reserve k for Nat;
reserve p for Prime;

theorem
  p*p <= k < 1369 implies
  p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or 
  p = 19 or p = 23 or p = 29 or p = 31
  proof
    assume p*p <= k < 1369;
    then p*p < 37*37 by XXREAL_0:2;
    hence thesis by Ttool37a,NAT_4:1;
  end;
