mersenneforum.org nth prime number in an arithmetic progression
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 2010-04-04, 17:34 #1 Unregistered   6,803 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
2010-04-04, 22:06   #2
CRGreathouse

Aug 2006

3×1,993 Posts

Quote:
 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

Last fiddled with by CRGreathouse on 2010-04-04 at 22:06

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