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Unregistered 2010-04-04 17:34

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 2010-04-04 22:06

[QUOTE=Unregistered;210575]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 ?[/QUOTE]

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 [url]http://www.math.ucla.edu/~tao/preprints/Expository/quantitative_AP.dvi[/url]


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