Source labels openChecked July 26, 2026

Erdős Problem 1139

Let $1\leq u_1 < u_2 < \cdots$ be the sequence of integers with at most $2$ prime factors. Is it true that $\limsup_{k \to \infty} \frac{u_{k+1}-u_k}{\log k}=\infty?$

Number theory AMS 11

Mathematical statement

Let $1\leq u_1 < u_2 < \cdots$ be the sequence of integers with at most $2$ prime factors. Is it true that $\limsup_{k \to \infty} \frac{u_{k+1}-u_k}{\log k}=\infty?$

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_1139

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_1139 :    answer(sorry) ↔      letI u := Nat.nth (fun n ↦ 0 < n ∧ Ω n ≤ 2)      atTop.limsup (fun k : ℕ ↦ (((u (k + 1) : ℝ) - (u k : ℝ)) / Real.log (↑k + 1) : EReal)) = ⊤ := 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/1139background