Project Euler Problem 027

import Data.Ord
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
--必要に応じてgroupする
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
divsum :: Integer -> Integer
divsum n =  (product. map tohi .group . factor) n - n where
    tohi [x] = x+1
    tohi l@(x:_) = (x^(length l+1)-1) `quot` (x-1)
isprime :: Integer -> Bool
isprime nn = if nn<0 then False
            else imp nn primes where
  imp n (x:xs) = if x*x>n then True
                 else if rem n x==0 then False
                      else imp n xs      
quad :: Num a => a -> a -> a -> a
quad a b n = n^(2::Integer)+a*n+b
consect :: Num a => Integer -> Integer -> a
consect aa bb = imp aa bb 0 where
  imp a b n = let r = quad a b n in
    if isprime r then 1 + imp a b (n+1)
    else 0
abrange :: [Integer]
abrange = [-999..999]

--(71,(-61,971))
ans :: (Integer, (Integer, Integer))
ans = maximumBy (comparing fst) [(c,(a,b))|a<-abrange,b<-abrange,let c=consect a b, c>40]
ansv :: Integer
ansv = let r = snd ans in (fst r)*(snd r)

-- -59231
main :: IO ()
main = print ansv