All open problems
Source labels openChecked July 26, 2026
Conjectures about Mersenne primes
Are there infinitely many Mersenne primes?
Mathematical statement
Are there infinitely many Mersenne primes?
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
infinitely_many_mersenne_primes
Complete statement target, proof intentionally absentLean 4
theorem infinitely_many_mersenne_primes : answer(sorry) ↔ Set.Infinite { p : ℕ | (mersenne p).Prime } := by sorry /--The first five Catalan-Mersenne numbers $c_0, \ldots, c_4$ are known to be prime.Catalan conjectured that they are prime "up to a certain limit".Are all Catalan-Mersenne numbers $c_n$ with $n \geq 5$ prime?-/@[category research open, AMS 11]theorem catalans_mersenne_conjecture : answer(sorry) ↔ ∀ n ≥ 5, Nat.Prime (catalanMersenne n) := 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