GPT-5.6 broke a 2018 record on gaps between prime numbers

A pure mathematics record held since 2018 by five leading number theorists has fallen to a language model, according to one of the field’s own researchers.

What was reported

Oxford number theorist Jared Lichtman reported on August 30, 2026 that GPT-5.6 has broken the record on large gaps between primes, improving the bound by a factor of roughly log base 3 of n over the previous best result. That result was set in 2018 by Kevin Ford, Ben Green, Sergei Konyagin, James Maynard and Terence Tao, a lineup that includes two Fields medalists; Maynard’s 2022 medal partly recognized his work on exactly this family of problems.

The new proof has been formalized in Lean by Alexeev, meaning a computer has verified every logical step. That detail moves the claim out of screenshot territory: whatever questions remain about how the result was found, its correctness is machine-checked.

The problem

Prime gaps ask a deceptively simple question: how long can the empty stretches between consecutive prime numbers get? Progress on the lower bound for large gaps is measured in decades, and the 2018 improvement had stood for eight years.

Why it matters

This is the third AI mathematics record reported in a single month, following a proof of the Crouzeix conjecture in mid-August and a new elliptic curve rank record a week ago. Frontier models are no longer reproducing known mathematics but extending it, and the results are arriving pre-verified in formal proof systems. The open question is no longer whether a model really proved something, but how far the pattern extends into problems mathematicians actually care about.