Tag: perl
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Integer Factorization: Web-Publish 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…
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Integer Factorization: “characterize” Script Updated
Advertisements Here is the link to the post from yesterday with the script in the form I updated today.
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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…
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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…
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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:
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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…
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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!
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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…
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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
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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…