2005 Input: Pi? Output: ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: *** Warning: unused characters: ?. Timing: real 0m0.046s user 0m0.010s sys 0m0.007s '20.133.' ************** PARI ***************** Host 20.133.32.18 (20.133.32.18) Time: Tue Jul 19 04:37:20 2005 Input: Pi*e Output: ? 3.1415926535897932384626433832795028841*e ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.008s sys 0m0.010s '20.133.' ************** PARI ***************** Host 20.133.32.18 (20.133.32.18) Time: Tue Jul 19 04:37:32 2005 Input: Pi*E Output: ? 3.1415926535897932384626433832795028841*E ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.012s sys 0m0.005s '20.133.' ************** PARI ***************** Host 20.133.32.18 (20.133.32.18) Time: Tue Jul 19 04:37:45 2005 Input: Pi*Euler Output: ? 1.8133764923916034996131345312710400190 ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.009s sys 0m0.008s '129.2.1' ************** PARI ***************** Host 129.2.103.42 (129.2.103.42) Time: Tue Jul 19 13:34:40 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.298s user 0m0.013s sys 0m0.012s '84.220.' ************** PARI ***************** Host 84.220.34.2 (84.220.34.2) Time: Tue Jul 19 14:37:56 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '84.220.' ************** PARI ***************** Host 84.220.34.2 (84.220.34.2) Time: Tue Jul 19 14:38:21 2005 Input: factorint (12345678912345678912345678912345678912345678978541258) Output: ? [2 1] [7 1] [73 1] [1983372899 1] [6090594796350741232274578500039244973161 1] ? Errors (if any) and Timing Info: Timing: real 0m0.210s user 0m0.148s sys 0m0.007s '84.220.' ************** PARI ***************** Host 84.220.34.2 (84.220.34.2) Time: Tue Jul 19 14:40:03 2005 Input: factorint (3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 29467 Killed /usr/bin/gp -q -emacs Timing: real 0m25.127s user 0m20.986s sys 0m0.015s '84.220.' ************** PARI ***************** Host 84.220.34.2 (84.220.34.2) Time: Tue Jul 19 14:41:27 2005 Input: factorint (3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 29479 Killed /usr/bin/gp -q -emacs Timing: real 0m25.128s user 0m20.977s sys 0m0.024s '82.57.7' ************** PARI ***************** Host 82.57.79.82 (82.57.79.82) Time: Tue Jul 19 14:44:57 2005 Input: factorint(5648978654213021567845312021245454210257879965468784512311) Output: ? [5648978654213021567845312021245454210257879965468784512311 1] ? Errors (if any) and Timing Info: Timing: real 0m0.047s user 0m0.022s sys 0m0.005s '82.57.7' ************** PARI ***************** Host 82.57.79.82 (82.57.79.82) Time: Tue Jul 19 14:45:15 2005 Input: factorint(15648978654213021567845312021245454210257879965468784512310) Output: ? [2 1] [5 1] [7 2] [317 1] [189853 1] [51781021 1] [312499039 1] [32793962536922258959998284592701 1] ? Errors (if any) and Timing Info: Timing: real 0m0.063s user 0m0.045s sys 0m0.012s '161.116' ************** PARI ***************** Host 161.116.84.15 (161.116.84.15) Time: Thu Jul 21 09:50:29 2005 Input: substitute(x^2+1,x,x+3); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: substitute(x^2+1,x,x+3); ^------------ Timing: real 0m0.026s user 0m0.012s sys 0m0.005s '161.116' ************** PARI ***************** Host 161.116.84.15 (161.116.84.15) Time: Thu Jul 21 09:50:47 2005 Input: substitute(x^2+1,x,x+3), Output: ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,. *** expected character: ',' instead of: substitute(x^2+1,x,x+3), ^------------ Timing: real 0m0.034s user 0m0.012s sys 0m0.004s '161.116' ************** PARI ***************** Host 161.116.84.15 (161.116.84.15) Time: Thu Jul 21 09:51:01 2005 Input: substitute[x^2+1,x,x+3], Output: ? ? Errors (if any) and Timing Info: *** expected character: ']' instead of: substitute[x^2+1,x,x+3], ^------ Timing: real 0m0.030s user 0m0.010s sys 0m0.007s '161.116' ************** PARI ***************** Host 161.116.84.15 (161.116.84.15) Time: Thu Jul 21 09:51:28 2005 Input: Substitute[x+3,x^2+1], Output: ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,. *** unexpected character: Substitute[x+3,x^2+1], ^------------ Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '161.116' ************** PARI ***************** Host 161.116.84.15 (161.116.84.15) Time: Thu Jul 21 09:51:37 2005 Input: Substitute[x+3,x^2+1]; Output: ? ? Errors (if any) and Timing Info: *** unexpected character: Substitute[x+3,x^2+1]; ^------------ Timing: real 0m0.034s user 0m0.010s sys 0m0.007s '80.118.' ************** PARI ***************** Host 80.118.155.102 (80.118.155.102) Time: Thu Jul 21 17:28:29 2005 Input: Pi Output: ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.284s user 0m0.010s sys 0m0.014s '147.213' ************** PARI ***************** Host 147.213.236.6 (147.213.236.6) Time: Fri Jul 22 05:48:16 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.012s sys 0m0.006s '155.247' ************** PARI ***************** Host 155.247.28.50 (155.247.28.50) Time: Fri Jul 22 13:15:52 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.216s user 0m0.009s sys 0m0.012s '155.247' ************** PARI ***************** Host 155.247.28.50 (155.247.28.50) Time: Fri Jul 22 13:16:28 2005 Input: 2+2 5*3 Output: ? 4 ? ? 15 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.008s sys 0m0.009s '155.247' ************** PARI ***************** Host 155.247.28.50 (155.247.28.50) Time: Fri Jul 22 13:16:45 2005 Input: 2+2 5*3 5/3 Output: ? 4 ? ? 15 ? ? 5/3 ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.011s sys 0m0.006s '155.247' ************** PARI ***************** Host 155.247.28.50 (155.247.28.50) Time: Fri Jul 22 13:17:07 2005 Input: 2+2 5*3 int x^2 ,dx Output: ? 4 ? ? 15 ? ? intx^2 ? Errors (if any) and Timing Info: *** Warning: unused characters: ,dx. Timing: real 0m0.039s user 0m0.013s sys 0m0.005s '81.56.1' ************** PARI ***************** Host 81.56.100.34 (81.56.100.34) Time: Sat Jul 23 04:09:02 2005 Input: 3+5 Output: ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.009s sys 0m0.009s '81.56.1' ************** PARI ***************** Host 81.56.100.34 (81.56.100.34) Time: Sat Jul 23 04:09:18 2005 Input: 12345679*8 Output: ? 98765432 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.007s sys 0m0.010s '81.56.1' ************** PARI ***************** Host 81.56.100.34 (81.56.100.34) Time: Sat Jul 23 04:10:00 2005 Input: ?u(n)=floor(1/n*sum(k=1,n,floor(10*sqrt(k))))-floor(1/3*sqrt(4*n+6)-1/2) ?for(n=1,1000,if(u(n)==1,print1(n,","))) Output: ? ? ? ? for(X=a,b,seq): the sequence is evaluated, X going from a up to b. ? Errors (if any) and Timing Info: *** u(n)=floor(1/n*sum(k=1,n,floor(10*sqrt(k))))-floor(1/3*sqrt(4*n+6)-1/2): unknown identifier. Timing: real 0m0.037s user 0m0.010s sys 0m0.007s '81.56.1' ************** PARI ***************** Host 81.56.100.34 (81.56.100.34) Time: Sat Jul 23 04:10:14 2005 Input: u(n)=floor(1/n*sum(k=1,n,floor(10*sqrt(k))))-floor(1/3*sqrt(4*n+6)-1/2) for(n=1,1000,if(u(n)==1,print1(n,","))) Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m3.163s user 0m2.612s sys 0m0.008s '81.56.1' ************** PARI ***************** Host 81.56.100.34 (81.56.100.34) Time: Sat Jul 23 04:10:20 2005 Input: u(n)=floor(1/n*sum(k=1,n,floor(10*sqrt(k))))-floor(1/3*sqrt(4*n+6)-1/2) for(n=1,1000,if(u(n)==1,print1(n,","))) Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m3.120s user 0m2.594s sys 0m0.013s '81.56.1' ************** PARI ***************** Host 81.56.100.34 (81.56.100.34) Time: Sat Jul 23 04:10:28 2005 Input: ?u(n)=floor(1/n*sum(k=1,n,floor(10*sqrt(k))))-floor(1/3*sqrt(4*n+6)-1/2) ?for(n=1,1000,if(u(n)==1,print1(n,","))) Output: ? ? for(X=a,b,seq): the sequence is evaluated, X going from a up to b. ? Errors (if any) and Timing Info: *** u(n)=floor(1/n*sum(k=1,n,floor(10*sqrt(k))))-floor(1/3*sqrt(4*n+6)-1/2): unknown identifier. Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '81.56.1' ************** PARI ***************** Host 81.56.100.34 (81.56.100.34) Time: Sat Jul 23 04:10:43 2005 Input: ?u(n)=floor(1/n*sum(k=1,n,floor(10*sqrt(k))))-floor(1/3*sqrt(4*n+6)-1/2) ?for(n=1,1000,if(u(n)=1,print1(n,","))) Output: ? ? for(X=a,b,seq): the sequence is evaluated, X going from a up to b. ? Errors (if any) and Timing Info: *** u(n)=floor(1/n*sum(k=1,n,floor(10*sqrt(k))))-floor(1/3*sqrt(4*n+6)-1/2): unknown identifier. Timing: real 0m0.025s user 0m0.011s sys 0m0.006s '81.56.1' ************** PARI ***************** Host 81.56.100.34 (81.56.100.34) Time: Sat Jul 23 04:10:46 2005 Input: ?u(n)=floor(1/n*sum(k=1,n,floor(10*sqrt(k))))-floor(1/3*sqrt(4*n+6)-1/2) ?for(n=1,1000,if(u(n)=1,print1(n,","))) Output: ? ? for(X=a,b,seq): the sequence is evaluated, X going from a up to b. ? Errors (if any) and Timing Info: *** u(n)=floor(1/n*sum(k=1,n,floor(10*sqrt(k))))-floor(1/3*sqrt(4*n+6)-1/2): unknown identifier. Timing: real 0m0.035s user 0m0.007s sys 0m0.010s '24.167.' ************** PARI ***************** Host 24.167.38.218 (24.167.38.218) Time: Sat Jul 23 09:35:43 2005 Input: 24737*2^991+1 Output: ? 517693523749349506216820125753852827887841227092964547799532292131198709993702048088168912046169305517623230936748285019817469002581460400322168936455700478369002740323880863059299067393413818235615141804531075491540754845960240845920074337097867783823725951696351550002765728018732362221078040255922177 ? Errors (if any) and Timing Info: Timing: real 0m0.311s user 0m0.012s sys 0m0.009s '81.221.' ************** PARI ***************** Host 81.221.156.186 (81.221.156.186) Time: Sat Jul 23 13:19:52 2005 Input: w=3.; for(n=2,100,w=(w^2-1)/2/n;print1(" "w)) Output: ? ? 2.0000000000000000000000000000000000000 0.50000000000000000000000000000000000000 -0.093750000000000000000000000000000000000 -0.099121093750000000000000000000000000000 -0.082514584064483642578125000000000000000 -0.070942238815476090150826036863561187471 -0.062185449921990497349588752074048673986 -0.055340720545444422891505474987272732236 -0.049846870232475551276844479589853860525 -0.045341604069455761035482032567720957074 -0.041581005789183696365433207696640858425 -0.038395039229136918151084998973776600032 -0.035661636462949751326071244281585598173 -0.033290941589492813758317192923328494066 -0.031215366037752655552718561583422177099 -0.029383105909503797590513960370855225375 -0.027753795363530857861327811243481890453 -0.026295519127445243501508696167908065593 -0.024982713641845454033496265325283606199 -0.023794663429025941644073508427860671638 -0.022714404863461349441285907982633609626 -0.021727914256776060073809682896395322139 -0.020823497869626045575687102376839395498 -0.019991327638729473590828323471156547252 -0.019223083592677710981727700637223769463 -0.018511675426984980092367214902962271061 -0.017851023533444392150981805054457914017 -0.017235885188944972663593460157473314700 -0.016661715404362558455399735269551688936 -0.016124554632899742377825508066437580568 -0.015620937480279541116473800695051448218 -0.015147817974427836331227164675444446093 -0.014702507994273729425905700453396737817 -0.014282626232266833101111696884128413191 -0.013886055647054296712878846126938021956 -0.013510907803494147452392405775325558742 -0.013155492833820072117787500441656312070 -0.012818294012926914214466335055050862046 -0.012497946141732477025325065972715194149 -0.012193217089539492125503590223686815102 -0.011902991969726278119962744837263736866 -0.011626259520722891066718373471852769423 -0.011362100341926781821946667756125381492 -0.011109676696397999858973419948949590415 -0.010868223642214146861131166793651431778 -0.010637041294838966143232744068781938851 -0.010415488055755123860109829446887347656 -0.010202974669475106350509024397436444979 -0.0099989589930789404934432012505158981192 -0.0098029413805789678998082092378337390723 -0.0096144605994258551203734059771093122541 -0.0094330902089375668662891263549013939112 -0.0092584353408250930204729967274272282096 -0.0090901298306821796449421840922606703050 -0.0089278336566041191247144617778432786265 -0.0087712306472473684800311922541542354789 -0.0086200264268356274871500399655758958083 -0.0084739465690203445373261038227698498187 -0.0083327349352462115694266204560521133690 -0.0081961521764631059615924837264219411338 -0.0080639743797540343475093075477179775962 -0.0079359918437873227820400002329773422066 -0.0078120079690113698522577986336354658454 -0.0076918382502422469450175854716891518807 -0.0075753093607903947749156414961720459380 -0.0074622583185678232941830324490419930824 -0.0073525317257410806273726127543153818241 -0.0072459850744726229774400534110301394642 -0.0071424821121450037141174532606859215810 -0.0070418942602061809059618835495095774761 -0.0069441000814251949669730800577384851173 -0.0068489847909182133602782850828365242340 -0.0067564398068063092634947440226677415133 -0.0066663623368075800208157047000199902451 -0.0065786549974552262722436526578611247133 -0.0064932254629767821907585030519033942747 -0.0064099861411736342945677648935277728805 -0.0063288538739093035565903506739368736153 -0.0062497496600540168950074903383497976566 -0.0061725983989455966339522072990450366906 -0.0060973286526158861844942642114185399979 -0.0060238724252006143936261291868288907722 -0.0059521649581012196885020673493043393902 -0.0058821445396018326582686474493705911122 -0.0058137523277652048392099429316387963854 -0.0057469321855394908313921910202783525585 -0.0056816305271048568766552831168623785935 -0.0056177961745761430909337542019360125399 -0.0055553802242563384314045545539014032455 -0.0054943359217063952834885658362900221926 -0.0054346185449607578626945516771454851182 -0.0053761852952756492936294047833958306897 -0.0053189951948493130951043454730378443136 -0.0052630089910006166837780060847908804019 -0.0052081890663352117014098669973951827442 -0.0051544993544672644657515862442317244444 -0.0051019052609000244722138268074034607676 -0.0050503735887005494982485927124357705796 -0.0049998724686330727796644471327030719692 ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.014s sys 0m0.010s '203.144' ************** PARI ***************** Host 203.144.160.244 (203.144.160.244) Time: Sat Jul 23 15:01:23 2005 Input: polgalois(x^5-10*x^3+20*x-8) Output: ? ? Errors (if any) and Timing Info: *** sorry, galois of reducible polynomial is not yet implemented. Timing: real 0m0.057s user 0m0.008s sys 0m0.010s '203.144' ************** PARI ***************** Host 203.144.160.244 (203.144.160.244) Time: Sat Jul 23 15:04:02 2005 Input: polgalois(x^3+30*x^2-1575*x+7500) Output: ? [6, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.010s sys 0m0.009s '203.144' ************** PARI ***************** Host 203.144.160.244 (203.144.160.244) Time: Sat Jul 23 15:04:49 2005 Input: factor(x^5-10*x^3+20*x-8) Output: ? [x + 2 1] [x^4 - 2*x^3 - 6*x^2 + 12*x - 4 1] ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.012s sys 0m0.006s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Mon Jul 25 19:10:09 2005 Input: s=ellinit([0,0,0,89,4]);elllseries(s,1) Output: ? 1.9969090498068267386859639844646523434 E-37 ? Errors (if any) and Timing Info: Timing: real 0m9.773s user 0m7.898s sys 0m0.022s '202.83.' ************** PARI ***************** Host 202.83.173.210 (202.83.173.210) Time: Wed Jul 27 03:34:45 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.256s user 0m0.010s sys 0m0.010s '202.83.' ************** PARI ***************** Host 202.83.173.210 (202.83.173.210) Time: Wed Jul 27 03:34:49 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.008s sys 0m0.009s '70.119.' ************** PARI ***************** Host 70.119.249.104 (70.119.249.104) Time: Wed Jul 27 04:36:23 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.009s sys 0m0.008s '140.78.' ************** PARI ***************** Host 140.78.107.99 (140.78.107.99) Time: Wed Jul 27 04:45:12 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.010s sys 0m0.007s '140.78.' ************** PARI ***************** Host 140.78.107.99 (140.78.107.99) Time: Wed Jul 27 05:09:23 2005 Input: 2+2 exp(PI*sqrt(163)) Output: ? 4 ? 1 + 12.767145334803704661710952009780892347*PI + 81.499999999999999999999999999999999999*PI^2 + 346.84078159550064330981419626571424210*PI^3 + 1107.0416666666666666666666666666666666*PI^4 + 2826.7523700033302429749856995655710731*PI^5 + 6014.9263888888888888888888888888888887*PI^6 + 10970.491340727210228688634976885430593*PI^7 + 17507.732167658730158730158730158730158*PI^8 + 24835.973451924100934392326406004516481*PI^9 + 31708.448259204144620811287477954144619*PI^10 + 36802.397024214804111872265492533965331*PI^11 + 39155.129289774814948426059537170648279*PI^12 + 38453.786634275724809199867149250233005*PI^13 + 35067.505902380740860403558816257228953*PI^14 + 29847.462958985443542378944501560895142*PI^15 + O(PI^16) ? Errors (if any) and Timing Info: Timing: real 0m0.067s user 0m0.009s sys 0m0.009s '140.78.' ************** PARI ***************** Host 140.78.107.99 (140.78.107.99) Time: Wed Jul 27 05:09:39 2005 Input: 2+2 exp(pi*sqrt(163)) Output: ? 4 ? 1 + 12.767145334803704661710952009780892347*pi + 81.499999999999999999999999999999999999*pi^2 + 346.84078159550064330981419626571424210*pi^3 + 1107.0416666666666666666666666666666666*pi^4 + 2826.7523700033302429749856995655710731*pi^5 + 6014.9263888888888888888888888888888887*pi^6 + 10970.491340727210228688634976885430593*pi^7 + 17507.732167658730158730158730158730158*pi^8 + 24835.973451924100934392326406004516481*pi^9 + 31708.448259204144620811287477954144619*pi^10 + 36802.397024214804111872265492533965331*pi^11 + 39155.129289774814948426059537170648279*pi^12 + 38453.786634275724809199867149250233005*pi^13 + 35067.505902380740860403558816257228953*pi^14 + 29847.462958985443542378944501560895142*pi^15 + O(pi^16) ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.010s '140.78.' ************** PARI ***************** Host 140.78.107.99 (140.78.107.99) Time: Wed Jul 27 05:09:46 2005 Input: 2+2 exp(pi*sqrt(163)) pi Output: ? 4 ? 1 + 12.767145334803704661710952009780892347*pi + 81.499999999999999999999999999999999999*pi^2 + 346.84078159550064330981419626571424210*pi^3 + 1107.0416666666666666666666666666666666*pi^4 + 2826.7523700033302429749856995655710731*pi^5 + 6014.9263888888888888888888888888888887*pi^6 + 10970.491340727210228688634976885430593*pi^7 + 17507.732167658730158730158730158730158*pi^8 + 24835.973451924100934392326406004516481*pi^9 + 31708.448259204144620811287477954144619*pi^10 + 36802.397024214804111872265492533965331*pi^11 + 39155.129289774814948426059537170648279*pi^12 + 38453.786634275724809199867149250233005*pi^13 + 35067.505902380740860403558816257228953*pi^14 + 29847.462958985443542378944501560895142*pi^15 + O(pi^16) ? pi ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.007s sys 0m0.010s '140.78.' ************** PARI ***************** Host 140.78.107.99 (140.78.107.99) Time: Wed Jul 27 05:10:21 2005 Input: 2+2 exp(pi*sqrt(163)) Pi Output: ? 4 ? 1 + 12.767145334803704661710952009780892347*pi + 81.499999999999999999999999999999999999*pi^2 + 346.84078159550064330981419626571424210*pi^3 + 1107.0416666666666666666666666666666666*pi^4 + 2826.7523700033302429749856995655710731*pi^5 + 6014.9263888888888888888888888888888887*pi^6 + 10970.491340727210228688634976885430593*pi^7 + 17507.732167658730158730158730158730158*pi^8 + 24835.973451924100934392326406004516481*pi^9 + 31708.448259204144620811287477954144619*pi^10 + 36802.397024214804111872265492533965331*pi^11 + 39155.129289774814948426059537170648279*pi^12 + 38453.786634275724809199867149250233005*pi^13 + 35067.505902380740860403558816257228953*pi^14 + 29847.462958985443542378944501560895142*pi^15 + O(pi^16) ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.011s sys 0m0.006s '140.78.' ************** PARI ***************** Host 140.78.107.99 (140.78.107.99) Time: Wed Jul 27 05:10:30 2005 Input: 2+2 exp(Pi*sqrt(163)) Pi Output: ? 4 ? 262537412640768743.99999999999925007253 ? 3.1415926535897932384626433832795028841 ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.011s sys 0m0.006s '140.78.' ************** PARI ***************** Host 140.78.107.99 (140.78.107.99) Time: Wed Jul 27 05:10:43 2005 Input: exp(Pi*sqrt(163)) Output: ? 262537412640768743.99999999999925007253 ? ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.014s sys 0m0.003s '82.239.' ************** PARI ***************** Host 82.239.138.144 (82.239.138.144) Time: Wed Jul 27 11:46:37 2005 Input: f:=x^2; Output: ? ? Errors (if any) and Timing Info: *** unexpected character: f:=x^2; ^----- Timing: real 0m0.247s user 0m0.011s sys 0m0.007s '164.67.' ************** PARI ***************** Host 164.67.190.56 (164.67.190.56) Time: Wed Jul 27 19:05:58 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.154s user 0m0.009s sys 0m0.007s '164.67.' ************** PARI ***************** Host 164.67.190.56 (164.67.190.56) Time: Wed Jul 27 19:06:03 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.007s sys 0m0.010s '164.67.' ************** PARI ***************** Host 164.67.190.56 (164.67.190.56) Time: Wed Jul 27 19:06:05 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.011s sys 0m0.006s '164.67.' ************** PARI ***************** Host 164.67.190.56 (164.67.190.56) Time: Wed Jul 27 19:06:06 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '80.6.94' ************** PARI ***************** Host 80.6.94.131 (80.6.94.131) Time: Thu Jul 28 07:25:21 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m1.575s user 0m0.010s sys 0m0.015s '128.187' ************** PARI ***************** Host 128.187.91.34 (128.187.91.34) Time: Thu Jul 28 13:03:05 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.324s user 0m0.010s sys 0m0.009s '131.107' ************** PARI ***************** Host 131.107.0.103 (131.107.0.103) Time: Thu Jul 28 13:13:10 2005 Input: ?derivative Output: ? ? Errors (if any) and Timing Info: *** derivative: unknown identifier. Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '131.107' ************** PARI ***************** Host 131.107.0.103 (131.107.0.103) Time: Thu Jul 28 13:13:17 2005 Input: ? Output: ? Help topics: 0: list of user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Further help (list of relevant functions): ?n (1<=n<=11). Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.009s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.249.160 (68.118.249.160) Time: Fri Jul 29 23:08:40 2005 Input: 2^2^2^2^2 Output: ? 2003529930406846464979072351560255750447825475569751419265016973710894059556311453089506130880933348101038234342907263181822949382118812668869506364761547029165041871916351587966347219442930927982084309104855990570159318959639524863372367203002916969592156108764948889254090805911457037675208500206671563702366126359747144807111774815880914135742720967190151836282560618091458852699826141425030123391108273603843767876449043205960379124490905707560314035076162562476031863793126484703743782954975613770981604614413308692118102485959152380195331030292162800160568670105651646750568038741529463842244845292537361442533614373729088303794601274724958414864915930647252015155693922628180691650796381064132275307267143998158508811292628901134237782705567421080070065283963322155077831214288551675554073345107213112427399562982719769150054883905223804357045848197956393157853510018992000024141963706813559840464039472194016069517690156119726982337890017641517190051133466306898140219383481435426387306539552969691388024158161859561100640362119796101859534802787167200122604642492385111393400464351623867567078745259464670903886547743483217897012764455529409092021959585751622973333576159552394885297579954028471943529913543763705986928913757153740001986394332464890052543106629669165243419174691389632476560289415199775477703138064781342309596190960654591300890188887588084733625956065444888501447335706058817090162108499714529568344061979690565469813631162053579369791403236328496233046421066136200220175787851857409162050489711781820400187282939943446186224328009837323764931814789848119452713007440220765680910376203999203492023906626264491909167985461515778839060397720759279378852241294301017458086862263369284725851403039615558564330385450688652213114813638408384778263790459607186876728509763471271988890680478243230394718650525660978150729861141430305816927924971409161059417185352275887504477592218301158780701975535722241400019548102005661773589781499532325208589753463547007786690406429016763808161740550405117670093673202804549339027992491867306539931640720492238474815280619166900933805732120816350707634351669869625020969023162859350071874190579161241536897514808261904847946571736601005892476655445840838334790544144817684255327207315586349347605137419779525190365032198020108764738368682531025183377533908861426184800374008082238104076468878471647552945326947661700424461063311238021134588694532200116564076327023074292426051582811070387018345324567635625951430032037432740780879056283663406965030844225855967039271869461158513793386475699748568670079823960604393478850861649260304945061743412365828352144806726676841807083754862211408236579802961200027441324438432402331257403545019352428776430880232850855886089962774458164680857875115807014743763867976955049991643998284357290415378143438847303484261903388841494031366139854257635577105335580206622185577060082551288893332226436281984838613239570676191409638533832374343758830859233722284644287996245605476932428998432652677378373173288063210753211238680604674708428051166488709084770291208161104912555598322366244868556651402684641209694982590565519216188104341226838996283071654868525536914850299539675503954938371853405900096[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.405s user 0m0.140s sys 0m0.016s '68.118.' ************** PARI ***************** Host 68.118.249.160 (68.118.249.160) Time: Fri Jul 29 23:09:56 2005 Input: 8^8^8 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.086s user 0m0.067s sys 0m0.015s '68.118.' ************** PARI ***************** Host 68.118.249.160 (68.118.249.160) Time: Fri Jul 29 23:10:04 2005 Input: 8^8^8 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.103s user 0m0.060s sys 0m0.023s '68.118.' ************** PARI ***************** Host 68.118.249.160 (68.118.249.160) Time: Fri Jul 29 23:10:23 2005 Input: 8^8 Output: ? 