Thread: 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?

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

The proof of this is very involved. It involves a great understanding in analysis and certain functions including the Riemann Zeta function 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