English

Explicit bounds for large gaps between squarefree integers

Number Theory 2023-08-29 v3

Abstract

We obtain explicit forms of the current best known asymptotic upper bounds for gaps between squarefree integers. In particular we show, for any x2x \ge 2, that every interval of the form (x,x+11x1/5logx](x, x + 11x^{1/5}\log x] contains a squarefree integer. The constant 11 can be improved further, if xx is assumed to be larger than a (very) large constant.

Keywords

Cite

@article{arxiv.2211.09975,
  title  = {Explicit bounds for large gaps between squarefree integers},
  author = {Angel Kumchev and Wade McCormick and Nathan McNew and Ariana Park and Russell Scherr and Willow Ziehr},
  journal= {arXiv preprint arXiv:2211.09975},
  year   = {2023}
}
R2 v1 2026-06-28T06:10:37.695Z