Command-line utility to quickly generate prime numbers (Haskell)

PrimeNumbers.hs

import           Control.Applicative
import           Control.Monad
import           Options
import           Safe


{-
  Command-line arguments:
    -m: biggest prime less than m   (required)
    -l: show full list              (optional)
  Example:
    $ ./PrimeNumbers -m 1000
      997
    $ ./PrimeNumbers -m 50 -l
      Prime numbers below 50:
      [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]
-}


--------------------------------------------------------------------------------
--| Process command line arguments and print results
main :: IO ()
main =
  runCommand $ \opts _ -> do

    let limit  = optMax opts
        primes = getPrimes limit

    -- Print largest prime below limit
    unless (optShowList opts) $
      print (lastDef 0 primes)

    -- Print the full list of primes if requested
    when (optShowList opts) $ do
      putStrLn ("Prime numbers below " ++ show limit ++ ":")
      print (getPrimes limit)

--------------------------------------------------------------------------------
-- | Returns a list of primes below limit: pi(limit)
getPrimes :: Integer -> [Integer]
getPrimes limit = [ n | n <- [2..limit] , 0 `notElem` remainders n ]
  where
    remainders n = map (n `mod`) $ takeWhile (\a -> a*a <= n) [2..n]

--------------------------------------------------------------------------------
-- | Command line flags
data PrimeOptions = PrimeOptions
  { optMax      :: Integer
  , optShowList :: Bool
  }

instance Options PrimeOptions where
  defineOptions = pure PrimeOptions
    <*> defineOption optionType_integer (\o -> o
                     { optionDescription = "Largest prime below max"
                     , optionShortFlags = "m"
                     , optionLongFlags = ["max"]
                     })
    <*> defineOption optionType_bool (\o -> o
                     { optionDescription = "Show full list"
                     , optionShortFlags = "l"
                     , optionLongFlags = ["list"]
                     , optionDefault = False
                     })