Source labels openChecked July 26, 2026

Erdős Problem 680: Ii

Can one prove this is false if we replace $k^2+1$ by $e^{(1+\epsilon)\sqrt{k}}+C_\epsilon$ , for all $\epsilon>0$ , where $C_\epsilon>0$ is some constant?

Number theory AMS 11

Mathematical statement

Can one prove this is false if we replace $k^2+1$ by $e^{(1+\epsilon)\sqrt{k}}+C_\epsilon$ , for all $\epsilon>0$ , where $C_\epsilon>0$ is some constant?

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.ii

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_680.parts.ii : answer(sorry) ↔ ∀ ε > 0, ∃ C > 0,    ¬ ∀ᶠ (n : ℕ) in Filter.atTop, ∃ k ≠ 0,    Nat.minFac (n + k) > exp ((1 + ε) * √k) + C := 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