Improve Haskell code for a few problems

Haskell/ProjectEuler.hs

@@ -14,19 +14,16 @@ isPrime 1 = False
 isPrime 2 = True
 isPrime 3 = True
 isPrime n =
-    odd n && n `mod` 3 /= 0 && null [ x | x <- candidates, n `mod` x == 0 || n `mod` (x+2) == 0 ]
+    n > 0 && odd n && n `mod` 3 /= 0 && null [ x | x <- candidates, n `mod` x == 0 || n `mod` (x+2) == 0 ]
     where candidates = [5,11..limit]
           limit = floor(sqrt(fromIntegral n)) + 1
 
-
 digitSum :: (Integral a, Show a) => a -> Int
 digitSum n = sum $ map digitToInt $ show n
 
-
 sumProperDivisors :: (Integral a) => a -> a
 sumProperDivisors n = sum [ if x /= y then x + y  else x | x <- [2..floor $ sqrt $ fromIntegral n], let y = n `div` x, n `mod` x == 0 ] + 1
 
-
 countDivisors :: (Integral a) => a -> Int
 countDivisors n = length $ nub $ concat [ [x, n `div` x] | x <- [1..limit], n `mod` x == 0 ]
     where limit = floor $ sqrt $ fromIntegral n
@@ -35,4 +32,3 @@ isPandigital :: Integer -> Bool
 isPandigital n = n_length == length (nub n_char) && '0' `notElem` n_char && digitToInt (maximum n_char) == n_length
     where n_char = show n
           n_length = length n_char
-

Haskell/p008.hs

@@ -23,7 +23,7 @@
 --
 -- Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?
 
-import Data.Char
+import Data.Char (digitToInt)
 
 nDigitProduct :: Int -> String -> Int
 nDigitProduct n s

Haskell/p012.hs

@@ -18,7 +18,6 @@
 -- What is the value of the first triangle number to have over five hundred divisors?
 
 import Data.List (nub)
-
 import ProjectEuler (countDivisors)
 
 triangNumbers :: [Int]

Haskell/p019.hs

@@ -11,7 +11,7 @@
 --
 -- How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?
 
-import Data.Time.Calendar
+import Data.Time.Calendar (Day, DayOfWeek(Sunday), dayOfWeek, fromGregorian)
 
 countSundaysFirst :: Day -> Day -> Int
 countSundaysFirst start end = let days = [start .. end]

Haskell/p023.hs

@@ -9,7 +9,7 @@
 -- as the sum of two abundant numbers is less than this limit.
 --
 -- Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.
-import Data.List
+import Data.List ((\\))
 import qualified Data.Set as Set
 
 import ProjectEuler (sumProperDivisors)

Haskell/p024.hs

@@ -5,7 +5,7 @@
 --
 -- What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?
 
-import Data.List
+import Data.List (sort, permutations)
 
 main = do
     let result = sort (permutations "0123456789") !! 999999

Haskell/p029.hs

@@ -10,7 +10,7 @@
 -- 4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
 --
 -- How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
-import Data.List
+import Data.List (nub)
 
 powerCombinations :: (Integral a) => a -> [a]
 powerCombinations n = nub [ x^y | x <- [2..n], y <- [2..n] ]

Haskell/p052.hs

@@ -1,7 +1,7 @@
 -- It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.
 --
 -- Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits.
-import Data.List
+import Data.List (sort)
 
 smallestPermutedMultiples :: Integer
 smallestPermutedMultiples = head  [ x | x <- [1..], sort (show x) == sort (show (2 * x)), sort (show x) == sort (show (3 * x)),  sort (show x) == sort (show (4 * x)),  sort (show x) == sort (show (5 * x)),  sort (show x) == sort (show (6 * x)) ]

Haskell/p054.hs

@@ -44,10 +44,9 @@
 --
 --      How many hands does Player 1 win?
 
-import Data.List
+import Data.List (sort, sortBy, groupBy, minimumBy, maximumBy)
-import Data.Function
+import Data.Function (on)
-import Data.Maybe
+import Data.Maybe (fromJust)
-import System.IO
 
 data Value = Two | Three | Four | Five | Six | Seven | Eight | Nine | Ten | Jack | Queen | King | Ace
              deriving (Eq, Ord, Show, Bounded, Enum)