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) = ∞?
Sources
FormalConjectures/ErdosProblems/
455.lean
Retained formal 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) = ∞?
True ↔ ∀ (q : ℕ → ℕ), StrictMono q → (∀ (n : ℕ), Nat.Prime (q n) ∧ q (n + 2) - q (n + 1) ≥ q (n + 1) - q n) → Filter.Tendsto (fun n => ↑(q n) / ↑n ^ 2) Filter.atTop Filter.atTopOpenStatement only, no proof