
theorem
  8297 is prime
proof
  now
    8297 = 2*4148 + 1; hence not 2 divides 8297 by NAT_4:9;
    8297 = 3*2765 + 2; hence not 3 divides 8297 by NAT_4:9;
    8297 = 5*1659 + 2; hence not 5 divides 8297 by NAT_4:9;
    8297 = 7*1185 + 2; hence not 7 divides 8297 by NAT_4:9;
    8297 = 11*754 + 3; hence not 11 divides 8297 by NAT_4:9;
    8297 = 13*638 + 3; hence not 13 divides 8297 by NAT_4:9;
    8297 = 17*488 + 1; hence not 17 divides 8297 by NAT_4:9;
    8297 = 19*436 + 13; hence not 19 divides 8297 by NAT_4:9;
    8297 = 23*360 + 17; hence not 23 divides 8297 by NAT_4:9;
    8297 = 29*286 + 3; hence not 29 divides 8297 by NAT_4:9;
    8297 = 31*267 + 20; hence not 31 divides 8297 by NAT_4:9;
    8297 = 37*224 + 9; hence not 37 divides 8297 by NAT_4:9;
    8297 = 41*202 + 15; hence not 41 divides 8297 by NAT_4:9;
    8297 = 43*192 + 41; hence not 43 divides 8297 by NAT_4:9;
    8297 = 47*176 + 25; hence not 47 divides 8297 by NAT_4:9;
    8297 = 53*156 + 29; hence not 53 divides 8297 by NAT_4:9;
    8297 = 59*140 + 37; hence not 59 divides 8297 by NAT_4:9;
    8297 = 61*136 + 1; hence not 61 divides 8297 by NAT_4:9;
    8297 = 67*123 + 56; hence not 67 divides 8297 by NAT_4:9;
    8297 = 71*116 + 61; hence not 71 divides 8297 by NAT_4:9;
    8297 = 73*113 + 48; hence not 73 divides 8297 by NAT_4:9;
    8297 = 79*105 + 2; hence not 79 divides 8297 by NAT_4:9;
    8297 = 83*99 + 80; hence not 83 divides 8297 by NAT_4:9;
    8297 = 89*93 + 20; hence not 89 divides 8297 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8297 & n is prime
  holds not n divides 8297 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
