Lecture 4: The Sequence of Prime Numbers

William Stein

Date: Math 124 $\quad$ HARVARD UNIVERSITY $\quad$ Fall 2001

This lecture is about the following three questions:

1. Are there infinitely many primes? (yes)
2. Are there infinitely many primes of the form $ax+b$? (yes, if $\gcd(a,b)=1$)
3. How many primes are there? (asymptotically $x/\log(x)$ primes less than $x$)