I came across a question today.
The number of 10-digit numbers such that the product of any two consecutive digits in the number is a prime number, is?
As much as I know the product of any two consecutive digits is a prime number only when one of them is $1$ and the other is a prime number (unless I am missing something). But I still can't see any way forward. So, how to do this?
EDIT: The answer to this problem is