Erdős Problem #366

Partial progress by Automated research pipeline (14 Apr 2026): conditional partial result.

Problem
Erdős problem #366 (number theory, powerful); current status: open (verifiable)
Credit
Automated research pipeline · AI on its own; related literature found afterwards
Checked
Listed in Tao's wiki
Timeline
First AI contribution 2026-04-14 · 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

Are there any 22-full nn such that n+1n+1 is 33-full? That is, if p∣np\mid n then p2∣np^2\mid n and if p∣n+1p\mid n+1 then p3∣n+1p^3\mid n+1.

Statement quoted from erdosproblems.com/366, maintained by Thomas Bloom. Original source: [Er76d,p.31][ErGr80,p.68]. Current status there: open (verifiable).

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 Outcome Literature
14 Apr, 2026 AI on its own; related literature found afterwards Automated research pipeline 🟡 Conditional partial result 🟡 Aktaş and Murty (2017)

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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