Tag: Programming
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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: 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,…
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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…
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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…
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Integer Factorization: Series of Ceiling Squares, Take 3 (or 4)
Advertisements I embarrassed myself twice this week, having to take down insufficiently debugged algorithms and Perl code for not testing thoroughly enough. However, I now have an algorithm I’ve once again tested, and will test some more (yes, opening the possibility that a bug will require me to correct/retract), and this one has a symmetric…
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Integer Factorization: The Hive Mind, Now Automated
Advertisements I’ve written a perl script to produce the “Beehive Plots” that I am currently using to search for patterns and relationships between odd positive integers, their (Adjusted) Ceiling Squares, and their Fermat factorizations, if they have them. Remember that to each possible factorization of a positive odd integer m=ab, where a and b are…
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Integer Factorization: A More Uniform Test, and a Similar Result
Advertisements For 100 pairs of randomly-chosen p and q less than 100,000,000: the Perl routine factor_it_4.pl performed as shown in the following scatter plot of m=pq vs. the number of iterations it required to factor m: Notice, as I mentioned in my blog post about the previous, less uniform test, that the number of iterations…
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Integer Factorization: Performance Stats/Graphs for factor_it_4.pl
Advertisements I ran factor_it_4.pl tonight on the collection of 10-digit and 12-digit discrete semiprimes I had generated earlier in my study. An image of the table I generated is below, along with scatter plots of particular behaviors. If someone wanted, I could certainly supply them with the raw data used to generate the graphs. I…