# Infinitely Many Primes

• June 23rd 2009, 09:35 PM
Cairo
Infinitely Many Primes
I've been asked to write an essay on

Some methods for proving that there are infinitely many primes of the form an+b (n=0,1,2,...), when (a,b)=1.

Can anybody help me with a plan of what should be included?
• June 23rd 2009, 09:39 PM
CaptainBlack
Quote:

Originally Posted by Cairo
I've been asked to write an essay on

Some methods for proving that there are infinitely many primes of the form an+b (n=0,1,2,...), when (a,b)=1.

Can anybody help me with a plan of what should be included?

Google for "primes in arithmetic progression". First hit is the Wikipedia article.

CB
• June 24th 2009, 06:12 PM
chiph588@
The proof of this is very involved. It involves a great understanding in analysis and certain functions including the Riemann Zeta function $\zeta(s)$ and Dirichlet L functions; hence one must know a great deal about Dirichlet characters.

A good reference for the full proof can be found in a number theory book by Ireland and Rosen which can be found here.

Amazon.com: A Classical Introduction to Modern Number Theory (Graduate Texts in Mathematics) (v. 84): Kenneth Ireland, Michael Rosen: Books