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For the Erdős–Pomerance functions $F(n)$ and $h_{\mathbb{P}}(n)$ counting how many consecutive integers are needed to contain a distinct multiple of each integer, respectively prime, up to $n$, the paper proves $F(n) \ge h_{\mathbb{P}}(n) \ge n\exp\left(\left(\frac{\log 2}{2} - o(1)\right)\frac{\log n}{\log\log n}\right)$, disproving Kominers' conjecture that $F(n) \ll n\log n$. The paper also significantly improves known upper bounds (which were on the order of $n^{3/2}$) to $F(n) \le n^{4/3 + o(1)}$ and $h_{\mathbb{P}}(n) \le n^{4/3 - o(1)}$.
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The note carries a dedicated Statement on AI saying that the main proofs in it were developed with the assistance of ChatGPT 5.x. That is a claim about the mathematics rather than the exposition, which is why this sits a tier above the rest of its batch.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
No independent check. The disclosure credits the model with the main proofs, so the result rests entirely on the author's own verification. Preprint, not refereed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.