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On the frequency of small gaps between the primes

Number Theory 2025-05-13 v1

Abstract

In a recent work Friedlander studied the problem of how large consecutive prime gaps should be in order that the sum of the reciprocals should be divergent. Supposing a very deep Hypothesis, a generalization of the Hardy--Littlewood prime kk-tuple conjecture, he gave an almost precise answer for it. In the present work we give an unconditional answer for a much weaker form of the same problem.

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Cite

@article{arxiv.2505.07630,
  title  = {On the frequency of small gaps between the primes},
  author = {Akos Magyar and Janos Pintz},
  journal= {arXiv preprint arXiv:2505.07630},
  year   = {2025}
}