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WikipediaNumber theory

Conjectures about Mersenne primes

The first five Catalan-Mersenne numbers c0,,c4c_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 cnc_n with n5n \geq 5 prime?

Mathematical statement

The first five Catalan-Mersenne numbers c0,,c4c_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 cnc_n with n5n \geq 5 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

Canonical source
Complete statement target, proof intentionally absentLean 4
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