1
Look at this beautiful picture I made in yEd:
It shows that some solutions to $2x + y = $ prime are preserved under action by the subgroup of the group of prime permutations $S_P$. In other words, letting $G \leqslant S_P$ be $G = \langle (3,2,5), (1,7,13)\rangle$, $G\circ (x,y)$ where $(x,y)...