Erdős Problem #1095

The problem

Let $g(k)>k+1$ be the smallest $n$ such that all prime factors of $\binom{n}{k}$ are $>k$ . Estimate $g(k)$ .

Statement quoted from erdosproblems.com/1095, maintained by Thomas Bloom. Original source: [EES74]. Current status there: open.

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Date	Kind	AI systems	Humans	Outcome	Literature
30 Dec, 2025	AI building on known literature	Aristotle	—	🟡 New proof of (slightly weaker) partial result (Lean)	🟡 Ecklund, Erdős, and Selfridge (1975)
13 Mar, 2026	AI working with humans	Claude Opus 4.6, Gemini 3.1 Pro, GPT-5.4 Pro	shtuka	🟡 Partial result	—

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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