reserve k for Nat;
reserve p for Prime;

theorem
  p*p <= k < 529 implies
  p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or 
  p = 19
  proof
    assume p*p <= k < 529;
    then p*p < 23*23 by XXREAL_0:2;
    hence thesis by Ttool23a,NAT_4:1;
  end;
