nth prime number in an arithmetic progression

It is well known that the number of primes in the arithmetic progression a, a + b, a + 2b, a + 3b , , , less than x is xlog(x)/phi(b).

Is there any good approximations (need lower bound acturally) for the nth prime number in this arithmetic progression ?


joseph

[CRGreathouse]

Originally Posted by Unregistered

It is well known that the number of primes in the arithmetic progression a, a + b, a + 2b, a + 3b , , , less than x is xlog(x)/phi(b).

Is there any good approximations (need lower bound acturally) for the nth prime number in this arithmetic progression ?

If I understand your question correctly:

This is a very hard question, but Ben Green and Terry Tao show that such progressions are Ω(log log log log log log log x). See http://www.math.ucla.edu/~tao/prepri...itative_AP.dvi