-- goldbach conjecture program
-- read in an even number and find two primes which sum to it

import Text.Printf

-- test if a number is prime starting at a given number
prime_from value test =
  if value <= test
    then True
    else if (mod value test) == 0
      then False
      else (prime_from value (test + 1))
  
-- test if a number is prime
isPrime value = 
  prime_from value 2

-- generate a list of prime numbers
gen_primes largest = [x | x <- [2 .. largest], isPrime x]

-- loop through the primes for one that works
goldbach_recurse value primes =
  let a = head primes in
  let b = value - a in
  if (isPrime b)
    then [a, b]
    else (goldbach_recurse value (tail primes))

-- call the above function and show results
goldbach value =
  goldbach_recurse value (gen_primes value)

-- main IO action
main  = do
  -- read in input as a String
  putStrLn "Enter an even number: "
  line <- getLine
  -- convert it to an Int
  let number = read line :: Int
  -- get the answer and print it
  let [a, b] = goldbach number
  printf "Two prime numbers that add to %d are %d and %d.\n" number a b