Tag: number theory

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:

Integer Factorization: A New Preliminary Algorithm Based on “Ceiling Squares”
Advertisements DISCLAIMER: The factorization method described here is not complete. This algorithm sets up a quadratic polynomial which produces points for a later comparison step. I will describe the comparison yet to be done, but it is not yet part of the existing algorithm I have written. I have decided to formulate, and will later […]

My Integer Factorization Study: Progress, 29 August 2022 (Pretty Dry Stuff)
Advertisements I’ve updated the testing “scratchpad” for the first example I’ve been working, and have added a second one. I’ll add a third one if I need more help in teasing a general algorithm out of all of this. That’s entirely possible. First, for m=1501, with more of the process written in: And then, for […]

My Integer Factorization Study: Inching Toward Realizations
Advertisements This last tack I’ve developed to look at Ceiling Squares, differences between perfect squares, and their relationships with factoring m=pq where p and q are odd prime numbers is getting exciting, but the excitement and inspiration seems a bit more mundane this time, more rooted in daytoday thought processes and not those early morning […]

My Integer Factorization Study: A Small Spark of Excitement
Advertisements I had an insight that might turn into an algorithmic method, after some further development and study. Given an odd integer m that is the product of two prime numbers, as I have explained previously, we can find the Ceiling Root c as the integer ceiling of the square root of m, so that […]

My Integer Factorization Study: The Next Step
Advertisements It has been another revelationsparce week. However, I am looking at the data and thinking about my current and emerging strategies daily. What I plan to do next is to begin construction of a table of the discrete semiprimes which differ from their Ceiling Squares by remainders which are not themselves perfect squares, grouped […]

My Integer Factorization Study: Boil Down the Intractable, It Can Still Stay Intractable.
Advertisements Quickly, I have found a way to characterize the flip side of the way integer factorization all boils down to the Ascent: The essential difficulty is the lumpiness of the whole Ceiling Root function: ceil(sqrt(m)). Even for prime numbers, it is not (yet) a smooth or closedform derivation very much more easily managed than […]