module Main
       where
 
import Data.List
 
divides :: Integer -> Integer -> Bool
divides d n = rem n d == 0
 
ld :: Integer -> Integer
ld x = ldf 2 x
 
ldf :: Integer -> Integer -> Integer
ldf m n | divides m n   = m
        | m^2 > n       = n
        | otherwise     = ldf (m + 1) n
 
prime0 :: Integer -> Bool
prime0 x | x < 1        = error "Not a positive integer!"
         | x == 1       = False
         | otherwise    = ld x == x
 
factors :: Integer -> [Integer]
factors n | n < 1       = error "Not a positive integer!"
          | n == 1      = []
          | otherwise   = p : factors (div n p) where p = ld n
 
main :: IO()
main = do
  putStrLn "Hello! This is a short program that aims at prime generation!"
  putStrLn "Test it yourself, here are some samples:"
  print $ factors 10
  print $ factors 15
  print $ "What about numbers and number of their divisors?"
  print $ [(x, factors x, length $ factors x) | x <- [2..100]]
  print "That above is messy, let's filter primes!"
  print $ filter prime0 [2..100]
  print "All fine and dandy, but what about really large numbers?"
  print $ factors 10001011107101
  print $ factors 11111111111111111
  print $ factors (2^20 - 1)
  print $ factors (2^31 - 1) -- Marsene Prime! This is a comment by the way.
  print "Yeah, that easy and fast!"
  print "This language and weird, quirky and I can totally get why people think"
  print "that it was made by sadists to masochists."
  print "But damn me if I am going to deny that it can approach C in terms of"
  print "efficiency. In right hand of course."
  print "As a bonus, here is a solution to first problem on Project Euler"
  print $ sum $ union [3,6..999] [5,10..999]
 

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