# Erdős Problem 251

A statement in qed.bot, the register of claims of AI work in mathematics. The register grades the evidence attached to each claim; it never rules on whether a proof is correct.

- Identifier: erdos:251
- Collection: Erdős
- Page: https://qed.bot/s/erdos-251
- Formal record: open; at its source: open
- Machine-checked: no independent check has verified it
- Fidelity F0: Absent. No formal statement is attached to the result.
- Source: https://www.erdosproblems.com/251

## AI claims

### GPT-5.4 Pro, 15 Apr 2026

Solution to variant problem

- Outcome: partial
- Autonomy A3: Autonomous. The system produced the result without significant human mathematical involvement.
- Evidence V1: Informal. A public write-up exists and has had community scrutiny.
- Fidelity F0: Absent. No formal statement is attached to the result.
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

## Claimed on erdosproblems.com

Proof claims posted on erdosproblems.com, which says that listing a claim is no guarantee of proof correctness. Nobody has examined them, and none counts in the register's totals.

- Stefan Ringer, using GPT 6 Astra, Fable 5.1: a partial proof claimed, 13 Sep 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/251/proof-claims#proof-claim-307

## Formal statements

- FormalConjectures/ErdosProblems/251.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/251.lean

Cite as: qed.bot, "Erdős Problem 251", https://qed.bot/s/erdos-251, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/