Haskell Primes

primes.hs

-- lazy evaluation lets you make mutually recursive definitions

-- a prime is a number whose only factor is itself
isPrime :: Integer -> Bool
isPrime 0 = False
isPrime 1 = False
isPrime 2 = True
isPrime n = head (factors n) == n

-- the factors of a number are all the prime numbers that make it up
factors :: Integer -> [Integer]
factors n =
  let d = take 1 [i | i <- (takeWhile (\x -> x < n `div` 2) primes), n `mod` i == 0]
  in
    if d == [] then
      [n]
    else
      (head d) : (factors (n `div` (head d)))

-- the primes are the list of numbers from 1 to infinity where isPrime is true
primes = [i | i <- [1..], isPrime i]