Infinite primes proof There is a proof for infinite prime numbers that i don't understand.

right in the middle of the proof:
"since every such $m$ can be written in a unique way as a product of the form:
$\prod_{p\leqslant x}p^{k_p}$. we see that the last sum is equal to: $\prod_{\binom{p\leqslant x}{p\in \mathbb{P}}}(\sum_{k\leqslant 0}\frac{1}{p^k})$.
I don't see that. can anyone can explain this step to me?

Just remember this equation:
$$\zeta(s) = \prod\left(1-\frac{1}{p^s}\right)^{-1}.$$
Where you know $\zeta(1)$ isn't convergent, so if there is a finite quantity of prime numbers, then right part is over, so there is infinite quantity of prime numbers.
