Answer:$373$. Assume that $pqrs$ is a very prime number which has $4$ digits. There are just $4$ very prime number which has $2$ digits which are $23,37,53,73$. $pq=23 \implies pqrs=2373$ but $3$ divides $2373$. $pq=37 \implies pqrs=3737$ but $37$ divides $3737$. $pq=53 \implies pqrs=5373$ but $3$ divides $5373$. $pq=73 \implies pqrs=7373$ but $73$ divides $7373$. So there are no very prime number which has $4$ or more digits. Let $pqr$ be the largest very prime number. $pq=73 \implies pqr=737$ but $11$ divides it. $pq=53 \implies 537$ but $3$ divides it. $pq=37 \implies 373$ and it's prime.