All open problems
Source labels openChecked July 26, 2026

WikipediaNumber theory

Twin prime conjecture

Are there infinitely many primes p such that p + 2 is prime?

Mathematical statement

Are there infinitely many primes p such that p + 2 is prime?

Statement source: Wikipedia statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

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

twin_primes

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem twin_primes :    answer(sorry)  {p :  | Prime p  Prime (p + 2)}.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