The number 197 is called a circular prime because all rotations of its digits (197, 971, and 719) are themselves prime.

There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.

How many circular primes are there below one million?

Hints:
There are two smaller problems within this larger one. The first is determining whether a number is prime. This is relatively straightforward, but the Wikipedia page on primality tests is a good reference for different methods.

The second problem is finding different permutations of digits. The STL algorithm library provides a method for finding permutations within an array, but an implementation on one data item would be easier to use in finding the solution.

(This problem came from Project Euler's site).