
theorem
  163 is prime
proof
  now
    163 = 2*81 + 1; hence not 2 divides 163 by NAT_4:9;
    163 = 3*54 + 1; hence not 3 divides 163 by NAT_4:9;
    163 = 5*32 + 3; hence not 5 divides 163 by NAT_4:9;
    163 = 7*23 + 2; hence not 7 divides 163 by NAT_4:9;
    163 = 11*14 + 9; hence not 11 divides 163 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 163 & n is prime
  holds not n divides 163 by XPRIMET1:10;
  hence thesis by NAT_4:14;
