-- Fractran prime generation algorithm
-- Implementation by Eliot Ball
-- See http://mathworld.wolfram.com/FRACTRAN.html for further details

-- The fractran program
frac = [[17, 91], [78, 85], [19, 51], [23, 38], [29, 33], [77, 29], [95, 23], [77, 19], [1, 17], [11, 13], [13, 11], [15, 2], [1, 7], [55, 1]]

-- Function to obtain the remainder when dividing n*f0 by f1
fpart :: Integer -> [Integer] -> Integer
fpart n f = mod (n * (head f)) (last f)

-- Function to multiply a number by the first fraction in the fractran program that gives an integral product
fmul :: Integer -> Integer
fmul n = head [div (n * (head f)) (last f) | f <- frac, fpart n f == 0]

-- An infinite list containing the sequence generated by the fractan program with initial seed n
sequ :: Integer -> [Integer]
sequ n = [n] ++ sequ (fmul n)

-- Function to check whether the real number n is an integer
isround :: Double -> Bool
isround n = fromIntegral (truncate n) == n

-- An infinite list of primes
primes = [truncate (pc n) | n <- (sequ 2), isround (pc n)]
 where
  pc n = logBase 2 (fromIntegral n)