Permutable Primes

A permutable prime is a prime number which can have its digits' positions switched through any permutation and still be a prime number.

For eg, $2$ is permutable prime as it contains only one digit. $13$ is a permutable prime as both $13$ and $31$ are prime. Note that each permutation of a permutable prime is considered as a unique solution. So $13$ and $31$ are considered as two different solutions.

How many permutable primes exist below $10000000$ in base $10$ ?

P.S. Both Number Theory and Computer Science solution exists for this problem.