How to optimize this Haskell code summing up the primes in sublinear time?

Question

Problem 10 from Project Euler is to find the sum of all the primes below given n.

I solved it simply by summing up the primes generated by the sieve of Eratosth

Answer 1

Try this and let me know how fast it is:

-- sum of primes

import Control.Monad (forM_, when)
import Control.Monad.ST
import Data.Array.ST
import Data.Array.Unboxed

sieve :: Int -> UArray Int Bool
sieve n = runSTUArray $ do
    let m = (n-1) `div` 2
        r = floor . sqrt $ fromIntegral n
    bits <- newArray (0, m-1) True
    forM_ [0 .. r `div` 2 - 1] $ \i -> do
        isPrime <- readArray bits i
        when isPrime $ do
            let a = 2*i*i + 6*i + 3
                b = 2*i*i + 8*i + 6
            forM_ [a, b .. (m-1)] $ \j -> do
                writeArray bits j False
    return bits

primes :: Int -> [Int]
primes n = 2 : [2*i+3 | (i, True) <- assocs $ sieve n]

main = do
    print $ sum $ primes 1000000

You can run it on ideone. My algorithm is the Sieve of Eratosthenes, and it should be quite fast for small n. For n = 2,000,000,000, the array size may be a problem, in which case you will need to use a segmented sieve. See my blog for more information about the Sieve of Eratosthenes. See this answer for information about a segmented sieve (but not in Haskell, unfortunately).