
Integer Factorization: Performance Stats/Graphs for factor_it_4.pl
Advertisements I ran factor_it_4.pl tonight on the collection of 10digit and 12digit 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 […]

Fear of Learning (copied from a Twitter Thread of Mine)
Advertisements Fear of learning, especially the kind of learning that makes a human being less susceptible to manipulative indoctrination, is at the core of radically Conservative state governments’ school curriculum policies. It is unsubtle antiintellectualism. The reasons are clear. To the @GOP and the Radical and Religious Right movements within you (to include Dominionist politics): You have […]

My Fastest Factorization Script So Far
Advertisements This won’t set any algorithmic speed records, but I am happy with it, for now. It comes in at 48 lines of Perl code. factor_it_4.pl is definitely faster than factor_it_3.pl, and routinely gets its answer in fewer than half the iterations of factor_it_2.pl. Once again, I am not experienced with writing arbitraryprecision arithmetic scripts […]

Integer Factorization: Quick Summary of Last Night’s Simplification “Revelation”
Advertisements Let m be an odd positive integer we wish to factor. Let c be the smallest integer (also positive) so that c2>m. (If m is a perfect square, we are done.) Set r=c2m. The least nonnegative value of x for which x2+2cx+r is a perfect square is a value of x which produces s=c+x […]

Integer Factorization: 9/18/2022 Update (short)
Advertisements It would seem, after reviewing factor_it_2.pl, that that code and the mathematics behind it are not due for an update – because they are beyond hope! 😀 No, really, I’ve moved far beyond those ideas, and they no longer seem fruitful enough to upgrade them. It would be like grafting a car onto a […]

Integer Factorization: Recent Work
Advertisements Ideas kept me up when the dogs got me up around 3 a.m. this morning for a walk and some water. That’s good, even though the ideas did not pan out to much. I had church to attend in a few hours, after all. But it occurs to me to share where it’s all […]

Integer Factorization: WebPublish in Haste, Repent at Leisure! 😀
Advertisements All right, I am very sorry… I did happen to see that huge error in arithmetic in computing the characteristic function, but not until late tonight. I have fixed it and placed the updated code in my original characterize.pl post. Again, I do apologize for that. But now I am excited again because until […]

Integer Factorization: “characterize” Script Updated
Advertisements Here is the link to the post from yesterday with the script in the form I updated today.

Integer Factorization: characterize.pl Update Forthcoming
Advertisements I found (occurring to me in the early morning hours) a way to correct some of the “lumpy” properties of the characterize.pl output. When the algorithm adds 1 to the Ceiling Root, as needed, to produce the Adjusted Ceiling Square, I had forgotten to make sure also that the points I want the characteristic […]

Integer Factorization: Postalgorithmicadjustment Thoughts
Advertisements It is plain to me that, after making the straightforward modifications to make sure that the characterization algorithm deals with adjusted ceiling squares of the correct “polarity” (according to m being congruent to 1 or 1 modulo 4), I need to look again at how I am choosing nice, smooth, linearly increasing ranges. These […]