Kummer–Vandiver conjecture

formal-conjectures · wikipedia · ams-11

Kummer–Vandiver conjecture states that for every prime $p$, the class number of the maximal
real subfield of $\mathbb{Q}(\zeta_p)$ is not divisible by $p$.
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Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://en.wikipedia.org/wiki/Kummer%E2%80%93Vandiver_conjecture
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/KummerVandiver.lean
Local target: Corpus.WikipediaKummerVandiver.kummer_vandiver
Source SHA-256: 9e1293b2be0ce36f05df606699a8ae9cc8a2bb8ec1bce6d48a119c3e378cde1c
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record