Goldbach conjecture: every even integer above two is a sum of two primes

Prove that every even natural number n ≥ 4 can be written n = p + q with both p and q prime. This is the binary (strong) conjecture; results about sums of three primes do not settle this request. The inline prime predicate means p ≥ 2 and every natural divisor of p is 1 or p. The target covers all even n, with no finite search cutoff. Research status checked 8 October 2026: no accepted general proof identified in the cited literature. This is a proposed formal statement; independent correspondence review is requested. A successful statement check establishes well-formedness, not the conjecture.

(fun prime : Nat → Prop =>
  ∀ n : Nat, 4 ≤ n → n % 2 = 0 → ∃ p q : Nat, prime p ∧ prime q ∧ n = p + q)
(fun p => 2 ≤ p ∧ ∀ d : Nat, d ∣ p → d = 1 ∨ d = p)

OA_statement : Prop