Define a prime number to be $\pm$ a usual prime number. Let $C = \{(X,Y,Z) \in \Bbb{Z}^3 : X - Y - Z = 0\}$. Define a composite number to not include $1$. Define $D_{x,y,z} = \{(X,Y,Z)\in C: X \in x\Bbb{Z}, \dots, Z \in z\Bbb{Z}\}$. It forms a $\Bbb{Z}$-submodule of $C$. Now take: $$ \pi: C \to...

Please vote for undeleting this answer: https://math.stackexchange.com/a/1933337/121097. It is correct, and for some reason that I don't know it was downvoted twice, and this probably determined the answerer to delete it. You can also upvote it, since it is way simpler than the accepted answer.