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Old 2005-12-30, 21:53   #5
akruppa's Avatar
Aug 2002

2,467 Posts

Yes, this is a special case of the "prime number theorem for arithmetic progressions." Simply put, it says that if you have an arithmetic progression a+b*x with gcd(a,b)=1 and x∈N, you get infinitely many primes. What is more, each such progression for different values of a (but the same b) gets an "equal share" of the primes. See Crandall and Pomerance, Prime Numbers, Theorem 1.1.5.

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