TITLE: Gap between an even integer and the next smaller prime?
QUESTION [11 upvotes]: I am desparately searching for a case that would skip the following conjecture (a variation of the Goldbach conjecture):
"Let $N$ an even integer, $P$ the very next prime smaller than $N$, and $D=N-P$. Then $D$ is always a prime. (Except $D=1$)"
Can anybody help me with a case to reject this conjecture?
Thank you in advance.

REPLY [16 votes]: The counterexample of Kyle Miller solve the problem, but we can say more. Since we can take prime gaps abitrarily large, we have that exists infinite even numbers such that $D$ is composite.