Woodall Primes

formal-conjectures · wikipedia · ams-11

There are infinitely many prime numbers of the form k * 2 ^ k - 1 for k > 1.

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/Woodall_number#Woodall_primes
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://oeis.org/A2234
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/WoodalPrimes.lean
Local target: Corpus.WikipediaWoodalPrimes.infinitely_many_woodall_primes
Source SHA-256: a50c7a5d668a844f0809b181d2a557973db857c21a0423779c3fbcad6d9c5cf9
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