import Prelude hiding (take)

fromTo :: Int -> Int -> [Int]
fromTo n m = if n>m then [] else n : fromTo (n+1) m

-- List of all ascending numbers starting from its argument:
from :: Int -> [Int]
from n = n : from (n+1)

-- Computes the prefix of a maximal given length from a list
take :: Int -> [a] -> [a]
take n xs | n <= 0    = []
          | otherwise = case xs of []     -> []
                                   (x:xs) -> x : take (n-1) xs

-- Compute the infinite list of all primes.
sieve :: [Int] -> [Int]
sieve (p:xs) = p : sieve (filter (\x -> x `mod` p /= 0) xs)

primes :: [Int]
primes = sieve (from 2)