the Legendre sieve method gives us an upper bound $S$ for the numbers that are not relatively prime to $P_{z}$ up to $x$ where $P_{z}$ is the product of prime number less than z
$S=x\prod_{p<z}(1-\frac{1}{p})+O(2^{\pi (z)})$
I don't understand why the error term is $2^{\pi (z)}$ can someone explain where it came from ?