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