reserve k for Nat;
reserve p for Prime;

theorem
  p*p <= k < 3481 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
  proof
    assume p*p <= k < 3481;
    then p*p < 59*59 by XXREAL_0:2;
    hence thesis by Ttool59a,NAT_4:1;
  end;
