Factoring[8 616 460 799] like 100 years ago

[Thomas Puettmann]

(09-08-2022 09:20 AM)C.Ret Wrote:  Otherwise, I also wanted to congratulate you on the video which is very well made; good video quality (especially the light is excellent - did you use a white glove box?)

All handmade, developed over the years. A part of my shelf is covered with plotter paper. The light is provided by two fixed and one variable LED panels.

(09-08-2022 09:20 AM)C.Ret Wrote:  As well as the idea of ​​not commenting in one language or another which makes it accessible to everyone. Now knowing the reason for these eight numbers at the bottom of each channel, I understand better why it could not be effectively shown in the video in a reasonably short time.

Actually, you just described the emergence of this video. First, I started to talk in English (for the general audience), then in German (for the fischertechnik freaks), but I was not happy (and, more important, my wife was also not happy). Now only the book cover at the end has a definite language, which was somehow the smallest inconsistency I could come up with.

(09-08-2022 09:20 AM)C.Ret Wrote:  I also like the added video after the end which explains using a hand's watch why it should read 3199 and not 3208. It is by building such a system that we understand the limits and discovers the imperfections or shortcomings of any technology and mechanics. This is a very good educational idea.

A good counter that works reliably at high speeds is high tech. The LEGO Lehmer sieve in EdS2's nice post uses an industrial counter for $50 (and, actually, it uses a fischertechnik relay). I didn't want to surrender at that point. Thus, I decided from the beginning to build a counter with a continuous carry mechanism.

I had a very rewarding discussions about the counter in the last days with the authors Jeffrey Shallit and Hugh Williams of the paper I recommended above. They have a document that shows that the French company who built this beautiful Carissan machine were masters in counters and built them for bicycles, automobiles, and turnstiles.

If you look at the Lehmer sieves, you see something similar. They also used technology that just became readily available: bicycle chains and later film tapes.

To me, this is a good explanation why these factoring machines were invented in this period and not, say, 100 years earlier.

(09-08-2022 09:20 AM)C.Ret Wrote:  Anyway, this all piqued my curiosity and I now have a few ideas to try to speed up this factorization on my poor, old and slow Ti-58c.

Thank you very much for your very interesting questions and comments!