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arXiv · 2505.07630

On the frequency of small gaps between the primes

Akos Magyar·Janos Pintz
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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 $k$-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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Akos Magyar, Janos Pintz. 2025-05-12. On the frequency of small gaps between the primes. https://arxiv.org/abs/2505.07630

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