Infinite Regular Primes

formal-conjectures · wikipedia · ams-11

We define the notion of regular primes, which are prime numbers that are coprime with the
cardinality of the class group of the p-th cyclotomic field. We also state that there are
infinitely many regular primes.

Conjecture: The set of regular primes is infinite.

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/Regular_prime
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/RegularPrimes.lean
Local target: Corpus.WikipediaRegularPrimes.regularprime_conjecture
Source SHA-256: 16c9e8095aa3b674a2dea5878ec259fd7c780e5960d413944597e922c21a828b
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.

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