16777216 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.008s sys 0m0.009s '68.118.' ************** PARI ***************** Host 68.118.249.160 (68.118.249.160) Time: Fri Jul 29 23:11:13 2005 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.056s user 0m0.010s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.249.160 (68.118.249.160) Time: Fri Jul 29 23:11:47 2005 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.007s sys 0m0.010s '68.118.' ************** PARI ***************** Host 68.118.249.160 (68.118.249.160) Time: Fri Jul 29 23:12:41 2005 Input: tan(100!) Output: ? ? Errors (if any) and Timing Info: *** loss of precision in mpsc1. Timing: real 0m0.045s user 0m0.007s sys 0m0.010s '68.118.' ************** PARI ***************** Host 68.118.249.160 (68.118.249.160) Time: Fri Jul 29 23:38:25 2005 Input: 8^8^4 Output: ? 1139165225263043370845938579315932008621298468028614501113799533426642439172469691567306477711637014807943967858591694430860851793602514412750433611928876871974929526595136714292202269877243080587167355589274624927976353262692345148008309507573685819955835876321194702904067672852630585653761861644571242372171305938720329762415531090187952999394484080243158140230933768654317732072862346478657014808167434738566098066865703948435697960690698143820219097883920407003040686456523245108233529281149726862222693477558297365169919254213176849897203892254348439995073129761356765109910020479495393380661515697239302324181939308678133940998328725955266515969502828655225480980895092809514369797858161129840554814496511186425336997926094809527662625334108406779145374499247692048395591015553528385731246203545724531612203607479377997576872569169483788053030378279576877386004030570986750132100204801763131711058475606646761383471125552169254602596735445058250180083098971630412612087756775480372453307530430780176105753868461990233541491448960739959862039983425453939789439104676251136386372904051680192229804685380001833428116313599063224324733076052699467854646844524311793304093924908423201911006864767668893649384894166113686442861779422695269897675881423889844545607914870835895733034509211170609262430862730433732018700756120651084270625980778311557017014461864993492408618705694231577726580111532021332153665526882140957678111916540129894079948804764692591360413784759938580255905838876028802617730882879188152977598786419451647310879729311103964732157446851230469475531585795984835148600800635479295397639938878156443965590224186419819882277032871060962194582102546090478144721190761850258369191900224395306794876873692428995158847840424991149849873176712167403972443558670000319304636037472002959025603251916173027249052271398946325044977689467938618590657389999474041948960845077947417835881611740370512056443386943277863227752971560792313074794845352366428347634202662555207631377062363568487792029076867739836043574078333859081888036937112370850492422001549656921701681029526177493392885476929327637876362831230387271521172866064514959007283516248976041897007280546298114410967020899920892992783547107860683924781183757248889096467252058762652847386776263197212357200557328449496699074620767409742604142415467296310832271903998101594665106284219030292188070116040897708658813530363560351706112268201291122525767182852438629664837145251620180457349044997862256070558396701044525115623372879871790731821932072989489288527618576766215951989257397203871071762595520655864377223544014415335327652614129459539821231945214018207065802759326443006923465371322335530156009106570559607238836509293786649162671442043589240990617598567679510550187130206141506559824507632434060587024813741001504771053996008411548678736619911891934721587458013429293204862213188135257875311834931539949587426657928499736854039644837553786289833154249741616522416723157610815085498392743549869831202012194890519566821874551709423529026358703978687243981808396743320354621416372223679065638882079936029130193279482952764468764628243892260347882895611313275007835651789502592007962235099135852331520947644313659812832[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.016s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.249.160 (68.118.249.160) Time: Fri Jul 29 23:38:45 2005 Input: 8^8^5 Output: ? 2835918541023101412057719148721366933683139086778481066131762807632741925957775628948066540787854603187068575057691689402466295229768620407547330613739622111393345975837753320776644576055850082940910383938995569263740596457155026158499381274098436706629656292086677095989594692947637506808424359749335491933607671391517183269085214349989804729680926509712724332524283058342226262911756739794287366453477009768186918641734363967718081710061289898739093259605769742923691941469016860584072808832389191844609441920992182674024020406712623204559356197013738165601520489632637099203509311177526676195319027142821078611084450556686179375783453286112924284699079960728471392802681087580743417090517458243120792270202870160899109425854222173238855551335367641610067672142583476866410380578883355882211664691545870539275172185105391650862080242792293804759723320202250343925566955887542238847857796707867662899795700617517688831893832725847274559581749776686803380163754369966919869376050393580460296994933190906911550126903448550305774589158186620983078908999903236227644139233809976497584112009977050099805918840081016003432473970308911084438473129843467937570260269213379752939477543971997194726942070765353973592486385100760395587500479777214271950072501486991898552548367802275440149428009874251681748050967371632131215749156057167172045724894962981581623974778041892195042816264748240409828325162358849726820178448319231515704199246757605068437756339320877259265139582667576416912720546962363103285192108896307473476174274621271178723981577554403202845541641676740313056153714688443906280584343003810512865753020368506352553087271480372982296670895782864322818123135443203302933644911189865459210072322304830184928332284628556640721055224855948984201084227397383953418710873850697333926367069105921914351974740343117190093631673349760517336561821950476729650328709569580778460992736323825642963583365348969622024158006936337813043054330055037527767221347528355433242539542466087899304256369258736508134686223595179047448047001570145849146324756490272595195715570875699646306203716838836776534970808933953870887765638487806377829463382076620271853656700098751083279985179713873149889062044382800988852083374146990693661853260052632458206399907468975693077054216597830691090317151877924382520671984587571794222230307871775240061008844110843501348636696997883714882549516887871502980647726480003147659120721535565761408623620927361294995925128519476368500602819769753648780596876800529612692423650565733586107499477227655721706437410586727475742909678343833373788354069124146112944669525984724481862838838524782985233874945805174389410610263619258088251459418297199582931873548719203700105452061591270897566681662633358675177010995405465742800561594881922684888138461444170188312727529433268077409276887287868534914247640154685042201957903048678934189372049332769554249290609764739868415390753029621222371515752703593076604391686794417963299405546092466894695933655399801404044606188239804056162765858304123506635552291730351734182790923095924386721539442469187144570286127258696129807741112223691079357847749581217856458810731198269061046697761614154582017265451058308833167071517330465171075354[+++] ? ? Errors (if any) and Timing Info: Timing: real 0m0.404s user 0m0.303s sys 0m0.017s '68.118.' ************** PARI ***************** Host 68.118.249.160 (68.118.249.160) Time: Fri Jul 29 23:39:05 2005 Input: tan(8^8^5) Output: ? ? ? ? Errors (if any) and Timing Info: *** loss of precision in mpsc1. Timing: real 0m0.029s user 0m0.008s sys 0m0.010s '68.118.' ************** PARI ***************** Host 68.118.249.160 (68.118.249.160) Time: Fri Jul 29 23:39:24 2005 Input: tan(8^8^4) Output: ? ? ? ? Errors (if any) and Timing Info: *** loss of precision in mpsc1. Timing: real 0m0.027s user 0m0.011s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.249.160 (68.118.249.160) Time: Fri Jul 29 23:41:48 2005 Input: length(8^8^8) Output: ** WARNING: Computation used more memory than allowed. ** ? ? ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.090s user 0m0.059s sys 0m0.024s '68.118.' ************** PARI ***************** Host 68.118.249.160 (68.118.249.160) Time: Fri Jul 29 23:42:09 2005 Input: allocatemem() length(8^8^8) Output: WARNING: PARI command contains unsafe command 'allocatemem', so it will not be executed. '68.118.' ************** PARI ***************** Host 68.118.249.160 (68.118.249.160) Time: Fri Jul 29 23:42:22 2005 Input: allocatemem() length(8^8^8) Output: WARNING: PARI command contains unsafe command 'allocatemem', so it will not be executed. '203.173' ************** PARI ***************** Host 203.173.22.189 (203.173.22.189) Time: Fri Jul 29 23:48:11 2005 Input: A round Container 11m across, and 1.2m deep, how many litres can the Container hold. Respectfully Ernst Olofsen Output: ? AroundContainer11macross ? RespectfullyErnstOlofsen ? Errors (if any) and Timing Info: *** Warning: unused characters: ,and1.2mdeep,howmanylitrescantheContainerhold.. Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Jul 31 01:22:06 2005 Input: gcd(1990,2280) Output: ? 10 ? Errors (if any) and Timing Info: Timing: real 0m0.296s user 0m0.010s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Jul 31 01:22:29 2005 Input: gcd(1990,2360) Output: ? 10 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.010s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Jul 31 01:22:58 2005 Input: gcd(1296,2360) Output: ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.006s sys 0m0.011s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Jul 31 01:23:18 2005 Input: gcd(1296,1490) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.010s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Jul 31 01:23:33 2005 Input: gcd(1296,1480) Output: ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.009s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Jul 31 01:23:39 2005 Input: gcd(1296,1520) Output: ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.014s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Jul 31 01:23:58 2005 Input: gcd(1296,1040) Output: ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.010s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Jul 31 01:24:11 2005 Input: gcd(1296,624) Output: ? 48 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.013s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Jul 31 01:24:32 2005 Input: gcd(1296,1920) Output: ? 48 ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.010s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Jul 31 01:25:13 2005 Input: gcd(1296,2880) Output: ? 144 ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.007s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Sun Jul 31 01:25:26 2005 Input: gcd(1296,2280) Output: ? 24 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.008s sys 0m0.009s '81.215.' ************** PARI ***************** Host 81.215.246.107 (81.215.246.107) Time: Sun Jul 31 11:39:05 2005 Input: 111 Output: ? 111 ? Errors (if any) and Timing Info: Timing: real 0m0.287s user 0m0.009s sys 0m0.009s '212.117' ************** PARI ***************** Host 212.117.127.42 (212.117.127.42) Time: Sun Jul 31 14:53:03 2005 Input: 12^2 Output: ? 144 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.009s sys 0m0.008s '84.189.' ************** PARI ***************** Host 84.189.233.61 (84.189.233.61) Time: Sun Jul 31 16:29:46 2005 Input: PZ3 := PolynomialRing(Integers(), 3); Pr2Z := ProjectiveSpace(PZ3); K := Curve(Pr2Z, X^15 + Y^15 + Z^15); K; Ka := AffinePatch(K, 2); P2Z := CoordinateRing(Ambient(Ka)); q(DefiningPolynomial(Ka)) where _, q := quo^2>; Output: ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,Y,Z>:=PolynomialRing(Integers(),3);. *** incorrect type in comparison. *** unexpected character: Pr2Z:=ProjectiveSpace(PZ3 ^-------------------- *** unexpected character: K:=Curve(Pr2Z,X^15+Y^1 ^-------------------- *** unexpected character: Ka:=AffinePatch(K,2); ^------------------ *** Warning: unused characters: ,V>:=CoordinateRing(Ambient(Ka));. *** incorrect type in comparison. *** unknown function or error in formal parameters: q(DefiningPolynomial(K ^-------------------- *** Warning: unused characters: ,q:=quo^2>;. Timing: real 0m0.064s user 0m0.010s sys 0m0.008s '24.222.' ************** PARI ***************** Host 24.222.34.35 (24.222.34.35) Time: Mon Aug 1 14:22:03 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.304s user 0m0.010s sys 0m0.010s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:27:50 2005 Input: ellinit([1,I,2,0,0]); Output: ? ? Errors (if any) and Timing Info: *** incorrect type in gsigne. Timing: real 0m0.142s user 0m0.014s sys 0m0.015s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:28:03 2005 Input: ellinit([1,i,2,0,0]); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.054s user 0m0.010s sys 0m0.008s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:28:21 2005 Input: ellinit([1,i,2,0,0]); I^2; Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.011s sys 0m0.006s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:28:32 2005 Input: ellinit([1,i,2,0,0]); i^2; Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.011s sys 0m0.006s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:28:41 2005 Input: i^2; Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.007s sys 0m0.010s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:28:49 2005 Input: i^2 Output: ? i^2 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.008s sys 0m0.008s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:29:42 2005 Input: I^2 Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.005s sys 0m0.011s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:30:01 2005 Input: I^2+8*I+9 Output: ? 8 + 8*I ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:30:21 2005 Input: ellinit([1,2,3,4,5]) Output: ? [1, 2, 3, 4, 5, 9, 11, 29, 35, -183, -3429, -10351, 6128487/10351, [-1.6189099322673713423780009396072169750, -0.31554503386631432881099953019639151247 - 2.0925470969119586079816894466366945829*I, -0.31554503386631432881099953019639151247 + 2.0925470969119586079816894466366945829*I]~, 2.7807400137667297710631976271813584993, -1.3903700068833648855315988135906792496 + 1.0687497763561930661592635474375038787*I, -1.5548241211621901642750745610982915039 + 0.E-38*I, 0.77741206058109508213753728054914575195 - 1.7273497563868398667141498789110695180*I, 2.9719152678179096707716479509361896059] ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.011s sys 0m0.010s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:30:32 2005 Input: ellinit([1,2,3,4,I]) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in gsigne. Timing: real 0m0.028s user 0m0.011s sys 0m0.010s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:30:46 2005 Input: ellinit([1,2,3,4,0+I]) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in gsigne. Timing: real 0m0.030s user 0m0.014s sys 0m0.007s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:34:44 2005 Input: jell(I) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: jell(I) ^------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: jell(x) ===> ellj(x) ellj(x): elliptic j invariant of x. Timing: real 0m0.030s user 0m0.009s sys 0m0.008s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:34:54 2005 Input: ellj(I) Output: ? 1728.0000000000000000000000000000000000 + 0.E-54*I ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.008s sys 0m0.008s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:35:51 2005 Input: initell Output: ? initell ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.007s sys 0m0.010s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:36:06 2005 Input: initell([1,2,3,4,5]) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: initell([1,2,3,4,5]) ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: initell(x) ===> ellinit(x) ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. Timing: real 0m0.032s user 0m0.008s sys 0m0.009s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:36:35 2005 Input: smallinitell([1,2,3,4,5]) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: smallinitell([1,2,3, ^-------------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: smallinitell(x) ===> ellinit(x,1) ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:37:01 2005 Input: ellinit([1,2,3,4,5],1) Output: ? [1, 2, 3, 4, 5, 9, 11, 29, 35, -183, -3429, -10351, 6128487/10351] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.010s sys 0m0.007s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:37:10 2005 Input: ellinit([1,2,3,4,I],1) Output: ? [1, 2, 3, 4, I, 9, 11, 9 + 4*I, -10 + 9*I, -183, 891 - 864*I, -3574 + 891*I, 21903212538/13567357 + 5460481917/13567357*I] ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.009s sys 0m0.009s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:37:36 2005 Input: ellinit([1,2,0,0,I],1) Output: ? [1, 2, 0, 0, I, 9, 0, 4*I, 9*I, 81, -729 - 864*I, 432 - 729*I, 314928/985 + 531441/985*I] ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.006s sys 0m0.011s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:41:18 2005 Input: E=ellinit([1,2,0,0,I],1) Output: ? [1, 2, 0, 0, I, 9, 0, 4*I, 9*I, 81, -729 - 864*I, 432 - 729*I, 314928/985 + 531441/985*I] ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.006s sys 0m0.011s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:41:23 2005 Input: E=ellinit([1,2,0,0,I],1) Output: ? [1, 2, 0, 0, I, 9, 0, 4*I, 9*I, 81, -729 - 864*I, 432 - 729*I, 314928/985 + 531441/985*I] ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.011s sys 0m0.006s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:41:41 2005 Input: E=ellinit([1,2,0,0,I],1) omega(E) Output: ? [1, 2, 0, 0, I, 9, 0, 4*I, 9*I, 81, -729 - 864*I, 432 - 729*I, 314928/985 + 531441/985*I] ? ? Errors (if any) and Timing Info: *** negative or zero argument in an arithmetic function Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:41:50 2005 Input: E=ellinit([1,2,0,0,2],1) omega(E) Output: ? [1, 2, 0, 0, 2, 9, 0, 8, 18, 81, -2457, -3186, -19683/118] ? ? Errors (if any) and Timing Info: *** negative or zero argument in an arithmetic function Timing: real 0m0.032s user 0m0.010s sys 0m0.007s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:42:06 2005 Input: E:=ellinit([1,2,0,0,2],1); omega(E) Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: E:=ellinit([1,2,0,0,2] ^-------------------- *** not an integer argument in an arithmetic function Timing: real 0m0.019s user 0m0.013s sys 0m0.003s '141.20.' ************** PARI ***************** Host 141.20.52.74 (141.20.52.74) Time: Tue Aug 2 05:42:14 2005 Input: E=ellinit([1,2,0,0,2],1); omega(E) Output: ? ? ? Errors (if any) and Timing Info: *** negative or zero argument in an arithmetic function Timing: real 0m0.035s user 0m0.010s sys 0m0.007s '141.20.' ************** PARI ***************** Host 141.20.193.208 (141.20.193.208) Time: Tue Aug 2 07:58:27 2005 Input: I^2 Output: ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.280s user 0m0.011s sys 0m0.009s '129.132' ************** PARI ***************** Host 129.132.2.215 (129.132.2.215) Time: Tue Aug 2 12:16:43 2005 Input: P := PolynomialRing(RationalField(), 3); I := ideal

; UnivariateEliminationIdealGenerator(I, 1); UnivariateEliminationIdealGenerator(I, 2); EliminationIdeal(I, {y, z}); Output: ? ? ? (y^2 + (-z^2 - 1))*x + 1 ? y*x^2 + ((z^2 - 1)*y + 1) ? ? ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,y,z>:=PolynomialRing(RationalField(),3);. *** incorrect type in comparison. *** unexpected character: I:=ideal; ^- *** unknown function or error in formal parameters: *** ...liminationIdealGenerator(I,1); ^----- *** unknown function or error in formal parameters: *** ...liminationIdealGenerator(I,2); ^----- *** unexpected character: EliminationIdeal(I,{y,z}); ^------- Timing: real 0m0.174s user 0m0.010s sys 0m0.010s '129.132' ************** PARI ***************** Host 129.132.2.215 (129.132.2.215) Time: Tue Aug 2 12:16:49 2005 Input: P := PolynomialRing(RationalField(), 3); I := ideal

