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An approximation to the twin prime conjecture and the parity phenomenon
Published 7 Apr 2010 in math.NT | (1004.1065v1)
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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