reserve k for Nat;
reserve p for Prime;

theorem
  p*p <= k < 19321 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 or p = 37 or p = 41 or p = 43 or 
  p = 47 or p = 53 or p = 59 or p = 61 or p = 67 or p = 71 or p = 73 or 
  p = 79 or p = 83 or p = 89 or p = 97 or p = 101 or p = 103 or p = 107 or 
  p = 109 or p = 113 or p = 127 or p = 131 or p = 137
  proof
    assume p*p <= k < 19321;
    then p*p < 139*139 by XXREAL_0:2;
    hence thesis by Ttool139a,NAT_4:1;
  end;
