Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 021-01. A quadratic bound for Jacobsthal's function
Manuscript map · lines 2905–2914
OpenAI@2026-10-07#rem:oai-p-021-01
Authors: OpenAI. Family 021.
Title: A quadratic bound for Jacobsthal's function.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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