Source labels openChecked July 26, 2026

Erdős Problem 889

Let $v(n,k)$ count the prime factors of $n+k$ which do not divide $n+i$ for $0\leq i < k$ . Is it true that $v_0(n)=\max_{k\geq 0}v(n,k)\to \infty$ as $n\to \infty$ ?

Number theory AMS 11

Mathematical statement

Let $v(n,k)$ count the prime factors of $n+k$ which do not divide $n+i$ for $0\leq i < k$ . Is it true that $v_0(n)=\max_{k\geq 0}v(n,k)\to \infty$ as $n\to \infty$ ?

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_889

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_889 : Tendsto v₀ atTop (𝓝 ⊤) := 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/889background