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Source labels openChecked July 26, 2026

WikipediaNumber theory

Prime Triplet Conjecture

Are there infinitely many tuples of three consecutive primes (p,q,r)(p, q, r) such that rp=6r - p = 6?

Mathematical statement

Are there infinitely many tuples of three consecutive primes (p,q,r)(p, q, r) such that rp=6r - p = 6?

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

prime_triplets

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem prime_triplets :    answer(sorry)  {p :  | 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