Source labels openChecked July 26, 2026

Conjectures about Mersenne primes

For any odd natural number p if two of the following conditions hold, then all three must hold: 1. $2^p-1$ is prime 2. $(2^p+1)/3$ is prime 3. Exists a number k such that $p = 2^k \\pm 1$ or $p = 4^k \\pm 3$

Number theory AMS 11

Mathematical statement

For any odd natural number p if two of the following conditions hold, then all three must hold:

$2^p-1$ is prime
$(2^p+1)/3$ is prime
Exists a number k such that $p = 2^k \\pm 1$ or $p = 4^k \\pm 3$

Statement source: Wikipedia statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

new_mersenne_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem new_mersenne_conjecture (p : ℕ) (hp : Odd p) :    NewMersenneConjectureStatement p := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization Wikipedia: Mersenne conjecturesbackground Wikipedia: Catalan's Mersenne conjecturebackground MathWorld: Catalan-Mersenne Numberbackground