I'm asking if this variant of weak Goldbach's Conjecture is already known.

Let $n$ be an odd number. Does there exists prime numbers $p_1$, $p_2$ and $p_3$ such that $p_1+p_2-p_3=n$? Ideally, can we find $p_1$, $p_2$ and $p_3$ so that they are small enough? For example, can we prove that for large enough $n$, we can find such triplet that all of them are smaller than $n$?