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arXiv · 1004.1065

An approximation to the twin prime conjecture and the parity phenomenon

Janos Pintz
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Abstract

Jing Run Chen proved in 1966 that $p+2$ has at most two prime factors for infinitely many primes $p$. However, due to the parity problem we do not know whether $p+2$ has an odd (or even) number of prime factors infinitely often. In the present work it is proved that $p+d$ has an odd number of prime factors for at least one value of d=2,4,...16.

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Janos Pintz. 2010-04-07. An approximation to the twin prime conjecture and the parity phenomenon. https://arxiv.org/abs/1004.1065

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