primes.hs

import System.Environment (getArgs)
import System.IO (hPutStrLn, stderr)
import Data.List (genericTake)
import Text.Read (readMaybe)

-- sqrt possibly inaccurate for large primes.
primes = 2 : [ n | n<-[3,5..], all (\x -> n `mod` x /= 0) $ takeWhile (<= (floor $ sqrt $ fromIntegral n)) primes]
-- guaranteed to be correct for all primes, but much slower:
-- primes = 2 : [ n | n<-[3,5..], all (\x -> n `mod` x /= 0) $ takeWhile (<= (quot n 2)) primes]
-- for all n out of [1..] there's a prime p so that n < p < 2*n (Bertrand's postulate)

main = do
    args <- getArgs
    let output = case args of
            []                                  -> Just primes
            [a] | Just n <- readMaybe a, n >= 0 -> Just $ genericTake n primes
            _                                   -> Nothing
    case output of
        Just o  -> putStr $ unlines $ show <$> o
        Nothing -> hPutStrLn stderr "wrong usage"

import qualified Data.Map as M

factor n = factor_ M.empty (takeWhile (<= n) primes) n
    where factor_ acc _ 1 = acc
          factor_ acc (p:ps) n
              | n `rem` p == 0 = factor_ (M.insertWith (+) p 1 acc) (p:ps) (n `div` p)
              | otherwise      = factor_ acc ps n