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

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

2010-04-07

arxiv.org/abs/1004.1067v1

Mathematics

Number Theory

Scientific paper

We show that if besides the primes some other sequences (involving the Liouville function and the primes) have a common distribution level exceeding 0.7231 then for any positive even integer $h$ there are arbitrarily long arithmetic progressions of primes $p$ such that $p+h$ is also prime for each element of the progression. In case of $h=2$ this means that under some plausible unproved hypotheses about regular distribution of the primes and other sequences in arithmetic progressions we really have arbitrarily long arithmetic progressions in the sequence of twin primes.

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