Bounded Gaps Between Primes: An Upper Bound of 236

Zhao Song; Song Yue

Paper 2026/1893

Bounded Gaps Between Primes: An Upper Bound of 236

Zhao Song

Song Yue

, Northeastern University

Abstract

Let $H_1:=\liminf_{n\to\infty}(p_{n+1}-p_n)$, where $p_n$ is the $n$-th prime. The twin-prime conjecture asserts that $H_1=2$. Zhang [Zha14] proved the first finite bound, $H_1<7\times10^7$. Maynard [May15] improved this bound to $H_1\le600$. Polymath [D. 14b] subsequently established $H_1\le246$. Stadlmann [Sta26] further improved the bound to $H_1\le240$. In this paper, we prove $H_1\leq236$.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: number theory prime numbers gap between prime numbers
Contact author(s): magic linuxkde @ gmail com
yue son @ northeastern edu
History: 2026-09-09: approved; 2026-09-04: received; See all versions
Short URL: https://ia.cr/2026/1893
License: CC BY-NC

BibTeX

@misc{cryptoeprint:2026/1893,
      author = {Zhao Song and Song Yue},
      title = {Bounded Gaps Between Primes: An Upper Bound of 236},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/1893},
      year = {2026},
      url = {https://eprint.iacr.org/2026/1893}
}