Source labels openChecked July 26, 2026

Erdős Problem 890: A

If $\omega_k(n)$ counts the number of distinct prime factors of $n$ which are $>k$ , then is it true that, for every $k\geq 1$ , $\liminf_{n\to \infty}\sum_{0\leq i < k}\omega_k(n+i)\leq k?$

Number theory AMS 11

Mathematical statement

If $\omega_k(n)$ counts the number of distinct prime factors of $n$ which are $>k$ , then is it true that, for every $k\geq 1$ , $\liminf_{n\to \infty}\sum_{0\leq i < k}\omega_k(n+i)\leq k?$

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_890.parts.a

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_890.parts.a :    answer(sorry) ↔    ∀ k ≥ 1, liminf (fun n ↦ (∑ i ∈ range k, (ω_gt k (n + i) : EReal))) atTop ≤ k := 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/890background