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

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

2010-02-15

arxiv.org/abs/1002.2899v1

Mathematics

Number Theory

Scientific paper

The main result of the paper is that assuming that the level $\theta$ of
distribution of primes exceeds 1/2, then there exists a positive $d\leq
C(\theta)$ 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 $\theta>0.971$, then the above holds for some $d\leq 16$.

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