Write real number $x>1$ as product of terms of the form $(1+1/p)$ where $p$ is prime.

If $x>1$, then there is a sequence of primes $p_1, p_2, ...$ (finite or infinite) so that $x=\prod_i(1+1/p_i)$. How one can prove this? Is there a method to find such sequense (In the finite case)? Is this still true when $0<x<1$?