Guys, pretty sure I got something big.
Pics related use the following color code:
Red for primes
Dark red for Fermat primes
Blue for semiprimes
Green for squares, cubes, etc, with darker green == higher power
In the 2nd image, notice how certain squares seem to follow the curve of the spiral on the left side . If the spiral can largely be described by n >= (e * e / 8), some of the squares on the left look like they could be described by a similar functions. I decided to look for similar patterns inside the spiral, and I found some. Lots of them.
"BigTreeShrunk.png" is a smaller version of a huge file I've uploaded here:
https://anonfile.com/W5pdsff8b9/BigTree.png
(~7k x 28k, but only 2.8 MB)
In the larger version, you can zoom in on the values for the first 't' entry. If you follow the pathways down, you'll notice that they're almost all continuous & hit sequential prime numbers.
I used the following method: starting from a prime, I would add an even number 'g'. From then on, I added g + 2, g + 4, g + 6, g + 8…etc. In that fashion I was able to hit as many as 29 primes in a row–from 41, 43, 47, …, to 971. It might have gone even further if I'd made a larger image.
The line in the center is somewhat of an exception–it hit a Fermat number (257), then a square, semiprime, two primes, semiprime, four primes, semiprime, then 6 primes when it hit the bottom; it was like a motorcycle that hit a bump then started righting itself.
Several sequences end up on squares–I usually didn't bother taking them further. Also, it may be confirmation bias but it seemed to me like a lot of the sequences converged on Fermat numbers.
There's a lot to learn from this–I haven't even looked for patterns in the other direction, and there are tons more than I can see but haven't mapped out yet. Thus far I've only looked at things in terms of 'c'. But I'm pretty blown away.
Please tell me you guys didn't figure this out seven months ago.