(** definition of a "prime number" *)
Definition is_prime (p:nat) := (p<>1)/\(forall (d:nat),(divides p d)->(d=1)\/(d=p)).

Lemma prime_cond : forall (p:nat),((p<>1)/\(forall (a:nat),(a<>1)->(a<>p)->~(divides p a))<->(is_prime p)).