# arithmetic progression by Dirichlet [duplicate]

The arithmetic progression $a_N=(p-1)N+1$ contains infinitely many primes $q$ by Dirichlet. I have searched this part in wiki, but I din't get any relevant proof. Can any one prove it how $a_N$ contains infinitely many primes and what is Dirichlet proof? please explain.

## marked as duplicate by davidlowryduda♦Oct 20 '17 at 5:26

• There are many places it is done, for example Apostol's book on Analytic Number Theory. For the case $cn+1$, which is the one you are interested in, there is also a proof that does not use Analytic Number Theory. But it is not easy. Neither proof can, I think, be usefully summarized in an MSE answer. – André Nicolas Feb 15 '14 at 4:11