English

On the Maximal Gap between Primes

General Mathematics 2025-11-05 v2

Abstract

In this paper, we show some results about the gap between a prime number and its consecutive prime number for large enough prime numbers. We show that the gap between a prime number pnp_n and its consecutive prime number is not larger than 2log2pn2\log^2{p_n}. We also show that the result implies the existence of a prime number in a certain type of interval for large enough numbers as a consequence.

Keywords

Cite

@article{arxiv.2510.17065,
  title  = {On the Maximal Gap between Primes},
  author = {Cheng-Ting Wang},
  journal= {arXiv preprint arXiv:2510.17065},
  year   = {2025}
}

Comments

found a major error in the main theorem, therefore I decided to withdraw before finding a way to repair the proof of the main claim(if possible)

R2 v1 2026-07-01T06:46:18.590Z