Haskell 007

haskell/e007.hs

@@ -0,0 +1,25 @@
+{- Find the 10001st prime.
+
+By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
+What is the 10001st prime number?
+-}
+
+import Text.Printf
+
+is_prime :: (Integral a) => a -> Bool
+is_prime n
+    | n == 1 = False
+    | n < 4 = True
+    | n `rem` 2 == 0 = False
+    | n < 9 = True
+    | n `rem` 3 == 0 = False
+    | otherwise = do
+        let f = sqrt (fromIntegral n)
+        let checkprime x = (n `rem` x == 0 || n `rem` (x + 2) == 0)
+        not (or (map checkprime (takeWhile (<= floor f) [5,11..])))
+
+primes = filter is_prime (2:[3,5..])
+
+main = do
+    printf "    6th prime: %d\n" (primes !! 5 :: Integer)
+    printf "10001th prime: %d\n" (primes !! 10000 :: Integer)