(** * Primality on Z *)

(** ZPrime, just like Prime but uses only Z. *)

Definition ZPrime (n : Z) : Prop :=
  (n > 1)%Z /\ (forall q : Z, (q >= 0)%Z -> ZDivides q n -> q = 1%Z \/ q = n).

Lemma primezprime : forall n : nat, Prime n -> ZPrime (Z_of_nat n).