; UnivariateEliminationIdealGenerator(I, 1); UnivariateEliminationIdealGenerator(I, 2); EliminationIdeal(I, {y, z}); Output: ? ? ? (y^2 + (-z^2 - 1))*x + 1 ? y*x^2 + ((z^2 - 1)*y + 1) ? ? ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: ,y,z>:=PolynomialRing(RationalField(),3);. *** incorrect type in comparison. *** unexpected character: I:=ideal; ^- *** unknown function or error in formal parameters: *** ...liminationIdealGenerator(I,1); ^----- *** unknown function or error in formal parameters: *** ...liminationIdealGenerator(I,2); ^----- *** unexpected character: EliminationIdeal(I,{y,z}); ^------- Timing: real 0m0.027s user 0m0.008s sys 0m0.010s '24.213.' ************** PARI ***************** Host 24.213.136.229 (24.213.136.229) Time: Tue Aug 2 19:17:13 2005 Input: gettime Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.045s user 0m0.008s sys 0m0.011s '24.213.' ************** PARI ***************** Host 24.213.136.229 (24.213.136.229) Time: Tue Aug 2 19:17:25 2005 Input: zeta(0.5) Output: ? -1.4603545088095868128894991525152980124 ? Errors (if any) and Timing Info: Timing: real 0m0.064s user 0m0.009s sys 0m0.012s '24.213.' ************** PARI ***************** Host 24.213.136.229 (24.213.136.229) Time: Tue Aug 2 19:17:38 2005 Input: gettime Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.083s user 0m0.013s sys 0m0.005s '24.213.' ************** PARI ***************** Host 24.213.136.229 (24.213.136.229) Time: Tue Aug 2 19:17:38 2005 Input: gettime Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.064s user 0m0.010s sys 0m0.006s '24.213.' ************** PARI ***************** Host 24.213.136.229 (24.213.136.229) Time: Tue Aug 2 19:17:46 2005 Input: zeta(5) Output: ? 1.0369277551433699263313654864570341680 ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.012s sys 0m0.006s '24.213.' ************** PARI ***************** Host 24.213.136.229 (24.213.136.229) Time: Tue Aug 2 19:20:40 2005 Input: quit Output: WARNING: PARI command contains unsafe command 'quit', so it will not be executed. '203.144' ************** PARI ***************** Host 203.144.160.245 (203.144.160.245) Time: Wed Aug 3 07:28:29 2005 Input: polgalois(X^3 + 3*X^2 - 3*X - 8) Output: ? [6, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m2.138s user 0m0.012s sys 0m0.015s '203.144' ************** PARI ***************** Host 203.144.160.245 (203.144.160.245) Time: Wed Aug 3 07:30:00 2005 Input: polgalois(X^3 + 3*X^2 + 3*X - 8) Output: ? [6, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m1.055s user 0m0.009s sys 0m0.010s '67.64.1' ************** PARI ***************** Host 67.64.140.101 (67.64.140.101) Time: Wed Aug 3 13:34:24 2005 Input: (e(^2(^(9))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (e(^2(^(9))) ^--------- Timing: real 0m0.205s user 0m0.012s sys 0m0.010s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Wed Aug 3 17:28:03 2005 Input: E=ellinit([0,0,0,423,2592])ellrootno(E)elllseries(E,1) Output: ? [0, 0, 0, 423, 2592, 0, 846, 10368, -178929, -20304, -2239488, -7746342336, 179406144/166031, [-5.6917494505693907639110889701348964075, 2.8458747252846953819555444850674482037 - 21.149397363897693839798378251632550507*I, 2.8458747252846953819555444850674482037 + 21.149397363897693839798378251632550507*I]~, 0.86138337921547975434290303910758422317, -0.43069168960773987717145151955379211158 + 0.36046248977161066754327022294416248063*I, -4.5606201239166216346788853458773783615 - 1.468312611037591057 E-38*I, 2.2803100619583108173394426729386891807 - 5.5556274404990173411476980295858111163*I, 0.31049639751989530382668559940269744866] ? Errors (if any) and Timing Info: *** Warning: unused characters: ellrootno(E)elllseries(E,1). Timing: real 0m0.179s user 0m0.010s sys 0m0.011s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Wed Aug 3 17:28:18 2005 Input: E=ellinit([0,0,0,423,2592]); elllseries(E,1) Output: ? ? 0.E-38 ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.012s sys 0m0.009s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Wed Aug 3 17:29:58 2005 Input: E=ellinit([0,0,0,421,2294]); elllseries(E,1) Output: ? ? -0.10780764855011616176058874763957930197 ? Errors (if any) and Timing Info: Timing: real 0m0.902s user 0m0.728s sys 0m0.015s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Wed Aug 3 17:30:16 2005 Input: E=ellinit([0,0,0,421,2294]); print(elllseries(E,1)); print(ellrootno(E)); Output: ? ? -0.10780764855011616176058874763957930197 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.897s user 0m0.741s sys 0m0.010s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Wed Aug 3 17:31:12 2005 Input: E=ellinit([0,0,0,421,2294]); print(elllseries(E,1)); print(ellrootno(E)); Output: ? ? -0.10780764855011616176058874763957930197 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.897s user 0m0.738s sys 0m0.009s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Wed Aug 3 17:32:59 2005 Input: E=ellinit([0,0,0,416,1104]); print(elllseries(E,1)); print(ellrootno(E)); Output: ? ? -0.12811134149200481825211120077456014010 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m1.532s user 0m1.272s sys 0m0.011s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Wed Aug 3 17:35:48 2005 Input: E=ellinit([0,0,0,423,2592]); print(elllseries(E,1)); print(ellrootno(E)); Output: ? ? 0.E-38 ? -1 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.010s sys 0m0.012s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Wed Aug 3 20:25:45 2005 Input: factor(967) Output: ? [967 1] ? Errors (if any) and Timing Info: Timing: real 0m0.051s user 0m0.006s sys 0m0.011s '65.212.' ************** PARI ***************** Host 65.212.189.254 (65.212.189.254) Time: Wed Aug 3 20:25:55 2005 Input: factor(966) Output: ? [2 1] [3 1] [7 1] [23 1] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.009s sys 0m0.008s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Thu Aug 4 01:22:14 2005 Input: decimalcycle(p0,q0)= { local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans } decimalcycle(7,17) Output: ? ? [4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9] ? Errors (if any) and Timing Info: Timing: real 0m0.051s user 0m0.007s sys 0m0.013s '154.20.' ************** PARI ***************** Host 154.20.122.85 (154.20.122.85) Time: Thu Aug 4 01:22:33 2005 Input: decimalcycle(p0,q0)= { local(y,p,q,p1,ans); p=p0; q=q0; while(gcd(q,10)-1, p=10*p/gcd(q,10); q=q/gcd(q,10) ); p1=p-floor(p/q)*q; y=floor(10*p1/q); p=10*p1-y*q; ans=[y]; while(p-p1, y=floor(10*p/q); p=10*p-q*y; ans=concat(ans,y) ); ans } decimalcycle(7,17) Output: ? ? [4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9] ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.009s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Aug 4 03:19:48 2005 Input: a = 236386073053717651268111535986524112316457347651048558229926140093208220049710086356992; b=472772146107435302536223071973048224632914695302097116459852171130520711256363590397527; ((a*a)-1)/b Output: ? ? ? ? 55878375533757538270990298293467676570876453032508014848162929806736088984271740624446648786511393252136583839281044089939659035286898470166842474994110434099602170067288063/472772146107435302536223071973048224632914695302097116459852171130520711256363590397527 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.008s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Aug 4 05:38:01 2005 Input: 2^607-1 Output: ? 531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127 ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.011s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Aug 4 05:42:35 2005 Input: a=265568996408383549344794103276234313664796558863515961599722069100201779930426121369581251132614642834444664743123250507673289668826353619704759989383293675971915635417696609515864064; b=531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728167; ((a*a)-1)/b Output: ? ? ? ? 70526891853356034531603979043031594940743371757357833919419337999977433871326190057052096664518845125780975284354914663582043862183185043558365634079656826243725326219902938648103648856146145787520889095860455531443591926858713371483719982145691511131075312745428721576814913895557944855745498204068445694181321575408727502406563906376986273529501741633684526596095/531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728167 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Aug 4 05:42:49 2005 Input: a=265568996408383549344794103276234313664796558863515961599722069100201779930426121369581251132614642834444664743123250507673289668826353619704759989383293675971915635417696609515864064.0; b=531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728167.0; ((a*a)-1)/b Output: ? ? ? ? 1.3278449820419177467239705163811715683 E182 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.008s sys 0m0.010s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Aug 4 05:58:48 2005 Input: gcd(6670,4070) Output: ? 10 ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.008s sys 0m0.009s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Aug 4 06:00:34 2005 Input: gcd(2822,902) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Aug 4 06:05:21 2005 Input: a:=25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357; MOD(a,10) Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: a:=2519590847565789349 ^-------------------- *** unknown function or error in formal parameters: MOD(a,10) ^--------- Timing: real 0m0.023s user 0m0.013s sys 0m0.004s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Aug 4 06:05:30 2005 Input: a:=25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357; mod(a,10) Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: a:=2519590847565789349 ^-------------------- *** obsolete function: mod(a,10) ^--------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.052s user 0m0.010s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Aug 4 06:05:41 2005 Input: a=25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357; mod(a,10) Output: ? ? ? Errors (if any) and Timing Info: *** obsolete function: mod(a,10) ^--------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.037s user 0m0.011s sys 0m0.007s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Aug 4 06:05:56 2005 Input: a=25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357; Mod(a,10) Output: ? ? Mod(7, 10) ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.010s sys 0m0.008s '61.9.13' ************** PARI ***************** Host 61.9.136.222 (61.9.136.222) Time: Thu Aug 4 06:06:13 2005 Input: a=25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357; Mod(a,60) Output: ? ? Mod(17, 60) ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.010s sys 0m0.007s '165.21.' ************** PARI ***************** Host 165.21.154.112 (165.21.154.112) Time: Thu Aug 4 14:21:29 2005 Input: C := Dual(BCH(GF(2),31,4)); w := MinimumWeight(C); S := {}; v1 := MinimumWord(C); C1 := PunctureCode(C, Support(v1)); w1 := MinimumWeight(C1); Min1 := MinimumWords(C1); for v2 in Min1 do C2 := PunctureCode(C1, Support(v2)); w2 := MinimumWeight(C2); Min2 := MinimumWords(C2); for v3 in Min2 do C3 := PunctureCode(C2, Support(v3)); w3 := MinimumWeight(C3); Min3 := MinimumWords(C3); for v4 in Min3 do C4 := PunctureCode(C3, Support(v4)); w4 := MinimumWeight(C4); Min4 := MinimumWords(C4); Include(~S,< w, w1, w2, w3, w4>); end for; end for; end for; S; Output: ? ? ? ? ? ? ? ? forv2inMin1do ? ? ? ? forv3inMin2do ? ? ? ? forv4inMin3do ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: C:=Dual(BCH(GF(2),31,4 ^-------------------- *** unexpected character: w:=MinimumWeight(C); ^------------------ *** unexpected character: S:={}; ^---- *** unexpected character: v1:=MinimumWord(C); ^---------------- *** unexpected character: C1:=PunctureCode(C,Supp ^-------------------- *** unexpected character: w1:=MinimumWeight(C1); ^------------------- *** unexpected character: Min1:=MinimumWords(C1); ^------------------ *** unexpected character: C2:=PunctureCode(C1,Sup ^-------------------- *** unexpected character: w2:=MinimumWeight(C2); ^------------------- *** unexpected character: Min2:=MinimumWords(C2); ^------------------ *** unexpected character: C3:=PunctureCode(C2,Sup ^-------------------- *** unexpected character: w3:=MinimumWeight(C3); ^------------------- *** unexpected character: Min3:=MinimumWords(C3); ^------------------ *** unexpected character: C4:=PunctureCode(C3,Sup ^-------------------- *** unexpected character: w4:=MinimumWeight(C4); ^------------------- *** unexpected character: Min4:=MinimumWords(C4); ^------------------ *** unexpected character: Include(~S,); ^-------------------- Timing: real 0m0.188s user 0m0.012s sys 0m0.013s '24.122.' ************** PARI ***************** Host 24.122.72.77 (24.122.72.77) Time: Thu Aug 4 20:43:47 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.240s user 0m0.011s sys 0m0.011s '24.122.' ************** PARI ***************** Host 24.122.72.77 (24.122.72.77) Time: Thu Aug 4 20:44:14 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.008s sys 0m0.008s '24.122.' ************** PARI ***************** Host 24.122.72.77 (24.122.72.77) Time: Thu Aug 4 20:44:24 2005 Input: 11 Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '24.122.' ************** PARI ***************** Host 24.122.72.77 (24.122.72.77) Time: Thu Aug 4 20:44:43 2005 Input: 2 2 2 2 2 2 2 Output: ? 2 ? 2 ? 2 ? 2 ? 2 ? 2 ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.007s sys 0m0.009s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 22:51:54 2005 Input: E:=[0,0,0,-21,20] Output: ? ? Errors (if any) and Timing Info: *** unexpected character: E:=[0,0,0,-21,20] ^--------------- Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 22:52:09 2005 Input: E=ellinit([0,0,0,-21,20]) Output: ? [0, 0, 0, -21, 20, 0, -42, 80, -441, 1008, -17280, 419904, 21952/9, [3.9999999999999999999999999999999999999, 1.0000000000000000000000000000000000000, -4.9999999999999999999999999999999999999]~, 1.3526394018325432850998294029751858960, 1.1559445901719566833899482171124535850*I, -1.0782790455627296476887278783647717339, -3.2440452917894879838309731959642827172*I, 1.5635761990017598817136629961924419654] ? Errors (if any) and Timing Info: Timing: real 0m0.073s user 0m0.011s sys 0m0.011s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 22:52:34 2005 Input: E=ellinit([0,0,0,-21,20]);print(ellrootno(E);print(elllseries(E,1); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...1,20]);print(ellrootno(E);print(elllseries(E, ^-------------------- Timing: real 0m0.028s user 0m0.010s sys 0m0.008s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 22:54:44 2005 Input: E=ellinit([0,0,0,-21,20]);print(ellrootno(E));print(elllseries(E,1)); Output: ? 1 1.3526394018325432850998294029751858960 ? Errors (if any) and Timing Info: Timing: real 0m0.059s user 0m0.033s sys 0m0.007s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 22:55:03 2005 Input: E=ellinit([0,0,0,245,2374]);print(ellrootno(E));print(elllseries(E,1)); Output: ? 1 -0.30976671466600772465587451759620234304 ? Errors (if any) and Timing Info: Timing: real 0m0.175s user 0m0.136s sys 0m0.006s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 22:55:37 2005 Input: E=ellinit([0,0,0,197,1686]);print(ellrootno(E));print(elllseries(E,1)); Output: ? 1 -0.65243476968391157221811324217649958059 ? Errors (if any) and Timing Info: Timing: real 0m0.179s user 0m0.138s sys 0m0.008s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 22:55:55 2005 Input: E Output: ? E ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.006s sys 0m0.010s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 22:57:30 2005 Input: E=ellinit([0,0,0,245,2374]); N=ellglobalred(E)[1]; u=sqrt(N); an=ellan(E,floor(u+1)); a=exp(-2*Pi/u); sum(n=1,floor(u+1),an[n]/n*a^n) Output: ? ? ? ? ? ? -0.15468927147918056775050512569858924498 ? Errors (if any) and Timing Info: Timing: real 0m0.042s user 0m0.014s sys 0m0.008s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 22:58:06 2005 Input: E=ellinit([0,0,0,245,2374]); N=ellglobalred(E)[1]; u=sqrt(N); an=ellan(E,2*floor(u+1)); a=exp(-2*Pi/u); 2*sum(n=1,2*floor(u+1),an[n]/n*a^n) elllseries(E,1) Output: ? ? ? ? ? ? -0.30976597037581112930533648135578309024 ? -0.30976671466600772465587451759620234304 ? Errors (if any) and Timing Info: Timing: real 0m0.187s user 0m0.135s sys 0m0.008s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 22:58:18 2005 Input: E=ellinit([0,0,0,245,2374]); N=ellglobalred(E)[1]; u=sqrt(N); an=ellan(E,4*floor(u+1)); a=exp(-2*Pi/u); 4*sum(n=1,2*floor(u+1),an[n]/n*a^n)-elllseries(E,1) Output: ? ? ? ? ? ? -0.30976522608561453395479844511536383744 ? Errors (if any) and Timing Info: Timing: real 0m0.181s user 0m0.137s sys 0m0.010s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 22:58:26 2005 Input: E=ellinit([0,0,0,245,2374]); N=ellglobalred(E)[1]; u=sqrt(N); an=ellan(E,4*floor(u+1)); a=exp(-2*Pi/u); 2*sum(n=1,4*floor(u+1),an[n]/n*a^n)-elllseries(E,1) Output: ? ? ? ? ? ? -4.2154084576217972166403396489682094478 E-12 ? Errors (if any) and Timing Info: Timing: real 0m0.173s user 0m0.135s sys 0m0.012s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 22:58:44 2005 Input: E=ellinit([0,0,0,197,1686]); N=ellglobalred(E)[1]; u=sqrt(N); an=ellan(E,4*floor(u+1)); a=exp(-2*Pi/u); 2*sum(n=1,4*floor(u+1),an[n]/n*a^n)-elllseries(E,1) Output: ? ? ? ? ? ? -1.1395347390946858848884955188072588123 E-12 ? Errors (if any) and Timing Info: Timing: real 0m0.179s user 0m0.142s sys 0m0.008s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 22:58:49 2005 Input: E=ellinit([0,0,0,197,1686]); N=ellglobalred(E)[1]; u=sqrt(N); an=ellan(E,4*floor(u+1)); a=exp(-2*Pi/u); 2*sum(n=1,4*floor(u+1),an[n]/n*a^n) elllseries(E,1) Output: ? ? ? ? ? ? -0.65243476968505110695720792806138807611 ? -0.65243476968391157221811324217649958059 ? Errors (if any) and Timing Info: Timing: real 0m0.189s user 0m0.138s sys 0m0.010s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 22:58:59 2005 Input: E=ellinit([0,0,0,229,1334]); N=ellglobalred(E)[1]; u=sqrt(N); an=ellan(E,4*floor(u+1)); a=exp(-2*Pi/u); 2*sum(n=1,4*floor(u+1),an[n]/n*a^n) elllseries(E,1) Output: ? ? ? ? ? ? -0.55733963623654442804187871224124432863 ? -0.55733963623738039162232053168446569721 ? Errors (if any) and Timing Info: Timing: real 0m0.220s user 0m0.179s sys 0m0.012s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 22:59:10 2005 Input: E=ellinit([0,0,0,357,2486]); N=ellglobalred(E)[1]; u=sqrt(N); an=ellan(E,4*floor(u+1)); a=exp(-2*Pi/u); 2*sum(n=1,4*floor(u+1),an[n]/n*a^n) elllseries(E,1) Output: ? ? ? ? ? ? -0.57409919492090813791102842654345118980 ? -0.57409919492112193872078533110503257438 ? Errors (if any) and Timing Info: Timing: real 0m0.297s user 0m0.234s sys 0m0.009s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 22:59:23 2005 Input: E=ellinit([0,0,0,277,2278]); N=ellglobalred(E)[1]; u=sqrt(N); an=ellan(E,4*floor(u+1)); a=exp(-2*Pi/u); 2*sum(n=1,4*floor(u+1),an[n]/n*a^n) elllseries(E,1) Output: ? ? ? ? ? ? -0.68109159410414992631565533304039260493 ? -0.68109159410461718971229554953254610097 ? Errors (if any) and Timing Info: Timing: real 0m0.317s user 0m0.248s sys 0m0.009s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:02:52 2005 Input: E=ellinit([0,0,0,-21,20]); N=ellglobalred(E)[1]; k=1; u1=N^.45; u2=N^.5; u3=N^.55; an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); c1 c2 c3 c1+c3-2*c2 Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? 0.59718194950321704513062721164752172616 ? 0.67614152148226572022674761364983592309 ? 0.75545293749505830368003417624480328616 ? 0.00035184403374390835716616059265316614912 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.012s sys 0m0.009s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:02:59 2005 Input: E=ellinit([0,0,0,-21,20]); N=ellglobalred(E)[1]; k=2; u1=N^.45; u2=N^.5; u3=N^.55; an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); c1 c2 c3 c1+c3-2*c2 Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? 0.59728340174205344157806170771171734022 ? 0.67632031768391429406527262252750151691 ? 0.75535563139842122727530685348209069094 ? -0.0000016022273539192771766838611950026668227 ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.015s sys 0m0.006s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:03:04 2005 Input: E=ellinit([0,0,0,-21,20]); N=ellglobalred(E)[1]; k=3; u1=N^.45; u2=N^.5; u3=N^.55; an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); c1 c2 c3 c1+c3-2*c2 Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? 0.59728331746314931820462861746006109072 ? 0.67631970169846874696690482102356541714 ? 0.75535608509280491172390708248337724392 ? -0.00000000084098326400527394210369249963779632304 ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.012s sys 0m0.009s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:03:25 2005 Input: E=ellinit([0,0,0,-21,20]);N=ellglobalred(E)[1];k=1;u1=N^.45; u2=N^.5; u3=N^.55; an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); c1 c2 c3 c1+c3-2*c2 Output: ? ? ? ? ? ? ? ? ? ? ? 0.59718194950321704513062721164752172616 ? 0.67614152148226572022674761364983592309 ? 0.75545293749505830368003417624480328616 ? 0.00035184403374390835716616059265316614912 ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.012s sys 0m0.009s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:03:35 2005 Input: E=ellinit([0,0,0,-21,20]);N=ellglobalred(E)[1];k=1;u1=N^.45;u2=N^.5;u3=N^.55;an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); c1 c2 c3 c1+c3-2*c2 Output: ? ? ? ? ? ? ? ? 0.59718194950321704513062721164752172616 ? 0.67614152148226572022674761364983592309 ? 0.75545293749505830368003417624480328616 ? 0.00035184403374390835716616059265316614912 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.014s sys 0m0.008s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:04:17 2005 Input: E=ellinit([0,0,0,245,2374]); N=ellglobalred(E)[1];k=1; u1=N^.45; u2=N^.5; u3=N^.55; an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); c1 c2 c3 c1+c3-2*c2 Output: ? ? ? ? ? ? ? ? ? ? ? ? ? -0.017925795060954183055042002594599128267 ? -0.15468927147918056775050512569858924498 ? -0.27014676554219132834202979251169942951 ? 0.021305982355215624103938456290879932187 ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.018s sys 0m0.007s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:05:10 2005 Input: E=ellinit([0,0,0,245,2374]); N=ellglobalred(E)[1]; k=1; u1=N^.45; u2=N^.5; u3=N^.55; r=ellrootno(E); an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); (c1+r*c3)-(c2+r*c2) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 0.021305982355215624103938456290879932187 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.018s sys 0m0.006s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:05:20 2005 Input: E=ellinit([0,0,0,2,2374]); N=ellglobalred(E)[1]; k=1; u1=N^.45; u2=N^.5; u3=N^.55; r=ellrootno(E); an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); (c1+r*c3)-(c2+r*c2) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 0.0026803945425037344078078707907098314967 ? Errors (if any) and Timing Info: Timing: real 0m4.405s user 0m3.643s sys 0m0.035s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:05:26 2005 Input: E=ellinit([0,0,0,2,23]); N=ellglobalred(E)[1]; k=1; u1=N^.45; u2=N^.5; u3=N^.55; r=ellrootno(E); an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); (c1+r*c3)-(c2+r*c2) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 0.0012753536525371802202172838124568850817 ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.029s sys 0m0.007s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:05:31 2005 Input: E=ellinit([0,0,0,2,23]); N=ellglobalred(E)[1]; k=3; u1=N^.45; u2=N^.5; u3=N^.55; r=ellrootno(E); an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); (c1+r*c3)-(c2+r*c2) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 0.0000000014887246204423851637711853090887536005 ? Errors (if any) and Timing Info: Timing: real 0m0.075s user 0m0.058s sys 0m0.008s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:05:38 2005 Input: # E=ellinit([0,0,0,2,23]); N=ellglobalred(E)[1]; k=3; u1=N^.45; u2=N^.5; u3=N^.55; r=ellrootno(E); an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); (c1+r*c3)-(c2+r*c2) Output: ? timer = 1 (on) ? time = 3 ms. ? time = 0 ms. ? time = 0 ms. ? time = 0 ms. ? time = 0 ms. ? time = 0 ms. ? time = 0 ms. ? time = 17 ms. ? time = 0 ms. ? time = 1 ms. ? time = 0 ms. ? time = 3 ms. ? time = 6 ms. ? time = 13 ms. ? time = 0 ms. 0.0000000014887246204423851637711853090887536005 ? Errors (if any) and Timing Info: Timing: real 0m0.069s user 0m0.056s sys 0m0.012s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:05:55 2005 Input: E=ellinit([0,0,0,2,23]); N=ellglobalred(E)[1]; k=3; u1=N^.45; u2=N^.5; u3=N^.55; r=ellrootno(E); an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); (c1+r*c3)-(c2+r*c2) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 0.0000000014887246204423851637711853090887536005 ? Errors (if any) and Timing Info: Timing: real 0m0.079s user 0m0.059s sys 0m0.007s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:06:06 2005 Input: E=ellinit([0,0,0,-21,20]); N=ellglobalred(E)[1]; k=3; u1=N^.45; u2=N^.5; u3=N^.55; r=ellrootno(E); an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); (c1+r*c3)-(c2+r*c2) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? -0.00000000084098326400527394210369249963779632304 ? Errors (if any) and Timing Info: Timing: real 0m0.041s user 0m0.015s sys 0m0.007s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:06:12 2005 Input: E=ellinit([0,0,0,-3,4]); N=ellglobalred(E)[1]; k=3; u1=N^.45; u2=N^.5; u3=N^.55; r=ellrootno(E); an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); (c1+r*c3)-(c2+r*c2) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 0.0000000014401031502387752929247009185874399100 ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.020s sys 0m0.006s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:06:23 2005 Input: E=ellinit([0,0,0,197,1686]); N=ellglobalred(E)[1]; k=3; u1=N^.45; u2=N^.5; u3=N^.55; r=ellrootno(E); an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); (c1+r*c3)-(c2+r*c2) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 0.085016789301790760471152919232746829767 ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.021s sys 0m0.009s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:06:48 2005 Input: E=ellinit([0,0,0,423,2592]); N=ellglobalred(E)[1]; k=3; u1=N^.45; u2=N^.5; u3=N^.55; r=ellrootno(E); an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); (c1+r*c3)-(c2+r*c2) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 0.0000000016954065203325184554054703730951973450 ? Errors (if any) and Timing Info: Timing: real 0m1.339s user 0m1.113s sys 0m0.012s '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:07:02 2005 Input: E=ellinit([0,0,0,423,2592]); N=ellglobalred(E)[1] factor(%) k=3; u1=N^.45; u2=N^.5; u3=N^.55; r=ellrootno(E); an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); (c1+r*c3)-(c2+r*c2) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '66.218.' ************** PARI ***************** Host 66.218.45.98 (66.218.45.98) Time: Thu Aug 4 23:07:09 2005 Input: E=ellinit([0,0,0,423,2592]); N=ellglobalred(E)[1] factor(N) k=3; u1=N^.45; u2=N^.5; u3=N^.55; r=ellrootno(E); an=ellan(E,k*floor(u3+1)); a1=exp(-2*Pi/u1); a2=exp(-2*Pi/u2); a3=exp(-2*Pi/u3); c1=sum(n=1,k*floor(u1+1),an[n]/n*a1^n); c2=sum(n=1,k*floor(u2+1),an[n]/n*a2^n); c3=sum(n=1,k*floor(u3+1),an[n]/n*a3^n); (c1+r*c3)-(c2+r*c2) Output: ? ? 