Project Euler, problem 3

euler3 = last . primeFactors allPrimes
  where
    primeFactors _ 1 = []
    primeFactors p@(y:ys) x | x `mod` y == 0 = y : primeFactors p (x `div` y)
                            | otherwise      = primeFactors ys x

    isPrime x = all (/= 0) . map (x `mod`) $ [2..sqrRoot x]
    sqrRoot = truncate . sqrt . fromIntegral
    allPrimes = 2 : filter (isPrime) [3,5..]

main = do
  putStrLn . show . euler3 $ 13195
  putStrLn . show . euler3 $ 600851475143