Problem 60

60.hs

@@ -0,0 +1,43 @@
+import Data.List
+
+upper = 10000
+
+isPrime :: Integer -> Bool
+isPrime x = null [k | k <- [2..x-1], k * k <= x, x `mod` k == 0]
+
+primes = [x | x <- [2..upper], isPrime x]
+    
+isPrimeNew :: Integer -> Bool
+isPrimeNew x
+    | x <= upper = elem x primes
+    | otherwise = isPrime x
+    
+order :: (Integer, Integer, Integer, Integer, Integer) -> (Integer, Integer, Integer, Integer, Integer) -> Ordering
+order (a1, b1, c1, d1, e1) (a2, b2, c2, d2, e2) =
+    compare (a1 + b1 + c1 + d1 + e1) (a2 + b2 + c2 + d2 + e2)
+  
+combosArePrime :: Integer -> Integer -> Integer -> Integer -> Integer -> Bool
+combosArePrime a b c d e = 
+    isPrimeNew (read (show a ++ show b)) && 
+    isPrimeNew (read (show b ++ show a)) &&
+    isPrimeNew (read (show a ++ show c)) && 
+    isPrimeNew (read (show c ++ show a)) &&
+    isPrimeNew (read (show b ++ show c)) && 
+    isPrimeNew (read (show c ++ show b)) &&
+    isPrimeNew (read (show a ++ show d)) &&
+    isPrimeNew (read (show d ++ show a)) &&
+    isPrimeNew (read (show b ++ show d)) &&
+    isPrimeNew (read (show d ++ show b)) &&
+    isPrimeNew (read (show c ++ show d)) &&
+    isPrimeNew (read (show a ++ show e)) &&
+    isPrimeNew (read (show e ++ show a)) &&
+    isPrimeNew (read (show b ++ show e)) &&
+    isPrimeNew (read (show e ++ show b)) &&
+    isPrimeNew (read (show c ++ show e)) &&
+    isPrimeNew (read (show d ++ show e)) &&
+    isPrimeNew (read (show e ++ show e))
+
+quints = sortBy order [(a, b, c, d, e) | a <- primes, b <- primes, c <- primes, d <- primes, e <- primes,
+    a < b, b < c, c < d, d < e, combosArePrime a b c d e]
+  
+main = print primes