prime_time.hs

-- from http://mathlesstraveled.com/2011/01/06/prime-time-in-haskell/
import Control.Arrow ((&&&), (>>>))
import Data.Function ((&))
import Data.List (find, intercalate, tails)
import Data.Numbers.Primes (isPrime, primes)

-- Finds runs of consecutive primes that sum to n
primeSums :: Int -> [(Int, Int)]
primeSums n =
    primes
        & takeWhile (< n)
        >>> tails
        >>> init
        >>> map (scanl (+) 0 >>> tail >>> takeWhile (<= n) >>> length &&& last)
        >>> zip [0 ..]
        >>> filter ((== n) . snd . snd)
        >>> map (fst &&& fst . snd)

-- Expands a run into list of primes
expandRun :: (Int, Int) -> [Int]
expandRun (i, n) = primes & drop i >>> take n

-- Self explanatory
isSumOfConsecutivePrimes :: Int -> Bool
isSumOfConsecutivePrimes = any (isPrime . snd) . primeSums

-- is Sum of Prime Consecutive Primes in Multiple Ways
iSoPCPiMW :: Int -> Int -> Bool
iSoPCPiMW k = (>= k) . length . filter (isPrime . snd) . primeSums

-- Main event
main :: IO ()
main =
    let ps = primeSums 2011
     in do
            print ps
            print $ map expandRun ps
            print $ isSumOfConsecutivePrimes 2011
            print $ find (iSoPCPiMW 4) [2012 ..]
            print . find isSumOfConsecutivePrimes $ dropWhile (<= 2011) primes