Conjectures about Mersenne primes
The first five Catalan-Mersenne numbers are known to be prime. Catalan conjectured that they are prime "up to a certain limit". Are all Catalan-Mersenne numbers with prime?
Mathematical statement
The first five Catalan-Mersenne numbers are known to be prime. Catalan conjectured that they are prime "up to a certain limit". Are all Catalan-Mersenne numbers with prime?
Statement source: Wikipedia statement material
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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
catalans_mersenne_conjecture
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