After learning a bit about alife I was able to write
another one. It took some false starts
to understand the problem, but afterward I was able to refactor the problem into a sort of alife that measured and carefully tweaked various variables in the simulator, as the algorithm
explored the paramater space. After a few hours of letting the thing run, it successfully returned a remainder of zero on 41.4% of semiprimes tested.

This is the bad boy right here:
tracks[14]
[15, 2731, 52, 144, 41.4]

As they say, "he ain't there yet, but he got the spirit."

A 'track' here is just a collection of critical values and a fitness score that was found given a few million runs. These variables are used as input to a factoring algorithm, attempting to factor
any number you give it. These parameters tune or configure the algorithm to try slightly different things. After some trial runs, the results are stored in the last entry in the list, and the whole process is repeated with slightly different numbers, ones that have been modified
and mutated so we can explore the space of possible parameters.

Naturally this is a bit of a hodgepodge, but the critical thing is that for each configuration of numbers representing a track (and its results), I chose the lowest fitness of three runs.
Meaning hypothetically theres room for improvement with a tweak of the core algorithm, or even modifications or mutations to the
track variables. I have no clue if this scales up to very large semiprime products, so that would be one of the next steps to test.

Fitness also doesn't account for return speed. Some of these may have a lower overall fitness, but might in fact have a lower basis
(the value of 'i' that needs to be found in order for the algorithm to return rem%a == 0) for correctly factoring a semiprime.

The key thing here is that because all the entries generated here are dependent on in an outer loop that specifies [i] must never be greater than a/4 (for whatever the lowest factor generated in this run is), we can potentially push down the value of i further with some modification.

The entire exercise took 2.1735 billion iterations (3-4 hours, wasn't paying attention) to find this particular configuration of variables for the current algorithm, but as before, I suspect I can probably push the fitness value (percentage of semiprimes covered) higher, either with a few
additional parameters, or a modification of the algorithm itself (with a necessary rerun to find another track of equivalent or greater fitness).

I'm starting to bump up to the limit of my resources, I keep hitting the ceiling in my RAD-style write->test->repeat development loop.
I'm primarily using the limited number of identities I know, my gut intuition, combine with looking at the numbers themselves, to deduce relationships as I improve these and other algorithms, instead of relying strictly on memorizing identities like most mathematicians do.
I'm thinking if I want to keep that rapid write->eval loop I'm gonna have to upgrade, or go to a server environment to keep things snappy.

I did find that "jiggling" the parameters after each trial helped to explore the parameter
space better, so I wrote some methods to do just that. But what I wouldn't mind doing
is taking this a bit of a step further, and writing some code to optimize the variables
of the jiggle method itself, by automating the observation of real-time track fitness,
and discarding those changes that lead to the system tending to find tracks with lower fitness.

I'd also like to break up the entire regime into a training vs test set, but for now
the results are pretty promising.

I knew if I kept researching I'd likely find extensions like this. Of course tested on
billions of semiprimes, instead of simply millions, or tested on very large semiprimes, the
effect might disappear, though the more i've tested, and the larger the numbers I've given it,
the more the effect has become prevalent.

Hitko suggested in the earlier thread, based on a simplification, that the original algorithm
was a tautology, but something told me for a change that I got one correct. Without that initial challenge I might have chalked this up to another false start instead of pushing through and making further breakthroughs.

I'd also like to thank all those who followed along, helped, or cheered on the madness:
In no particular order ,demolishun, scor, root, iiii, karlisk, netikras, fast-nop, hazarth, chonky-quiche, Midnight-shcode, nanobot, c0d4, jilano, kescherrant, electrineer, nomad,
vintprox, sariel, lensflare, jeeper.

The original write up for the ideas behind the concept can be found at:
https://devrant.com/rants/7650612/...

If I left your name out, you better speak up, theres only so many invitations to the orgy.
Firecode already says we're past max capacity!