Source labels openChecked July 26, 2026

Smallest number k such that kn + 1 is prime

Conjecture: for every $n > 1$ there exists a number $k < n$ such that $nk + 1$ is a prime.

Number theory AMS 11

Mathematical statement

Conjecture: for every $n > 1$ there exists a number $k < n$ such that $nk + 1$ is a prime.

Statement source: OEIS 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

exists_k

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem exists_k {n : ℕ} (hn : 1 < n) : ∃ k < n, (n * k + 1).Prime := 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 A34693background