{"id":"openai-math/A-quadratic-bound-for-Jacobsthals-function","pdf":"https://github.com/openai/math/blob/main/preprints/A-quadratic-bound-for-Jacobsthals-function-September-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-quadratic-bound-for-Jacobsthals-function-September-25-2026","tags":["number-theory","sieve-theory","jacobsthal-function"],"score":0,"title":"A quadratic bound for Jacobsthal's function","domain":"Number theory","family":"021","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"Let $`h(k)`$ be the least integer such that every interval of $`h(k)`$ consecutive integers contains an integer coprime to any prescribed positive integer having at most k distinct prime divisors. We prove $`h(k)\\ll k^2/(\\log\\log(3k))^2`$, giving an affirmative answer to Jacobsthal's quadratic-bound question.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":true,"family_title":"A quadratic bound for Jacobsthal’s function"}