Not quite tweetable. :(

Primes.hs

module Primes where

import Control.Monad

primesFrom []     = []
primesFrom (x:xs) = x : primesFrom (filter ((0 /=) . (`mod` x)) xs)

main = do
  let c = primesFrom [2..200]
  print $ length $ do
    p <- c
    q <- c
    r <- c
    guard (p + q^2 + r^3 == 200)
    return (p, q, r)