-- Find the lowest sum for a set of five primes for which any two primes
-- concatenate to produce another prime.

import Euler
import Debug.Trace
import Data.Array.Unboxed ((!))

nDigits n = ceiling $ logBase 10 $ max 1 $ fromIntegral n
a ## b = (a * (10 ^ nDigits b)) + b

main = print $ head $ do
   a <- drop 4 primes
   b <- takeWhile (< a) primes
   guard $ all isPrime $ [(## b), (b ##)] <*> [a]
   --traceM $ show (a,b)
   c <- takeWhile (< b) primes
   guard $ all isPrime $ [(## c), (c ##)] <*> [a,b]
   --traceM $ show (a,b,c)
   d <- takeWhile (< c) primes
   guard $ all isPrime $ [(## d), (d ##)] <*> [a,b,c]
   e <- takeWhile (< d) primes
   guard $ all isPrime $ [(## e), (e ##)] <*> [a,b,c,d]
   let xs = [a,b,c,d,e]
   return (sum xs, xs)