Integer Factorization: Update for 25 September 2023


An incidental quirk i noticed in outputs led me to scurry to program a based thereon, but which produced a speed-up in only one out of the fifty test numbers (10 to 12 digits) of my discrete semiprime data suite.

What that exciting/disappointing work caused me to pause has resumed: a more or less systematic examination and characterization of the following two systems of organizing the odd positive integers: sorting by Remainder r in m=c^2-r, and by the slope of the Remainder Line on the Zone Grid corresponding to the Characteristic Polynomial x^2+2cx+r.

I am seeing old relationships and possibly new ones: The behavior of the intersection of the Zone Boundary Lines with the Remainder Line is something I have already used in but also something on which I can base improvements; but also i may be seeing a strong correlation between the slope of the Remainder Line and the Zone Boundary or Boundaries where the Line will hit at an integer point.

Still thrilling, it’s also still sometimes pushing me to get up and get cracking on it. During a set of weeks busy in other, more practical ways, plus obsession over a novel and a play to rehearse besides, balancing and maintaining energy is tricky, but it’s happening. That’s saying something, so it’s a good thing I’ve just finished saying it here.

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