Erdős Problem #451

Partial progress by Wouter van Doorn and Quanyu Tang with Aristotle and GPT-5.5 Pro (19 Jun 2026): partial result (Lean).

Problem
Erdős problem #451 (number theory); current status: open
Credit
Wouter van Doorn and Quanyu Tang with Aristotle and GPT-5.5 Pro · AI working with humans
Checked
Lean formalizationListed in Tao's wiki
Timeline
First AI contribution 2026-06-19 · wiki data as of 2026-06-30
Sources
Problem page (erdosproblems.com)Tao's AI-contributions wiki
PARTIALPer Tao's AI-contributions wiki

The problem

Estimate nkn_k, the smallest integer >2k>2k such that ∏1≤i≤k(nk−i)\prod_{1\leq i\leq k}(n_k-i) has no prime factor in (k,2k)(k,2k).

Statement quoted from erdosproblems.com/451, maintained by Thomas Bloom. Original source: [Er79d,p.78][ErGr80,p.89]. 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
26 Apr-19 Jun, 2026 AI working with humans Aristotle, GPT-5.5 Pro Wouter van Doorn, Quanyu Tang 🟡 Partial result (Lean)

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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