
theorem
  8731 is prime
proof
  now
    8731 = 2*4365 + 1; hence not 2 divides 8731 by NAT_4:9;
    8731 = 3*2910 + 1; hence not 3 divides 8731 by NAT_4:9;
    8731 = 5*1746 + 1; hence not 5 divides 8731 by NAT_4:9;
    8731 = 7*1247 + 2; hence not 7 divides 8731 by NAT_4:9;
    8731 = 11*793 + 8; hence not 11 divides 8731 by NAT_4:9;
    8731 = 13*671 + 8; hence not 13 divides 8731 by NAT_4:9;
    8731 = 17*513 + 10; hence not 17 divides 8731 by NAT_4:9;
    8731 = 19*459 + 10; hence not 19 divides 8731 by NAT_4:9;
    8731 = 23*379 + 14; hence not 23 divides 8731 by NAT_4:9;
    8731 = 29*301 + 2; hence not 29 divides 8731 by NAT_4:9;
    8731 = 31*281 + 20; hence not 31 divides 8731 by NAT_4:9;
    8731 = 37*235 + 36; hence not 37 divides 8731 by NAT_4:9;
    8731 = 41*212 + 39; hence not 41 divides 8731 by NAT_4:9;
    8731 = 43*203 + 2; hence not 43 divides 8731 by NAT_4:9;
    8731 = 47*185 + 36; hence not 47 divides 8731 by NAT_4:9;
    8731 = 53*164 + 39; hence not 53 divides 8731 by NAT_4:9;
    8731 = 59*147 + 58; hence not 59 divides 8731 by NAT_4:9;
    8731 = 61*143 + 8; hence not 61 divides 8731 by NAT_4:9;
    8731 = 67*130 + 21; hence not 67 divides 8731 by NAT_4:9;
    8731 = 71*122 + 69; hence not 71 divides 8731 by NAT_4:9;
    8731 = 73*119 + 44; hence not 73 divides 8731 by NAT_4:9;
    8731 = 79*110 + 41; hence not 79 divides 8731 by NAT_4:9;
    8731 = 83*105 + 16; hence not 83 divides 8731 by NAT_4:9;
    8731 = 89*98 + 9; hence not 89 divides 8731 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8731 & n is prime
  holds not n divides 8731 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
