An approximation to the twin prime conjecture and the parity phenomenon

Details An approximation to the twin prime conjecture and the parity phenomenon An approximation to the twin prime conjecture and the parity phenomenon

2010-04-07

arxiv.org/abs/1004.1065v1

Mathematics

Number Theory

Scientific paper

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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