Back to Problems

erdos_455:

Specification

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) = ∞`?

Actions

Submit a Proof

Have a proof attempt? Submit it for zero-trust verification.

Submit Proof
Lean 4 Statement 
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
ID: ErdosProblems__455__erdos_455_
Browse 300 unsolved math conjectures formalized in Lean 4
Browse

All Problems

Explore all 300 unsolved conjectures.

View problems →
ASI Prize documentation for formal verification pipeline
Docs

Verification Pipeline

How zero-trust verification works.

Read docs →
Evaluation Results

Recent Submissions

No submissions yet. Be the first to attempt this problem.