Source labels openChecked July 26, 2026

Erdős Problem 1137

Let $d_n=p_{n+1}-p_n$ , where $p_n$ denotes the $n$ th prime. Is it true that $\frac{\max_{n < x}d_{n}d_{n-1}}{(\max_{n < x}d_n)^2}\to 0$ as $x\to \infty$ ?

Number theory AMS 11

Mathematical statement

Let $d_n=p_{n+1}-p_n$ , where $p_n$ denotes the $n$ th prime. Is it true that $\frac{\max_{n < x}d_{n}d_{n-1}}{(\max_{n < x}d_n)^2}\to 0$ as $x\to \infty$ ?

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_1137

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_1137 :    answer(sorry) ↔     Tendsto (fun x ↦        (((range x).sup (fun n ↦ (primeGap n) * (primeGap (n - 1))) : ℕ) : ℝ) /        (((range x).sup primeGap : ℕ) : ℝ) ^ 2) atTop (𝓝 0) := 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/1137background