
theorem
  6733 is prime
proof
  now
    6733 = 2*3366 + 1; hence not 2 divides 6733 by NAT_4:9;
    6733 = 3*2244 + 1; hence not 3 divides 6733 by NAT_4:9;
    6733 = 5*1346 + 3; hence not 5 divides 6733 by NAT_4:9;
    6733 = 7*961 + 6; hence not 7 divides 6733 by NAT_4:9;
    6733 = 11*612 + 1; hence not 11 divides 6733 by NAT_4:9;
    6733 = 13*517 + 12; hence not 13 divides 6733 by NAT_4:9;
    6733 = 17*396 + 1; hence not 17 divides 6733 by NAT_4:9;
    6733 = 19*354 + 7; hence not 19 divides 6733 by NAT_4:9;
    6733 = 23*292 + 17; hence not 23 divides 6733 by NAT_4:9;
    6733 = 29*232 + 5; hence not 29 divides 6733 by NAT_4:9;
    6733 = 31*217 + 6; hence not 31 divides 6733 by NAT_4:9;
    6733 = 37*181 + 36; hence not 37 divides 6733 by NAT_4:9;
    6733 = 41*164 + 9; hence not 41 divides 6733 by NAT_4:9;
    6733 = 43*156 + 25; hence not 43 divides 6733 by NAT_4:9;
    6733 = 47*143 + 12; hence not 47 divides 6733 by NAT_4:9;
    6733 = 53*127 + 2; hence not 53 divides 6733 by NAT_4:9;
    6733 = 59*114 + 7; hence not 59 divides 6733 by NAT_4:9;
    6733 = 61*110 + 23; hence not 61 divides 6733 by NAT_4:9;
    6733 = 67*100 + 33; hence not 67 divides 6733 by NAT_4:9;
    6733 = 71*94 + 59; hence not 71 divides 6733 by NAT_4:9;
    6733 = 73*92 + 17; hence not 73 divides 6733 by NAT_4:9;
    6733 = 79*85 + 18; hence not 79 divides 6733 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6733 & n is prime
  holds not n divides 6733 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