47816928 ? [2 5] [3 2] [166031 1] ? ? ? ? ? ? ? ? ? ? ? ? ? 0.0000000016954065203325184554054703730951973450 ? Errors (if any) and Timing Info: Timing: real 0m1.341s user 0m1.110s sys 0m0.017s '209.214' ************** PARI ***************** Host 209.214.56.16 (209.214.56.16) Time: Fri Aug 5 19:42:18 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.262s user 0m0.009s sys 0m0.013s '80.127.' ************** PARI ***************** Host 80.127.39.162 (80.127.39.162) Time: Sat Aug 6 07:21:59 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m2.863s user 0m0.015s sys 0m0.010s '83.197.' ************** PARI ***************** Host 83.197.222.129 (83.197.222.129) Time: Mon Aug 8 14:49:19 2005 Input: 2^88 Output: ? 309485009821345068724781056 ? Errors (if any) and Timing Info: Timing: real 0m0.050s user 0m0.011s sys 0m0.007s '83.197.' ************** PARI ***************** Host 83.197.222.129 (83.197.222.129) Time: Mon Aug 8 14:55:12 2005 Input: 2^88 Output: ? 309485009821345068724781056 ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.011s sys 0m0.008s '83.197.' ************** PARI ***************** Host 83.197.222.129 (83.197.222.129) Time: Mon Aug 8 14:56:36 2005 Input: 2^85 Output: ? 38685626227668133590597632 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.007s sys 0m0.010s '128.84.' ************** PARI ***************** Host 128.84.234.183 (128.84.234.183) Time: Mon Aug 8 15:17:27 2005 Input: Factor(x^3 +x^2 -104*x +371); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Factor(x^3+x^2-104*x+371); ^------------------ Timing: real 0m0.043s user 0m0.011s sys 0m0.006s '128.84.' ************** PARI ***************** Host 128.84.234.183 (128.84.234.183) Time: Mon Aug 8 15:17:36 2005 Input: Factor(x^3 +x^2 -104*x +371,x); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Factor(x^3+x^2-104*x+371,x); ^-------------------- Timing: real 0m0.029s user 0m0.010s sys 0m0.007s '12.221.' ************** PARI ***************** Host 12.221.95.99 (12.221.95.99) Time: Mon Aug 8 15:35:33 2005 Input: R < x > := PolynomialRing(Integers()); f := x^2 + 2; K < w > := NumberField(f); U:=UnitGroup(K); GL3 := GeneralLinearGroup(3, K); g1 := [2,-1-w,1-w,-1]; g2 := [1+w,1-w,2,-1-w]; G := MatrixGroup < 2, K | g1,g2>; Order(G); IsSolvable(G); Q:=G/Center(G); Order(Q); Output: ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: R:=PolynomialRing(Int ^-------------------- *** unexpected character: f:=x^2+2; ^------- *** unexpected character: K:=NumberField(f); ^----------------- *** unexpected character: U:=UnitGroup(K); ^-------------- *** unexpected character: GL3:=GeneralLinearGroup( ^-------------------- *** unexpected character: g1:=[2,-1-w,1-w,-1]; ^----------------- *** unexpected character: g2:=[1+w,1-w,2,-1-w]; ^------------------ *** unexpected character: G:=MatrixGroup<2,K|g1, ^-------------------- *** expected character: '=' instead of: Order(G); ^- *** expected character: '=' instead of: IsSolvable(G); ^- *** unexpected character: Q:=G/Center(G); ^------------- *** expected character: '=' instead of: Order(Q); ^- Timing: real 0m0.032s user 0m0.010s sys 0m0.009s '168.150' ************** PARI ***************** Host 168.150.235.66 (168.150.235.66) Time: Tue Aug 9 00:47:40 2005 Input: log 10 (52) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: log10(52) ^--------- Timing: real 0m0.234s user 0m0.007s sys 0m0.011s '83.197.' ************** PARI ***************** Host 83.197.92.233 (83.197.92.233) Time: Tue Aug 9 10:21:27 2005 Input: 481^0,5 Output: ? 1 ? Errors (if any) and Timing Info: *** Warning: unused characters: ,5. Timing: real 0m0.251s user 0m0.011s sys 0m0.009s '83.197.' ************** PARI ***************** Host 83.197.92.233 (83.197.92.233) Time: Tue Aug 9 10:21:54 2005 Input: 481^(1/2) Output: ? 21.931712199461308816548071696127563650 ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.010s sys 0m0.008s '83.197.' ************** PARI ***************** Host 83.197.92.233 (83.197.92.233) Time: Tue Aug 9 10:32:22 2005 Input: 432165438765654376547654/5432 Output: ? 216082719382827188273827/2716 ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.009s sys 0m0.008s '83.197.' ************** PARI ***************** Host 83.197.92.233 (83.197.92.233) Time: Tue Aug 9 10:32:44 2005 Input: 432165438765654376547654/5431 Output: ? 432165438765654376547654/5431 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.008s sys 0m0.009s '83.197.' ************** PARI ***************** Host 83.197.92.233 (83.197.92.233) Time: Tue Aug 9 10:33:00 2005 Input: =432165438765654376547654/5431 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: =4321654387656543765 ^-------------------- Timing: real 0m0.019s user 0m0.007s sys 0m0.010s '83.197.' ************** PARI ***************** Host 83.197.92.233 (83.197.92.233) Time: Tue Aug 9 10:33:37 2005 Input: 432165438765654376547654^(1/2) Output: ? 657392910492.38915301444833196764640118 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.006s '83.197.' ************** PARI ***************** Host 83.197.92.233 (83.197.92.233) Time: Tue Aug 9 10:34:16 2005 Input: 4321654387656543765476547654765476547654^(1/2) Output: ? 65739291049238915301.444891417391561807 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.007s sys 0m0.010s '83.197.' ************** PARI ***************** Host 83.197.92.233 (83.197.92.233) Time: Tue Aug 9 10:34:21 2005 Input: 4321654387656543765476547654765476547654^(1/2) Output: ? 65739291049238915301.444891417391561807 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.011s sys 0m0.007s '83.197.' ************** PARI ***************** Host 83.197.92.233 (83.197.92.233) Time: Tue Aug 9 10:35:21 2005 Input: 4321654387656543765476547654765476547654^(1/7) Output: ? 459447.31611857125677678086393259885064 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.011s sys 0m0.006s '83.197.' ************** PARI ***************** Host 83.197.92.233 (83.197.92.233) Time: Tue Aug 9 10:35:44 2005 Input: 4321654387656543765476547654765476547654^(1/47) Output: ? 6.9712667793595136259618999674074627706 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.012s sys 0m0.005s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 12:57:18 2005 Input: polroots(x^10-15*x^8+65*x^6-90*x^4+31*x^2-1) Output: ? [-2.9370372638532651942003323203314218203 + 0.E-38*I, -2.0446974972862653285641888375739238995 + 0.E-38*I, -1.3053233953965109395769792403637766425 + 0.E-38*I, -0.67323891597597051107511059583052100412 + 0.E-38*I, -0.18948469799599269967575558635612584053 + 0.E-38*I, 0.18948469799599269967575558635612584053 + 0.E-38*I, 0.67323891597597051107511059583052100412 + 0.E-38*I, 1.3053233953965109395769792403637766425 + 0.E-38*I, 2.0446974972862653285641888375739238995 + 0.E-38*I, 2.9370372638532651942003323203314218203 + 0.E-38*I]~ ? Errors (if any) and Timing Info: Timing: real 0m0.101s user 0m0.023s sys 0m0.012s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 12:58:45 2005 Input: S(n,k)=(1/factorial(k))*sum(i=0,k-1,((-1)^i)*binomial(k,i)*(k-i)^n; S(3,2) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...^i)*binomial(k,i)*(k-i)^n; ^- *** unknown function or error in formal parameters: S(3,2) ^------ Timing: real 0m0.021s user 0m0.009s sys 0m0.009s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 12:59:14 2005 Input: S(n,k)=(1/factorial(k))*sum(i=0,k-1,((-1)^i)*binomial(k,i)*(k-i)^n); S(3,2) Output: ? ? 3.0000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.009s sys 0m0.009s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 13:00:44 2005 Input: S(n,k)=(1/factorial(k))*sum(i=0,k-1,((-1)^i)*binomial(k,i)*(k-i)^n); m(n,x)=sum(k=0,n,((-1)^k)*S(n,n-k)); m(2,x); Output: ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.008s sys 0m0.010s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 13:01:03 2005 Input: S(n,k)=(1/factorial(k))*sum(i=0,k-1,((-1)^i)*binomial(k,i)*(k-i)^n); print(m(n,x)=sum(k=0,n,((-1)^k)*S(n,n-k))); m(2,x); Output: ? ? 0 ? ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.013s sys 0m0.006s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 13:01:50 2005 Input: m(n,x)= { S(n,k)=(1/factorial(k))*sum(i=0,k-1,((-1)^i)*binomial(k,i)*(k-i)^n); print(sum(k=0,n,((-1)^k)*S(n,n-k))); } m(2,x); Output: ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.007s sys 0m0.012s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 13:01:57 2005 Input: m(n,x)= { S(n,k)=(1/factorial(k))*sum(i=0,k-1,((-1)^i)*binomial(k,i)*(k-i)^n); print(sum(k=0,n,((-1)^k)*S(n,n-k))); } Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.009s sys 0m0.010s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 13:02:15 2005 Input: m(n,x)= { S(n,k)=(1/factorial(k))*sum(i=0,k-1,((-1)^i)*binomial(k,i)*(k-i)^n); print(sum(k=0,n,((-1)^k)*S(n,n-k))); } m(2,x); Output: ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.007s sys 0m0.011s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 13:02:54 2005 Input: m(n,x)= { S(n,k)=(1/factorial(k))*sum(i=0,k-1,((-1)^i)*binomial(k,i)*(k-i)^n); print(sum(k=0,n,((-1)^k)*S(n,n-k)*x^(2*n-2*k))); } Output: ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 13:03:05 2005 Input: m(n,x)= { S(n,k)=(1/factorial(k))*sum(i=0,k-1,((-1)^i)*binomial(k,i)*(k-i)^n); print(sum(k=0,n,((-1)^k)*S(n,n-k)*x^(2*n-2*k))); } m(2,x); Output: ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.013s sys 0m0.005s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 13:04:36 2005 Input: m(n,x)= { S(n,k)=(1/factorial(k))*sum(i=0,k-1,((-1)^i)*binomial(k,i)*(k-i)^n); print(sum(k=0,n,((-1)^k)*S(n,n-k)*x^(2*n-2*k))); } m(2,x); Output: ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.012s sys 0m0.005s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 13:04:56 2005 Input: m(n,x)= { S(n,k)=(1/factorial(k))*sum(i=0,k-1,((-1)^i)*binomial(k,i)*(k-i)^n); sum(k=0,n,((-1)^k)*S(n,n-k)*x^(2*n-2*k)); } m(2,x); Output: ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.008s sys 0m0.009s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 13:05:10 2005 Input: m(n,x)= { S(n,k)=(1/factorial(k))*sum(i=0,k-1,((-1)^i)*binomial(k,i)*(k-i)^n); sum(k=0,n,((-1)^k)*S(n,n-k)*x^(2*n-2*k)); } S(3,2); Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: S(3,2); ^------- Timing: real 0m0.035s user 0m0.012s sys 0m0.006s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 13:05:31 2005 Input: m(n,x)= { f(n,k)=(1/factorial(k))*sum(i=0,k-1,((-1)^i)*binomial(k,i)*(k-i)^n); sum(k=0,n,((-1)^k)*f(n,n-k)*x^(2*n-2*k)); } f(3,2) Output: ? ? ? ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: f(3,2) ^------ Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 13:07:04 2005 Input: f(n,k)=(1/factorial(k))*sum(i=0,k-1,((-1)^i)*binomial(k,i)*(k-i)^n); m(n,x)=sum(k=0,n,((-1)^k)*f(n,n-k)*x^(2*n-2*k)); f(3,2); m(2,x); Output: ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.013s sys 0m0.007s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 13:07:16 2005 Input: f(n,k)=(1/factorial(k))*sum(i=0,k-1,((-1)^i)*binomial(k,i)*(k-i)^n); m(n,x)=sum(k=0,n,((-1)^k)*f(n,n-k)*x^(2*n-2*k)); f(3,2); print(m(2,x)); Output: ? ? ? ? ? ? 1.0000000000000000000000000000000000000*x^4 - 1.0000000000000000000000000000000000000*x^2 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.011s sys 0m0.007s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 13:07:51 2005 Input: f(n,k)=(1/factorial(k))*sum(i=0,k-1,((-1)^i)*binomial(k,i)*(k-i)^n); m(n,x)=sum(k=0,n,((-1)^k)*f(n,n-k)*x^(2*n-2*k)); print(m(3,x)); Output: ? ? ? ? 0.99999999999999999999999999999999999999*x^6 - 3.0000000000000000000000000000000000000*x^4 + 1.0000000000000000000000000000000000000*x^2 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.008s sys 0m0.009s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 13:13:54 2005 Input: f(n,n)=1; f(n,1)=1; f(n,0)=0; f(n,k)=k*f(n-1,k)+f(n-1,k-1); print(f(3,2)); Output: ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** user function f: variable n declared twice. *** unknown function or error in formal parameters: f(n,1)=1; ^--------- *** unknown function or error in formal parameters: f(n,0)=0; ^--------- *** deep recursion: k*f(n-1,k)+f(n-1,k-1); ^-------------------- Timing: real 0m0.074s user 0m0.026s sys 0m0.030s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 15:52:39 2005 Input: polroots(x^8-10*x^6+25*x^4-15*x^2+1); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.050s user 0m0.022s sys 0m0.005s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 15:52:50 2005 Input: polyroots(x^8-10*x^6+25*x^4-15*x^2+1); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: polyroots(x^8-10*x^6+25*x^4-15* ^-------------------- Timing: real 0m0.018s user 0m0.008s sys 0m0.009s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 15:53:48 2005 Input: polroots(x^8-10*x^6+25*x^4-15*x^2+1); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.019s sys 0m0.008s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 15:54:13 2005 Input: polroots(x^8-10*x^6+25*x^4-15*x^2+1) Output: ? [-2.5514964429757895360954318703607363974 + 0.E-38*I, -1.6284019760468784955900732568191488719 + 0.E-38*I, -0.87302295017318657226464526426297680993 + 0.E-38*I, -0.27568792929582667149017153152830234661 + 0.E-38*I, 0.27568792929582667149017153152830234661 + 0.E-38*I, 0.87302295017318657226464526426297680993 + 0.E-38*I, 1.6284019760468784955900732568191488719 + 0.E-38*I, 2.5514964429757895360954318703607363974 + 0.E-38*I]~ ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.019s sys 0m0.008s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 15:55:30 2005 Input: polroots(x^10-15*x^8+65*x^6-90*x^4+31*x^2-1) Output: ? [-2.9370372638532651942003323203314218203 + 0.E-38*I, -2.0446974972862653285641888375739238995 + 0.E-38*I, -1.3053233953965109395769792403637766425 + 0.E-38*I, -0.67323891597597051107511059583052100412 + 0.E-38*I, -0.18948469799599269967575558635612584053 + 0.E-38*I, 0.18948469799599269967575558635612584053 + 0.E-38*I, 0.67323891597597051107511059583052100412 + 0.E-38*I, 1.3053233953965109395769792403637766425 + 0.E-38*I, 2.0446974972862653285641888375739238995 + 0.E-38*I, 2.9370372638532651942003323203314218203 + 0.E-38*I]~ ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.026s sys 0m0.005s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 15:56:37 2005 Input: polroots(x^12-21*x^10+140*x^8-350*x^6+301*x^4-63*x^2+1) Output: ? [-3.2881124987244585532256274494179876511 + 0.E-38*I, -2.4213678181459921881018294225128340032 + 0.E-38*I, -1.7001346382029912050059275394780824610 + 0.E-38*I, -1.0679187167638310302697817833075801817 + 0.E-38*I, -0.52641847170033845302273998786090177345 + 0.E-38*I, -0.13141348484638649157561541744841729507 + 0.E-38*I, 0.13141348484638649157561541744841729507 + 0.E-38*I, 0.52641847170033845302273998786090177345 + 0.E-38*I, 1.0679187167638310302697817833075801817 + 0.E-38*I, 1.7001346382029912050059275394780824610 + 0.E-38*I, 2.4213678181459921881018294225128340032 + 0.E-38*I, 3.2881124987244585532256274494179876511 + 0.E-38*I]~ ? Errors (if any) and Timing Info: Timing: real 0m0.049s user 0m0.029s sys 0m0.009s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 15:58:17 2005 Input: polroots(x^14-28*x^12+266*x^10-1050*x^8+1701*x^6-966*x^4+127*x^2-1) Output: ? [-3.6124510360842219771995008146711633578 + 0.E-38*I, -2.7673598944840744082364535389451209733 + 0.E-38*I, -2.0631423901776288395781211867243925567 + 0.E-38*I, -1.4394359016675863263156300774422024132 + 0.E-38*I, -0.88454720282863641649354976240828623578 + 0.E-38*I, -0.41540042567215047041722709197463151176 + 0.E-38*I, -0.091669086703853090393179203266445359659 + 0.E-38*I, 0.091669086703853090393179203266445359659 + 0.E-38*I, 0.41540042567215047041722709197463151176 + 0.E-38*I, 0.88454720282863641649354976240828623578 + 0.E-38*I, 1.4394359016675863263156300774422024132 + 0.E-38*I, 2.0631423901776288395781211867243925567 + 0.E-38*I, 2.7673598944840744082364535389451209733 + 0.E-38*I, 3.6124510360842219771995008146711633578 + 0.E-38*I]~ ? Errors (if any) and Timing Info: Timing: real 0m0.080s user 0m0.033s sys 0m0.012s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 16:00:04 2005 Input: polroots(x^16-36*x^14+462*x^12-2646*x^10+6951*x^8-7770*x^6+3025*x^4-255*x^2+1) Output: ? [-3.9152762397043324123107182382990325331 + 0.E-38*I, -3.0888157436488878661785100136849563918 + 0.E-38*I, -2.3999265630728300200039447195102173168 + 0.E-38*I, -1.7868348797726021161302916131136524223 + 0.E-38*I, -1.2323168953277890158667434609444801750 + 0.E-38*I, -0.73879968255867477054995789703365876889 + 0.E-38*I, -0.32992738116837426287088499893460233349 + 0.E-38*I, -0.064194194248340968083832861794848964567 + 0.E-38*I, 0.064194194248340968083832861794848964567 + 0.E-38*I, 0.32992738116837426287088499893460233349 + 0.E-38*I, 0.73879968255867477054995789703365876889 + 0.E-38*I, 1.2323168953277890158667434609444801750 + 0.E-38*I, 1.7868348797726021161302916131136524223 + 0.E-38*I, 2.3999265630728300200039447195102173168 + 0.E-38*I, 3.0888157436488878661785100136849563918 + 0.E-38*I, 3.9152762397043324123107182382990325331 + 0.E-38*I]~ ? Errors (if any) and Timing Info: Timing: real 0m0.066s user 0m0.042s sys 0m0.009s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 16:01:41 2005 Input: polroots(x^18-45*x^16+750x^14-5880*x^12+22827*x^10-42525*x^8+34105*x^6-9330*x^4+511*x^2-1) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: polroots(x^18-45*x^16+750 *** x^14-5880*x^12+22827 ^-------------------- Timing: real 0m0.033s user 0m0.011s sys 0m0.006s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Tue Aug 9 16:01:55 2005 Input: polroots(x^18-45*x^16+750*x^14-5880*x^12+22827*x^10-42525*x^8+34105*x^6-9330*x^4+511*x^2-1) Output: ? [-4.2003124177284583445821767022791681590 + 0.E-38*I, -3.3901217801544794681383220988567292618 + 0.E-38*I, -2.7149349003938807011625504759826279185 + 0.E-38*I, -2.1125810907447785312484755488526798753 + 0.E-38*I, -1.5632534070390195327340376458820115006 + 0.E-38*I, -1.0630467164580793684859204995834997361 + 0.E-38*I, -0.62079565821007806064683035480909577441 + 0.E-38*I, -0.26330777728481173761500317960145706761 + 0.E-38*I, -0.045075048825799037644294444989077978214 + 0.E-38*I, 0.045075048825799037644294444989077978214 + 0.E-38*I, 0.26330777728481173761500317960145706761 + 0.E-38*I, 0.62079565821007806064683035480909577441 + 0.E-38*I, 1.0630467164580793684859204995834997361 + 0.E-38*I, 1.5632534070390195327340376458820115006 + 0.E-38*I, 2.1125810907447785312484755488526798753 + 0.E-38*I, 2.7149349003938807011625504759826279185 + 0.E-38*I, 3.3901217801544794681383220988567292618 + 0.E-38*I, 4.2003124177284583445821767022791681590 + 0.E-38*I]~ ? Errors (if any) and Timing Info: Timing: real 0m0.091s user 0m0.043s sys 0m0.013s '59.133.' ************** PARI ***************** Host 59.133.126.56 (59.133.126.56) Time: Wed Aug 10 07:09:45 2005 Input: bloxb1:= [ { 3, 10, 17, 20, 23, 30, 36, 40, 47, 53, 55 }, { 5, 11, 14, 17, 18, 20, 26, 33, 34, 44, 50 }, { 2, 7, 11, 13, 17, 19, 24, 32, 41, 45, 55 }, { 11, 13, 15, 18, 38, 39, 42, 43, 46, 47, 53 }, { 1, 7, 14, 15, 22, 25, 30, 33, 39, 40, 45 }, { 1, 4, 5, 9, 11, 16, 19, 37, 40, 47, 49 }, { 12, 16, 18, 19, 22, 26, 30, 31, 38, 52, 55 }, { 5, 8, 29, 30, 34, 37, 38, 41, 45, 51, 53 }, { 5, 6, 9, 15, 18, 23, 32, 36, 45, 52, 54 }, { 15, 24, 26, 28, 34, 37, 40, 46, 48, 54, 55 }, { 6, 16, 24, 31, 32, 33, 40, 42, 44, 51, 53 }, { 5, 7, 16, 20, 21, 30, 32, 43, 46, 48, 56 }, { 1, 3, 6, 11, 20, 28, 31, 35, 38, 45, 48 }, { 2, 15, 16, 17, 23, 27, 33, 35, 37, 38, 56 }, { 3, 4, 8, 12, 16, 17, 39, 44, 45, 46, 54 }, { 3, 4, 15, 26, 30, 32, 35, 41, 42, 49, 50 }, { 2, 3, 7, 9, 14, 31, 37, 46, 50, 52, 53 }, { 5, 7, 10, 12, 15, 27, 28, 31, 41, 44, 47 }, { 1, 3, 12, 18, 21, 24, 33, 36, 37, 41, 43 }, { 1, 2, 5, 12, 23, 39, 42, 48, 50, 51, 55 }, { 8, 9, 19, 20, 22, 23, 28, 33, 41, 42, 46 }, { 9, 10, 12, 13, 26, 33, 45, 48, 49, 53, 56 }, { 10, 18, 19, 21, 27, 35, 40, 45, 46, 50, 51 }, { 9, 12, 17, 25, 28, 29, 32, 38, 40, 43, 50 }, { 1, 9, 13, 17, 21, 27, 30, 31, 34, 42, 54 }, { 8, 10, 11, 21, 23, 25, 26, 31, 32, 37, 39 }, { 4, 22, 23, 24, 31, 34, 43, 45, 47, 50, 56 }, { 6, 9, 10, 14, 16, 34, 35, 39, 41, 43, 55 }, { 1, 7, 19, 23, 26, 29, 35, 43, 44, 53, 54 }, { 2, 14, 16, 21, 26, 28, 29, 36, 42, 45, 47 }, { 6, 7, 8, 21, 33, 38, 47, 49, 50, 54, 55 }, { 8, 14, 15, 17, 19, 31, 36, 43, 48, 49, 51 }, { 1, 4, 8, 14, 18, 27, 28, 32, 53, 55, 56 }, { 2, 8, 9, 18, 24, 25, 30, 35, 44, 47, 48 }, { 2, 18, 20, 29, 31, 39, 40, 41, 49, 54, 56 }, { 1, 2, 10, 22, 32, 34, 36, 38, 44, 46, 49 }, { 11, 16, 22, 25, 27, 36, 41, 48, 50, 53, 54 }, { 6, 11, 12, 14, 23, 24, 27, 29, 30, 46, 49 }, { 2, 4, 10, 11, 28, 30, 33, 43, 51, 52, 54 }, { 4, 5, 13, 25, 29, 31, 33, 35, 36, 46, 55 }, { 3, 19, 27, 29, 32, 33, 34, 39, 47, 48, 52 }, { 3, 7, 13, 16, 18, 23, 25, 28, 34, 49, 51 }, { 4, 6, 7, 10, 17, 18, 22, 29, 37, 42, 48 }, { 5, 17, 21, 22, 24, 28, 35, 39, 49, 52, 53 }, { 6, 13, 19, 28, 30, 36, 37, 39, 44, 50, 56 }, { 12, 13, 14, 20, 22, 32, 35, 37, 47, 51, 54 }, { 1, 8, 10, 13, 15, 16, 20, 24, 29, 50, 52 }, { 2, 4, 6, 12, 15, 19, 20, 21, 25, 34, 53 }, { 3, 9, 11, 15, 21, 22, 29, 44, 51, 55, 56 }, { 1, 6, 17, 25, 26, 41, 46, 47, 51, 52, 56 }, { 4, 13, 14, 21, 23, 38, 40, 41, 44, 48, 52 }, { 3, 5, 10, 14, 19, 24, 25, 38, 42, 54, 56 }, { 20, 25, 27, 37, 42, 43, 44, 45, 49, 52, 55 }, { 7, 8, 11, 12, 34, 35, 36, 40, 42, 52, 56 }, { 4, 7, 9, 20, 24, 26, 27, 36, 38, 39, 51 }, { 2, 3, 5, 6, 8, 13, 22, 26, 27, 40, 43 } ]; Output: ? ? 3 ? ? Errors (if any) and Timing Info: *** unexpected character: bloxb1:=[ ^-- *** Warning: unused characters: ,10,17,20,23,30,36,40,47,53,55},{5,11,14,17,18,20,26,33,34,44,50},{2,7,11,13,17,19,24,32,41,45,55},{11,13,15,18,38,39,[+++]. *** unexpected character: ]; ^-- Timing: real 0m3.738s user 0m0.017s sys 0m0.017s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 10:11:43 2005 Input: polisirreducible(x^2-1) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.319s user 0m0.013s sys 0m0.013s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 10:11:50 2005 Input: polisirreducible(x^2+1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.013s sys 0m0.005s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 10:12:18 2005 Input: polisirreducible(x^4-3*x^2+1) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.013s sys 0m0.004s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 10:13:43 2005 Input: polisirreducible(x^6-6*x^4+7*x^2-1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.011s sys 0m0.009s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 10:14:25 2005 Input: polisirreducible(x^8-10*x^6+25*x^4-15*x^2+1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.010s sys 0m0.008s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 10:14:30 2005 Input: polisirreducible(x^8-10*x^6+25*x^4-15*x^2+1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.013s sys 0m0.006s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 10:15:24 2005 Input: polisirreducible(x^10-15*x^8+65*x^6-90*x^4+31*x^2-1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.009s sys 0m0.009s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 10:16:16 2005 Input: polisirreducible(x^12-21*x^10+140*x^8-350*x^6+301*x^4-63*x^2+1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.014s sys 0m0.006s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 10:16:23 2005 Input: polisirreducible(x^12-21*x^10+140*x^8-350*x^6+301*x^4-63*x^2+1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.010s sys 0m0.010s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 10:17:36 2005 Input: polisirreducible(x^14-28*x^12+266*x^10-1050*x^8+1701*x^6-966*x^4+127*x^2-1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.012s sys 0m0.008s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 10:17:39 2005 Input: polisirreducible(x^14-28*x^12+266*x^10-1050*x^8+1701*x^6-966*x^4+127*x^2-1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.010s sys 0m0.010s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 10:18:22 2005 Input: polisirreducible(x^4-3*x^2+1) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.011s sys 0m0.007s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 10:23:42 2005 Input: polisirreducible(x^4-3*x^2+1) polroots(x^4-3*x^2+1) Output: ? 