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I didn't leave, I just got busy working 60 hour weeks in between studying.

I found a new method called matrix decomposition (not the known method of the same name).

Premise is that you break a semiprime down into its component numbers and magnitudes, lets say 697 for example. It becomes 600, 90, and 7.

Then you break each of those down into their prime factorizations (with exponents).
So you get something like

>>> decon(697)
offset: 3, exp: [[Decimal('2'), Decimal('3')], [Decimal('3'), Decimal('1')], [Decimal('5'), Decimal('2')]]
offset: 2, exp: [[Decimal('2'), Decimal('1')], [Decimal('3'), Decimal('2')], [Decimal('5'), Decimal('1')]]
offset: 1, exp: [[Decimal('7'), Decimal('1')]]

And it turns out that in larger numbers there are distinct patterns that act as maps at each offset (or magnitude) of the product, mapping to the respective magnitudes and digits of the factors.

For example I can pretty reliably predict from a product, where the '8's are in its factors.

Apparently theres a whole host of rules like this.
So what I've done is gone an started writing an interpreter with some pseudo-assembly I defined. This has been ongoing for maybe a month, and I've had very little time to work on it in between at my job (which I'm about to be late for here if I don't start getting ready, lol).

Anyway, long and the short of it, the plan is to generate a large data set of primes and their products, and then write a rules engine to generate sets of my custom assembly language, and then fitness test and validate them, winnowing what doesn't work.

The end product should be a function that lets me map from the digits of a product to all the digits of its factors.

It technically already works, like I've printed out a ton of products and eyeballed patterns to derive custom rules, its just not the complete set yet. And instead of spending months or years doing that I'm just gonna finish the system to automatically derive them for me. The rules I found so far have tested out successfully every time, and whether or not the engine finds those will be the test case for if the broader system is viable, but everything looks legit.

I wouldn't have persued this except when I realized the production of semiprimes *must* be non-eularian (long story), it occured to me that there must be rich internal representations mapping products to factors, that we were simply missing.

I'll go into more details in a later post, maybe not today, because I'm working till close tonight (won't be back till 3 am), but after 4 1/2 years the work is bearing fruit.

Also, its good to see you all again. I fucking missed you guys.