Project Euler #3 in pure CoffeeScript

Euler3.coffee

# Project Euler #3 -> http://projecteuler.net/index.php?section=problems&id=3
# Q: What is the largest prime factor of the number 600851475143 ?

# Generate a Sieve of Eratosthenes (an array loaded with prime numbers)
primes = []
sieve = (set, pos) ->
  return false if pos >= set.length
  if set[pos] * set[pos] < set[set.length-1]
    primes = (x for x in set when x == set[pos] or x % set[pos] != 0)
  return sieve(primes,pos+1)
sieve([2..200000],0)

# Factor a number into its primes - we use our Sieve above to quickly check if number is prime
factors = []
factorial = (primes, target, count) ->
  if primes[count] < target
    if target % primes[count] == 0
      factors.push(primes[count])
      target = target / primes[count]
    else
      count++

    if (num for num in primes when num == target).length > 0
      factors.push(target)
    else
      factorial(primes, target, count)

factorial(primes, 600851475143, 0)
console.log(factors)