Bounds on prime gaps as a consequence of the divergence of the series of reciprocal primes

Douglas Azevedo

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arXiv · 1706.09058

Bounds on prime gaps as a consequence of the divergence of the series of reciprocal primes

Douglas Azevedo

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Abstract

In this paper, using the well known fact that the series of reciprocals of primes diverges, we obtain a general inequality for gaps of consecutive primes that holds for infinitely many primes. As it is shown the key ingredient for this direct approach is a consequence of the the Kummer's characterization of summable sequences of positive terms. Some interesting consequences are then presented. In particular, we show how the twin-prime conjecture is related to our main result.

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Douglas Azevedo. 2017-06-27. Bounds on prime gaps as a consequence of the divergence of the series of reciprocal primes. https://arxiv.org/abs/1706.09058

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