Erdős Problem 455
Let q : ℕ → ℕ be a strictly increasing sequence of primes such that q (n + 2) - q (n + 1) ≥ q (n + 1) - q n. Must lim q n / (n ^ 2) = ∞?
Mathematical statement
Let q : ℕ → ℕ be a strictly increasing sequence of primes such that
q (n + 2) - q (n + 1) ≥ q (n + 1) - q n. Must lim q n / (n ^ 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_455
theorem erdos_455: answer(sorry) ↔ ∀ q : ℕ → ℕ, StrictMono q → (∀ n, (q n).Prime ∧ q (n + 2) - q (n + 1) ≥ q (n + 1) - q n) → Tendsto (fun n : ℕ => (q n : ℝ) / n ^ 2) atTop 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