English

Primes in almost all short intervals

Number Theory 2025-09-26 v6

Abstract

The author sharpens a result of Jia (1996), showing that the interval [n,n+n121.5+ε][n, n+n^{\frac{1}{21.5}+\varepsilon}] contains prime numbers for almost all nn. Watt's mean value bound, a delicate sieve decomposition and more accurate estimates for integrals are used to good effect.

Keywords

Cite

@article{arxiv.2407.05651,
  title  = {Primes in almost all short intervals},
  author = {Runbo Li},
  journal= {arXiv preprint arXiv:2407.05651},
  year   = {2025}
}

Comments

28 pages

R2 v1 2026-06-28T17:32:24.394Z