Haskell: Sieve of Eratosthenes

Recently I needed to compute prime numbers starting from 2 and on to x , Sieve of Eratosthenes seemed like a simple and straightforward (albeit not too fast) way to get this done


eliminator :: Int -> [Int] -> [Int]
eliminator _ [] = []
eliminator start list = filter (\x -> x `rem` start /= 0) list

sieve :: [Int] -> [Int]
sieve [] = []
sieve (x:xs) = x : (sieve $ eliminator x xs)

*Main> sieve [2..100]
[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]

There is one known limitation -- sieve assumes that the first number in the sequence is a prime.