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arXiv · 1002.2899

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

Janos Pintz
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Abstract

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

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Janos Pintz. 2010-02-15. Are there arbitrarily long arithmetic progressions in the sequence of twin primes?. https://arxiv.org/abs/1002.2899

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