Tag: number theory

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…

Integer Factorization: Making the Crooked Straight
Advertisements My current approach to integer factorization, elements of which I have described in the last several days on this blog, involves a process I discovered last night that surprised me with its beauty and simplicity: It is a twodimensional method, straightforwardly described and probably easily programmed, for visualizing quadraticallydistributed numbers, namely consecutive perfect squares…

Integer Factorization: Plotting the Bee Line
Advertisements I came up with an idea late last night (after midnight turned March 3 to March 4) that is a bit exciting, although I know enough from the past months of study to temper my excitement with some realism as to the chance of it translating into an actual algorithmic breakthrough. So far, the…

Congruence Consequences I’d Forgotten
Advertisements My integer factorization study has me looking a great deal at differences of perfect squares, one even and one odd. This is an easily justified path to take, since powers of two will be apparent and can divide out as soon as we start, regardless of the numerical base we are using. But I…