# Exponetial speed

1. Dec 15, 2013

Is anyone aware of any factoring algorithms that factor in exponential speed?
Working on improving mine and need a comparison.

Have not had much luck finding such.
Thanks

2. Dec 15, 2013

### Staff: Mentor

Isn't trial division exponential? For a number of length n, you need at most $\left(\sqrt{2}\right)^n$ attempts to find a factor and there is at most one really time-consuming step, so all other factors can be neglected. Assuming base 2, base 10 just changes this to $\left(\sqrt{10}\right)^n$.
Good algorithms are much better, so I don't see why you want a comparison with exponential algorithms.

3. Dec 31, 2013

My reference is to reducing beyond the root exponentially. For very large numbers this greatly reduces time and makes factoring of large numbers possible within a useful period of time.
Thanks,

4. Dec 31, 2013

### Staff: Mentor

Which reference, and what do you mean with "reducing beyond the root exponentially"?

Better than existing algorithms? Those are way below exponential time...