problem_60.hs

module Main where

import System
import Data.List
import Primes

primes :: [Integer]
primes = filter (prime) [2..]

concatenations :: Show a => [a] -> [Integer]
concatenations (x:xs) = (foldl (++) [] $ map (pairify x) xs) ++ (concatenations xs)
  where pairify x y = map (\s -> (read s)::Integer) [(show x) ++ (show y), (show y) ++ (show x)]
concatenations [] = []

solutions = [(a,b,c,d,e) | a <- drop 4 primes
                         , b <- takeWhile (<a) (drop 3 primes)
                         , c <- takeWhile (<b) (drop 2 primes)
                         , d <- takeWhile (<c) (drop 1 primes)
                         , e <- takeWhile (<d) primes
                         , all prime (concatenations [a,b,c,d])]

-- Uncomment below to solve the example problem
-- solutions = [(a,b,c,d) | a <- drop 3 primes
--                        , b <- takeWhile (<a) (drop 2 primes)
--                        , c <- takeWhile (<b) (drop 1 primes)
--                        , d <- takeWhile (<c) primes
--                        , all prime (concatenations [a,b,c,d])]

main = do print $ head solutions