Tag: perl

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 – New Code for characterize.pl
Advertisements I believe this is running correctly. I’ll certainly correct it if it is not. EDIT: I have indeed updated the code. I suspect it’s almost if not entirely in its final form. A couple of small values in the entire set of discrete semiprimes whose primes are less than 100 showed negative discriminants, but…

Integer Factorization: A Preliminary Characterization Script, in Perl
Advertisements I am posting a Perl script here that illustrates the algorithm I described in my previous post, a first step to what I hope could be a new approach to integer factorization. The characterize.pl source code follows: Sample runs follow:

My Integer Factorization Study: Locating an Odd Integer on Yesterday’s Chart
Advertisements I figured out the formula for determining the row (y) and column (x) position of an arbitrary odd positive integer on the chart I created and shared yesterday. It gives the row and column, and also the quadratic polynomials satisfied by all the odd integers in the row and column, respectively. This all bears…

Factorization Perl Script Update
Advertisements I cleaned up the code for cf_exam.pl just now. Making the script better also made it a little shorter, but I doubt that it is any faster. Anyway, have at it!

Integer Factorization: A New and Very Simple Script
Advertisements A little over a month’s worth of mathematical and numerical study and effort, ending in an amazing week of realization about the structure of numbers and their factors, have led me to a finished product which, despite probably not being revolutionary, leaves me feeling very satisfied about what I have learned, and all the…

My Integer Factorization Study: Final Report (Google Docs)
Advertisements Here is the link to my Google Docs summary of the mathematical study I have just completed, including all the information in my previous blog post, and more. https://docs.google.com/document/d/1OP7B7STeHaVhFaRU_DfjVCx2QUspB4jvPFUAlyhh8GI/edit?usp=sharing

My Integer Factorization Study: Maybe No New Discoveries, but a Fairly Good Program (I Think)
Advertisements After extensive study, and a great many discoveries which seemed exciting to me but that after investigation boiled down to properties of established concepts, I have been able to construct an algorithm that uses the difference between m and the smallest greater perfect square s to search for appropriate values of c and thus…