
theorem
  8599 is prime
proof
  now
    8599 = 2*4299 + 1; hence not 2 divides 8599 by NAT_4:9;
    8599 = 3*2866 + 1; hence not 3 divides 8599 by NAT_4:9;
    8599 = 5*1719 + 4; hence not 5 divides 8599 by NAT_4:9;
    8599 = 7*1228 + 3; hence not 7 divides 8599 by NAT_4:9;
    8599 = 11*781 + 8; hence not 11 divides 8599 by NAT_4:9;
    8599 = 13*661 + 6; hence not 13 divides 8599 by NAT_4:9;
    8599 = 17*505 + 14; hence not 17 divides 8599 by NAT_4:9;
    8599 = 19*452 + 11; hence not 19 divides 8599 by NAT_4:9;
    8599 = 23*373 + 20; hence not 23 divides 8599 by NAT_4:9;
    8599 = 29*296 + 15; hence not 29 divides 8599 by NAT_4:9;
    8599 = 31*277 + 12; hence not 31 divides 8599 by NAT_4:9;
    8599 = 37*232 + 15; hence not 37 divides 8599 by NAT_4:9;
    8599 = 41*209 + 30; hence not 41 divides 8599 by NAT_4:9;
    8599 = 43*199 + 42; hence not 43 divides 8599 by NAT_4:9;
    8599 = 47*182 + 45; hence not 47 divides 8599 by NAT_4:9;
    8599 = 53*162 + 13; hence not 53 divides 8599 by NAT_4:9;
    8599 = 59*145 + 44; hence not 59 divides 8599 by NAT_4:9;
    8599 = 61*140 + 59; hence not 61 divides 8599 by NAT_4:9;
    8599 = 67*128 + 23; hence not 67 divides 8599 by NAT_4:9;
    8599 = 71*121 + 8; hence not 71 divides 8599 by NAT_4:9;
    8599 = 73*117 + 58; hence not 73 divides 8599 by NAT_4:9;
    8599 = 79*108 + 67; hence not 79 divides 8599 by NAT_4:9;
    8599 = 83*103 + 50; hence not 83 divides 8599 by NAT_4:9;
    8599 = 89*96 + 55; hence not 89 divides 8599 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8599 & n is prime
  holds not n divides 8599 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
