Awesome! But I love the authors' qualifying statement, "The new algorithm is not really practical in its current form, because the proof given in our paper only works for ludicrously large numbers. Even if each digit was written on a hydrogen atom, there would not be nearly enough room available in the observable universe to write them down."
That's a downside. But then again, it's with the really enormous numbers that N log(N) most outperforms N^2.