English

On the ratio of consecutive gaps between primes

Number Theory 2014-07-09 v2

Abstract

In the present work we prove a common generalization of Maynard-Tao's recent result about consecutive bounded gaps between primes and on the Erd\H{o}s-Rankin bound about large gaps between consecutive primes. The work answers in a strong form a 60 years old problem of Erd\"os, which asked whether the ratio of two consecutive primegaps can be infinitely often arbitrarily small, and arbitrarily large, respectively.

Keywords

Cite

@article{arxiv.1406.2658,
  title  = {On the ratio of consecutive gaps between primes},
  author = {Janos Pintz},
  journal= {arXiv preprint arXiv:1406.2658},
  year   = {2014}
}
R2 v1 2026-06-22T04:35:22.552Z