English

An approximation to the twin prime conjecture and the parity phenomenon

Number Theory 2010-04-08 v1

Abstract

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

Keywords

Cite

@article{arxiv.1004.1065,
  title  = {An approximation to the twin prime conjecture and the parity phenomenon},
  author = {Janos Pintz},
  journal= {arXiv preprint arXiv:1004.1065},
  year   = {2010}
}