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- - **nth prime number in an arithmetic progression**
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nth prime number in an arithmetic progressionIt 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 |

[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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