Erdős Problem 234
Is it true that for all c ≥ 0, the density f c of integers for which (p (n + 1) - p n) / log n < c exists and is a continuous function of c?
Mathematical statement
Is it true that for all c ≥ 0, the density f c of integers for which
(p (n + 1) - p n) / log n < c exists and is a continuous function of c?
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_234
theorem erdos_234 : answer(sorry) ↔ ∃ f : ℝ≥0 → ℝ, Continuous f ∧ ∀ c : ℝ≥0, HasDensity {n : ℕ | primeGap n / log n < c} (f c) := 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