Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.
Definition in prerequisite notation
Prime(p) ∧ (¬z = 0 ∧ (Lt(z,p) ∧ Dvd(p,z · z + 1)))Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
(((~(p = 1) /\ forall frm_prime_left_cor_secondwave_prime frm_prime_right_cor_secondwave_prime. p = frm_prime_left_cor_secondwave_prime * frm_prime_right_cor_secondwave_prime -> frm_prime_left_cor_secondwave_prime = 1 \/ frm_prime_right_cor_secondwave_prime = 1)) /\ (((~(z = 0)) /\ (((exists cor_gap_secondwave_bound. cor_gap_secondwave_bound + S (z) = (p)) /\ (exists cor_factor_secondwave. z * z + 1 = p * cor_factor_secondwave))))))The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.