
theorem
  167 is prime
proof
  now
    167 = 2*83 + 1; hence not 2 divides 167 by NAT_4:9;
    167 = 3*55 + 2; hence not 3 divides 167 by NAT_4:9;
    167 = 5*33 + 2; hence not 5 divides 167 by NAT_4:9;
    167 = 7*23 + 6; hence not 7 divides 167 by NAT_4:9;
    167 = 11*15 + 2; hence not 11 divides 167 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 167 & n is prime
  holds not n divides 167 by XPRIMET1:10;
  hence thesis by NAT_4:14;
end;
