English

Are there arbitrarily long arithmetic progressions in the sequence of twin primes?

Number Theory 2010-02-16 v1

Abstract

The main result of the paper is that assuming that the level θ\theta of distribution of primes exceeds 1/2, then there exists a positive dC(θ)d\leq C(\theta) such that there are arbitrarily long arithmetic progressions with the property that p=p+dp'=p+d is the next prime for each element of the progression. If θ>0.971\theta>0.971, then the above holds for some d16d\leq 16.

Keywords

Cite

@article{arxiv.1002.2899,
  title  = {Are there arbitrarily long arithmetic progressions in the sequence of twin primes?},
  author = {Janos Pintz},
  journal= {arXiv preprint arXiv:1002.2899},
  year   = {2010}
}
R2 v1 2026-06-21T14:47:09.688Z