Largest integer divisible by two primes (Euler, 347)

-- ### Project Euler, problem 347 ### --
import Data.List (nub)

firstPrimes n = takeWhile (<=n) primes

primes = 2 : filter isPrime [3,5..]
  where
    isPrime n = all (/=0) . map (n `mod`) $ [2..squareRoot n]
    squareRoot = truncate . sqrt . fromIntegral

factors n = f n (reverse $ firstPrimes n)
  where
    f _ [] = []
    f 1 _ = []
    f m l@(x:xs) | m `mod` x == 0 = x : f (m `div` x) l
                 | otherwise      = f m xs

fn_m a b lim = myHead . map fst . filter (λ(x, xs) -> (b `elem` xs) && (a `elem` xs)) . filter ((== 2) . length . snd) . zip [lim, lim-1..2] $ map (nub . factors) [lim, lim-1..2]
  where
    myHead [] = 0
    myHead xs = head xs

fn_s n = sum $ map (λ(x,y) -> fn_m x y n) l
  where
    l = myZip (firstPrimes $ n-1) (tail $ firstPrimes n)

myZip _ [] = []
myZip [] _ = []
myZip a@(x:xs) b@(y:ys) = map (λn -> (x, n)) b ++ myZip xs ys

main = do
  putStrLn . show $ fn_m 2 3 100   -- control of "fn_m" (function M(p,q,N))
  putStrLn . show $ fn_s 100       -- control of "fn_s" (function S(N))
  putStrLn . show $ fn_s 10000000  -- problem