
theorem
  9533 is prime
proof
  now
    9533 = 2*4766 + 1; hence not 2 divides 9533 by NAT_4:9;
    9533 = 3*3177 + 2; hence not 3 divides 9533 by NAT_4:9;
    9533 = 5*1906 + 3; hence not 5 divides 9533 by NAT_4:9;
    9533 = 7*1361 + 6; hence not 7 divides 9533 by NAT_4:9;
    9533 = 11*866 + 7; hence not 11 divides 9533 by NAT_4:9;
    9533 = 13*733 + 4; hence not 13 divides 9533 by NAT_4:9;
    9533 = 17*560 + 13; hence not 17 divides 9533 by NAT_4:9;
    9533 = 19*501 + 14; hence not 19 divides 9533 by NAT_4:9;
    9533 = 23*414 + 11; hence not 23 divides 9533 by NAT_4:9;
    9533 = 29*328 + 21; hence not 29 divides 9533 by NAT_4:9;
    9533 = 31*307 + 16; hence not 31 divides 9533 by NAT_4:9;
    9533 = 37*257 + 24; hence not 37 divides 9533 by NAT_4:9;
    9533 = 41*232 + 21; hence not 41 divides 9533 by NAT_4:9;
    9533 = 43*221 + 30; hence not 43 divides 9533 by NAT_4:9;
    9533 = 47*202 + 39; hence not 47 divides 9533 by NAT_4:9;
    9533 = 53*179 + 46; hence not 53 divides 9533 by NAT_4:9;
    9533 = 59*161 + 34; hence not 59 divides 9533 by NAT_4:9;
    9533 = 61*156 + 17; hence not 61 divides 9533 by NAT_4:9;
    9533 = 67*142 + 19; hence not 67 divides 9533 by NAT_4:9;
    9533 = 71*134 + 19; hence not 71 divides 9533 by NAT_4:9;
    9533 = 73*130 + 43; hence not 73 divides 9533 by NAT_4:9;
    9533 = 79*120 + 53; hence not 79 divides 9533 by NAT_4:9;
    9533 = 83*114 + 71; hence not 83 divides 9533 by NAT_4:9;
    9533 = 89*107 + 10; hence not 89 divides 9533 by NAT_4:9;
    9533 = 97*98 + 27; hence not 97 divides 9533 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9533 & n is prime
  holds not n divides 9533 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
