Pierpont primes

formal-conjectures · wikipedia · ams-11

A Pierpont prime is a prime of the form $2^a 3^b + 1$, where $a$ and $b$ are
nonnegative integers. Marc Gleason conjectured that there are infinitely many.

There are infinitely many Pierpont primes.

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/Pierpont_prime
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://oeis.org/A005109
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/PierpontPrime.lean
Local target: Corpus.WikipediaPierpontPrime.infinitely_many_pierpont_primes
Source SHA-256: f62451cd8f350a3ec81b9e1e1f55ddcd2fc65a529f8f34088a4e6cc21fefb4ce
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