
theorem
  1999 is prime
proof
  now
    1999 = 2*999 + 1; hence not 2 divides 1999 by NAT_4:9;
    1999 = 3*666 + 1; hence not 3 divides 1999 by NAT_4:9;
    1999 = 5*399 + 4; hence not 5 divides 1999 by NAT_4:9;
    1999 = 7*285 + 4; hence not 7 divides 1999 by NAT_4:9;
    1999 = 11*181 + 8; hence not 11 divides 1999 by NAT_4:9;
    1999 = 13*153 + 10; hence not 13 divides 1999 by NAT_4:9;
    1999 = 17*117 + 10; hence not 17 divides 1999 by NAT_4:9;
    1999 = 19*105 + 4; hence not 19 divides 1999 by NAT_4:9;
    1999 = 23*86 + 21; hence not 23 divides 1999 by NAT_4:9;
    1999 = 29*68 + 27; hence not 29 divides 1999 by NAT_4:9;
    1999 = 31*64 + 15; hence not 31 divides 1999 by NAT_4:9;
    1999 = 37*54 + 1; hence not 37 divides 1999 by NAT_4:9;
    1999 = 41*48 + 31; hence not 41 divides 1999 by NAT_4:9;
    1999 = 43*46 + 21; hence not 43 divides 1999 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1999 & n is prime
  holds not n divides 1999 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
