49th Mathematical Olympiad in Ukraine

As the product of the digits this number has is prime, then these digits are $1,1,p$ (not necessarily in this order) and the digit $p$ is a prime number. Obviously, $p\ne 7$ because otherwise the sum of the digits is divisible by $3$ and the number isn't prime. The digits $2$ and $5$ can stay only between both digits $1$, then we obtain the numbers $121$ and $151$. If $p=3$, then we have numbers $113$, $131$ and $311$. The biggest from these numbers is $311$.