Baseless number encoder

PrimeEnc.hs

import Data.Numbers.Primes (primes, primeFactors)
import Data.List (elemIndex)
import Control.Monad (forM_)

data N = P N | Z | Prod [N] deriving (Eq, Show)

primes' = 1 : primes
primeIndex n = let Just idx = elemIndex n primes' in idx

encode :: Int -> N
encode 0 = Z
encode 1 = P Z
encode n = Prod $ map (P . encode . primeIndex) $ primeFactors n

decode :: N -> Int
decode Z = 0
decode (P n) = primes' !! decode n
decode (Prod ns) = product $ map decode ns

main = forM_ [0..2^32-1] $ \n -> encode n `seq` return ()