Tag: integer factorization
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Integer Factorization: Playing With the Zones
Advertisements It occurred to me tonight to start looking at the successive remainders on the Zone Grid in a different way. During my studies of this arrangement of number lines vertically shifted by quadratic amounts on the Cartesian Plane, I discovered that a “skew” linear transformation of the zone lines and the Remainder Line preserves…
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Integer Factorization: Update for 21 March 2023
Advertisements This update refers to concepts defined in earlier posts, without explaining them extensively here. I have placed links at the bottom of this post to recent explanatory posts. In designing my most recent approach, I produced a two-dimensional travel path taken by successive remainders c2-m, (c+1)2-m, … (c+n)2-m, … where m is the odd…
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A Method of Construction and a Theorem for Integer Factorization
Advertisements By J. Calvin Smith, B.A., Mathematics, Georgia College, Milledgeville, Georgia, United States of America (1979) – Retired Member, American Mathematical Society Written 14 March 2023 at Mountain River Chalet (the author’s home), Talking Rock, Georgia, USA. The following definitions, theorem, and construction are the end result of research by the author into factorization of…
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Integer Factorization: An Informal Report
Advertisements Here is an informal article, in PDF, about the work I’ve done lately, including some of the new revelations about which I’ve blogged.
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Integer Factorization: Going Forward
Advertisements What do I do next? Well, I’m inclined to think I should look at how I’m making the Zone Jumps, which don’t get bigger as rapidly as I’d like, into multi-Zone jumps that do. This will involve understanding the quadratic increase of the numerators of the intercept points with Zone boundaries, and the linear…
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Integer Factorization: Revision to jumpfactor.pl, March 8, 2023
Advertisements I added a usage line, and also programmed the loop to look only at numerators which are even, cutting the number of iterations of the main loop in half. Thus repurposed variable “idx” as the Zone number, and added another variable to serve as the iteration counter. The revised code will be, and will…
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Integer Factorization: An Observation About jumpfactor.pl
Advertisements I’m taking the results from jumpfactor.pl, and its algorithm for making the “jumps” in order to try to figure out ways to combine the jumps into few or (I hope) one jump to the Zone that will permit factorization. What I’ve observed is that the rational point where the Remainder Line hits each Zone…
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Integer Factorization: New Algorithm and Routine – jumpfactor.pl
Advertisements Reality has tempered and sobered my earlier excitement, but I still think this new approach holds promise. And there’s a lot I can’t yet tell about the new Perl factorization script jumpfactor.pl just yet – it’s brand new code, after all. On the sobering side, my initial assessment that the inter-Zone jumps grew rapidly…
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Integer Factorization: It’s Getting Thrilling (Again)
Advertisements I am so excited. Yes, I’m struggling mightily to contain that excitement with a large dose of realism – nah, still VERY excited about this. I’m in the midst of programming a new factorization algorithm and Perl script, jumpfactor.pl. I’ve finished writing and initially testing the code for calculating some initial values, and will,…