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Old 2010-04-04, 17:34   #1
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Default 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 ?


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Old 2010-04-04, 22:06   #2
CRGreathouse
 
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Quote:
Originally Posted by Unregistered View Post
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

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