(** After factorization by a gcd, the original numbers are relatively prime. *)

Theorem Zrel_prime_neq_mod_0: forall a b, 1 < b -> rel_prime a b -> a mod b <> 0.
Inductive prime (p:Z) : Prop :=
prime_intro :
1 < p -> (forall n:Z, 1 <= n < p -> rel_prime n p) -> prime p.