Catalan-Mersenne numbers

formal-conjectures · oeis · ams-11

Catalan-Mersenne numbers: $a(0) = 2$; for $n \ge 0$, $a(n+1) = 2^{a(n)} - 1$.

Catalan-Mersenne conjecture: All terms of the Catalan-Mersenne sequence are prime.

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://oeis.org/A007013
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/7013.lean
Local target: Corpus.OEIS7013.conjecture
Source SHA-256: f249301d00d861737420c3d7ada913fcc9813dcf18cda1df9d8f46bdfcb2e36f
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