Source labels openChecked July 26, 2026

Grimm's conjecture

Grimm's Conjecture, weaker version* If $n, n+1, \dots, n+k-1$ are all composite numbers, then their product has at least $k$ distinct prime divisors.

Number theory AMS 11

Mathematical statement

Grimm's Conjecture, weaker version* If $n, n+1, \dots, n+k-1$ are all composite numbers, then their product has at least $k$ distinct prime divisors.

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

grimm_conjecture_weak

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem grimm_conjecture_weak (n k : ℕ) (hn : 1 ≤ n) (hk : 1 ≤ k)    (h : ∀ i : Fin k, (n + i).Composite) :    ∃ ps : Fin k ↪ ℕ,  ∀ i : Fin k, (ps i).Prime ∧ ∃ j : Fin k, ps i ∣ (n + j) := 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

Pinned Formal Conjectures sourceformalization Wikipediabackground