Open problemChecked July 24, 2026

Goldbach's Conjecture

A famously elementary statement about writing even numbers as sums of primes.

Number theory Prime numbers Additive combinatorics

Mathematical statement

Every even integer $n>2$ can be written as $n=p+q$ with $p$ and $q$ prime.

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

GoldbachConjecture.goldbach

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem goldbach :    answer(sorry) ↔ ∀ n : ℕ, 2 < n → Even n →      ∃ p q, Prime p ∧ Prime q ∧ n = p + q := 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

Goldbach's conjecture overviewbackground