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The first fruits of almost five years of labor:
7.8% of semiprimes give the magnitude of their lowest prime factor via the following equation:
((p/(((((p/(10**(Mag(p)-1))).sqrt())-x) + x)*w))/10)

I've also learned, given exponents of some variables, to relate other variables to them on a curve to better sense make of the larger algebraic structure. This has mostly been stumbling in the dark but after a while it has become easier to translate these into methods that allow plugging in one known variable to derive an unknown in a series of products.

For example I have a series of variables d4a, d4u, d4z, d4omega, etc, and these are translateable now, through insights that become various methods, into other types of (non-d4) series. What these variables actually represent is less relevant, only that it is possible to translate between them.

I've been doing some initial learning about neural nets (implementation, rather than theoretics as I normally read about). I'm thinking what I might do is build a GPT style sequence generator, and train it on the 'unknowns' from semiprime products with known factors.

The whole point of the project is that a bunch of internal variables can easily be derived, (d4a, c/d4, u*v) from a product, its root, and its mantissa, that relate to *unknown* variables--unknown variables such as u, v, c, and d4, that if known directly give a constant time answer to the factors of the original product.

I think theres sufficient data at this point to train such a machine, I just don't think I'm up to it yet because I'm lacking in the calculus department.

2000+ variables that are derivable from a product, without knowing its factors, which are themselves products of unknown variables derived from the internal algebraic relations of a product--this ought to be enough of an attack surface to do something with.

I'm willing to collaborate with someone familiar with recurrent neural nets and get them up to speed through telegram/element/discord if they're willing to do the setup and training for a neural net of this sort, one that can tease out hidden relationships and map known variables to the unknown set for a given product.