A Goldbach partition $2n = p + q$ with $p$ and $q$ primes and $p \leqslant q$ is usually called minimal if the numbers $2n - k$ ($k = 1,\ldots, p-1$) are all composite.
Reading through the literature, I see that the minimal Goldbach partitions of even integers have been studied a lot (for instance in https://dms.umontreal.ca/~andrew/PDF/Goldbach1.pdf).
Has anybody ever worked on what I'd call maximal Goldbach partitions? By a maximal Goldbach partition I mean a partition $2n = p + q$ with $p$ and $q$ primes, $p \leqslant q$ and $q-p \geqslant 0$ as small as possible. (E.g. $13+17$ would be the maximal Goldbach-partition of $30$.)