# Project Euler 解答

## Project Euler Problem 003

Project Euler Problem 003

```-- 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

{- 簡易版
primes = 2: f  [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
-- -}

dst :: Integer
dst = 600851475143

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
solve :: Integer
solve = last \$ factor dst  -- 6857 -- [71,839,1471,6857]
-- 6857
main :: IO ()
main = print solve
```
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