February 12, 2023 or so

How was I able to figure out the gears needed for those patterns? It turns out there is the Prime Factor Method. Put the prime factors of the stationary gear over those of the moving gear and strike out any common factors. For the first few 35s patterns:

Well, we don’t want to do that more than once per ring or gear! Hmmm… how to store that so we can look it up easily as needed? Ah, paraphrasing Dilbert - “We like spreadsheets”. 

This is just a small part of the spreadsheet, it goes from the smallest combo that works (below) to the largest the 360 ring - maybe 275 Gear. I only build it as I need to, but right now it has about 70 rows and 40 columns

Believe it or not, the smallest possible gear, the 5 tooth, will work in a 10 tooth ring.