-- 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?

import Data.List (inits, tails)
import ProjectEuler (isPrime, primeSieve)

isCircularPrime :: Int -> Bool
isCircularPrime n
    | n == 2                               = True
    | any (`elem` ['0','2'..'8']) (show n) = False
    | all (isPrime . read) rotations       = True
    | otherwise                            = False
    where rotations = zipWith (++) (tails (show n)) (init (inits (show n)))
--isCircularPrime n = let rotations = zipWith (++) (tails (show n)) (init (inits (show n)))
--                    in  all (isPrime . read) rotations

main = do
    let result = length $ filter isCircularPrime (takeWhile (<1000000) primeSieve)
    putStrLn $ "Project Euler, Problem 35\n"
        ++ "Answer: " ++ show result