
theorem
  2003 is prime
proof
  now
    2003 = 2*1001 + 1; hence not 2 divides 2003 by NAT_4:9;
    2003 = 3*667 + 2; hence not 3 divides 2003 by NAT_4:9;
    2003 = 5*400 + 3; hence not 5 divides 2003 by NAT_4:9;
    2003 = 7*286 + 1; hence not 7 divides 2003 by NAT_4:9;
    2003 = 11*182 + 1; hence not 11 divides 2003 by NAT_4:9;
    2003 = 13*154 + 1; hence not 13 divides 2003 by NAT_4:9;
    2003 = 17*117 + 14; hence not 17 divides 2003 by NAT_4:9;
    2003 = 19*105 + 8; hence not 19 divides 2003 by NAT_4:9;
    2003 = 23*87 + 2; hence not 23 divides 2003 by NAT_4:9;
    2003 = 29*69 + 2; hence not 29 divides 2003 by NAT_4:9;
    2003 = 31*64 + 19; hence not 31 divides 2003 by NAT_4:9;
    2003 = 37*54 + 5; hence not 37 divides 2003 by NAT_4:9;
    2003 = 41*48 + 35; hence not 41 divides 2003 by NAT_4:9;
    2003 = 43*46 + 25; hence not 43 divides 2003 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2003 & n is prime
  holds not n divides 2003 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
