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On critical small intervals containing primes.

Втр, 08/18/2009 - 11:53 — SomNambul
Authors: Vladimir Shevelev
Subjects: Number Theory
link: http://arxiv.org/abs/0908.2319
Abstract

Let p be an odd prime, such that p_n<p/2<p_{n+1}, where p_n is the n-th
prime. We study the following question: with what probability P there exists a
prime in the interval (p, 2p_{n+1})? We show, that for p tends to the infinity,
P>= 1/2(1-epsilon) and conjecture that P<= 1/2(1+epsilon).

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