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Math Help - Infinitely Many Primes

  1. #1
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    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?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Cairo View Post
    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
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  3. #3
    MHF Contributor chiph588@'s Avatar
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    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
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