All open problems
Source labels openChecked July 26, 2026
Prime Triplet Conjecture
Are there infinitely many tuples of three consecutive primes such that ?
Mathematical statement
Are there infinitely many tuples of three consecutive primes such that ?
Statement source: Wikipedia statement material
Statement terms: CC-BY-SA-4.0
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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
prime_triplets
Complete statement target, proof intentionally absentLean 4
theorem prime_triplets : answer(sorry) ↔ {p : ℕ | Prime p ∧ (Prime (p + 2) ∨ Prime (p + 4)) ∧ Prime (p + 6)}.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