
theorem
  9733 is prime
proof
  now
    9733 = 2*4866 + 1; hence not 2 divides 9733 by NAT_4:9;
    9733 = 3*3244 + 1; hence not 3 divides 9733 by NAT_4:9;
    9733 = 5*1946 + 3; hence not 5 divides 9733 by NAT_4:9;
    9733 = 7*1390 + 3; hence not 7 divides 9733 by NAT_4:9;
    9733 = 11*884 + 9; hence not 11 divides 9733 by NAT_4:9;
    9733 = 13*748 + 9; hence not 13 divides 9733 by NAT_4:9;
    9733 = 17*572 + 9; hence not 17 divides 9733 by NAT_4:9;
    9733 = 19*512 + 5; hence not 19 divides 9733 by NAT_4:9;
    9733 = 23*423 + 4; hence not 23 divides 9733 by NAT_4:9;
    9733 = 29*335 + 18; hence not 29 divides 9733 by NAT_4:9;
    9733 = 31*313 + 30; hence not 31 divides 9733 by NAT_4:9;
    9733 = 37*263 + 2; hence not 37 divides 9733 by NAT_4:9;
    9733 = 41*237 + 16; hence not 41 divides 9733 by NAT_4:9;
    9733 = 43*226 + 15; hence not 43 divides 9733 by NAT_4:9;
    9733 = 47*207 + 4; hence not 47 divides 9733 by NAT_4:9;
    9733 = 53*183 + 34; hence not 53 divides 9733 by NAT_4:9;
    9733 = 59*164 + 57; hence not 59 divides 9733 by NAT_4:9;
    9733 = 61*159 + 34; hence not 61 divides 9733 by NAT_4:9;
    9733 = 67*145 + 18; hence not 67 divides 9733 by NAT_4:9;
    9733 = 71*137 + 6; hence not 71 divides 9733 by NAT_4:9;
    9733 = 73*133 + 24; hence not 73 divides 9733 by NAT_4:9;
    9733 = 79*123 + 16; hence not 79 divides 9733 by NAT_4:9;
    9733 = 83*117 + 22; hence not 83 divides 9733 by NAT_4:9;
    9733 = 89*109 + 32; hence not 89 divides 9733 by NAT_4:9;
    9733 = 97*100 + 33; hence not 97 divides 9733 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9733 & n is prime
  holds not n divides 9733 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
