reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem
  for p be prime Nat, a be non trivial Nat holds
    (p |-count a)*(a |-count p|^n) <= n
proof
  let p be prime Nat, a be non trivial Nat;
  A1: p > 1 by NAT_4:14;
  p|^((p |-count a)*(a |-count p|^n)) <= p|^n by Count7;
  hence thesis by A1,PEPIN:66;
end;
