
theorem
  8713 is prime
proof
  now
    8713 = 2*4356 + 1; hence not 2 divides 8713 by NAT_4:9;
    8713 = 3*2904 + 1; hence not 3 divides 8713 by NAT_4:9;
    8713 = 5*1742 + 3; hence not 5 divides 8713 by NAT_4:9;
    8713 = 7*1244 + 5; hence not 7 divides 8713 by NAT_4:9;
    8713 = 11*792 + 1; hence not 11 divides 8713 by NAT_4:9;
    8713 = 13*670 + 3; hence not 13 divides 8713 by NAT_4:9;
    8713 = 17*512 + 9; hence not 17 divides 8713 by NAT_4:9;
    8713 = 19*458 + 11; hence not 19 divides 8713 by NAT_4:9;
    8713 = 23*378 + 19; hence not 23 divides 8713 by NAT_4:9;
    8713 = 29*300 + 13; hence not 29 divides 8713 by NAT_4:9;
    8713 = 31*281 + 2; hence not 31 divides 8713 by NAT_4:9;
    8713 = 37*235 + 18; hence not 37 divides 8713 by NAT_4:9;
    8713 = 41*212 + 21; hence not 41 divides 8713 by NAT_4:9;
    8713 = 43*202 + 27; hence not 43 divides 8713 by NAT_4:9;
    8713 = 47*185 + 18; hence not 47 divides 8713 by NAT_4:9;
    8713 = 53*164 + 21; hence not 53 divides 8713 by NAT_4:9;
    8713 = 59*147 + 40; hence not 59 divides 8713 by NAT_4:9;
    8713 = 61*142 + 51; hence not 61 divides 8713 by NAT_4:9;
    8713 = 67*130 + 3; hence not 67 divides 8713 by NAT_4:9;
    8713 = 71*122 + 51; hence not 71 divides 8713 by NAT_4:9;
    8713 = 73*119 + 26; hence not 73 divides 8713 by NAT_4:9;
    8713 = 79*110 + 23; hence not 79 divides 8713 by NAT_4:9;
    8713 = 83*104 + 81; hence not 83 divides 8713 by NAT_4:9;
    8713 = 89*97 + 80; hence not 89 divides 8713 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8713 & n is prime
  holds not n divides 8713 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
