  In a recent work \cite{key-11}, A. Fish proved that if $E_{1}$ and $E_{2}$
are two subsets of $\mathbb{Z}$ of positive upper Banach density, then there
exists $k\in\mathbb{Z}$ such that
$k\cdot\mathbb{Z}\subset\left(E_{1}-E_{1}\right)\cdot\left(E_{2}-E_{2}\right).$
In this article we will show that a similar result is true for the set of
primes $\mathbb{P}$ (which has density $0$). We will prove that there exists
$k\in\mathbb{N}$ such that
$k\cdot\mathbb{N}\subset\left(\mathbb{P}-\mathbb{P}\right)\cdot\left(\mathbb{P}-\mathbb{P}\right),$
where $\mathbb{P}-\mathbb{P}=\left\{
p-q:p>q\,\text{and}\,p,q\in\mathbb{P}\right\} .$
