Project Euler Problem 047

import Data.List hiding (union)

--003より
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 nn = factorimpl nn 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
fac4 :: Integer -> Bool
fac4 n= length (group $ factor n ) == 4
geta :: (Eq a, Num a) => [a] -> [a]
geta lst = if con lst then take 4 lst
           else geta (tail lst)
con :: (Eq a, Num a) => [a] -> Bool
con (a:b:c:d:_) | b==a+1&&c==a+2&&d==a+3=True
con _ = False
ans1 :: Integer
ans1 = head $ geta $ filter fac4 [1..] --134043 by [134043,134044,134045,134046]
-- 134043
main :: IO ()
main = print ans1