import Data.List
import Data.Ord

isPrime :: Integer -> Bool
primes :: Integer ->[Integer]

isLengthLessThan :: Int -> [a] -> Bool
isLengthLessThan 0 _      = False
isLengthLessThan _ []     = True
isLengthLessThan n (_:ys) = isLengthLessThan (n-1) ys

isPrime x
    | x == 2       = True
    | mod x 2 == 0 = False
    | otherwise    = isLengthLessThan 2 [y | y <- [1,3.. roof], mod x y == 0]
    where roof = 1 + truncate (sqrt $fromIntegral x)

primes x
    | isPrime x = [x]
    | otherwise = factor : primes(div x factor)
    where factor = head $filter checkdiv [2..]
          checkdiv n = x `mod` n == 0