Euler question 7

src/projectEuler/question7.hs

@@ -0,0 +1,32 @@
+-- https://projecteuler.net/problem=7
+-- Find the 10_001 prime number
+
+primes1 :: [Integer]
+primes1 = 2:3:prs
+  where
+    1:p:candidates = [6*k+r | k <- [0..], r <- [1,5]]
+    prs            = p : filter isPrime candidates
+    isPrime n      = not (any (divides n) (takeWhile (\p -> p*p <= n) prs))
+    divides n p    = n `mod` p == 0
+
+
+primes2 = 2:([3..] `minus` composites)
+  where
+    composites = union [multiples p | p <- primes2]
+
+    multiples n = map (n*) [n..]
+
+    (x:xs) `minus` (y:ys) | x < y = x:(xs `minus` (y:ys))
+                          | x == y = xs `minus` ys
+                          | x > y = (x:xs) `minus` ys
+    union = foldr merge [ ]
+      where
+        merge (x:xs) ys = x:merge' xs ys
+        merge' (x:xs) (y:ys) | x < y = x:merge' xs (y:ys)
+                            | x == y = x:merge' xs ys
+                            | x > y = y:merge' (x:xs) ys
+
+
+primes3 = sieve [2..]
+  where
+    sieve (p : xs) = p : sieve [x | x <- xs, x `mod` p > 0]