gistfile1.hs

-- The smallest number expressible as the sum of a prime square,
-- prime cube, and prime fourth power is 28. In fact, there are
-- exactly four numbers below fifty that can be expressed in
-- such a way:
-- 
-- 28 = 2^(2) + 2^(3) + 2^(4) 33 = 3^(2) + 2^(3) + 2^(4) 49 =
-- 5^(2) + 2^(3) + 2^(4) 47 = 2^(2) + 3^(3) + 2^(4)
-- 
-- How many numbers below fifty million can be expressed as the
-- sum of a prime square, prime cube, and prime fourth power?
-- 

module Main where

import Data.List
import Primes
import System

primes = filter (prime) [2..]

squares n = takeWhile (< n) $ map (^2) primes
cubes n = takeWhile (< n) $ map (^3) primes
fourths n = takeWhile (< n) $ map (^4) primes

sums n = nub [a + b + c | a <- (squares n)
                        , b <- (cubes n)
                        , c <- (fourths n)
                        , a + b + c < n]

main = do args <- getArgs
          let n = (read (args !! 0))::Int
          print $ sums n
          print $ length $ sums n