
theorem
  263 is prime
proof
  now
    263 = 2*131 + 1; hence not 2 divides 263 by NAT_4:9;
    263 = 3*87 + 2; hence not 3 divides 263 by NAT_4:9;
    263 = 5*52 + 3; hence not 5 divides 263 by NAT_4:9;
    263 = 7*37 + 4; hence not 7 divides 263 by NAT_4:9;
    263 = 11*23 + 10; hence not 11 divides 263 by NAT_4:9;
    263 = 13*20 + 3; hence not 13 divides 263 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 263 & n is prime
  holds not n divides 263 by XPRIMET1:12;
  hence thesis by NAT_4:14;
end;
