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Research / Aug 25, 2026

Improved record lower bound for large prime gaps (Erdős

How large can gaps between consecutive primes be relative to iterated logarithms?

Model / AI: GPT-5.6 Sol

verified (improved bound)self-reported (improved bound)
Aug 25, 2026

Smoothed probabilistic-tilt sieve

Model / AI: GPT-5.6 Sol

verified (improved bound)self-reported (improved bound)

A model-authored manuscript replaces an intermediate sieve in the 2018 Ford–Green–Konyagin–Maynard–Tao argument and claims a factor log_3 T/(log_4 T)^2 improvement. Ben Green publicly reported becoming broadly convinced after consulting Tao and Maynard; a separate Lean transcription was later posted.

Source read 2026-09-08. Read the manuscript and public source synthesis recording Green's review. The Lean transcription was not rebuilt and no journal review was found.