module LennartPrimes (primesUpTo) where

infixr :>

data StreamInt = !Int :> StreamInt

(!>) :: StreamInt -> Int -> Int
(x :> _)  !> 0 = x
(_ :> xs) !> n = xs !> (n-1)

-- By replacing lprimes on the next line by '5 :> gen 7 4 2' this algorithm
-- runs in very little space, but is somewhat slower.
primes = 2 :> 3 :> lprimes
  where isPrime (p:>ps) n = n `rem` p /= 0 && (p*p > n || isPrime ps n)
        lprimes = 5 :> gen 7 4 2
        gen n a b = if isPrime lprimes n then n :> gen (n+a) b a
                                         else gen (n+a) b a

primesUpTo n = [ fromIntegral (primes !> (i-1)) | i <- [1..fromIntegral n] ]