{"id":"palomar/PALOMAR-2026-11-03-000025","url":"https://github.com/sthubbar/goldbach-lean/tree/d0d978d2cf565be71d6949ce529ed5503affa72e/entries/goldbachshort1075","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-11-03-000025-v1.json","repo":"https://github.com/sthubbar/goldbach-lean","tags":["math.NT","msc:11P32","msc:11N05"],"score":0,"title":"Goldbach numbers in short intervals of length x^(26/1075+ε)","trust":"high","domain":"math.NT","source":"palomar","authors":["Steve Hubbard"],"reviews":0,"subject":"math.NT","summary":"A Lean 4 proof that for every ε > 0 and all large natural x there is a Goldbach number, an even sum of two primes, in the interval from x to x + 3 x^(26/1075+ε). The theorem is conditional on two cited results taken as explicit hypotheses, never as axioms, and neither is proved here: LiRow052, R. Li, arXiv 2308.04458, Theorem 2, the row θ = 0.52, primes in the intervals from n - n^(0.52+ε) to n with a lower bound of the right order, with some positive constant since the printed constant differs between versions of the paper; and LiPrintedExceptionalCount, R. Li, arXiv 2407.05651 v6, Theorem…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-11-03","reactions":{},"formalized":true,"formalizes":[{"title":"Primes in almost all short intervals","identifier":"arXiv:2407.05651v6","relationship":"adapts"},{"title":"The number of primes in short intervals and numerical calculations for Harman's sieve","identifier":"arXiv:2308.04458","relationship":"adapts"}]}