20100404, 17:34  #1 
2×769 Posts 
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 
20100404, 22:06  #2  
Aug 2006
3·1,993 Posts 
Quote:
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 Last fiddled with by CRGreathouse on 20100404 at 22:06 

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