Recently, while working on something else, I invented as a side effect, a new(?) algorithm
to find factors of an integer N.
Specifically, I believe I could prove that it will always find a nontrivial factor of N
in time bounded by O(N^0.251) steps, each step an arithmetic operation on
O(logN)-digit numbers. Really, runtime is O(N^(1/4)*logN^somepower) but I have
not carefully thought about the log terms.
Question: Is this new & interesting?
This factoring algorithm is clearly a lot slower asymptotically than the best
(quadratic sieve, ECM, NF-sieve) and comparable in time bound to Pollard-rho method
(except I think my algorithm will usually perform worse than Pollard rho in practice),
so my runtime is unexciting. BUT my algorithm is deterministic and rigorous.
I think perhaps those other better algorithms are randomized and/or their
time bounds are nonrigorous.
So in that (not very interesting) sense, maybe I have a new record.
Or, maybe I do not even have that. You tell me please.