The number, 197, is called a circular prime because all rotations of the 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?
Similar to last question, we need to find the limit to how far we should search for these numbers. Consider a 5 digit number. Then, the maximum digit factorials is 5 * 9! = 1814400. Let's look at 8 digits: 8 * 9! = 2903040, only has 7 digit. How about 7 digit? 7 * 9! = 2540160, which has 7 digit like we wanted! It's impossible for an 8 digit number to have its digit factorial to equal to its number. The maximum is 2903040 which only has 7 digits. So, we only have to check up to 2540160. Coding factorials and checking this is simple!
Answer: 40730
Runtime: 29.3 seconds