jmc

If $10x+y$ is prime, then $y$ cannot be 2 or 5. So if $x$ and $y$ are prime digits, then $y$ must be 3 or 7 and $x$ must be one of the other three prime digits. Checking the six resulting cases, we find that the prime numbers of the form $10x+y$ where $x$ and $y$ are both prime digits are 23, 53, 73, and 37. The values of $xy(10x+y)$ for these four numbers are 138, 795, 1533, and 777. The largest of these values which is less than 1000 is $\boxed{795}$.