(** Prime(n) if all prime divisors > sqrt(n). *)

(* Specifications: *)
Theorem primepropdiv :
forall n : nat,
n > 1 -> (forall q : nat, Prime q -> Divides q n -> q * q > n) -> Prime n.
Lemma primediv1p : forall p n : nat, Prime p -> Divides n p -> n = 1 \/ n = p.
(** Two is a prime. *)
Lemma prime2 : Prime 2.
Definition ZPrime (n : Z) : Prop :=
(n > 1)%Z /\ (forall q : Z, (q >= 0)%Z -> ZDivides q n -> q = 1%Z \/ q = n).