Sieve of Eratosthenes as infinite list of primes in Haskell

gistfile1.hs

module Primes where

main :: IO ()
main = print $ take 1000 primes
 
(√) :: Int -> Int
(√) = floor . sqrt . fromIntegral
 
primes :: [Int]
primes = 2 : sieve [3, 5..]
  where sieve (x:xs)
		| isPrime x = x:sieve xs
		| otherwise = sieve xs
 
none :: (a -> Bool) -> [a] -> Bool
none f = not . any f
 
isPrime :: Int -> Bool
isPrime x = none (\p -> rem x p == 0) $ possibleFactorsOf x
	where possibleFactorsOf x = takeWhile (\p -> (√)x >= p) primes