Source labels openChecked July 26, 2026

Erdős Problem 853: Ii

Let $d_n = p_{n+1} - p_n$ , where $p_n$ is the $n$ th prime. Let $r(x)$ be the smallest even integer $t$ such that $d_n = t$ has no solutions for $n \le x$ .

Number theory AMS 11

Mathematical statement

Let $d_n = p_{n+1} - p_n$ , where $p_n$ is the $n$ th prime. Let $r(x)$ be the smallest even integer $t$ such that $d_n = t$ has no solutions for $n \le x$ .

Is it true that $r(x) / \log x \to \infty$ ?

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_853.parts.ii

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_853.parts.ii :    atTop.Tendsto (fun n ↦ r n / Real.log n) atTop := 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/853background