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Sign inThe preprint claims that for every real λ with 0 < λ < 1, the interval (x, x + x^λ] contains asymptotically x^λ / log x primes. This would improve the Baker–Harman–Pintz gap exponent 0.525 to any positive power and would give Legendre's conjecture, Andrica's conjecture and Brocard's conjecture for all sufficiently large n. First posted 17 July 2023; version 4 dated 7 May 2026.
The arXiv page lists no journal reference and the comments say it was submitted to Annals of Mathematics; no independent confirmation was found by 17 October 2026. The claim is extraordinary: the Riemann Hypothesis gives the asymptotic only for λ > 1/2, so the preprint claims more than RH implies. The Formal Conjectures file labels the large-n statement solved, citing Ferreira, which reflects the claim, not a refereed acceptance.
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The result would be a major advance on prime gaps; a specialist should check the key estimates and constants.
Compare with Maier's matrix method and the parity barrier, which limit what short-interval methods are known to reach.
A Lean proof of the eventual statement in the Formal Conjectures corpus would settle the large-n case.
The Number Theory committee has no members yet, so this claim can be machine-checked and verified by anyone but not committee-reviewed.
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