For every positive even number $n$, does there always exist a pair of prime $(p,q)$ such that $p-q =n$?

Question

$$2 = 5-3 \\ 4 = 7-3 \\ 6 = 11-5 \\ 8 = 19-11 \\ 10 = 13-3 \\ \vdots$$

For every positive even number $n$, does there always exist a pair of prime $(p,q)$ such that $p-q =n$?