diff --git a/Zora.cabal b/Zora.cabal
--- a/Zora.cabal
+++ b/Zora.cabal
@@ -1,5 +1,5 @@
 Name:		   Zora
-Version:	   1.1.15
+Version:	   1.1.16
 Synopsis:      Graphing library wrapper + assorted useful functions 
 Description:   A library of assorted useful functions for working with lists, doing mathematical operations and graphing custom data types.
 Category:      Unclassified
@@ -8,7 +8,7 @@
 License-File:  LICENSE
 Stability:	Experimental
 Author:		Brett Wines
-Maintainer: brettwines@gmail.com
+Maintainer: bgwines@cs.stanford.edu
 Homepage:	http://github.com/bgwines/zora
 Build-Type: Simple
 Source-Repository head
diff --git a/Zora/List.hs b/Zora/List.hs
--- a/Zora/List.hs
+++ b/Zora/List.hs
@@ -62,6 +62,7 @@
 , bsearch
 , bsearch_1st_geq
 , elem_counts
+, elem_counts_by
 , running_bests
 , running_bests_by
 , (<$*>)
@@ -501,6 +502,15 @@
     = map (\l -> (head l, length' l))
     . List.group
     . List.sort
+
+-- | /O(nlog(n))/ Counts the number of time each element appears in the given list. For example:
+--
+--  > elem_counts [1,2,1,4] == [(1,2),(2,1),(4,1)]
+elem_counts_by :: (Ord b) => (a -> b) -> [a] -> [(a, Integer)]
+elem_counts_by cmp
+    = map (\l -> (head l, length' l))
+    . List.groupBy (\a b -> cmp a == cmp b)
+    . List.sortBy (Ord.comparing cmp)
 
 -- | Shorthand for applying the same parameter twice.
 --
diff --git a/Zora/Math.hs b/Zora/Math.hs
--- a/Zora/Math.hs
+++ b/Zora/Math.hs
@@ -128,16 +128,9 @@
 		d :: Integer
 		d = (n - 1) `div` (2^s)
 
-prime_rec :: Integer -> Integer -> Bool
-prime_rec n k
-	| (n <= 1) = False
-	| (fromInteger k >= ((fromInteger n) / 2) + 1.0) = True
-	| ((n `mod` k) == 0) = False
-	| otherwise = prime_rec n (k+1)
-
--- | /O(n)/ Returns whether the parameter is a prime number.
+-- | /O(k n log(n)^-1)/, where /k/ is the number of primes dividing /n/ (double-counting for powers). /n log(n)^-1/ is an approximation for <http://en.wikipedia.org/wiki/Prime-counting_function the number of primes below a number>. Returns whether the parameter is a prime number.
 prime :: Integer -> Bool
-prime n = prime_rec n 2
+prime n = (factor n) == [n]
 
 -- | /O(min(n, m))/ Returns whether the the two parameters are <http://en.wikipedia.org/wiki/Coprime coprime>, that is, whether they share any divisors.
 coprime :: Integer -> Integer -> Bool
@@ -218,7 +211,7 @@
 
 factors_to_divisors :: [(Integer, Integer)] -> [Integer]
 factors_to_divisors
-	= init
+	= (\l -> if l == [] then [] else init l)
 	. List.sort
 	. map product
 	. map (map (\(p, a) -> p^a))