# Permutable Primes

Computer Science Level 3

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.

×