Back to Problems

balanced_primes

Specification

Let $p_k$ be the $k$-th prime number. Are there infinitely many $n$ such that $(p_n + p_{n+2}) / 2$ is prime?

Actions

Submit a Proof

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

Submit Proof
Lean 4 Statement 
theorem balanced_primes :
    answer(sorry) ↔ {n : ℕ | Prime ((Nat.nth Prime n + Nat.nth Prime (n + 2)) / 2)}.Infinite
ID: Wikipedia__BalancedPrimes__balanced_primes
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.