0 ? [-1.6180339887498948482045868343656381177 + 0.E-38*I, -0.61803398874989484820458683436563811772 + 0.E-38*I, 0.61803398874989484820458683436563811772 + 0.E-38*I, 1.6180339887498948482045868343656381177 + 0.E-38*I]~ ? Errors (if any) and Timing Info: Timing: real 0m0.055s user 0m0.015s sys 0m0.006s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 10:32:25 2005 Input: polisirreducible(x^14-28*x^12+266*x^10-1050*x^8+1701*x^6-966*x^4+127*x^2-1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.012s sys 0m0.007s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 10:54:51 2005 Input: polisirreducible(x^16-36*x^14+462*x^12-2646*x^10+6951*x^8-7770*x^6+3025*x^4-255*x^2+1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.012s sys 0m0.008s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 10:59:51 2005 Input: polisirreducible(x^18-45*x^16+750x^14-5880*x^12+22827*x^10-42525*x^8+34105*x^6-9330*x^4+511*x^2-1) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...educible(x^18-45*x^16+750 *** x^14-5880*x^12+22827 ^-------------------- Timing: real 0m0.024s user 0m0.012s sys 0m0.006s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 11:00:05 2005 Input: polisirreducible(x^18-45*x^16+750*x^14-5880*x^12+22827*x^10-42525*x^8+34105*x^6-9330*x^4+511*x^2-1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.015s sys 0m0.005s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 12:18:48 2005 Input: s(n,k)=(1/factorial(k)*sum(i=0,k, ((-1)^i)*binomial(k,i)*(k-i)^n); s(3,2) Output: ? ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...i)*binomial(k,i)*(k-i)^n); ^- *** unknown function or error in formal parameters: s(3,2) ^------ Timing: real 0m0.033s user 0m0.006s sys 0m0.011s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 12:19:19 2005 Input: s(n,k)=(1/factorial(k)*sum(i=0,k,((-1)^i)*binomial(k,i)*(k-i)^n); s(3,2) Output: ? ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...i)*binomial(k,i)*(k-i)^n); ^- *** unknown function or error in formal parameters: s(3,2) ^------ Timing: real 0m0.021s user 0m0.007s sys 0m0.010s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 12:19:47 2005 Input: s(n,k)={(1/factorial(k)*sum(i=0,k,((-1)^i)*binomial(k,i)*(k-i)^n)}; s(3,2) Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: s(n,k)={(1/factorial(k)*sum ^-------------------- *** unknown function or error in formal parameters: s(3,2) ^------ Timing: real 0m0.028s user 0m0.007s sys 0m0.010s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 12:20:06 2005 Input: f(n,k)={(1/factorial(k)*sum(i=0,k,((-1)^i)*binomial(k,i)*(k-i)^n)}; f(3,2) Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: f(n,k)={(1/factorial(k)*sum ^-------------------- *** unknown function or error in formal parameters: f(3,2) ^------ Timing: real 0m0.031s user 0m0.009s sys 0m0.008s '137.43.' ************** PARI ***************** Host 137.43.122.228 (137.43.122.228) Time: Wed Aug 10 12:20:22 2005 Input: f(n,k)={(1/factorial(k)*sum(i=0,k,((-1)^i)*binomial(k,i)*(k-i)^n)}; print(f(3,2)); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: f(n,k)={(1/factorial(k)*sum ^-------------------- *** unknown function or error in formal parameters: print(f(3,2)); ^-------- Timing: real 0m0.026s user 0m0.010s sys 0m0.007s '81.69.5' ************** PARI ***************** Host 81.69.59.13 (81.69.59.13) Time: Wed Aug 10 15:08:12 2005 Input: 64*9878657 Output: ? 632234048 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '201.8.6' ************** PARI ***************** Host 201.8.60.25 (201.8.60.25) Time: Thu Aug 11 07:57:15 2005 Input: (a+b+c)^3 Output: ? a^3 + (3*b + 3*c)*a^2 + (3*b^2 + 6*c*b + 3*c^2)*a + (b^3 + 3*c*b^2 + 3*c^2*b + c^3) ? Errors (if any) and Timing Info: Timing: real 0m0.281s user 0m0.008s sys 0m0.010s '68.111.' ************** PARI ***************** Host 68.111.49.126 (68.111.49.126) Time: Fri Aug 12 08:55:41 2005 Input: polgalois(512*x^6-768*x^4-32*x^3+288*x^2+24*x-15) Output: ? [12, -1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.098s user 0m0.017s sys 0m0.011s '213.7.1' ************** PARI ***************** Host 213.7.162.164 (213.7.162.164) Time: Fri Aug 12 20:43:55 2005 Input: 2^3 Output: ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.158s user 0m0.013s sys 0m0.008s '213.7.1' ************** PARI ***************** Host 213.7.162.164 (213.7.162.164) Time: Fri Aug 12 20:44:11 2005 Input: intformal(x^2) Output: ? 1/3*x^3 ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.007s sys 0m0.010s '213.7.1' ************** PARI ***************** Host 213.7.162.164 (213.7.162.164) Time: Fri Aug 12 20:44:29 2005 Input: intformal(x^2/exp(x^2)) Output: ? 1/3*x^3 - 1/5*x^5 + 1/14*x^7 - 1/54*x^9 + 1/264*x^11 - 1/1560*x^13 + 1/10800*x^15 - 1/85680*x^17 + O(x^19) ? Errors (if any) and Timing Info: Timing: real 0m0.047s user 0m0.012s sys 0m0.007s '201.137' ************** PARI ***************** Host 201.137.39.170 (201.137.39.170) Time: Sat Aug 13 19:33:42 2005 Input: 2^2^2 Output: ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.294s user 0m0.008s sys 0m0.015s '201.137' ************** PARI ***************** Host 201.137.39.170 (201.137.39.170) Time: Sat Aug 13 19:34:29 2005 Input: 2^3^2^3 Output: ? 11423562217377937432834817564864391054921813476074403186202876186307194708759156620192815736856953160782704625320798799480493785783539071475308181558958409886139180507766255745268835295645117313504338819263740326883325464574267555496207694285869572314648316514329215930122751571464318862255979369772869442140816230512157201729281184157721386877314303827951055243527097308944107496195827273952935604677267766071546533446890697483255207837930462782684172148575680225197203487779905492453075630072358789672398534046574327392486173694016134122557759726226515008486798286901592462027191956990502296836826476904023063730093767352130344242019656202260888892026453895468229206988071920295008873379682446553369924894350070488891702010078541708225795234839095211089097709112162085120097647338122139833228110600082989392591338433777616544053684799646500413069770687086581487137502485652747714529441936196186003229177757067964120330231232040963858808839184289548225605031170276587718715043046407159535959626211055259297605210472194352154412308176378305978722042762270067173474951806087819815154079666858570587012720661422637817709796687416276036064210127293014198595450513696623633614994073435824842954082330215697686198561610404629566074790086569059643951234599817490323492052082224793909497188899924748028310673588762417682527348630665205417209359086662377804683776356513790589272591978956170307165117107589512088595323312169179624851488689039519409637419425694423986296239609301255502738931127000906125692128912846840805341230670024948640174953768772224370653045179249084484537443164603352860688179124388887671769490857961498972552585448374811136545337429493009247982272748138694950049819837487875349582757538405984852225375998205031894594085879229119678150100444102619057722203800499447489455107613497927587194865059674725545869846288173614441578176037582721675130519361949018877981483652351653188988167198715064479729607107795243426756944986254682519699815429352363416415356114173952 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.009s sys 0m0.009s '201.137' ************** PARI ***************** Host 201.137.39.170 (201.137.39.170) Time: Sat Aug 13 20:26:47 2005 Input: //d := func< m | DivisorSigma(1, m) - m >; //for m := 2 to 90000 do // n := d(m); // if d(n) eq m then // print m, n; // end if; //end for; 2^3 Output: ? ? ? ? ? ? ? ? ? 8 ? Errors (if any) and Timing Info: *** unexpected character: //d:=func; for m := 2 to 90000 do n := d(m); if d(n) eq m then print m, n; end if; end for; 2^3 Output: ? ? ? ? ? ? ? ? ? 8 ? Errors (if any) and Timing Info: *** unexpected character: d:=func; ***for m := 2 to 90000 do *** n := d(m); *** if d(n) eq m then *** print m, n; *** end if; ***end for; 2^3 Output: ? ? ? ? ? ? ? ? ? 8 ? Errors (if any) and Timing Info: *** unexpected character: ***d:=func; ***for m := 2 to 90000 do *** n := d(m); *** if d(n) eq m then *** print m, n; *** end if; ***end for; 2^3 Output: ? ? ? ? ? ? ? ? ? 8 ? Errors (if any) and Timing Info: *** unexpected character: d:=func Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.027s user 0m0.007s sys 0m0.012s '211.26.' ************** PARI ***************** Host 211.26.119.57 (211.26.119.57) Time: Sun Aug 21 03:18:38 2005 Input: Mod(893^607,1363) Output: ? Mod(141, 1363) ? ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.009s sys 0m0.009s '211.26.' ************** PARI ***************** Host 211.26.119.57 (211.26.119.57) Time: Sun Aug 21 03:19:22 2005 Input: Mod(1265^607,1363) Output: ? Mod(304, 1363) ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.008s sys 0m0.009s '211.26.' ************** PARI ***************** Host 211.26.119.57 (211.26.119.57) Time: Sun Aug 21 03:19:54 2005 Input: Mod(406^607,1363) Output: ? Mod(261, 1363) ? ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.007s sys 0m0.010s '211.26.' ************** PARI ***************** Host 211.26.119.57 (211.26.119.57) Time: Sun Aug 21 03:20:15 2005 Input: Mod(171^607,1363) Output: ? Mod(214, 1363) ? ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.007s sys 0m0.010s '211.26.' ************** PARI ***************** Host 211.26.119.57 (211.26.119.57) Time: Sun Aug 21 03:20:44 2005 Input: Mod(241^607,1363) Output: ? Mod(614, 1363) ? ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.010s sys 0m0.007s '211.26.' ************** PARI ***************** Host 211.26.119.57 (211.26.119.57) Time: Sun Aug 21 03:21:01 2005 Input: Mod(980^607,1363) Output: ? Mod(170, 1363) ? ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.011s sys 0m0.006s '211.26.' ************** PARI ***************** Host 211.26.119.57 (211.26.119.57) Time: Sun Aug 21 03:21:20 2005 Input: Mod(1040^607,1363) Output: ? Mod(426, 1363) ? ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.010s sys 0m0.008s '211.26.' ************** PARI ***************** Host 211.26.119.57 (211.26.119.57) Time: Sun Aug 21 03:21:41 2005 Input: Mod(12^607,1363) Output: ? Mod(220, 1363) ? ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.010s sys 0m0.007s '211.26.' ************** PARI ***************** Host 211.26.119.57 (211.26.119.57) Time: Sun Aug 21 03:21:58 2005 Input: Mod(1152^607,1363) Output: ? Mod(404, 1363) ? ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.008s sys 0m0.009s '211.26.' ************** PARI ***************** Host 211.26.119.57 (211.26.119.57) Time: Sun Aug 21 03:22:34 2005 Input: Mod(573^607,1363) Output: ? Mod(100, 1363) ? ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.012s sys 0m0.005s '81.250.' ************** PARI ***************** Host 81.250.17.22 (81.250.17.22) Time: Sun Aug 21 12:56:28 2005 Input: 123456789*987654321 Output: ? 121932631112635269 ? Errors (if any) and Timing Info: Timing: real 0m0.282s user 0m0.014s sys 0m0.014s '84.135.' ************** PARI ***************** Host 84.135.45.137 (84.135.45.137) Time: Sun Aug 21 15:10:06 2005 Input: 100! Output: ? 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.049s user 0m0.010s sys 0m0.007s '72.128.' ************** PARI ***************** Host 72.128.91.216 (72.128.91.216) Time: Mon Aug 22 01:56:06 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.278s user 0m0.011s sys 0m0.006s '132.68.' ************** PARI ***************** Host 132.68.248.74 (132.68.248.74) Time: Mon Aug 22 11:08:02 2005 Input: A := Matrix(2,2,(1,2,3,4)); A; SmithForm(A); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: A:=Matrix(2,2,(1,2,3,4 ^-------------------- *** expected character: '=' instead of: SmithForm(A); ^- Timing: real 0m0.279s user 0m0.012s sys 0m0.009s '80.119.' ************** PARI ***************** Host 80.119.114.123 (80.119.114.123) Time: Mon Aug 22 12:25:19 2005 Input: int(1/(1+x),x=0..32) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: int(1/(1+x),x=0..32) ^-------------------- Timing: real 0m0.020s user 0m0.011s sys 0m0.006s '84.176.' ************** PARI ***************** Host 84.176.250.197 (84.176.250.197) Time: Mon Aug 22 17:53:47 2005 Input: 00110010100101001001001001010001001001:11001001001001001001 Output: ? 11001001001001001001 ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.009s sys 0m0.010s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 22 18:31:03 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.097s user 0m0.040s sys 0m0.010s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 22 18:31:33 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.051s user 0m0.038s sys 0m0.010s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 22 18:31:45 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,3 3,11 11,41 ? Errors (if any) and Timing Info: Timing: real 0m0.070s user 0m0.041s sys 0m0.008s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 22 18:32:00 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2-1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 1,3 2,3 1,4 3,4 1,5 4,5 1,6 5,6 1,7 6,7 1,8 3,8 7,8 1,9 8,9 1,10 9,10 1,11 10,11 1,12 11,12 1,13 12,13 1,14 13,14 1,15 4,15 14,15 1,16 15,16 1,17 16,17 1,18 17,18 1,19 18,19 1,20 19,20 1,21 8,21 20,21 1,22 21,22 1,23 22,23 1,24 5,24 23,24 1,25 24,25 1,26 25,26 1,27 26,27 1,28 27,28 1,29 28,29 1,30 29,30 1,31 30,31 1,32 31,32 1,33 32,33 1,34 33,34 1,35 6,35 34,35 1,36 35,36 1,37 36,37 1,38 37,38 1,39 38,39 1,40 39,40 1,41 40,41 1,42 41,42 1,43 42,43 1,44 43,44 1,45 44,45 1,46 45,46 1,47 46,47 1,48 7,48 47,48 1,49 48,49 1,50 49,50 1,51 50,51 1,52 51,52 1,53 52,53 1,54 53,54 1,55 21,55 54,55 1,56 15,56 55,56 1,57 56,57 1,58 57,58 1,59 58,59 1,60 59,60 1,61 60,61 1,62 61,62 1,63 8,63 62,63 1,64 63,64 1,65 64,65 1,66 65,66 1,67 66,67 1,68 67,68 1,69 68,69 1,70 69,70 1,71 70,71 1,72 71,72 1,73 72,73 1,74 73,74 1,75 74,75 1,76 75,76 1,77 76,77 1,78 77,78 1,79 78,79 1,80 9,80 79,80 1,81 80,81 1,82 81,82 1,83 82,83 1,84 83,84 1,85 84,85 1,86 85,86 1,87 86,87 1,88 87,88 1,89 88,89 1,90 89,90 1,91 90,91 1,92 91,92 1,93 92,93 1,94 93,94 1,95 94,95 1,96 95,96 1,97 96,97 1,98 97,98 1,99 10,99 98,99 1,100 99,100 ? Errors (if any) and Timing Info: Timing: real 0m0.065s user 0m0.047s sys 0m0.005s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 22 18:32:43 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,3 3,11 11,41 ? Errors (if any) and Timing Info: Timing: real 0m0.056s user 0m0.041s sys 0m0.006s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 22 18:32:53 2005 Input: for(b=1,200, for(a=1,b, if( frac((a^2+b^2+2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,3 3,11 11,41 41,153 ? Errors (if any) and Timing Info: Timing: real 0m0.177s user 0m0.136s sys 0m0.008s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 22 18:33:17 2005 Input: for(b=1,200, for(a=1,b, if( frac((a^2+b^2+3)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 1,4 2,7 4,19 7,26 19,91 26,97 ? Errors (if any) and Timing Info: Timing: real 0m0.183s user 0m0.136s sys 0m0.008s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 22 18:34:12 2005 Input: for(b=1,200, for(a=1,b, if( frac((a^2+b^2)/(a*b-1))==0 , print(a,",",b), ) ) ) Output: ? ? Errors (if any) and Timing Info: *** division by zero in dvmdii Timing: real 0m0.037s user 0m0.007s sys 0m0.010s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 22 18:34:22 2005 Input: for(b=1,200, for(a=1,b, if( frac((a^2+b^2)/(a*b+1))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,8 3,27 8,30 4,64 30,112 5,125 ? Errors (if any) and Timing Info: Timing: real 0m0.172s user 0m0.137s sys 0m0.009s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 22 18:34:43 2005 Input: for(b=1,200, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 101,101 102,102 103,103 104,104 105,105 106,106 107,107 108,108 109,109 110,110 111,111 112,112 113,113 114,114 115,115 116,116 117,117 118,118 119,119 120,120 121,121 122,122 123,123 124,124 125,125 126,126 127,127 128,128 129,129 130,130 131,131 132,132 133,133 134,134 135,135 136,136 137,137 138,138 139,139 140,140 141,141 142,142 143,143 144,144 145,145 146,146 147,147 148,148 149,149 150,150 151,151 152,152 153,153 154,154 155,155 156,156 157,157 158,158 159,159 160,160 161,161 162,162 163,163 164,164 165,165 166,166 167,167 168,168 169,169 170,170 171,171 172,172 173,173 174,174 175,175 176,176 177,177 178,178 179,179 180,180 181,181 182,182 183,183 184,184 185,185 186,186 187,187 188,188 189,189 190,190 191,191 192,192 193,193 194,194 195,195 196,196 197,197 198,198 199,199 200,200 ? Errors (if any) and Timing Info: Timing: real 0m0.162s user 0m0.130s sys 0m0.007s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 22 18:35:02 2005 Input: for(b=1,200, for(a=1,b, if( frac((a^2+b^2)/(a*b+2))==0 , print(a,",",b), ) ) ) Output: ? 1,3 2,4 3,5 4,6 5,7 6,8 7,9 8,10 9,11 10,12 11,13 12,14 13,15 14,16 15,17 16,18 17,19 18,20 19,21 20,22 21,23 22,24 23,25 24,26 25,27 26,28 27,29 28,30 29,31 4,32 30,32 31,33 32,34 33,35 34,36 35,37 36,38 37,39 38,40 39,41 40,42 41,43 42,44 43,45 44,46 45,47 46,48 47,49 48,50 49,51 50,52 51,53 52,54 53,55 54,56 55,57 56,58 57,59 58,60 59,61 60,62 61,63 62,64 63,65 64,66 65,67 66,68 67,69 68,70 69,71 70,72 71,73 72,74 73,75 74,76 75,77 76,78 77,79 78,80 79,81 80,82 81,83 82,84 83,85 84,86 85,87 86,88 87,89 88,90 89,91 90,92 91,93 92,94 93,95 94,96 95,97 96,98 97,99 98,100 99,101 100,102 101,103 102,104 103,105 104,106 105,107 6,108 106,108 107,109 108,110 109,111 110,112 111,113 112,114 113,115 114,116 115,117 116,118 117,119 118,120 119,121 120,122 121,123 122,124 123,125 124,126 125,127 126,128 127,129 128,130 129,131 130,132 131,133 132,134 133,135 134,136 135,137 136,138 137,139 138,140 139,141 140,142 141,143 142,144 143,145 144,146 145,147 146,148 147,149 148,150 149,151 150,152 151,153 152,154 153,155 154,156 155,157 156,158 157,159 158,160 159,161 160,162 161,163 162,164 163,165 164,166 165,167 166,168 167,169 168,170 169,171 170,172 171,173 172,174 173,175 174,176 175,177 176,178 177,179 178,180 179,181 180,182 181,183 182,184 183,185 184,186 185,187 186,188 187,189 188,190 189,191 190,192 191,193 192,194 193,195 194,196 195,197 196,198 197,199 198,200 ? Errors (if any) and Timing Info: Timing: real 0m0.172s user 0m0.137s sys 0m0.009s '141.30.' ************** PARI ***************** Host 141.30.112.23 (141.30.112.23) Time: Tue Aug 23 06:47:43 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.342s user 0m0.006s sys 0m0.017s '200.177' ************** PARI ***************** Host 200.177.41.159 (200.177.41.159) Time: Tue Aug 23 12:35:04 2005 Input: x.^2 Output: ? ? Errors (if any) and Timing Info: *** unknown member function: x.^2 ^-- Timing: real 0m0.288s user 0m0.008s sys 0m0.015s '24.130.' ************** PARI ***************** Host 24.130.52.157 (24.130.52.157) Time: Wed Aug 24 07:35:24 2005 Input: 5-2 Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.271s user 0m0.010s sys 0m0.011s '62.45.1' ************** PARI ***************** Host 62.45.130.218 (62.45.130.218) Time: Wed Aug 24 15:23:38 2005 Input: 1C5A8CA77FF3000 Output: ? 1 ? Errors (if any) and Timing Info: *** Warning: unused characters: C5A8CA77FF3000. Timing: real 0m0.067s user 0m0.011s sys 0m0.006s '130.217' ************** PARI ***************** Host 130.217.76.77 (130.217.76.77) Time: Wed Aug 24 22:26:30 2005 Input: R := PolynomialRing(RationalField()); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: R:=PolynomialRing(Rat ^-------------------- Timing: real 0m0.096s user 0m0.011s sys 0m0.008s '130.217' ************** PARI ***************** Host 130.217.76.77 (130.217.76.77) Time: Wed Aug 24 22:26:46 2005 Input: R = PolynomialRing(RationalField()); Output: ? ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: R=PolynomialRing( *** RationalField()); ^----------------- Timing: real 0m0.021s user 0m0.011s sys 0m0.006s '130.217' ************** PARI ***************** Host 130.217.76.77 (130.217.76.77) Time: Wed Aug 24 22:26:57 2005 Input: R = PolynomialRing(RationalField()); Output: ? ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: R=PolynomialRing( *** RationalField()); ^----------------- Timing: real 0m0.020s user 0m0.008s sys 0m0.010s '130.217' ************** PARI ***************** Host 130.217.76.77 (130.217.76.77) Time: Wed Aug 24 22:27:42 2005 Input: a = 2 Output: ? 2 ? ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.012s sys 0m0.005s '130.217' ************** PARI ***************** Host 130.217.76.77 (130.217.76.77) Time: Wed Aug 24 22:28:38 2005 Input: a = 2; Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.008s sys 0m0.008s '24.185.' ************** PARI ***************** Host 24.185.19.204 (24.185.19.204) Time: Thu Aug 25 00:16:05 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.077s user 0m0.013s sys 0m0.005s '24.185.' ************** PARI ***************** Host 24.185.19.204 (24.185.19.204) Time: Thu Aug 25 00:16:22 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.012s sys 0m0.005s '210.136' ************** PARI ***************** Host 210.136.161.196 (210.136.161.196) Time: Thu Aug 25 10:30:45 2005 Input: prime(500) Output: ? 3571 ? Errors (if any) and Timing Info: Timing: real 0m0.252s user 0m0.007s sys 0m0.014s '24.163.' ************** PARI ***************** Host 24.163.228.78 (24.163.228.78) Time: Thu Aug 25 14:51:18 2005 Input: prime(1001) Output: ? 7927 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '70.171.' ************** PARI ***************** Host 70.171.5.123 (70.171.5.123) Time: Thu Aug 25 14:52:18 2005 Input: prime(1001) Output: ? 7927 ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.011s sys 0m0.006s '70.171.' ************** PARI ***************** Host 70.171.5.123 (70.171.5.123) Time: Thu Aug 25 14:52:30 2005 Input: prime(10010987) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.031s user 0m0.009s sys 0m0.008s '70.171.' ************** PARI ***************** Host 70.171.5.123 (70.171.5.123) Time: Thu Aug 25 14:52:37 2005 Input: prime(10010) Output: ? 104831 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.006s sys 0m0.010s '70.171.' ************** PARI ***************** Host 70.171.5.123 (70.171.5.123) Time: Thu Aug 25 14:52:46 2005 Input: 2^3452345234523452345 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8.0 Mbytes [hint] you can increase GP stack with allocatemem() Timing: real 0m0.031s user 0m0.009s sys 0m0.008s '67.171.' ************** PARI ***************** Host 67.171.38.11 (67.171.38.11) Time: Thu Aug 25 14:53:06 2005 Input: 1001 Output: ? 1001 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '67.171.' ************** PARI ***************** Host 67.171.38.11 (67.171.38.11) Time: Thu Aug 25 14:53:17 2005 Input: prime(1001) Output: ? 7927 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.013s sys 0m0.004s '67.171.' ************** PARI ***************** Host 67.171.38.11 (67.171.38.11) Time: Thu Aug 25 14:53:26 2005 Input: prime(10001) Output: ? 104743 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.010s sys 0m0.006s '67.171.' ************** PARI ***************** Host 67.171.38.11 (67.171.38.11) Time: Thu Aug 25 14:55:38 2005 Input: prime(100001) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.029s user 0m0.013s sys 0m0.004s '69.248.' ************** PARI ***************** Host 69.248.83.208 (69.248.83.208) Time: Thu Aug 25 14:56:29 2005 Input: 1001 Output: ? 