
theorem
  8287 is prime
proof
  now
    8287 = 2*4143 + 1; hence not 2 divides 8287 by NAT_4:9;
    8287 = 3*2762 + 1; hence not 3 divides 8287 by NAT_4:9;
    8287 = 5*1657 + 2; hence not 5 divides 8287 by NAT_4:9;
    8287 = 7*1183 + 6; hence not 7 divides 8287 by NAT_4:9;
    8287 = 11*753 + 4; hence not 11 divides 8287 by NAT_4:9;
    8287 = 13*637 + 6; hence not 13 divides 8287 by NAT_4:9;
    8287 = 17*487 + 8; hence not 17 divides 8287 by NAT_4:9;
    8287 = 19*436 + 3; hence not 19 divides 8287 by NAT_4:9;
    8287 = 23*360 + 7; hence not 23 divides 8287 by NAT_4:9;
    8287 = 29*285 + 22; hence not 29 divides 8287 by NAT_4:9;
    8287 = 31*267 + 10; hence not 31 divides 8287 by NAT_4:9;
    8287 = 37*223 + 36; hence not 37 divides 8287 by NAT_4:9;
    8287 = 41*202 + 5; hence not 41 divides 8287 by NAT_4:9;
    8287 = 43*192 + 31; hence not 43 divides 8287 by NAT_4:9;
    8287 = 47*176 + 15; hence not 47 divides 8287 by NAT_4:9;
    8287 = 53*156 + 19; hence not 53 divides 8287 by NAT_4:9;
    8287 = 59*140 + 27; hence not 59 divides 8287 by NAT_4:9;
    8287 = 61*135 + 52; hence not 61 divides 8287 by NAT_4:9;
    8287 = 67*123 + 46; hence not 67 divides 8287 by NAT_4:9;
    8287 = 71*116 + 51; hence not 71 divides 8287 by NAT_4:9;
    8287 = 73*113 + 38; hence not 73 divides 8287 by NAT_4:9;
    8287 = 79*104 + 71; hence not 79 divides 8287 by NAT_4:9;
    8287 = 83*99 + 70; hence not 83 divides 8287 by NAT_4:9;
    8287 = 89*93 + 10; hence not 89 divides 8287 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8287 & n is prime
  holds not n divides 8287 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
