
theorem
  8999 is prime
proof
  now
    8999 = 2*4499 + 1; hence not 2 divides 8999 by NAT_4:9;
    8999 = 3*2999 + 2; hence not 3 divides 8999 by NAT_4:9;
    8999 = 5*1799 + 4; hence not 5 divides 8999 by NAT_4:9;
    8999 = 7*1285 + 4; hence not 7 divides 8999 by NAT_4:9;
    8999 = 11*818 + 1; hence not 11 divides 8999 by NAT_4:9;
    8999 = 13*692 + 3; hence not 13 divides 8999 by NAT_4:9;
    8999 = 17*529 + 6; hence not 17 divides 8999 by NAT_4:9;
    8999 = 19*473 + 12; hence not 19 divides 8999 by NAT_4:9;
    8999 = 23*391 + 6; hence not 23 divides 8999 by NAT_4:9;
    8999 = 29*310 + 9; hence not 29 divides 8999 by NAT_4:9;
    8999 = 31*290 + 9; hence not 31 divides 8999 by NAT_4:9;
    8999 = 37*243 + 8; hence not 37 divides 8999 by NAT_4:9;
    8999 = 41*219 + 20; hence not 41 divides 8999 by NAT_4:9;
    8999 = 43*209 + 12; hence not 43 divides 8999 by NAT_4:9;
    8999 = 47*191 + 22; hence not 47 divides 8999 by NAT_4:9;
    8999 = 53*169 + 42; hence not 53 divides 8999 by NAT_4:9;
    8999 = 59*152 + 31; hence not 59 divides 8999 by NAT_4:9;
    8999 = 61*147 + 32; hence not 61 divides 8999 by NAT_4:9;
    8999 = 67*134 + 21; hence not 67 divides 8999 by NAT_4:9;
    8999 = 71*126 + 53; hence not 71 divides 8999 by NAT_4:9;
    8999 = 73*123 + 20; hence not 73 divides 8999 by NAT_4:9;
    8999 = 79*113 + 72; hence not 79 divides 8999 by NAT_4:9;
    8999 = 83*108 + 35; hence not 83 divides 8999 by NAT_4:9;
    8999 = 89*101 + 10; hence not 89 divides 8999 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8999 & n is prime
  holds not n divides 8999 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
