module Lib (fib, primes, primeFactors) where

fib :: [Integer]
fib = 1 : 2 : zipWith (+) fib (tail fib)

isPrime :: Integer -> Bool
isPrime n = n > 1 && null [[] | k <- [2 .. (floor $ sqrt $ fromIntegral n)], mod n k == 0]

primes :: [Integer]
primes = 2 : filter isPrime [3, 4 ..]

primeFactors :: Integer -> [Integer]
primeFactors n = genPrimeFactors n 2
  where
    genPrimeFactors :: Integer -> Integer -> [Integer]
    genPrimeFactors n c
      | c * c > n = [n]
      | mod n c /= 0 = genPrimeFactors n (c + 1)
      | otherwise = c : genPrimeFactors (div n c) c