{- |
Description: Goldbach's conjecture
Copyright: Copyright (C) 2021 Yoo Chung
License: GPL-3.0-or-later
Maintainer: dev@chungyc.org

Part of Ninety-Nine Haskell "Problems".  Some solutions are in "Solutions.P40".
-}
module Problems.P40 (goldbach) where

import qualified Solutions.P40 as Solution

-- | Goldbach's conjecture says that every positive even number greater than 2 is the sum of two prime numbers.
-- For example: \(28 = 5 + 23\).
-- It is one of the most famous facts in number theory that has not been proved to be correct in the general case.
-- It has been numerically confirmed up to very large numbers.
--
-- Write a function to find two prime numbers that sum up to a given even integer.
--
-- === Examples
--
-- >>> goldbach 12
-- (5,7)
goldbach :: Integral a => a -> (a,a)
goldbach :: forall a. Integral a => a -> (a, a)
goldbach = a -> (a, a)
forall a. Integral a => a -> (a, a)
Solution.goldbach