# [RC5] Long-term projects: exponential and logarithmic growth

Elektron elektron_rc5 at yahoo.ca
Sun Sep 5 03:08:56 EDT 2004

```On 4 Sep, 2004, at 22:10, Daniel Quintiliani wrote:

> Remember a month ago I suggested that with long-term distributed
> computing projects,
> logarithmic growth is a better estimate than exponential growth
> because people leave the
> project or die as processing power grows?

Actually, people probably 'left' OGR because of a lack of packets, and
now, because there's somehow more interest in RC5 (especially in
coding/designing cores). Or perhaps it's because of other distributed
projects.

As it stands, RC5-72 looks like it might be approaching some kind of
growth. Of course, the RC5-64 keyrate looks like it was approximately
stable for over a year (perhaps our computer power doesn't double every
18 months). But RC5-72 is really an exercise in futility, because when
people see that it'll take several hundred years, it just doesn't seem
worthwhile.

That is, of course, why I run OGR. It's at least doable in a reasonable
timeframe, though my computer (PPC 7450 ish) is much better at RC5 than
OGR, relatively speaking.

We don't have the full history for RC5-64, but at least, people don't
seem to have left, and people don't seem to be leaving RC5-72 either
(like what appears to have happened with OGR).

Looking at the graphs, though, RC5-72 looks like it roughly
approximates some kind of linear growth (the dip in keyrate this summer
and last can probably be explained by people turning computers off
during the summer). If I estimate it was around 100 Gkeys/s last
september, and 170 Gkeys/s this september, we have a growth rate of
70e9/31536000 = 2219 keys/s/s. Our keyrate is then 1e11 + 2219t,
integrating, 1e11t + 1110t^2. Solving the quadratic, 1110t^2 + 1e11t -
2^72 = 0, t = 2018062629 (or roughly negative that, which we're not
interested in), or just under 64 years.

Some FPGAs may change all that though.

- Purr

```