G'day all.
Quoting Dan Weston
Why all the fuss? n! is in fact very easily *completely* factored into prime numbers [...]
It's even easier than that. primePowerOf :: Integer -> Integer -> Integer primePowerOf n p = (n - s p n) `div` (p-1) where s p 0 = 0 s p n = let (q,r) = n `divMod` p in s p q + r factorisedFactorial :: Integer -> [(Integer,Integer)] factorisedFactorial n = [ (p, primePowerOf n p) | p <- primesUpTo n ] factorial :: Integer -> Integer factorial = product . zipWith (^) . factorisedFactorial (Implement primesUpTo using your favourite prime sieve.) Manipulating prime factors like this is sometimes MUCH faster than computing products for this kind of combinatorial work, because Integer division is quite expensive. Cheers, Andrew Bromage