# Tag: mathematics

• ## 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: Post-algorithmic-adjustment 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 […]

• ## 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: The Adjusted Ceiling Square and Characteristic Polynomial

Advertisements I’ve got a good bit of housework to get going today, and some necessary but necessarily small amount of shopping to do as well, but I want to get this idea down first. The Adjusted Ceiling Square of odd positive integer m is the least perfect square greater than m that is odd if […]

• ## My Integer Factorization Study: Update – 9/14/2022

Advertisements I’ve changed the platform for composing my mathematical reports – above and beyond blogging them here – to use Apple’s Pages program on my MacBook Pro. It’s taking some orientation – equations must be in an appropriate mathematics markup language (I am choosing LaTeX) – and I need to export the end product in […]

• ## Integer Factorization: Dreams and Plans

Advertisements I am working several ideas, and haven’t dropped any of the recent ones I’ve started examining. The weeds/woods are deep and thick. It’s all worthwhile. Plus, I woke up before my Sunday alarm today from dreams that played with the Fermat difference-of-squares approach and my current algorithm that uses it. MIRIAM is still with […]

• ## Integer Factorization: The Obvious Obstacle I Always Seem to Hit with a Thump

Advertisements It occurs to me my new factorization method is likely not to be any faster than the old, because of a simple observation: I am still iterating values to add to the Ceiling Square of m and testing. There will not be an improvement, at least not the one I seek, until I can […]

• ## Integer Factorization: The Remaining Puzzle in Its Newest Form

Advertisements Here is what I have established now, and have used in forming the algorithm I shared this past week: I have chosen to repeat a small set of definitions and concepts I have established in other posts and papers, for clarity. Let m be an odd positive integer we wish to factor. Let c […]

• ## Integer Factorization: So It Comes Down to This, Take 276

Advertisements . . . you know, this used to be fun 😀 . . . J/K, y’all, you know I’m enjoying the heck out of this number study, still. Life’s stresses have had a way of, strangely, normalizing the still very active Inspiration Process (MIRIAM), working together, of course, with the probability of anything that […]

• ## 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: