
theorem
  8699 is prime
proof
  now
    8699 = 2*4349 + 1; hence not 2 divides 8699 by NAT_4:9;
    8699 = 3*2899 + 2; hence not 3 divides 8699 by NAT_4:9;
    8699 = 5*1739 + 4; hence not 5 divides 8699 by NAT_4:9;
    8699 = 7*1242 + 5; hence not 7 divides 8699 by NAT_4:9;
    8699 = 11*790 + 9; hence not 11 divides 8699 by NAT_4:9;
    8699 = 13*669 + 2; hence not 13 divides 8699 by NAT_4:9;
    8699 = 17*511 + 12; hence not 17 divides 8699 by NAT_4:9;
    8699 = 19*457 + 16; hence not 19 divides 8699 by NAT_4:9;
    8699 = 23*378 + 5; hence not 23 divides 8699 by NAT_4:9;
    8699 = 29*299 + 28; hence not 29 divides 8699 by NAT_4:9;
    8699 = 31*280 + 19; hence not 31 divides 8699 by NAT_4:9;
    8699 = 37*235 + 4; hence not 37 divides 8699 by NAT_4:9;
    8699 = 41*212 + 7; hence not 41 divides 8699 by NAT_4:9;
    8699 = 43*202 + 13; hence not 43 divides 8699 by NAT_4:9;
    8699 = 47*185 + 4; hence not 47 divides 8699 by NAT_4:9;
    8699 = 53*164 + 7; hence not 53 divides 8699 by NAT_4:9;
    8699 = 59*147 + 26; hence not 59 divides 8699 by NAT_4:9;
    8699 = 61*142 + 37; hence not 61 divides 8699 by NAT_4:9;
    8699 = 67*129 + 56; hence not 67 divides 8699 by NAT_4:9;
    8699 = 71*122 + 37; hence not 71 divides 8699 by NAT_4:9;
    8699 = 73*119 + 12; hence not 73 divides 8699 by NAT_4:9;
    8699 = 79*110 + 9; hence not 79 divides 8699 by NAT_4:9;
    8699 = 83*104 + 67; hence not 83 divides 8699 by NAT_4:9;
    8699 = 89*97 + 66; hence not 89 divides 8699 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8699 & n is prime
  holds not n divides 8699 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
