# Erdős Problem 123

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:123
- Collection: Erdős
- Page: https://qed.bot/s/erdos-123
- Formal record: mixed; at its source: proved (Lean)
- Prize: $250
- Machine-checked: yes, by qed.bot
- Fidelity F2: The statement corpus cites this proof against its own statement.
- Source: https://www.erdosproblems.com/123

## AI claims

No AI contribution is recorded against this statement.

## 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.

- Principia Math, using GPT 5.6, Opus 4.8: a full proof claimed, 20 Jul 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/123/proof-claims#proof-claim-97
- Colin Snyder, using GPT 5.6 (custom harness): a full proof claimed, 15 Jul 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/123/proof-claims#proof-claim-25

## Checks

- verified, by qed.bot: 96 theorems on the standard axioms only (https://github.com/plby/lean-proofs/blob/a28a04b6b8ce43d5260a7466677c1f23833bfc38/src/latest/ErdosProblems/Erdos123.lean)

## Formal statements

- FormalConjectures/ErdosProblems/123.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/123.lean

Cite as: qed.bot, "Erdős Problem 123", https://qed.bot/s/erdos-123, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/