
theorem
  8719 is prime
proof
  now
    8719 = 2*4359 + 1; hence not 2 divides 8719 by NAT_4:9;
    8719 = 3*2906 + 1; hence not 3 divides 8719 by NAT_4:9;
    8719 = 5*1743 + 4; hence not 5 divides 8719 by NAT_4:9;
    8719 = 7*1245 + 4; hence not 7 divides 8719 by NAT_4:9;
    8719 = 11*792 + 7; hence not 11 divides 8719 by NAT_4:9;
    8719 = 13*670 + 9; hence not 13 divides 8719 by NAT_4:9;
    8719 = 17*512 + 15; hence not 17 divides 8719 by NAT_4:9;
    8719 = 19*458 + 17; hence not 19 divides 8719 by NAT_4:9;
    8719 = 23*379 + 2; hence not 23 divides 8719 by NAT_4:9;
    8719 = 29*300 + 19; hence not 29 divides 8719 by NAT_4:9;
    8719 = 31*281 + 8; hence not 31 divides 8719 by NAT_4:9;
    8719 = 37*235 + 24; hence not 37 divides 8719 by NAT_4:9;
    8719 = 41*212 + 27; hence not 41 divides 8719 by NAT_4:9;
    8719 = 43*202 + 33; hence not 43 divides 8719 by NAT_4:9;
    8719 = 47*185 + 24; hence not 47 divides 8719 by NAT_4:9;
    8719 = 53*164 + 27; hence not 53 divides 8719 by NAT_4:9;
    8719 = 59*147 + 46; hence not 59 divides 8719 by NAT_4:9;
    8719 = 61*142 + 57; hence not 61 divides 8719 by NAT_4:9;
    8719 = 67*130 + 9; hence not 67 divides 8719 by NAT_4:9;
    8719 = 71*122 + 57; hence not 71 divides 8719 by NAT_4:9;
    8719 = 73*119 + 32; hence not 73 divides 8719 by NAT_4:9;
    8719 = 79*110 + 29; hence not 79 divides 8719 by NAT_4:9;
    8719 = 83*105 + 4; hence not 83 divides 8719 by NAT_4:9;
    8719 = 89*97 + 86; hence not 89 divides 8719 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8719 & n is prime
  holds not n divides 8719 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
