haskell: add p3

Signed-off-by: Amneesh Singh <natto@weirdnatto.in>

haskell/Lib.hs

@@ -1,4 +1,13 @@
-module Lib where
+module Lib (fib, primeFactors) where
 
-fib :: [ Integer ]
+fib :: [Integer]
 fib = 1 : 2 : zipWith (+) fib (tail fib)
+
+primeFactors :: Integer -> [Integer]
+primeFactors n = genPrimeFactors n 2
+  where
+    genPrimeFactors :: Integer -> Integer -> [Integer]
+    genPrimeFactors n c
+      | c == n = [n]
+      | mod n c /= 0 = genPrimeFactors n (c + 1)
+      | otherwise = c : genPrimeFactors (div n c) c

haskell/p3.hs

@@ -0,0 +1,7 @@
+import Lib (primeFactors)
+
+main :: IO ()
+main = putStr $ show solve
+
+solve :: Integer
+solve = last $ primeFactors 600851475143