For any $x\in \mathbb{N}$ does there exist $m\in \mathbb{N}$ such that $2x+1+2m, 2x+1+4m$ are both prime?

Question

Could someone please give me a proof (or counter example) for this (I believe it is true):

For any $x$ (Whole Number) there exists some $m$ (Also Whole) such that $2x+1+2m$ and $2x+1+4m$ are both prime.

An equivalent is for any odd $n$ there exists some even $y$ such that $n+y$ and $n+2y$ are both prime. I am pretty sure a proof would be based around Dirichlet's Theorem.