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With recent changes I managed to eliminate having to explore branches to more than d+1, where d=depth.

This occurred because I realized that while semiprimes do not have one unique path through an undirected graph, parallels can nevertheless be drawn between the operation of multiplication and convolution. But that unlike convolution, at least in the nieve case, there always exists a deconvolution as it were.

And that because smaller magnitude digits in a semiprime have inordinate impacts on larger digits, that this convolution-like process (where we can add p up to q times to get n, or q up to p times to get n) should have a bias affect that flows from rightmost digits to leftmost (larger magnitude) columns of a number. Meaning effectively, where we might bruteforce the factors (p, q) of a semiprime n, by trying each digit 0-9 at each magnitude up to the largest magnitude of the root of n, there must exist a metric that controls for the selection of branching such that the correct combinations of digits at some search depth, ultimately lead to the production of n, and that this problem should be convertible to a shallow depth search of a branch.

The next logical leap was that if digits in different columns to the right, have more affect on digits closer to them on the left (versus farther away), then there must be a maximal depth that this is true for.

Ergo the prior problem of combinatorial explosion should reduce down to a linear problem.

What it looks like is the search space for factoring a semiprime n, or breaking a public key, should be reduceable to k<=100, (k)floor(log(n, 10)) regardless of the bitlength of the key.

And that is what I have seen so far in my testing.

Right now I'm working on implementing a generalization so the code fully runs across all magnitudes of a key we're looking to decrypt, but the core algorithm seems to do its job quite well. I'm also battle-testing it to look for edge cases and non-filterable branches that have to be dealed with but so far I haven't encountered any in my tests.

We're in the home stretch from everything I can see, God willing.