
theorem
  8329 is prime
proof
  now
    8329 = 2*4164 + 1; hence not 2 divides 8329 by NAT_4:9;
    8329 = 3*2776 + 1; hence not 3 divides 8329 by NAT_4:9;
    8329 = 5*1665 + 4; hence not 5 divides 8329 by NAT_4:9;
    8329 = 7*1189 + 6; hence not 7 divides 8329 by NAT_4:9;
    8329 = 11*757 + 2; hence not 11 divides 8329 by NAT_4:9;
    8329 = 13*640 + 9; hence not 13 divides 8329 by NAT_4:9;
    8329 = 17*489 + 16; hence not 17 divides 8329 by NAT_4:9;
    8329 = 19*438 + 7; hence not 19 divides 8329 by NAT_4:9;
    8329 = 23*362 + 3; hence not 23 divides 8329 by NAT_4:9;
    8329 = 29*287 + 6; hence not 29 divides 8329 by NAT_4:9;
    8329 = 31*268 + 21; hence not 31 divides 8329 by NAT_4:9;
    8329 = 37*225 + 4; hence not 37 divides 8329 by NAT_4:9;
    8329 = 41*203 + 6; hence not 41 divides 8329 by NAT_4:9;
    8329 = 43*193 + 30; hence not 43 divides 8329 by NAT_4:9;
    8329 = 47*177 + 10; hence not 47 divides 8329 by NAT_4:9;
    8329 = 53*157 + 8; hence not 53 divides 8329 by NAT_4:9;
    8329 = 59*141 + 10; hence not 59 divides 8329 by NAT_4:9;
    8329 = 61*136 + 33; hence not 61 divides 8329 by NAT_4:9;
    8329 = 67*124 + 21; hence not 67 divides 8329 by NAT_4:9;
    8329 = 71*117 + 22; hence not 71 divides 8329 by NAT_4:9;
    8329 = 73*114 + 7; hence not 73 divides 8329 by NAT_4:9;
    8329 = 79*105 + 34; hence not 79 divides 8329 by NAT_4:9;
    8329 = 83*100 + 29; hence not 83 divides 8329 by NAT_4:9;
    8329 = 89*93 + 52; hence not 89 divides 8329 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8329 & n is prime
  holds not n divides 8329 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
