Gap between an even integer and the next smaller prime?

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.

Solution 1:

$122$ is even, and it is between $113$ and $127$. The difference, $122-113$, is $9$, definitely composite.

How I searched: primes greater than two are odd, so the difference between an even number and a prime is odd, so what is the smallest composite odd number? Then, the search was for a pair of neighboring primes at least nine apart.

Solution 2:

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.