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

Lemma gcd_prime : forall (p:nat),(p<>1)->(forall (d a:nat),(is_gcd d a p)->(d=1)\/(d=p))->(is_prime p).