Source labels openChecked July 26, 2026

Erdős Problem 218: Le

The set of indices $n$ for which a prime gap is followed by a larger or equal prime gap has a natural density of $\frac 1 2$ .

Number theory AMS 11

Mathematical statement

The set of indices $n$ for which a prime gap is followed by a larger or equal prime gap has a natural density of $\frac 1 2$ .

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_218.variants.le

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_218.variants.le : {n | primeGap n ≤ primeGap (n + 1)}.HasDensity <| 1 / 2 := 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/218background