{- | Description: List of Goldbach pairs 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.P41". -} module Problems.P41 (goldbachList) where import qualified Solutions.P41 as Solution -- | Given a range of integers by its lower and upper limit, -- return a list of all Goldbach compositions for the even numbers in the range. -- -- In most cases, if an even number is written as the sum of two prime numbers, one of them is very small. -- Very rarely, it cannot be a sum of primes for which at least one is smaller than, say, 50. -- Try to find out how many such cases there are in the range \([2,3000]\). -- -- === Examples -- -- >>> goldbachList 9 20 -- [(3,7),(5,7),(3,11),(3,13),(5,13),(3,17)] -- -- >>> filter (\(m,n) -> m > 100 && n > 100) $ goldbachList 2 3000 -- [(103,2539)] goldbachList :: Integral a => a -> a -> [(a,a)] goldbachList :: forall a. Integral a => a -> a -> [(a, a)] goldbachList = forall a. Integral a => a -> a -> [(a, a)] Solution.goldbachList