primes

primes.hs

module Main where

import Data.List (genericTake)

{-
let p(i) be the i(th) prime number starting from 2
[p1,p2,p3,p4,p5...]
[(p2-p1),(p3-p2),(p4-p3),(p5-p4)...]
[{(p3-p2)-(p2-p1)},{(p4-p3)-(p3-p2)},{(p5-p4)-(p4-p3)}...]
... etc. applied n times
-}

main :: IO()
main = do
    -- input format: "a b"
    input <- getLine
    let args = words input
        a = read (head args) :: Integer
        b = read (last args) :: Integer
    print . applyN a seqDiff . primes $ b

-- applyN n f == (f . f . f...n times)
applyN :: Integral a => a -> (b -> b) -> b -> b
applyN n f x
    | n > 0 = applyN (n-1) f $ f x
    | otherwise = x

-- seqDiff [x1,x2,x3...] == [x2-x1,x3-x2...]
seqDiff :: Num a => [a] -> [a]
seqDiff [] = []
seqDiff [x] = []
seqDiff [x1,x2] = [x2-x1]
seqDiff (x1:x2:xs) = x2-x1:seqDiff (x2:xs)

-- primes n == [p1,p2,p3...nth prime]
primes :: Integral a => a -> [a]
primes n = genericTake n . filterPrime $ [2..]
    where filterPrime (p:xs) =
              p : filterPrime (filter (\x -> x `mod` p /= 0) xs)