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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.

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I just realized I can remove the x, lol.

Was a hold over from another equation.
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If you’ve gone through all this I feel like sitting down and learning some calculus isn’t out of reach
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@jeeper I lack the prerequisite knowledge of linear algebra. I've only learned what I've needed so far.

Where would you recommend I start? What material should I study?
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@Wisecrack

Calculus (or should I say analysis) does not really have linear algebra as a prerequisite. In fact, they usually are taught at the same time, since they deal in completely unrelated aspects.

Analysis is a big enough field, but since you are dealing with machine learning, I guess you should start with successions, series and limits.

I find that bounds analysis is often critical in ensuring systems are convergent.

Loss and activation functions touch more into geometric (algebraic) concepts, but they are mostly "visually" evident, even without formal proof, and besides, there's usually little to gain in trying things beside tried and true ones like relu, sigmoid, and the like.
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In the end, I'd say applied statistics are a much bigger contributor.
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@Wisecrack idk if Khan Academy is still free by that has some great math curriculum. Also I think there are Harvard lectures on calculus and other maths on YouTube. I think you should look at some full courses and read the intros and see what you see as important. You could consider buying old text books. Even ones a few editions old can be had for under \$10 and the concepts are the same, they just change up the problems.
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Also calculus 1 and sometimes calc 2 are usually prerequisite for linear algebra in colleges.
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@Wisecrack
Hey it is always a pleasure to read new things from You!
Really appreciate these micro blogs so keep up the good work dudeðŸ˜€
Fyi there are some open courses from MIT

https://ocw.mit.edu/courses/...
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@figoore hey thanks figoore. I'm glad you enjoy it.

These posts started out as shitposts and are now only semi-shitposty.

I'm thinking I'll start a forum or some shit where I can post notes and updates. Thought about it for a while. Only issue I really encounter on devrant is theres less room for collaborative discussion/work, and less tools. For example code gets mangled, and pastebin is hit or miss on whether it deletes some code.

Main motivation is the semiprime factoring project has 1272 significant variables and identities as of now, and just this month I'm probably going to double or quadruple that number, along with adding a dozen conversion methods between different function slopes.

Thats before I've fully applied matrix algebra, and I haven't even tried applying calculus, linear algebra, or machine learning.

I have at least three major automation and exploratory projects going on there too. It's way too much for me to continue.
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Then theres other work such as proving the equivalence of a restricted form of the collatz conjecture to certain limited version of state machines, and I'm gonna need a ton of help to learn how to write proofs, though the basic premise is there.

And theres been certain work to map the product of semiprimes a*b to some OTHER non semiprime product (more than two non-trivial primes) composed of n>2 factors. which makes *very* large numbers that are too big to factor with cutting-edge methods (ECM), small enough to then be factored by ECM. And I've broke ground on that but it still needs a lot more work to map all the semiprime product factor trees to non-semiprime product factor trees. I'd like to do that visually if possible, but I don't have the money to take the time off, so I'll undoubtedly need help from others to do components like visual rendering.

It's a lot of open frontier to explore and I think it'd be more fruitful with more people.
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And finally I've been learning about shannon entropy, and I think there may be new measures of entropy that supervene it on sufficiently large data sets but I'm still learning and formulating raw conjectures about that.

And as absurd as it sound, there may or may not be allowabled interpretations of division-by-zero in relation to useful *categorization* of certain kinds of matrices.
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A lot of the study starts out as ridiculous 'what ifs', like "what if we COULD do this thing that generally not allowed? What if we could do this thing just under very specific circumstances?" and "what if these two completely unrelated problems are actually related? And if so, how?"

And thats something I really enjoy exploring, these experiments in possibilities. And I'm glad others like yourself do too, otherwise I'm just shouting into the wind.

Eventually I'll have to get partners or help, and a dedicated place online to act as a hub for it all, like a forum or wiki, but fwiw thank you for your support. Means something to me that people want to read it.

Again, thank you and everyone that comes to read these posts.
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edit: allowable NOT allowable(d).

lol.
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