Source labels openChecked July 26, 2026

Erdős Problem 457: Qnk

More generally, let $q(n, k)$ denote the least prime which does not divide $\prod_{1 \le i \le k}(n + i)$ . This problem asks whether $q(n, \log n) \ge (2 + \epsilon) \log n$ infinitely often.

Number theory AMS 11

Mathematical statement

More generally, let $q(n, k)$ denote the least prime which does not divide $\prod_{1 \le i \le k}(n + i)$ . This problem asks whether $q(n, \log n) \ge (2 + \epsilon) \log n$ infinitely often.

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

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

erdos_457.variants.qnk

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_457.variants.qnk : answer(sorry) ↔ ∃ ε > (0 : ℝ),    { (n : ℕ) | (2 + ε) * Real.log n ≤ q n (Real.log n) }.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

Pinned Formal Conjectures sourceformalization erdosproblems.com/457background