Back to Problems

sylvester_schur

Specification

Sylvester and Schur: for $1 \le i \le n/2$ there is a prime $p > i$ dividing `n.choose i`.

Actions

Submit a Proof

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

Submit Proof
Lean 4 Statement
theorem sylvester_schur (n i : ℕ) (hi : 1 ≤ i) (hi_half : i ≤ n / 2) :
    ∃ p : ℕ, p.Prime ∧ i < p ∧ p ∣ Nat.choose n i
ID: ErdosProblems__699__sylvester_schur
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.