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 -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.
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}
}