Open problemChecked July 24, 2026

Twin Prime Conjecture

The question of whether prime pairs separated by two continue forever.

Number theory Prime numbers Sieve theory

Mathematical statement

There are infinitely many primes $p$ for which $p+2$ is also 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

TwinPrimes.twin_primes

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem twin_primes :    answer(sorry) ↔      {p : ℕ | 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

Twin prime conjecture overviewbackground