jmc

To show this statement to be false, we need a non-prime value of $n$ such that $n-2$ is prime. Since $13$ and $23$ are prime, they won't prove anything relating to the truth of the statement. Now we just check the statement for $n=9,12,16$. If $n=12$ or $n=16$, then $n-2$ is $10$ or $14$, which aren't prime. However, $n=9$ makes $n-2=7$, which is prime, so $n=9$ proves the statement false. Therefore, the answer is $\boxed{9}$, 9.