Perfect numbers
Infinitely many even perfect numbers conjecture.* Are there infinitely many even perfect numbers?
Mathematical statement
Infinitely many even perfect numbers conjecture.* Are there infinitely many even perfect numbers?
This is equivalent to asking whether there are infinitely many Mersenne primes, since by the Euclid–Euler theorem an even number is perfect if and only if it has the form where is a Mersenne prime. Reference:* Wikipedia
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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
infinitely_many_even_perfect
theorem infinitely_many_even_perfect : answer(sorry) ↔ {n : ℕ | Perfect n ∧ Even n}.Infinite := 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