From f5d5a26d4b9796a0f8ffb6c06101e56ead2b8490 Mon Sep 17 00:00:00 2001
From: Jesse McDonald <nybble41@gmail.com>
Date: Sat, 22 Aug 2015 19:39:42 -0500
Subject: [PATCH] Add solution for problem 51.

---
 Problem051.hs | 30 ++++++++++++++++++++++++++++++
 1 file changed, 30 insertions(+)
 create mode 100644 Problem051.hs

diff --git a/Problem051.hs b/Problem051.hs
new file mode 100644
index 0000000..2d317b6
--- /dev/null
+++ b/Problem051.hs
@@ -0,0 +1,30 @@
+-- By replacing the 1st digit of the 2-digit number *3, it turns out that six
+-- of the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime.
+--
+-- By replacing the 3rd and 4th digits of 56**3 with the same digit, this
+-- 5-digit number is the first example having seven primes among the ten
+-- generated numbers, yielding the family: 56003, 56113, 56333, 56443, 56663,
+-- 56773, and 56993. Consequently 56003, being the first member of this family,
+-- is the smallest prime with this property.
+--
+-- Find the smallest prime which, by replacing part of the number (not
+-- necessarily adjacent digits) with the same digit, is part of an eight prime
+-- value family.
+
+import Euler
+import Debug.Trace
+
+isPrime :: Integer -> Bool
+isPrime n = n >= 2 && all (\p -> n `mod` p /= 0) smallPrimes
+   where smallPrimes = takeWhile (<= floor (sqrt (fromIntegral n))) primes
+
+main = print $ head $ do
+   base <- primes
+   let digits = toDigits base
+   template <- sequenceA <$> mapM (\n -> [const n, id]) digits
+   let family = nub $ filter isPrime $ map fromDigits $
+                filter ((/= 0) . head) $ map template [0..9]
+   guard $ take 1 family == [base]
+   guard $ length family >= 8
+   traceM $ show family
+   return base