Add `isPrime` and `divides` to Euler.hs.

Euler.hs

@@ -9,9 +9,11 @@ module Euler
   , whenM
   , unlessM
   , primesTo
-  , isPrimeArray
+  , isPrimeArrayTo
   , primes
+  , isPrime
   , primeFactors
+  , divides
   , zipArraysWith
   , RangeIx(..)
   , divisors
@@ -60,26 +62,30 @@ whenM   mc m = mc >>= (\c -> when   c m)
 unlessM mc m = mc >>= (\c -> unless c m)
 
 primesTo n = LST.runST $ do
-   isPrime <- LST.strictToLazyST (newArray (2, n) 1 :: ST s (STUArray s Integer Word8))
+   isPrimeArr <- LST.strictToLazyST (newArray (2, n) 1 :: ST s (STUArray s Integer Word8))
    let primesFrom m = if m > n then return [] else do
-         p <- LST.strictToLazyST (readArray isPrime m)
+         p <- LST.strictToLazyST (readArray isPrimeArr m)
-         if p == 0 then primesFrom (m+1) else do
+         if p == 0 then primesFrom (m+1) else fmap (m:) $ do
-            LST.strictToLazyST $ forM_ [2*m,3*m..n] $ \i -> writeArray isPrime i 0
+            LST.strictToLazyST $ forM_ [2*m,3*m..n] $ \i -> do
-            (m:) <$> primesFrom (m+1)
+               writeArray isPrimeArr i 0
+            primesFrom (m+1)
    primesFrom 2
 
-isPrimeArray n = runSTUArray $ do
+isPrimeArrayTo n = runSTUArray $ do
-   isPrime <- newArray (2, n) 1 :: ST s (STUArray s Integer Word8)
+   isPrimeArr <- newArray (2, n) 1 :: ST s (STUArray s Integer Word8)
-   forM_ [2..n] $ \m -> whenM ((/= 0) <$> readArray isPrime m) $ do
+   forM_ [2..n] $ \m -> whenM ((/= 0) <$> readArray isPrimeArr m) $ do
-      forM_ [2*m,3*m..n] $ \i -> writeArray isPrime i 0
+      forM_ [2*m,3*m..n] $ \i -> writeArray isPrimeArr i 0
-   return isPrime
+   return isPrimeArr
 
 primes :: [Integer]
---primes = let go (!p:xs) = p : go [ x | x <- xs, x `mod` p /= 0 ] in go [2..]
+--primes = let go (!p:xs) = p : go [ x | x <- xs, not (p `divides` x) ] in go [2..]
 primes = go 1000000
    where
       go n = primesTo n ++ dropWhile (<= n) (go (2*n))
 
+isPrime :: Integer -> Bool
+isPrime n = n >= 2 && not (any (`divides` n) $ takeWhile ((<=n).(^2)) primes)
+
 primeFactors :: Integer -> [Integer]
 primeFactors n = go n primes
    where
@@ -90,6 +96,9 @@ primeFactors n = go n primes
          | (q, 0) <- n `divMod` p = p : go q (p:ps)
          | otherwise = go n ps
 
+divides :: Integral a => a -> a -> Bool
+a `divides` b = b `mod` a == 0
+
 class Ix a => RangeIx a where
    intersectBounds :: (a, a) -> (a, a) -> (a, a)
 

Problem027.hs

@@ -8,9 +8,6 @@
 
 import Euler
 
-isPrime :: Integer -> Bool
-isPrime n = n >= 2 && not (any (\p -> n `mod` p == 0) $ takeWhile (< n) primes)
-
 nPrimes a b = length $ takeWhile isPrime $ map (\n -> n^2 + a*n + b) [0..]
 
 main = print $ uncurry (*) $ snd $ maximumBy (compare `on` fst) $

Problem035.hs

@@ -17,7 +17,5 @@ rotations n = map (fromDigits . take (length digits))
 
 main = do
    let limit      = 1000000 - 1
-   let isPrimeArr = isPrimeArray limit
-   let isPrime n  = (isPrimeArr!n) /= 0
    let circular n = all isPrime $ rotations n
    print $ length $ filter circular [2..limit]

Problem037.hs

@@ -5,8 +5,4 @@ import Euler
 import Data.Array.Unboxed
 
 truncations n = map fromDigits $ filter (not . null) $ inits (toDigits n) ++ tails (toDigits n)
-
-isPrimeArr = isPrimeArray 1000000
-isPrime n  = n >= 2 && isPrimeArr!n /= 0
-
 main = print $ sum $ take 11 $ filter (all isPrime . truncations) [11..]

Problem041.hs

@@ -9,7 +9,4 @@ import Euler
 pandigitals = map fromDigits $ go 9
    where go 0 = []; go n = reverse (sort (permutations [1..n])) ++ go (n-1)
 
-isPrime n = not $ any (\p -> n `mod` p == 0) $
-   takeWhile (<= floor (sqrt (fromIntegral n))) primes
-
 main = print $ head $ filter isPrime pandigitals

Problem051.hs

@@ -14,10 +14,6 @@
 import Euler
 import Debug.Trace
 
-isPrime :: Integer -> Bool
-isPrime n = n >= 2 && all (\p -> n `mod` p /= 0) smallPrimes
-   where smallPrimes = takeWhile (<= floor (sqrt (fromIntegral n))) primes
-
 main = print $ head $ do
    base <- primes
    let digits = toDigits base

Problem058.hs

@@ -18,8 +18,6 @@ module Main where
 
 import Euler
 
-isPrime n = n >= 2 && not (any (\p -> n `mod` p == 0) $ takeWhile ((<= n) . (^2)) primes)
-
 -- diagonals of an m by m spiral; m = 2*n + 1.
 allDiags = 1 : zipWith (+) allDiags (concat $ map (replicate 4) [2,4..])
 allDiags' = map isPrime allDiags