Category: My Math Studies

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…

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.

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 multiZone jumps that do. This will involve understanding the quadratic increase of the numerators of the intercept points with Zone boundaries, and the linear…

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…

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…

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 interZone jumps grew rapidly…

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,…

Integer Factorization: A Brief Observation Before I Start Coding jumpfactor.pl
Advertisements I noticed and thought about something that bemuses me concerning the new integer factorization algorithm in my mind about to turn itself into Perl code on ChrIIstopher, my MacBook Pro: I am using both varieties of Ceiling Squares that I have developed and defined during this study: the initial one, which is the least…

Integer Factorization: Describing My New Approach
Advertisements Enough teasing and tantalizing. I’m at the stage now where it would do me good to describe the new integer factorization algoritm idea a little bit better, so that I will have a clear conception of it in my own mind as I move from designing it to programming it. As we take the…

Integer Factorization: Calculating the Jumps (A Preliminary Photo)
Advertisements This is just a screenshot of my digital graph paper as I continue the work, which is going to be tricky and a bit difficult, on a new algorithm. If this idea is as good as it seems, it will be an improvement on my best integer factorization routine. My Ceiling Squares idea will…