A new ceiling for Λ: the de Bruijn–Newman constant is at most 0.1787854
A researcher presents a computer-assisted proof lowering the known ceiling of the de Bruijn–Newman constant, a value linked to the Riemann hypothesis. The work utilizes interval arithmetic to refine the bound to 0.1787854.
Why it matters
Advancing the understanding of the Riemann hypothesis is a major milestone in number theory with implications for prime number distribution.
I'm Jude Gomila and I've been exploring the zeta function in private since 2025. This post is part of a series of posts on discoveries obtained from human/ai collaboration. This post is about the de Bruijn–Newman constant Λ — a single real number with this property: the Riemann hypothesis holds exactly when Λ ≤ 0. Nobody can prove that yet, but its known ceiling can be lowered, and this is my computer-assisted proof taking it from 0.2 to 0.1787854, unconditionally, with no unproved conjecture anywhere in the chain. I'll walk you through the whole proof, step by step. Every claim links back to my audit repository and the independent review record. Feedback, bugs and upgrade comments are welcome as GitHub issues .
= 129/800 + 87677/5,000,000: an exact rational, obtained by exact arithmetic from 3,149,013 + 883 + 1 machine-checked interval certificates.
Get smarter about the news
Sign up free for a feed built around what you actually care about, Dive Deeper research on any story, and the full text of every article.
Create free accountAlready have an account? Sign in