My solution to problem #3 on projecteuler.net

euler_three.rb

def factorize(list, num, p)
  while true
    list.each_with_index { |e, i| list[i] = 0 if e!=p && e%p == 0 }
    list.each{|e| p = e and break if e > p}
    if num % p == 0
#      p num                                                                                                                                                                                          
      return factorize(list[p..Math.sqrt(num/=p)], num, p)
    end
    return num if list.empty?
  end
end

big = 600851475143
big_list = (2..Math.sqrt(big)).to_a
p factorize(big_list, big, 2)