Open problemChecked July 24, 2026

Odd Perfect Number Conjecture

The ancient question of whether every perfect number must be even.

Number theory Perfect numbers Divisors

Mathematical statement

Every perfect number $n$ , satisfying $n=\sum_{d\mid n,\ d<n}d$ , is even.

Statement source: Therefore editorial statement

Statement terms: Source-specific

Editorial wording by Therefore. No statement reuse license is granted.

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

PerfectNumbers.odd_perfect_number_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem odd_perfect_number_conjecture    (n : ℕ) (hn : Perfect n) : Even 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

Odd perfect numbers referencebackground