1001 ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.012s sys 0m0.005s '82.64.2' ************** PARI ***************** Host 82.64.233.192 (82.64.233.192) Time: Fri Aug 26 10:23:15 2005 Input: 71721075 Output: ? 71721075 ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.008s sys 0m0.009s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Fri Aug 26 13:13:23 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.102s user 0m0.044s sys 0m0.007s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Fri Aug 26 13:18:53 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Errors (if any) and Timing Info: Timing: real 0m0.063s user 0m0.041s sys 0m0.007s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Fri Aug 26 13:19:16 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Errors (if any) and Timing Info: Timing: real 0m0.069s user 0m0.037s sys 0m0.012s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Fri Aug 26 14:34:01 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Errors (if any) and Timing Info: Timing: real 0m0.058s user 0m0.039s sys 0m0.009s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Fri Aug 26 18:44:06 2005 Input: frac(2^8/3) Output: ? 1/3 ? Errors (if any) and Timing Info: Timing: real 0m0.064s user 0m0.010s sys 0m0.009s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Fri Aug 26 18:44:26 2005 Input: frac(2^8/3) Output: ? 1/3 ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.010s sys 0m0.007s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Fri Aug 26 18:44:40 2005 Input: round(2^8/3) Output: ? 85 ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.010s sys 0m0.007s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Fri Aug 26 18:45:14 2005 Input: round(2^6/3),round(2^7/3),round(2^8/3) Output: ? 21 ? Errors (if any) and Timing Info: *** Warning: unused characters: ,round(2^7/3),round(2^8/3). Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Fri Aug 26 18:45:34 2005 Input: round(2^6/3) ; round(2^7/3); round(2^8/3) Output: ? 85 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.007s sys 0m0.010s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Fri Aug 26 18:45:48 2005 Input: round(2^6/3) round(2^7/3) round(2^8/3) Output: ? 21 ? 43 ? 85 ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.008s sys 0m0.009s '84.11.7' ************** PARI ***************** Host 84.11.75.132 (84.11.75.132) Time: Sat Aug 27 04:34:16 2005 Input: 127 Output: ? 127 ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.010s sys 0m0.006s '84.129.' ************** PARI ***************** Host 84.129.226.219 (84.129.226.219) Time: Sat Aug 27 11:09:13 2005 Input: prime(2^16+1) Output: ? ? Errors (if any) and Timing Info: *** not enough precalculated primes Timing: real 0m0.277s user 0m0.010s sys 0m0.015s '84.129.' ************** PARI ***************** Host 84.129.226.219 (84.129.226.219) Time: Sat Aug 27 11:10:18 2005 Input: factor(2^16+1) Output: ? [65537 1] ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.011s sys 0m0.007s '84.129.' ************** PARI ***************** Host 84.129.226.219 (84.129.226.219) Time: Sat Aug 27 11:10:40 2005 Input: factor(2^32+1) Output: ? [641 1] [6700417 1] ? Errors (if any) and Timing Info: Timing: real 0m0.038s user 0m0.009s sys 0m0.008s '84.129.' ************** PARI ***************** Host 84.129.226.219 (84.129.226.219) Time: Sat Aug 27 11:11:13 2005 Input: factor(2^64+1) Output: ? [274177 1] [67280421310721 1] ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.012s sys 0m0.007s '84.129.' ************** PARI ***************** Host 84.129.226.219 (84.129.226.219) Time: Sat Aug 27 11:11:38 2005 Input: factor(2^31-1) Output: ? [2147483647 1] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '84.129.' ************** PARI ***************** Host 84.129.226.219 (84.129.226.219) Time: Sat Aug 27 11:12:01 2005 Input: factor(7090581) Output: ? [3 1] [17 1] [41 1] [3391 1] ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.009s sys 0m0.008s '67.81.1' ************** PARI ***************** Host 67.81.165.240 (67.81.165.240) Time: Sat Aug 27 22:14:20 2005 Input: 1 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.008s sys 0m0.008s '68.12.2' ************** PARI ***************** Host 68.12.245.48 (68.12.245.48) Time: Sun Aug 28 06:12:30 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Errors (if any) and Timing Info: Timing: real 0m0.116s user 0m0.042s sys 0m0.010s '81.221.' ************** PARI ***************** Host 81.221.159.34 (81.221.159.34) Time: Sun Aug 28 06:14:52 2005 Input: e:=ellinit([0,0,1,-7,6]); ellglobalred(e) ellap(e,5) Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: e:=ellinit([0,0,1,-7,6 ^-------------------- *** bad argument for an elliptic curve related function *** bad argument for an elliptic curve related function Timing: real 0m0.069s user 0m0.009s sys 0m0.008s '81.221.' ************** PARI ***************** Host 81.221.159.34 (81.221.159.34) Time: Sun Aug 28 06:15:19 2005 Input: e:=ellinit([0,0,1,-7,6]); ellglobalred(e) ellap(e,5) Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: e:=ellinit([0,0,1,-7,6 ^-------------------- *** bad argument for an elliptic curve related function *** bad argument for an elliptic curve related function Timing: real 0m0.021s user 0m0.005s sys 0m0.011s '81.221.' ************** PARI ***************** Host 81.221.159.34 (81.221.159.34) Time: Sun Aug 28 06:16:50 2005 Input: e:=ellinit([0,0,1,-7,6]); ellglobalred(e) ellap(e,5) Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: e:=ellinit([0,0,1,-7,6 ^-------------------- *** bad argument for an elliptic curve related function *** bad argument for an elliptic curve related function Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '81.221.' ************** PARI ***************** Host 81.221.159.34 (81.221.159.34) Time: Sun Aug 28 06:17:09 2005 Input: e=ellinit([0,0,1,-7,6]); ellglobalred(e) ellap(e,5) Output: ? ? [5077, [1, 0, 0, 0], 1] ? -4 ? Errors (if any) and Timing Info: Timing: real 0m0.113s user 0m0.011s sys 0m0.011s '213.185' ************** PARI ***************** Host 213.185.37.138 (213.185.37.138) Time: Sun Aug 28 08:48:28 2005 Input: real x; integrate(x,x) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: integrate(x,x) ^ Timing: real 0m0.291s user 0m0.013s sys 0m0.007s '68.101.' ************** PARI ***************** Host 68.101.205.133 (68.101.205.133) Time: Sun Aug 28 19:28:46 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.843s user 0m0.039s sys 0m0.021s '68.101.' ************** PARI ***************** Host 68.101.205.133 (68.101.205.133) Time: Sun Aug 28 19:28:53 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.172s user 0m0.041s sys 0m0.009s '137.111' ************** PARI ***************** Host 137.111.216.17 (137.111.216.17) Time: Mon Aug 29 02:45:23 2005 Input: lcm(30,25) Output: ? 150 ? Errors (if any) and Timing Info: Timing: real 0m0.048s user 0m0.011s sys 0m0.005s '137.111' ************** PARI ***************** Host 137.111.216.17 (137.111.216.17) Time: Mon Aug 29 02:45:39 2005 Input: lcm(30,25)/60 Output: ? 5/2 ? Errors (if any) and Timing Info: Timing: real 0m0.033s user 0m0.010s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.216.17 (137.111.216.17) Time: Mon Aug 29 02:46:06 2005 Input: (lcm(lcm(30,25),35)/60 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (lcm(lcm(30,25),35)/60 ^ Timing: real 0m0.020s user 0m0.007s sys 0m0.009s '137.111' ************** PARI ***************** Host 137.111.216.17 (137.111.216.17) Time: Mon Aug 29 02:46:13 2005 Input: (lcm(lcm(30,25),35))/60 Output: ? 35/2 ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.010s sys 0m0.007s '137.111' ************** PARI ***************** Host 137.111.216.17 (137.111.216.17) Time: Mon Aug 29 02:47:12 2005 Input: (lcm(lcm(30*2,25*2),35*2))/60 Output: ? 35 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.010s sys 0m0.007s '82.229.' ************** PARI ***************** Host 82.229.112.58 (82.229.112.58) Time: Mon Aug 29 09:48:20 2005 Input: factor(1968189198) Output: ? [2 1] [3 1] [328031533 1] ? Errors (if any) and Timing Info: Timing: real 0m0.315s user 0m0.012s sys 0m0.009s '82.229.' ************** PARI ***************** Host 82.229.112.58 (82.229.112.58) Time: Mon Aug 29 09:48:32 2005 Input: factor(19681891961694196849849849849649967) Output: ? [3 1] [47341261559 1] [233387348651 1] [593783946121 1] ? Errors (if any) and Timing Info: Timing: real 0m0.209s user 0m0.107s sys 0m0.021s '82.229.' ************** PARI ***************** Host 82.229.112.58 (82.229.112.58) Time: Mon Aug 29 09:48:40 2005 Input: factor(19681891961694196849849849849649967) Output: ? [3 1] [47341261559 1] [233387348651 1] [593783946121 1] ? Errors (if any) and Timing Info: Timing: real 0m0.166s user 0m0.106s sys 0m0.020s '82.229.' ************** PARI ***************** Host 82.229.112.58 (82.229.112.58) Time: Mon Aug 29 09:48:45 2005 Input: factor(19681891961694196849849847748637863789849649967) Output: ? [449 1] [82699 1] [42668761 1] [117164912903 1] [106026063723380724899 1] ? Errors (if any) and Timing Info: Timing: real 0m0.155s user 0m0.097s sys 0m0.023s '82.229.' ************** PARI ***************** Host 82.229.112.58 (82.229.112.58) Time: Mon Aug 29 09:48:50 2005 Input: factor(1968189196169419684984984774863786378984783678678637869649967) Output: ? [15103903 1] [49120308871 1] [2652873653747151238252948075848658581477959 1] ? Errors (if any) and Timing Info: Timing: real 0m0.918s user 0m0.760s sys 0m0.012s '82.229.' ************** PARI ***************** Host 82.229.112.58 (82.229.112.58) Time: Mon Aug 29 09:49:00 2005 Input: factor(1968189196169419684984984774863786378984783678678637869649967) Output: ? [15103903 1] [49120308871 1] [2652873653747151238252948075848658581477959 1] ? Errors (if any) and Timing Info: Timing: real 0m0.927s user 0m0.760s sys 0m0.008s '82.229.' ************** PARI ***************** Host 82.229.112.58 (82.229.112.58) Time: Mon Aug 29 09:49:35 2005 Input: factor(1968189196169419684984984774863786378984783678645637867867878637869649967) Output: ? [41 1] [19919 1] [239190114311 1] [54825353909702331965410901 1] [183776842266758882945431288643 1] ? Errors (if any) and Timing Info: Timing: real 0m30.612s user 0m20.707s sys 0m0.148s '82.229.' ************** PARI ***************** Host 82.229.112.58 (82.229.112.58) Time: Mon Aug 29 09:50:05 2005 Input: factor(1968189196169419684984984774863786378984783678645637867867) Output: ? [19 1] [173 1] [24203 1] [295353857 1] [83763591858438271676446532584975041044471 1] ? Errors (if any) and Timing Info: Timing: real 0m0.177s user 0m0.138s sys 0m0.008s '82.229.' ************** PARI ***************** Host 82.229.112.58 (82.229.112.58) Time: Mon Aug 29 09:50:09 2005 Input: factor(1968189196169419684984984774863786378984783678645637867867) Output: ? [19 1] [173 1] [24203 1] [295353857 1] [83763591858438271676446532584975041044471 1] ? Errors (if any) and Timing Info: Timing: real 0m0.183s user 0m0.139s sys 0m0.008s '82.229.' ************** PARI ***************** Host 82.229.112.58 (82.229.112.58) Time: Mon Aug 29 09:50:16 2005 Input: factor(19681891961694196849849847748637863789847836786456378678456367) Output: ? [67 1] [3617 1] [5645779 1] [14385324336162066929054893122015128816974019972807 1] ? Errors (if any) and Timing Info: Timing: real 0m0.064s user 0m0.049s sys 0m0.008s '82.229.' ************** PARI ***************** Host 82.229.112.58 (82.229.112.58) Time: Mon Aug 29 09:50:22 2005 Input: factor(19681891961694196849849847748637863789847836786456378786378678456367) Output: ? [19 1] [53 1] [61 1] [1621 1] [1889 1] [14229773 1] [7353508404677550468428518064782885418599590623333 1] ? Errors (if any) and Timing Info: Timing: real 0m0.056s user 0m0.035s sys 0m0.010s '82.229.' ************** PARI ***************** Host 82.229.112.58 (82.229.112.58) Time: Mon Aug 29 09:50:55 2005 Input: factor(196818919616941968498498477486378637898478367864563787863786784563671) Output: ? [199 1] [81551714423 1] [4635966266653 1] [2616016051958815934347732741162094729989891 1] ? Errors (if any) and Timing Info: Timing: real 0m24.965s user 0m17.795s sys 0m0.114s '82.229.' ************** PARI ***************** Host 82.229.112.58 (82.229.112.58) Time: Mon Aug 29 09:51:17 2005 Input: factor(1968189196169419684984984774863786378984783678645787863786784563671) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 10528 Killed /usr/bin/gp -q -emacs Timing: real 0m29.918s user 0m20.981s sys 0m0.021s '82.229.' ************** PARI ***************** Host 82.229.112.58 (82.229.112.58) Time: Mon Aug 29 09:52:03 2005 Input: factor(196818919616941968498498477486378637898478367864578786376784563671) Output: ? [3 4] [2417 1] [1005321971513211299072406245301432946150356619340263597750423 1] ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.020s sys 0m0.010s '82.229.' ************** PARI ***************** Host 82.229.112.58 (82.229.112.58) Time: Mon Aug 29 09:52:09 2005 Input: factor(1968189196169419684984984774863786378984718367864578786376784563671) Output: ? [257 1] [3242363 1] [2664989959 1] [4615958390207 1] [192005921670089197310805334626141437 1] ? Errors (if any) and Timing Info: Timing: real 0m0.696s user 0m0.571s sys 0m0.010s '82.229.' ************** PARI ***************** Host 82.229.112.58 (82.229.112.58) Time: Mon Aug 29 09:53:15 2005 Input: factor(19681891961694196849849847748637863789847183678645787863767845636721) Output: ? [3 1] [23819 1] [26521483899019 1] [2534019507415153 1] [4098399510529986143471764828323779 1] ? Errors (if any) and Timing Info: Timing: real 0m9.680s user 0m8.012s sys 0m0.071s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 29 13:09:14 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Errors (if any) and Timing Info: Timing: real 0m0.084s user 0m0.045s sys 0m0.005s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 29 14:49:09 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Errors (if any) and Timing Info: Timing: real 0m0.052s user 0m0.040s sys 0m0.008s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 29 14:49:25 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.069s user 0m0.039s sys 0m0.010s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 29 14:49:37 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b+1))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,8 3,27 8,30 4,64 ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.042s sys 0m0.006s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 29 14:50:02 2005 Input: for(b=1,400, for(a=1,b, if( frac((a^2+b^2)/(a*b+1))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,8 3,27 8,30 4,64 30,112 5,125 6,216 27,240 7,343 ? Errors (if any) and Timing Info: Timing: real 0m0.641s user 0m0.530s sys 0m0.006s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 29 14:50:45 2005 Input: for(b=1,400, for(a=1,b, if( frac((a^2+b^2)/(a*b+2))==0 , print(a,",",b), ) ) ) Output: ? 1,3 2,4 3,5 4,6 5,7 6,8 7,9 8,10 9,11 10,12 11,13 12,14 13,15 14,16 15,17 16,18 17,19 18,20 19,21 20,22 21,23 22,24 23,25 24,26 25,27 26,28 27,29 28,30 29,31 4,32 30,32 31,33 32,34 33,35 34,36 35,37 36,38 37,39 38,40 39,41 40,42 41,43 42,44 43,45 44,46 45,47 46,48 47,49 48,50 49,51 50,52 51,53 52,54 53,55 54,56 55,57 56,58 57,59 58,60 59,61 60,62 61,63 62,64 63,65 64,66 65,67 66,68 67,69 68,70 69,71 70,72 71,73 72,74 73,75 74,76 75,77 76,78 77,79 78,80 79,81 80,82 81,83 82,84 83,85 84,86 85,87 86,88 87,89 88,90 89,91 90,92 91,93 92,94 93,95 94,96 95,97 96,98 97,99 98,100 99,101 100,102 101,103 102,104 103,105 104,106 105,107 6,108 106,108 107,109 108,110 109,111 110,112 111,113 112,114 113,115 114,116 115,117 116,118 117,119 118,120 119,121 120,122 121,123 122,124 123,125 124,126 125,127 126,128 127,129 128,130 129,131 130,132 131,133 132,134 133,135 134,136 135,137 136,138 137,139 138,140 139,141 140,142 141,143 142,144 143,145 144,146 145,147 146,148 147,149 148,150 149,151 150,152 151,153 152,154 153,155 154,156 155,157 156,158 157,159 158,160 159,161 160,162 161,163 162,164 163,165 164,166 165,167 166,168 167,169 168,170 169,171 170,172 171,173 172,174 173,175 174,176 175,177 176,178 177,179 178,180 179,181 180,182 181,183 182,184 183,185 184,186 185,187 186,188 187,189 188,190 189,191 190,192 191,193 192,194 193,195 194,196 195,197 196,198 197,199 198,200 199,201 200,202 201,203 202,204 203,205 204,206 205,207 206,208 207,209 208,210 209,211 210,212 211,213 212,214 213,215 214,216 215,217 216,218 217,219 218,220 219,221 220,222 221,223 222,224 223,225 224,226 225,227 226,228 227,229 228,230 229,231 230,232 231,233 232,234 233,235 234,236 235,237 236,238 237,239 238,240 239,241 240,242 241,243 242,244 243,245 244,246 245,247 246,248 247,249 248,250 249,251 32,252 250,252 251,253 252,254 253,255 8,256 254,256 255,257 256,258 257,259 258,260 259,261 260,262 261,263 262,264 263,265 264,266 265,267 266,268 267,269 268,270 269,271 270,272 271,273 272,274 273,275 274,276 275,277 276,278 277,279 278,280 279,281 280,282 281,283 282,284 283,285 284,286 285,287 286,288 287,289 288,290 289,291 290,292 291,293 292,294 293,295 294,296 295,297 296,298 297,299 298,300 299,301 300,302 301,303 302,304 303,305 304,306 305,307 306,308 307,309 308,310 309,311 310,312 311,313 312,314 313,315 314,316 315,317 316,318 317,319 318,320 319,321 320,322 321,323 322,324 323,325 324,326 325,327 326,328 327,329 328,330 329,331 330,332 331,333 332,334 333,335 334,336 335,337 336,338 337,339 338,340 339,341 340,342 341,343 342,344 343,345 344,346 345,347 346,348 347,349 348,350 349,351 350,352 351,353 352,354 353,355 354,356 355,357 356,358 357,359 358,360 359,361 360,362 361,363 362,364 363,365 364,366 365,367 366,368 367,369 368,370 369,371 370,372 371,373 372,374 373,375 374,376 375,377 376,378 377,379 378,380 379,381 380,382 381,383 382,384 383,385 384,386 385,387 386,388 387,389 388,390 389,391 390,392 391,393 392,394 393,395 394,396 395,397 396,398 397,399 398,400 ? Errors (if any) and Timing Info: Timing: real 0m0.652s user 0m0.535s sys 0m0.009s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 29 14:51:11 2005 Input: for(b=1,400, for(a=1,b, if( frac((a^2+b^2)/(a*b+3))==0 , print(a,",",b), ) ) ) Output: ? 1,2 1,7 3,9 2,11 9,24 7,34 11,53 24,63 6,72 34,163 63,165 9,243 53,254 ? Errors (if any) and Timing Info: Timing: real 0m1.412s user 0m0.521s sys 0m0.007s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 29 14:51:37 2005 Input: for(b=1,400, for(a=1,b, if( frac((a^2+b^2+2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,3 3,11 11,41 41,153 ? Errors (if any) and Timing Info: Timing: real 0m0.650s user 0m0.532s sys 0m0.008s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Mon Aug 29 14:52:07 2005 Input: for(b=1,1000, for(a=1,b, if( frac((a^2+b^2+2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,3 3,11 11,41 41,153 153,571 ? Errors (if any) and Timing Info: Timing: real 0m3.982s user 0m3.314s sys 0m0.006s '139.78.' ************** PARI ***************** Host 139.78.112.126 (139.78.112.126) Time: Mon Aug 29 15:28:10 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Errors (if any) and Timing Info: Timing: real 0m0.060s user 0m0.039s sys 0m0.008s '152.6.1' ************** PARI ***************** Host 152.6.18.163 (152.6.18.163) Time: Tue Aug 30 16:24:21 2005 Input: GCD(12345645645645645645645674564564567,12456456456456123123123745645645645677777); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: GCD(1234564564564564 ^-------------------- Timing: real 0m0.048s user 0m0.010s sys 0m0.006s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Tue Aug 30 18:06:16 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Errors (if any) and Timing Info: Timing: real 0m0.108s user 0m0.043s sys 0m0.006s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Tue Aug 30 18:06:37 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Errors (if any) and Timing Info: Timing: real 0m0.053s user 0m0.037s sys 0m0.012s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Tue Aug 30 18:06:54 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b+7))==0 , print(a,",",b), ) ) ) Output: ? 1,3 2,3 1,18 2,29 3,41 1,43 7,49 5,66 ? Errors (if any) and Timing Info: Timing: real 0m0.052s user 0m0.040s sys 0m0.008s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Tue Aug 30 18:07:27 2005 Input: for(b=1,400, for(a=1,b, if( frac((a^2+b^2)/(a*b+7))==0 , print(a,",",b), ) ) ) Output: ? 1,3 2,3 1,18 2,29 3,41 1,43 7,49 5,66 6,223 18,233 49,336 29,375 14,392 ? Errors (if any) and Timing Info: Timing: real 0m0.644s user 0m0.523s sys 0m0.007s '139.78.' ************** PARI ***************** Host 139.78.112.146 (139.78.112.146) Time: Tue Aug 30 18:08:13 2005 Input: for(b=1,400, for(a=1,b, if( frac((a^2+b^2)/(a*b+1))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,8 3,27 8,30 4,64 30,112 5,125 6,216 27,240 7,343 ? Errors (if any) and Timing Info: Timing: real 0m0.658s user 0m0.532s sys 0m0.006s '137.111' ************** PARI ***************** Host 137.111.216.17 (137.111.216.17) Time: Tue Aug 30 21:30:52 2005 Input: 2^31 Output: ? 2147483648 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '134.10.' ************** PARI ***************** Host 134.10.176.122 (134.10.176.122) Time: Tue Aug 30 23:57:08 2005 Input: 555555^5 Output: ? 52921884791126860213551721875 ? Errors (if any) and Timing Info: Timing: real 0m0.109s user 0m0.009s sys 0m0.008s '134.10.' ************** PARI ***************** Host 134.10.176.122 (134.10.176.122) Time: Tue Aug 30 23:57:24 2005 Input: 555555^555555 Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 29577 Killed /usr/bin/gp -q -emacs Timing: real 0m26.877s user 0m20.973s sys 0m0.029s '68.100.' ************** PARI ***************** Host 68.100.7.105 (68.100.7.105) Time: Wed Aug 31 00:19:08 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: ? ? [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.070s user 0m0.007s sys 0m0.011s '82.225.' ************** PARI ***************** Host 82.225.209.38 (82.225.209.38) Time: Wed Aug 31 09:10:41 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.236s user 0m0.010s sys 0m0.013s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Thu Sep 1 02:02:19 2005 Input: for (b=1,100, for (a=1,b, if (frac(360(b-a)/ab)==0, print (a,",",b),) ) ) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...100,for(a=1,b,if(frac(360 *** (b-a)/ab)==0,print(a ^-------------------- Timing: real 0m0.310s user 0m0.013s sys 0m0.014s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Thu Sep 1 02:02:55 2005 Input: for (b=1,100, for (a=1,b, if (frac(360(b-a)/ab)==0, print (a,",",b),) ) ) Output: ? ? ? ? a,b ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: for(b=1,100, ^ *** expected character: ')' instead of: for(a=1,b, ^ *** expected character: ')' instead of: if(frac(360(b-a)/ab)==0, ^------------- *** Warning: unused characters: ,). *** Warning: unused characters: ). *** Warning: unused characters: ). Timing: real 0m0.033s user 0m0.012s sys 0m0.006s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Thu Sep 1 02:03:12 2005 Input: for (b=1,100, for (a=1,b, if (frac(360(b-a)/ab)==0, print (a,",",b),) ) ) Output: ? ? ? ? a,b ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: for(b=1,100, ^ *** expected character: ')' instead of: for(a=1,b, ^ *** expected character: ')' instead of: if(frac(360(b-a)/ab)==0, ^------------- *** Warning: unused characters: ,). *** Warning: unused characters: ). *** Warning: unused characters: ). Timing: real 0m0.036s user 0m0.010s sys 0m0.007s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Thu Sep 1 02:04:38 2005 Input: for(b=1,100, for(a=1,b, if (frac(360(b-a)/ab)==0, print (a,",",b);) ); ); Output: ? ? ? ? a,b ? ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: for(b=1,100, ^ *** expected character: ')' instead of: for(a=1,b, ^ *** expected character: ')' instead of: if(frac(360(b-a)/ab)==0, ^------------- *** Warning: unused characters: ). *** Warning: unused characters: );. *** Warning: unused characters: );. Timing: real 0m0.019s user 0m0.008s sys 0m0.010s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Thu Sep 1 02:05:06 2005 Input: for(b=1,100,for(a=1,b,if (frac(360(b-a)/ab)==0,print (a,",",b)))) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...100,for(a=1,b,if(frac(360 *** (b-a)/ab)==0,print(a ^-------------------- Timing: real 0m0.034s user 0m0.007s sys 0m0.011s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Thu Sep 1 02:05:12 2005 Input: for(b=1,100,for(a=1,b,if (frac(360(b-a)/ab)==0,print (a,",",b)))) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...100,for(a=1,b,if(frac(360 *** (b-a)/ab)==0,print(a ^-------------------- Timing: real 0m0.031s user 0m0.012s sys 0m0.005s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Thu Sep 1 02:06:13 2005 Input: for(b=1,100, for(a=1,b, if (frac(360(b-a)/ab)==0, print (a,",",b),) ) ) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...100,for(a=1,b,if(frac(360 *** (b-a)/ab)==0,print(a ^-------------------- Timing: real 0m0.026s user 0m0.011s sys 0m0.006s '129.105' ************** PARI ***************** Host 129.105.81.56 (129.105.81.56) Time: Thu Sep 1 12:49:48 2005 Input: Q:=RationalField(); Output: ? ? Errors (if any) and Timing Info: *** unexpected character: Q:=RationalField(); ^----------------- Timing: real 0m0.325s user 0m0.010s sys 0m0.010s '218.228' ************** PARI ***************** Host 218.228.222.14 (218.228.222.14) Time: Thu Sep 1 14:20:09 2005 Input: ?5 Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Errors (if any) and Timing Info: Timing: real 0m0.260s user 0m0.011s sys 0m0.012s '218.228' ************** PARI ***************** Host 218.228.222.14 (218.228.222.14) Time: Thu Sep 1 14:21:22 2005 Input: ?5 Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.007s sys 0m0.010s '218.228' ************** PARI ***************** Host 218.228.222.14 (218.228.222.14) Time: Thu Sep 1 14:21:34 2005 Input: ?ellisoncurve Output: ? ellisoncurve(e,x): true(1) if x is on elliptic curve e, false(0) if not. ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.009s sys 0m0.009s '218.228' ************** PARI ***************** Host 218.228.222.14 (218.228.222.14) Time: Thu Sep 1 14:21:50 2005 Input: ?5 Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Errors (if any) and Timing Info: Timing: real 0m0.228s user 0m0.006s sys 0m0.010s '218.228' ************** PARI ***************** Host 218.228.222.14 (218.228.222.14) Time: Thu Sep 1 14:22:05 2005 Input: ?5 ?ellzeta Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? ellzeta(om,z): om=[om1,om2], value of the Weierstrass zeta function of the lattice generated by om at z. ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.010s sys 0m0.007s '218.228' ************** PARI ***************** Host 218.228.222.14 (218.228.222.14) Time: Thu Sep 1 14:22:51 2005 Input: ?5 ?ellak Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? ellak(e,n): computes the n-th Fourier coefficient of the L-function of the elliptic curve e. ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.010s sys 0m0.007s '218.228' ************** PARI ***************** Host 218.228.222.14 (218.228.222.14) Time: Thu Sep 1 14:23:13 2005 Input: ?5 ?ellinit Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6], gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. ? Errors (if any) and Timing Info: Timing: real 0m0.062s user 0m0.011s sys 0m0.007s '218.228' ************** PARI ***************** Host 218.228.222.14 (218.228.222.14) Time: Thu Sep 1 14:24:30 2005 Input: ?5 ?ellan Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? ellan(e,n): computes the first n Fourier coefficients of the L-function of the elliptic curve e (n<2^24 on a 32-bit machine). ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.012s sys 0m0.005s '218.228' ************** PARI ***************** Host 218.228.222.14 (218.228.222.14) Time: Thu Sep 1 14:25:01 2005 Input: ?5 ?ellbil Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? ellbil(e,z1,z2): canonical bilinear form for the points z1,z2 on the elliptic curve e. Either z1 or z2 can also be a vector/matrix of points. ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '218.228' ************** PARI ***************** Host 218.228.222.14 (218.228.222.14) Time: Thu Sep 1 14:25:19 2005 Input: ?5 ?ellwp Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? ellwp(e,{z=x},{flag=0}): Complex value of Weierstrass P function at z on the lattice generated over Z by e=[om1,om2] (e as given by ellinit is also accepted). Optional flag means 0 (default), compute only P(z), 1 compute [P(z),P'(z)], 2 consider om as an elliptic curve and compute P(z) for that curve (identical to ellztopoint in that case). If z is omitted or is a simple variable, return formal expansion in z. ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.010s sys 0m0.007s '139.78.' ************** PARI ***************** Host 139.78.10.104 (139.78.10.104) Time: Thu Sep 1 15:08:47 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Errors (if any) and Timing Info: Timing: real 0m0.151s user 0m0.037s sys 0m0.013s '139.78.' ************** PARI ***************** Host 139.78.10.104 (139.78.10.104) Time: Thu Sep 1 15:08:55 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Errors (if any) and Timing Info: Timing: real 0m0.071s user 0m0.039s sys 0m0.011s '62.82.2' ************** PARI ***************** Host 62.82.250.148 (62.82.250.148) Time: Thu Sep 1 19:04:12 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.303s user 0m0.007s sys 0m0.017s '62.82.2' ************** PARI ***************** Host 62.82.250.148 (62.82.250.148) Time: Thu Sep 1 19:04:22 2005 Input: 1 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.010s sys 0m0.007s '62.82.2' ************** PARI ***************** Host 62.82.250.148 (62.82.250.148) Time: Thu Sep 1 19:04:32 2005 Input: true Output: ? true ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.010s sys 0m0.007s '62.82.2' ************** PARI ***************** Host 62.82.250.148 (62.82.250.148) Time: Thu Sep 1 19:04:45 2005 Input: x = 5 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.007s sys 0m0.010s '68.9.18' ************** PARI ***************** Host 68.9.180.75 (68.9.180.75) Time: Thu Sep 1 23:15:05 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.312s user 0m0.010s sys 0m0.008s '68.9.18' ************** PARI ***************** Host 68.9.180.75 (68.9.180.75) Time: Thu Sep 1 23:15:24 2005 Input: 137*137 Output: ? 18769 ? Errors (if any) and Timing Info: Timing: real 0m0.050s user 0m0.010s sys 0m0.008s '85.68.1' ************** PARI ***************** Host 85.68.185.41 (85.68.185.41) Time: Fri Sep 2 09:07:07 2005 Input: > 2+4; Output: ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: > ^- Timing: real 0m0.331s user 0m0.011s sys 0m0.011s '139.78.' ************** PARI ***************** Host 139.78.39.131 (139.78.39.131) Time: Fri Sep 2 11:28:51 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.225s user 0m0.044s sys 0m0.006s '139.78.' ************** PARI ***************** Host 139.78.39.131 (139.78.39.131) Time: Fri Sep 2 11:29:12 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.068s user 0m0.043s sys 0m0.006s '139.78.' ************** PARI ***************** Host 139.78.39.131 (139.78.39.131) Time: Fri Sep 2 11:30:03 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.074s user 0m0.041s sys 0m0.009s '137.43.' ************** PARI ***************** Host 137.43.122.87 (137.43.122.87) Time: Fri Sep 2 12:34:31 2005 Input: f(n,k)= { round((1/round(factorial(k),&e))*sum(i=0,k-1,((-1)^i) *binomial(k,i)*(k-i)^n),&e); } m(n,x)= { sum(k=0,n,((-1)^k)*f(n,n-k)*x^(2*n-2*k-2)); } find(d,l)= { for(j=d,d+l, if(polisirreducible(m(j,x))==0, print(m(j,x)","j), next ) ); } find(2,200) Output: ? ? ? ? ? ? ? ? x^2 - 1,2 x^4 - 3*x^2 + 1,3 Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 32192 Killed /usr/bin/gp -q -emacs Timing: real 0m27.088s user 0m20.935s sys 0m0.068s '139.78.' ************** PARI ***************** Host 139.78.115.143 (139.78.115.143) Time: Fri Sep 2 13:27:52 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Errors (if any) and Timing Info: Timing: real 0m0.153s user 0m0.045s sys 0m0.006s '128.111' ************** PARI ***************** Host 128.111.88.139 (128.111.88.139) Time: Fri Sep 2 15:45:43 2005 Input: quadclassunit(-143947) Output: ? [57, [57], [Qfb(29, 3, 1241)], 1, 1.004244064350438656] ? Errors (if any) and Timing Info: Timing: real 0m0.209s user 0m0.014s sys 0m0.013s '81.178.' ************** PARI ***************** Host 81.178.114.159 (81.178.114.159) Time: Fri Sep 2 17:17:00 2005 Input: (x+1)^20 Output: ? x^20 + 20*x^19 + 190*x^18 + 1140*x^17 + 4845*x^16 + 15504*x^15 + 38760*x^14 + 77520*x^13 + 125970*x^12 + 167960*x^11 + 184756*x^10 + 167960*x^9 + 125970*x^8 + 77520*x^7 + 38760*x^6 + 15504*x^5 + 4845*x^4 + 1140*x^3 + 190*x^2 + 20*x + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.148s user 0m0.011s sys 0m0.007s '81.178.' ************** PARI ***************** Host 81.178.114.159 (81.178.114.159) Time: Fri Sep 2 17:17:33 2005 Input: (x+1)^20 Output: ? x^20 + 20*x^19 + 190*x^18 + 1140*x^17 + 4845*x^16 + 15504*x^15 + 38760*x^14 + 77520*x^13 + 125970*x^12 + 167960*x^11 + 184756*x^10 + 167960*x^9 + 125970*x^8 + 77520*x^7 + 38760*x^6 + 15504*x^5 + 4845*x^4 + 1140*x^3 + 190*x^2 + 20*x + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.008s sys 0m0.010s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Fri Sep 2 17:23:06 2005 Input: gp > for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.146s user 0m0.041s sys 0m0.008s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Fri Sep 2 17:23:48 2005 Input: gp > for(b=1,100, for(a=1,b, if( frac((360*(b-a))/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,2 1,3 2,3 3,3 1,4 2,4 3,4 4,4 1,5 2,5 3,5 4,5 5,5 1,6 2,6 3,6 4,6 5,6 6,6 7,7 1,8 2,8 3,8 4,8 5,8 6,8 8,8 1,9 2,9 3,9 4,9 5,9 6,9 8,9 9,9 1,10 2,10 3,10 4,10 5,10 6,10 8,10 9,10 10,10 11,11 1,12 2,12 3,12 4,12 5,12 6,12 8,12 9,12 10,12 12,12 13,13 14,14 1,15 2,15 3,15 4,15 5,15 6,15 8,15 9,15 10,15 12,15 15,15 16,16 17,17 1,18 2,18 3,18 4,18 5,18 6,18 8,18 9,18 10,18 12,18 15,18 18,18 19,19 1,20 2,20 3,20 4,20 5,20 6,20 8,20 9,20 10,20 12,20 15,20 18,20 20,20 21,21 22,22 23,23 1,24 2,24 3,24 4,24 5,24 6,24 8,24 9,24 10,24 12,24 15,24 18,24 20,24 24,24 25,25 26,26 27,27 28,28 29,29 1,30 2,30 3,30 4,30 5,30 6,30 8,30 9,30 10,30 12,30 15,30 18,30 20,30 24,30 30,30 31,31 32,32 33,33 34,34 35,35 1,36 2,36 3,36 4,36 5,36 6,36 8,36 9,36 10,36 12,36 15,36 18,36 20,36 24,36 30,36 36,36 37,37 38,38 39,39 1,40 2,40 3,40 4,40 5,40 6,40 8,40 9,40 10,40 12,40 15,40 18,40 20,40 24,40 30,40 36,40 40,40 41,41 42,42 43,43 44,44 1,45 2,45 3,45 4,45 5,45 6,45 8,45 9,45 10,45 12,45 15,45 18,45 20,45 24,45 30,45 36,45 40,45 45,45 46,46 47,47 16,48 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 7,56 56,56 57,57 58,58 59,59 1,60 2,60 3,60 4,60 5,60 6,60 8,60 9,60 10,60 12,60 15,60 18,60 20,60 24,60 30,60 36,60 40,60 45,60 60,60 61,61 62,62 14,63 63,63 64,64 65,65 66,66 67,67 68,68 69,69 21,70 70,70 71,71 1,72 2,72 3,72 4,72 5,72 6,72 8,72 9,72 10,72 12,72 15,72 18,72 20,72 24,72 30,72 36,72 40,72 45,72 60,72 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 16,80 48,80 80,80 81,81 82,82 83,83 35,84 84,84 85,85 86,86 87,87 88,88 89,89 1,90 2,90 3,90 4,90 5,90 6,90 8,90 9,90 10,90 12,90 15,90 18,90 20,90 24,90 30,90 36,90 40,90 45,90 60,90 72,90 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.054s user 0m0.038s sys 0m0.012s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Fri Sep 2 17:24:43 2005 Input: gp > for(b=1,20, for(a=1,b, if( frac((360*(b-a))/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,2 1,3 2,3 3,3 1,4 2,4 3,4 4,4 1,5 2,5 3,5 4,5 5,5 1,6 2,6 3,6 4,6 5,6 6,6 7,7 1,8 2,8 3,8 4,8 5,8 6,8 8,8 1,9 2,9 3,9 4,9 5,9 6,9 8,9 9,9 1,10 2,10 3,10 4,10 5,10 6,10 8,10 9,10 10,10 11,11 1,12 2,12 3,12 4,12 5,12 6,12 8,12 9,12 10,12 12,12 13,13 14,14 1,15 2,15 3,15 4,15 5,15 6,15 8,15 9,15 10,15 12,15 15,15 16,16 17,17 1,18 2,18 3,18 4,18 5,18 6,18 8,18 9,18 10,18 12,18 15,18 18,18 19,19 1,20 2,20 3,20 4,20 5,20 6,20 8,20 9,20 10,20 12,20 15,20 18,20 20,20 ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.027s user 0m0.014s sys 0m0.006s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Fri Sep 2 17:26:25 2005 Input: gp > for(b=1,100, for(a=b-1,b, if( frac((360*(b-a))/(a*b))==0 , print(a,",",b), ) ) ) Output: ? ? ? Errors (if any) and Timing Info: *** division by zero in dvmdii Timing: real 0m0.031s user 0m0.013s sys 0m0.005s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Fri Sep 2 17:26:53 2005 Input: gp > for(b=2,100, for(a=b-1,b, if( frac((360*(b-a))/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,2 2,2 2,3 3,3 3,4 4,4 4,5 5,5 5,6 6,6 7,7 8,8 8,9 9,9 9,10 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.036s user 0m0.013s sys 0m0.006s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Fri Sep 2 17:27:53 2005 Input: gp > for(b=2,30, for(a=b-1,b, if( frac((360*(b-a))/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,2 2,2 2,3 3,3 3,4 4,4 4,5 5,5 5,6 6,6 7,7 8,8 8,9 9,9 9,10 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.020s user 0m0.007s sys 0m0.011s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Fri Sep 2 17:28:06 2005 Input: gp > for(b=2,20, for(a=b-1,b, if( frac((360*(b-a))/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,2 2,2 2,3 3,3 3,4 4,4 4,5 5,5 5,6 6,6 7,7 8,8 8,9 9,9 9,10 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Fri Sep 2 17:28:40 2005 Input: gp > for(b=2,20, for(a=b-1,b-1, if( frac((360*(b-a))/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,2 2,3 3,4 4,5 5,6 8,9 9,10 ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.021s user 0m0.012s sys 0m0.006s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Fri Sep 2 17:30:17 2005 Input: gp > for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? ? ? 1,1 1,2 2,5 5,13 13,34 34,89 ? ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.055s user 0m0.039s sys 0m0.010s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Fri Sep 2 17:30:28 2005 Input: gp > for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.058s user 0m0.044s sys 0m0.005s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Fri Sep 2 17:30:31 2005 Input: gp > for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,1 1,2 2,5 5,13 13,34 34,89 ? ? ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.073s user 0m0.041s sys 0m0.008s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Fri Sep 2 17:30:39 2005 Input: gp > for(b=2,20, for(a=b-1,b-1, if( frac((360*(b-a))/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,2 2,3 3,4 4,5 5,6 8,9 9,10 ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.021s user 0m0.008s sys 0m0.010s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Fri Sep 2 17:31:31 2005 Input: gp > for(b=2,20, for(a=b-1,b+1, if( frac((360*(b-a))/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,2 2,2 3,2 2,3 3,3 4,3 3,4 4,4 5,4 4,5 5,5 6,5 5,6 6,6 7,7 8,8 9,8 8,9 9,9 10,9 9,10 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.024s user 0m0.012s sys 0m0.005s '139.78.' ************** PARI ***************** Host 139.78.10.72 (139.78.10.72) Time: Fri Sep 2 17:31:41 2005 Input: gp > for(b=2,20, for(a=b-1,b-1, if( frac((360*(b-a))/(a*b))==0 , print(a,",",b), ) ) ) Output: ? 1,2 2,3 3,4 4,5 5,6 8,9 9,10 ? Errors (if any) and Timing Info: *** incorrect type in comparison. Timing: real 0m0.038s user 0m0.010s sys 0m0.008s '66.75.2' ************** PARI ***************** Host 66.75.246.252 (66.75.246.252) Time: Sat Sep 3 11:54:32 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.200s user 0m0.006s sys 0m0.008s '194.47.' ************** PARI ***************** Host 194.47.241.206 (194.47.241.206) Time: Sat Sep 3 15:26:59 2005 Input: 5+7 Output: ? 12 ? Errors (if any) and Timing Info: Timing: real 0m0.200s user 0m0.006s sys 0m0.007s '128.84.' ************** PARI ***************** Host 128.84.234.183 (128.84.234.183) Time: Mon Sep 5 09:35:49 2005 Input: Factor(x^2+1,5); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Factor(x^2+1,5); ^-------- Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '128.84.' ************** PARI ***************** Host 128.84.234.183 (128.84.234.183) Time: Mon Sep 5 09:36:03 2005 Input: factor(x^2+1,5); Output: ? ? Errors (if any) and Timing Info: *** partial factorization is not meaningful here. Timing: real 0m0.029s user 0m0.008s sys 0m0.004s '128.119' ************** PARI ***************** Host 128.119.47.86 (128.119.47.86) Time: Tue Sep 6 09:07:52 2005 Input: 3+5 Output: ? 8 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.119' ************** PARI ***************** Host 128.119.47.86 (128.119.47.86) Time: Tue Sep 6 09:08:02 2005 Input: prime(124) Output: ? 683 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:47:54 2005 Input: exp(-2*Pi) Output: ? 0.0018674427317079888144302129348270303934 ? Errors (if any) and Timing Info: Timing: real 0m0.025s user 0m0.006s sys 0m0.007s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:48:20 2005 Input: a = 8/Pi exp(-2*Pi) Output: ? 2.5464790894703253723021402139602297925 ? 0.0018674427317079888144302129348270303934 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:48:59 2005 Input: a = 8/Pi p = 211 N = p^2 exp(-2*Pi/a/N/Log(N)) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: exp(-2*Pi/a/N/Log(N)) ^- Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:49:27 2005 Input: a = 8/Pi p = 211 N = p^2 theta = exp(-2*Pi/a/N/Log(N)) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: theta=exp(-2*Pi/a/N/Log(N ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:50:00 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/ln(N) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? ? Errors (if any) and Timing Info: *** obsolete function: f=-2*Pi/a/N/ln(N) ^----- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: ln(x) ===> log(x) log(x,{flag=0}): natural logarithm of x. flag is optional, and can be 0: default, or 1: calls logagm, computed using the agm. Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:50:15 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:50:28 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) theta = exp(f) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: theta=exp(f) ^------- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:50:39 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) theta = e(f) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: theta=e(f) ^----- Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:50:53 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) c = exp(f) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:51:45 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) theta = exp(f) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: theta=exp(f) ^------- Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:51:51 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) theta = exp(f) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: theta=exp(f) ^------- Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:52:00 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:52:09 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f); Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:52:17 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:52:31 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:53:06 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2)-th^p/(1-th^(2p)) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: th/(1-th^2)-th^p/(1-th^(2p)) ^--- Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:53:10 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2)-th^p/(1-th^(2p)) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: th/(1-th^2)-th^p/(1-th^(2p)) ^--- Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:53:30 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:53:48 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^p/(1-th^{2p}) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? ? Errors (if any) and Timing Info: *** unexpected character: th^p/(1-th^{2p}) ^----- Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:53:51 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^p/(1-th^{2p}) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? ? Errors (if any) and Timing Info: *** unexpected character: th^p/(1-th^{2p}) ^----- Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:54:04 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^p/(1-th^{2p}) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? ? Errors (if any) and Timing Info: *** unexpected character: th^p/(1-th^{2p}) ^----- Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:54:11 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^p/(1-th^{2p}) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? ? Errors (if any) and Timing Info: *** unexpected character: th^p/(1-th^{2p}) ^----- Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 20:55:00 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '132.239' ************** PARI ***************** Host 132.239.145.207 (132.239.145.207) Time: Thu Sep 8 20:58:35 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:04:41 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) add(i,i=1..3) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? ? Errors (if any) and Timing Info: *** unknown member function: add(i,i=1..3) ^-- Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:04:43 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) add(i,i=1..3) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? ? Errors (if any) and Timing Info: *** unknown member function: add(i,i=1..3) ^-- Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:04:55 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i,i=1..3) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: sum(i,i=1..3) ^-------- Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:05:00 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i,i=1..3) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: sum(i,i=1..3) ^-------- Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:05:11 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i,i:=1..3) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: sum(i,i:=1..3) ^--------- Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:05:20 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i,i=1..3) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: sum(i,i=1..3) ^-------- Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:07:09 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1..3,i) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: sum(i=1..3,i) ^- Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:07:11 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1..3,i) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: sum(i=1..3,i) ^- Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:07:20 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1 to 3,i) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: sum(i=1to3,i) ^------ Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:07:22 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1 to 3,i) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: sum(i=1to3,i) ^------ Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:07:24 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1 to 3,i) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: sum(i=1to3,i) ^------ Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:07:25 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1 to 3,i) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: sum(i=1to3,i) ^------ Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:09:11 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1,3,i) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:09:34 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1,3,i) sum(i=1,3,legendre(i/5)) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? 6 ? ? Errors (if any) and Timing Info: *** obsolete function: legendre(i/5)) ^-------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: legendre(n) ===> pollegendre(n) pollegendre(n,{v=x}): legendre polynomial of degree n (n C-integer), in variable v. Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:09:36 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1,3,i) sum(i=1,3,legendre(i/5)) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? 6 ? ? Errors (if any) and Timing Info: *** obsolete function: legendre(i/5)) ^-------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: legendre(n) ===> pollegendre(n) pollegendre(n,{v=x}): legendre polynomial of degree n (n C-integer), in variable v. Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:09:38 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1,3,i) sum(i=1,3,legendre(i/5)) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? 6 ? ? Errors (if any) and Timing Info: *** obsolete function: legendre(i/5)) ^-------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: legendre(n) ===> pollegendre(n) pollegendre(n,{v=x}): legendre polynomial of degree n (n C-integer), in variable v. Timing: real 0m0.013s user 0m0.003s sys 0m0.010s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:09:42 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1,3,i) sum(i=1,3,legendre(i/5)) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? 6 ? ? Errors (if any) and Timing Info: *** obsolete function: legendre(i/5)) ^-------------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file). New syntax: legendre(n) ===> pollegendre(n) pollegendre(n,{v=x}): legendre polynomial of degree n (n C-integer), in variable v. Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:12:48 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1,3,i) sum(i=1,3,kronecker(i/5)) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? 6 ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: sum(i=1,3,kronecker(i/5)) ^-- Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:12:49 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1,3,i) sum(i=1,3,kronecker(i/5)) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? 6 ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: sum(i=1,3,kronecker(i/5)) ^-- Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:12:51 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1,3,i) sum(i=1,3,kronecker(i/5)) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? 6 ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: sum(i=1,3,kronecker(i/5)) ^-- Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:13:13 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1,3,kronecker(i,5)) sum(i=1,3,kronecker(i/5)) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? -1 ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: sum(i=1,3,kronecker(i/5)) ^-- Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:14:08 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1,p-1,kronecker(i,p)*th^i) sum(i=1,3,kronecker(i/5)) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? 0.0032757197203134718355036823544587297285 ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: sum(i=1,3,kronecker(i/5)) ^-- Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:14:30 2005 Input: a = 8/Pi p = 211 N = p^2 f = -2*Pi/a/N/log(N) th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p) Output: ? 2.5464790894703253723021402139602297925 ? 211 ? 44521 ? -0.0000051777401973916058325694436232119162506 ? 0.99999482227320708203503921591773848698 ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? 2.9999998794399600806276835568565607606 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:15:23 2005 Input: a = 8/Pi; p= 211; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) th/(1-th^2) th^211/(1-th^422) sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p) Output: ? 0.99999482227320708203503921591773848698 ? ? 96567.224491034004048987147530528213764 ? 457.66448000768031601248405009882486632 ? 2.9999998794399600806276835568565607606 ? Errors (if any) and Timing Info: Timing: real 0m0.045s user 0m0.008s sys 0m0.014s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:16:07 2005 Input: a = 8/Pi; p= 211; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) th/(1-th^2)-th^p/(1-th^(2*p)) th^211/(1-th^422) sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p) Output: ? 0.99999482227320708203503921591773848698 ? ? 96109.560011026323732974663480429388898 ? 457.66448000768031601248405009882486632 ? 2.9999998794399600806276835568565607606 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:16:43 2005 Input: a = 8/Pi; p= 211; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) th/(1-th^2)-th^p/(1-th^(2*p))+sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p) sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p) Output: ? 0.99999482227320708203503921591773848698 ? ? 96112.560010905763693055291163986245459 ? ? 2.9999998794399600806276835568565607606 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.006s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:24:29 2005 Input: a = 8/Pi; p= 211; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) th/(1-th^2)-th^p/(1-th^(2*p))+sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p)-sum(i=1,p-1,kronecker(2i,p)*th^(2*i))/(1-th^(2*p)) sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p) Output: ? 0.99999482227320708203503921591773848698 ? ? ? ? 2.9999998794399600806276835568565607606 ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...)-sum(i=1,p-1,kronecker(2 *** i,p)*th^(2*i))/(1-th ^-------------------- Timing: real 0m0.013s user 0m0.011s sys 0m0.001s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:24:42 2005 Input: a = 8/Pi; p= 211; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) th/(1-th^2)-th^p/(1-th^(2*p))+sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p)-sum(i=1,p-1,kronecker(2*i,p)*th^(2*i))/(1-th^(2*p)) sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p) Output: ? 0.99999482227320708203503921591773848698 ? ? 96115.560010423523582368450090611526265 ? ? 2.9999998794399600806276835568565607606 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.009s sys 0m0.006s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:24:59 2005 Input: a = 8/Pi; p= 211; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) g = th/(1-th^2)-th^p/(1-th^(2*p))+sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p)-sum(i=1,p-1,kronecker(2*i,p)*th^(2*i))/(1-th^(2*p)) Output: ? 0.99999482227320708203503921591773848698 ? ? 96115.560010423523582368450090611526265 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.010s sys 0m0.005s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:25:10 2005 Input: a = 8/Pi; p= 163; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) g = th/(1-th^2)-th^p/(1-th^(2*p))+sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p)-sum(i=1,p-1,kronecker(2*i,p)*th^(2*i))/(1-th^(2*p)) Output: ? 0.99999088419708908679985730956685807497 ? ? 54515.053467039434369092038381879223692 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.009s sys 0m0.006s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:35:14 2005 Input: a = 8/Pi; p= 163; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) g = th/(1-th^2)-th^p/(1-th^(2*p))+sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p)-sum(i=1,p-1,kronecker(2*i,p)*th^(2*i))/(1-th^(2*p)) p^3 Output: ? 0.99999088419708908679985730956685807497 ? ? 54515.053467039434369092038381879223692 ? 4330747 ? ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.007s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:35:24 2005 Input: a = 8/Pi; p= 163; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) g = th/(1-th^2)-th^p/(1-th^(2*p))+sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p)-sum(i=1,p-1,kronecker(2*i,p)*th^(2*i))/(1-th^(2*p)) g/p^3 Output: ? 0.99999088419708908679985730956685807497 ? ? 54515.053467039434369092038381879223692 ? 0.012587909999600400200956564394521135428 ? ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '132.239' ************** PARI ***************** Host 132.239.145.207 (132.239.145.207) Time: Thu Sep 8 21:36:50 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.013s user 0m0.006s sys 0m0.009s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:37:00 2005 Input: a = 8/Pi; p= 163; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) g = th/(1-th^2)-th^p/(1-th^(2*p))+sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p)-sum(i=1,p-1,kronecker(2*i,p)*th^(2*i))/(1-th^(2*p)) g/p^3 C1 := ((2/3)^2)*(log(p))^2*p^2 Output: ? 0.99999088419708908679985730956685807497 ? ? 54515.053467039434369092038381879223692 ? 0.012587909999600400200956564394521135428 ? ? Errors (if any) and Timing Info: *** unexpected character: C1:=((2/3)^2)*(log(p))^ ^-------------------- Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:37:08 2005 Input: a = 8/Pi; p= 163; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) g = th/(1-th^2)-th^p/(1-th^(2*p))+sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p)-sum(i=1,p-1,kronecker(2*i,p)*th^(2*i))/(1-th^(2*p)) g/p^3 C1 = ((2/3)^2)*(log(p))^2*p^2 Output: ? 0.99999088419708908679985730956685807497 ? ? 54515.053467039434369092038381879223692 ? 0.012587909999600400200956564394521135428 ? 306385.33709078613054401520183283806379 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.006s sys 0m0.009s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:37:40 2005 Input: a = 8/Pi; p= 163; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) g = th/(1-th^2)-th^p/(1-th^(2*p))+sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p)-sum(i=1,p-1,kronecker(2*i,p)*th^(2*i))/(1-th^(2*p)) g/p^3 C1 = ((2/3)^2)*(log(p))^2*p^2 2*log(C1)/sqrt(C1) Output: ? 0.99999088419708908679985730956685807497 ? ? 54515.053467039434369092038381879223692 ? 0.012587909999600400200956564394521135428 ? 306385.33709078613054401520183283806379 ? 0.045644527184918329619718420953168415696 ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.005s sys 0m0.004s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:37:55 2005 Input: a = 8/Pi; p= 163; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) g = th/(1-th^2)-th^p/(1-th^(2*p))+sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p)-sum(i=1,p-1,kronecker(2*i,p)*th^(2*i))/(1-th^(2*p)) g/p^3 C1 = ((2/3)^2)*(log(p))^2*p^2 2*log(C1)/sqrt(C1)*g/p^3 Output: ? 0.99999088419708908679985730956685807497 ? ? 54515.053467039434369092038381879223692 ? 0.012587909999600400200956564394521135428 ? 306385.33709078613054401520183283806379 ? 0.00057456920017806574671282371027806958269 ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.005s sys 0m0.011s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:38:10 2005 Input: a = 8/Pi; p= 163; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) g = th/(1-th^2)-th^p/(1-th^(2*p))+sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p)-sum(i=1,p-1,kronecker(2*i,p)*th^(2*i))/(1-th^(2*p)) g/p^3 C1 = ((2/3)^2)*(log(p))^2*p^2 2*log(C1)/sqrt(C1) Output: ? 0.99999088419708908679985730956685807497 ? ? 54515.053467039434369092038381879223692 ? 0.012587909999600400200956564394521135428 ? 306385.33709078613054401520183283806379 ? 0.045644527184918329619718420953168415696 ? Errors (if any) and Timing Info: Timing: real 0m0.047s user 0m0.007s sys 0m0.007s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:38:41 2005 Input: a = 8/Pi; p= 163; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) g = th/(1-th^2)-th^p/(1-th^(2*p))+sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p)-sum(i=1,p-1,kronecker(2*i,p)*th^(2*i))/(1-th^(2*p)) g/p^3 C1 = ((2/3)^2)*(log(p))^2*p^2 2*log(C1)/sqrt(C1)*g/p^3 Output: ? 0.99999088419708908679985730956685807497 ? ? 54515.053467039434369092038381879223692 ? 0.012587909999600400200956564394521135428 ? 306385.33709078613054401520183283806379 ? 0.00057456920017806574671282371027806958269 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:52:20 2005 Input: a = 8/Pi; p= 163; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) g = th/(1-th^2)-th^p/(1-th^(2*p))+sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p)-sum(i=1,p-1,kronecker(2*i,p)*th^(2*i))/(1-th^(2*p)) g/p^3 C1 = ((2/3)^2)*(log(p))^2*p^2 2*log(C1)/sqrt(C1)*g/p^3 Output: ? 0.99999088419708908679985730956685807497 ? ? 54515.053467039434369092038381879223692 ? 0.012587909999600400200956564394521135428 ? 306385.33709078613054401520183283806379 ? 0.00057456920017806574671282371027806958269 ? Errors (if any) and Timing Info: Timing: real 0m0.402s user 0m0.011s sys 0m0.008s '70.51.2' ************** PARI ***************** Host 70.51.218.153 (70.51.218.153) Time: Thu Sep 8 21:52:39 2005 Input: a = 8/Pi; p= 163; N=p^2; f = -2*Pi/a/N/log(N); th = exp(f) g = th/(1-th^2)-th^p/(1-th^(2*p))+sum(i=1,p-1,kronecker(i,p)*th^i)/(1-th^p)-sum(i=1,p-1,kronecker(2*i,p)*th^(2*i))/(1-th^(2*p)) g/p^3 C1 = ((2/3)^2)*(log(p))^2*p^2 16*Pi^3*2*log(C1)/sqrt(C1)*g/p^3 Output: ? 0.99999088419708908679985730956685807497 ? ? 54515.053467039434369092038381879223692 ? 0.012587909999600400200956564394521135428 ? 306385.33709078613054401520183283806379 ? 0.28504402548319486797166857816678624087 ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '128.84.' ************** PARI ***************** Host 128.84.234.183 (128.84.234.183) Time: Mon Sep 12 22:54:56 2005 Input: Discrim(x^2 - 134*x + 115); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Discrim(x^2-134*x+115); ^-------------- Timing: real 0m0.268s user 0m0.007s sys 0m0.007s '128.84.' ************** PARI ***************** Host 128.84.234.183 (128.84.234.183) Time: Mon Sep 12 22:55:05 2005 Input: Discriminant(x^2 - 134*x + 115); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Discriminant(x^2-134*x+115); ^-------------- Timing: real 0m0.013s user 0m0.004s sys 0m0.008s '128.84.' ************** PARI ***************** Host 128.84.234.183 (128.84.234.183) Time: Mon Sep 12 22:55:17 2005 Input: Discriminant(x^2 - 134*x + 115); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: Discriminant(x^2-134*x+115); ^-------------- Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Wed Sep 14 14:45:32 2005 Input: factor (10) Output: ? [2 1] [5 1] ? Errors (if any) and Timing Info: Timing: real 0m0.118s user 0m0.006s sys 0m0.007s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Wed Sep 14 14:46:13 2005 Input: factor 95800 Output: ? factor95800 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.007s sys 0m0.005s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Wed Sep 14 14:46:33 2005 Input: factor (95800) Output: ? [2 3] [5 2] [479 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Wed Sep 14 14:48:38 2005 Input: factor (217519) Output: ? [217519 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Wed Sep 14 14:49:34 2005 Input: factor (414560) Output: ? [2 5] [5 1] [2591 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Wed Sep 14 14:51:05 2005 Input: factor (422481) Output: ? [3 1] [140827 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Wed Sep 14 15:24:26 2005 Input: 95800^4 Output: ? ? 84229075969600000000 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.005s sys 0m0.007s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Wed Sep 14 15:26:37 2005 Input: 95800^4 217519^4 Output: ? 84229075969600000000 ? 2238663363846304960321 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Wed Sep 14 15:30:20 2005 Input: 95800^4 217519^4 414560^4 Output: ? 84229075969600000000 ? 2238663363846304960321 ? 29535857400192040960000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '130.91.' ************** PARI ***************** Host 130.91.119.63 (130.91.119.63) Time: Wed Sep 14 15:38:06 2005 Input: 95800^4 217519^4 414560^4 422481^4 Output: ? 84229075969600000000 ? 2238663363846304960321 ? 29535857400192040960000 ? 31858749840007945920321 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '84.228.' ************** PARI ***************** Host 84.228.60.169 (84.228.60.169) Time: Sat Sep 17 01:29:43 2005 Input: 123 Output: ? 123 ? Errors (if any) and Timing Info: Timing: real 0m0.183s user 0m0.004s sys 0m0.009s '84.228.' ************** PARI ***************** Host 84.228.60.169 (84.228.60.169) Time: Sat Sep 17 01:30:08 2005 Input: factor(123) Output: ? [3 1] [41 1] ? ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '84.228.' ************** PARI ***************** Host 84.228.60.169 (84.228.60.169) Time: Sat Sep 17 01:31:15 2005 Input: factor(10^200+23) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 6822 Killed /usr/bin/gp -q -emacs Timing: real 0m21.054s user 0m20.994s sys 0m0.008s '84.228.' ************** PARI ***************** Host 84.228.60.169 (84.228.60.169) Time: Sat Sep 17 01:31:22 2005 Input: factor(10^200+23) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 6826 Killed /usr/bin/gp -q -emacs Timing: real 0m21.060s user 0m20.991s sys 0m0.009s '84.228.' ************** PARI ***************** Host 84.228.60.169 (84.228.60.169) Time: Sat Sep 17 01:31:41 2005 Input: factor(10^200+23) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 6831 Killed /usr/bin/gp -q -emacs Timing: real 0m21.047s user 0m20.992s sys 0m0.009s '84.228.' ************** PARI ***************** Host 84.228.60.169 (84.228.60.169) Time: Sat Sep 17 01:31:53 2005 Input: factor(10^200+23) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 6836 Killed /usr/bin/gp -q -emacs Timing: real 0m21.011s user 0m20.992s sys 0m0.010s '24.60.1' ************** PARI ***************** Host 24.60.189.211 (24.60.189.211) Time: Sun Sep 18 16:22:17 2005 Input: factor(2352151325) Output: ? [5 2] [94086053 1] ? Errors (if any) and Timing Info: Timing: real 0m0.295s user 0m0.007s sys 0m0.006s '69.133.' ************** PARI ***************** Host 69.133.71.21 (69.133.71.21) Time: Thu Sep 22 13:03:28 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.352s user 0m0.007s sys 0m0.012s '139.78.' ************** PARI ***************** Host 139.78.37.181 (139.78.37.181) Time: Thu Sep 22 17:21:55 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/((a*b)+1)==0 , print(a,",",b), ) ) ) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...ac((a^2+b^2)/((a*b)+1)==0 *** ,print(a,",",b),))) ^------------------- Timing: real 0m0.170s user 0m0.004s sys 0m0.008s '139.78.' ************** PARI ***************** Host 139.78.37.181 (139.78.37.181) Time: Thu Sep 22 17:22:32 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/((a*b)+1)==0 , print(a,",",b), ) ) ) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...ac((a^2+b^2)/((a*b)+1)==0 *** ,print(a,",",b),))) ^------------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '139.78.' ************** PARI ***************** Host 139.78.37.181 (139.78.37.181) Time: Thu Sep 22 17:24:22 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b+1))==0 , print(a,",",b), ) ) ) Output: ? 1,1 2,8 3,27 8,30 4,64 ? Errors (if any) and Timing Info: Timing: real 0m0.076s user 0m0.027s sys 0m0.002s '139.78.' ************** PARI ***************** Host 139.78.37.181 (139.78.37.181) Time: Thu Sep 22 17:24:31 2005 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b+1)) )==0 , print(a,",",b), ) ) ) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...f(frac((a^2+b^2)/(a*b+1)) ^ *** Warning: unused characters: )==0,print(a,",",b),))). Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '130.83.' ************** PARI ***************** Host 130.83.244.129 (130.83.244.129) Time: Sat Sep 24 12:31:25 2005 Input: ##### Modular polynomials and their partial derivatives ##### phi(X,Y) = X^3+Y^3-X^2*Y^2+2^4*3*31*(X^2*Y+X*Y^2)-2^4*3^4*5^3*(X^2+Y^2)+3^4*5^3*4027*X*Y+2^8*3^7*5^6*(X+Y)-2^12*3^9*5^9 phi(X,Y)=X^3 + Y^3 - X^2*Y^2 + 1488*(X*Y^2+X^2*Y) - 162000*(X^2+Y^2) + 40773375*X*Y + 8748000000*(X+Y) - 157464000000000; phip(X,Y) = deriv(phi(X,Y), X); phip(X,Y)=3*X^2 + (-2*Y^2 + 2976*Y - 324000)*X + (1488*Y^2 + 40773375*Y + 8748000000); { fi(A,B)=(-1023490369077469249536000000000*B^6 - 7107572007482425344000000000*B^5 - 16584334684125659136000000*B^4 - 13304354323562496000000*B^3 - 710919696678912000*B^2 - 13060694016000*B - 80621568)*A^6 + (-7107572007482425344000000000*B^6 - 49358138940850176000000000*B^5 - 115168990861983744000000*B^4 - 92391349469184000000*B^3 - 4936942338048000*B^2 - 90699264000*B - 559872)*A^5 + (-16584334684125659136000000*B^6 - 115168990861983744000000*B^5 - 267290642485518336000*B^4 - 208927024413696000*B^3 - 3938781821184*B^2 - 487648512*B - 1296)*A^4 + (-13304354323562496000000*B^6 - 92391349469184000000*B^5 - 208927024413696000*B^4 - 142143382656000*B^3 + 25854818976*B^2 - 1447632*B - 1)*A^3 + (-710919696678912000*B^6 - 4936942338048000*B^5 - 3938781821184*B^4 + 25854818976*B^3 + 39301119*B^2 - 1920*B)*A^2 + (-13060694016000*B^6 - 90699264000*B^5 - 487648512*B^4 - 1447632*B^3 - 1920*B^2 - B)*A + (-80621568*B^6 - 559872*B^5 - 1296*B^4 - B^3) } fip(X,Y) = deriv(fi(X,Y), X); { fip(A,B)=(-6140942214464815497216000000000*B^6 - 42645432044894552064000000000*B^5 - 99506008104753954816000000*B^4 - 79826125941374976000000*B^3 - 4265518180073472000*B^2 - 78364164096000*B - 483729408)*A^5 + (-35537860037412126720000000000*B^6 - 246790694704250880000000000*B^5 - 575844954309918720000000*B^4 - 461956747345920000000*B^3 - 24684711690240000*B^2 - 453496320000*B - 2799360)*A^4 + (-66337338736502636544000000*B^6 - 460675963447934976000000*B^5 - 1069162569942073344000*B^4 - 835708097654784000*B^3 - 15755127284736*B^2 - 1950594048*B - 5184)*A^3 + (-39913062970687488000000*B^6 - 277174048407552000000*B^5 - 626781073241088000*B^4 - 426430147968000*B^3 + 77564456928*B^2 - 4342896*B - 3)*A^2 + (-1421839393357824000*B^6 - 9873884676096000*B^5 - 7877563642368*B^4 + 51709637952*B^3 + 78602238*B^2 - 3840*B)*A + (-13060694016000*B^6 - 90699264000*B^5 - 487648512*B^4 - 1447632*B^3 - 1920*B^2 - B) } ##### Example curves ##### p1 = t^11+t^2+1; a1 = Mod(Mod(1,2)*(t^4+t^2+t),p1); d1 = poldegree( p1 ); n1 = ceil( d1/2 ) + 1; p2 = t^120 + t^4 + t^3 + t + 1; a2 = Mod( Mod(1, 2)*t^119 + Mod(1, 2)*t^3 + Mod(1, 2)*t^2 + Mod(1, 2), p2 ); d2 = poldegree( p2 ); n2 = ceil( d2/2 ) + 1; p3 = t^3 + t + 1; a3 = Mod(Mod(1,2)*t,p3); d3 = poldegree( p3 ); n3 = ceil( d3/2 ) + 1; p4 = t^32 + t^7 + t^6 + t^2 + 1 a4 = Mod(Mod(1,2)*t,p4); d4 = poldegree( p4 ); n4 = ceil( d4/2 ) + 1; one=Mod(Mod(1,2),mp); zero=Mod(Mod(0,2),mp); E=[one,zero,zero,zero,a]; ev=ellinit(E); ##### Code section begins ##### ceillog2( X ) = matsize(binary(X-1))[2]; getpol( X ) = if( type(X)=="t_VEC", X=X[1] ); component( X, 1 ) getmod( X ) = if( type(X)=="t_VEC", X=X[1] ); component(pollead(component(X,2)),1) getdim( X ) = matsize(X)[2]; { docheck( AA, d, i ) = d = getdim(AA); for( i=1, d, if( fi(AA[i],AA[i%d+1]) != 0, print("terr: ",i) ); ); } lift2zq( X ) = Mod(lift(lift(X)), getpol(X)); liftn( X, n ) = lift2zq(X)*Mod(1,1<>n)*Mod(1,getmod(X)), getpol(X) )) shl2( X, n ) = if(X==0, 0, Mod( (lift(lift(X))<0, iX = iX*(2-X*iX); i--; ); return( iX ); } { padicsqrt( X, pow2, X0, X1 ) = pow2 = component(X,1); X1 = Mod(1, pow2); until( X1 == X0, X0 = X1; X1 -= Mod( lift(X1*(X*X1^2-1))/2, pow2 ); ); return( X1*X ); } { updateAs( currprec, A, d, i, t, m, f, D, P ) = d = getdim(A); D = vector(d-1); P = vector(d); for( i=1, d-1, if(DEBUG, print(i)); t = qadicinv( fip(A[i],A[i+1]) ); D[i] = t * fip(A[i+1],A[i]); P[i] = t * shr2( fi(A[i],A[i+1]), currprec ); ); m = fip( A[1], A[d] ); f = shr2( fi(A[d], A[1]), currprec ); for( i=1, d-1, f -= m*P[i]; m *= -D[i]; if( m==0, break() ); ); m += fip( A[d], A[1] ); P[d] = f * qadicinv( m ); A[d] -= shl2( P[d], currprec ); forstep( i=d-1, 1, -1, P[i] -= D[i]*P[i+1]; A[i] -= shl2( P[i], currprec ); ); return( A ); } { doA( a, d, A, i ) = d = poldegree(getpol(a)); A = vector(d); A[1] = a; A[d] = A[1]^2; forstep( i=d-1, 2, -1, A[i] = A[i+1]^2; ); return( A ); } { doAA( n, A, n1=1, n0, i ) = if( type(A) == "t_POLMOD", A = doA(A); n1 = 1; ); i = ceillog2( ceil(n/n1) ); while( i>0, i--; n0 = n1; n1 *= 2; if( n1>n, n1=n ); print("lift A to prec ",n1); A = liftn( A, n1 ); A = updateAs( n0, A ); if(DEBUG, docheck(A)); ); return( A ); } { doZZ0( AA, d, Z, i ) = d = getdim(AA); Z = vector(d); for( i=1, d, Z[i] = liftn( AA[i%d+1], 2 ); Z[i] *= (1 + 432*Z[i]); Z[i] = -Z[i]; ); return(Z); } { liftz( A, Z0, Z, i ) = Z = Z0; until( Z == Z0, Z0 = Z; Z -= shr2( (8*Z+1)*Z*Z + A, 1 ) * qadicinv( (12*Z+1)*Z ); ); return( Z ); } { doZZ( n, Z, AA, d, p, ZZ ) = d = getdim(AA); ZZ = Z; for( i=1, d, ZZ[i] = liftz( liftn(AA[i],n+1), liftn(ZZ[i],n+1) ); ); return(liftn(ZZ,n)); } { sqrtrace( n, A, Z, p, d ) = d = getdim(A); A = liftn( A, n ); Z = liftn( Z, n ); return( [prod(i=1,d,1-504*Z[i]+19008*A[i]), prod(i=1,d,(1+240*Z[i]*(12*Z[i]+1))*(1+864*A[i]))] ); } { ecpc( mp, a, d, n, A, AA, ZZ, T, c ) = i ) = d = poldegree( mp ); n = ceil(d/2) + 1; A = doA( a ); AA = doAA( n, A ); ZZ = doZZ0( AA ); ZZ = doZZ( n-1, ZZ, AA ); T = sqrtrace( n+2, AA, ZZ ); c = centerlift( padicsqrt(simplify(lift(T[1])/lift(T[2]))) * Mod(1,1<<(n+1)) ); c = if( c%4 != 1, -c, c ); return( (1<