Some final thoughts and closing out this question

Thank you so much for your help and kind responses regarding my prime randomness post.  Here is the additional bounty I mentioned for the extended discussion.

I think it might be possible to distill the gears into a legitmate function, but I doubt that it is something I can accomplish, as my math skills top-out well before anything that is degree-worthy.  However, that won't stop me from playing with it.

Regarding the Python code, I went back to an older functional version and edited more carefully.  I tried to upload it in a text file, but so far I don't see it anywhere.  Hopefully it will appear.

Once we took to conversing via the 500-character comment tool, this became somewhat of a mess.  Should I consolodate the subsequent questions into the main body, or will it be ok to leave it as is?  This is my first use of matchmaticians, but from what I understand this should be left coherent enough for someone else to use/purchase.

Also, did you want to integrate your further comments into the main answer?  I'm not sure if all that disappears, or stays with the main body after the answer is accepted.