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