Source labels openChecked July 26, 2026

Erdős Problem 680: I

Is it true that, for all sufficiently large $n$ , there exists some $k$ such that $p(n+k)>k^2+1,$ where $p(m)$ denotes the least prime factor of $m$ ?

Number theory AMS 11

Mathematical statement

Is it true that, for all sufficiently large $n$ , there exists some $k$ such that

p(n+k)>k^2+1,

where $p(m)$ denotes the least prime factor of $m$ ?

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_680.parts.i

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_680.parts.i :    answer(sorry) ↔ ∀ᶠ (n : ℕ) in .atTop, ∃ k ≠ 0, (n + k).minFac > k^2 + 1 := 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/680background