Tag: mathematics

Integer Factorization: Ascent/Remainder Chains
Advertisements This post will use concepts from past posts about Ceiling Squares/Roots. Most ideas I will present without proof, but the mathematics behind them will not, I don’t think, exceed the need of simple algebraic calculation to verify the concepts and properties. If a theoremandproof development of these ideas is warranted and I can sketch…

Integer Factorization: The Latest quickfact.pl Script
Advertisements Nothing earthshaking or historic is here. This is just my latest and greatest attempt to create a Perl script that improves on Fermat factorization, with the simplest and shortest code possible. As always, if anyone wants to try this algorithm out in a language, or an extension of Perl, that can use arbitraryprecision integers,…

Integer Factorization: Recap, October 17, 2023
Advertisements It is time for a review of what I have found in my study, in order for me to figure out where to head next. INTRODUCTORY CONCEPTS AND REMARKS Let m be an odd positive integer. When m = ab for a and b also odd positive integers, this gives a factorization of m.…

Integer Factorization: A Not Yet Closed Gap
Advertisements My studies keep leading me back to the seemingly intractable regions of chaos. I wonder if I will ever see something in all of this that will lead me to any clear path to a solution. Having cleared up the way of constructing the gaps for m=c2r between the first two Remainder Series quantities,…

Integer Factorization: Constellations ProbablyPostscript
Advertisements By measuring only the gaps between even perfect squares and even Remainder Series terms, and between odd and odd, The constellations I was seeing shrank by half in both directions… and showed me something quite unremarkable as a result. Such is math. What it showed me was basically an arrangement of X’s and dots…

Integer Factorization: Dopey Me
Advertisements I think I’m going to have to reconfigure my whole constellation idea due to a fact that should have been obvious to me, ‘cept’n I’m dopey sometimes. What I’ve just noticed is that subtracting even Remainder Series from odd Zone Boundary squares and vice versa is unnecessary because although the linear series that results…

Integer Factorization: a Small Observation on Remainder Series Constellations
Advertisements In my past few days’ study of the “constellations” made by lining up the gaps between the perfect squares and the Remainder Series values for discrete semiprimes (explanation is in earlier posts), I only this morning discovered something I’d missed: There is one pair of discrete semiprimes that has the exact same gaps, and…

Constellation 2071
Advertisements Its smallest prime factor is 19. Thus, it’s a bit of a bigger view. I can start to see some parabolic patterns. This is interesting.

Integer Factorization: Meet the MetaConstellation
Advertisements I am so in the weeds with this, now. LOL Sometimes, when the MIRIAM process (Moving Inspiration Rapidly Into Accepting Minds) gives me a glimpse of somewhere in this integer factorization study that I can go, something that I can do to assemble an idea into reality … the process tells me NOTHING about…

Something Is Taking Form…
Advertisements … Or is it? Your guess is as good as mine right now. Stay tuned to my Integer Factorization posts, here on this blog. There may be something afoot. (I certainly hope so!)