Project Euler Problem 007

import Data.List hiding (union)
--003より
--http://www.haskell.org/haskellwiki/Prime_numbers
primes :: [Integer]
primes = 2 : ([3,5..] `minus` join [[p*p, p*p+2*p..] | p <- primes']) 
  where
    primes' = 3 : ([5,7..] `minus` join [[p*p, p*p+2*p..] | p <- primes'])   
    join  ((x:xs):t)    = x : union xs (join (pairs t))
    pairs ((x:xs):ys:t) = (x : union xs ys) : pairs t                      
    union (x:xs) (y:ys) = case (compare x y) of 
      LT -> x : union  xs  (y:ys)
      EQ -> x : union  xs     ys 
      GT -> y : union (x:xs)  ys
    union  xs     []    = xs
    union  []     ys    = ys
    minus (x:xs) (y:ys) = case (compare x y) of 
      LT -> x : minus  xs  (y:ys)
      EQ ->     minus  xs     ys
      GT ->     minus (x:xs)  ys
    minus  xs     _     = xs

factor :: Integer -> [Integer]
factor n = factorimpl n primes where
  factorimpl n pri@(p:xs) =
    if p*p>n then [n]
    else if n`rem` p == 0 then
      p:factorimpl (n `quot` p) pri
         else
           factorimpl n xs
solve :: Int -> Integer
solve n = last $ take n primes
m :: Integer
m = solve 10001
-- 104743
main :: IO ()
main = print m

-- シンプルな別解
{-
primes = 2:f [3] [3,5..] where
  f (x:xs) ys = ps ++ f(xs++ps) [z|z<-qs,z`rem`x/=0] where
    (ps,qs) = span(< x*x) ys
m = primes !! (10^4) --104743
-- -}