Tag: mathematics

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 […]

My Integer Factorization Study: The Complicated but Important Task of Visualizing the Ascent
Advertisements I find myself, mathematically, almost ready to say with certainty, “It boils down to this.” I am speaking in terms of the Ascent, that concept to which I gave a name a month or three ago which is the difference between the Ceiling Square of a positive odd integer m and the larger of […]

My Integer Factorization Study: A Visualization Anomaly
Advertisements Or: The Asymmetric Behavior of the Ceiling Square Remainder My Inspiration Process has been more active, more related to working on thought processes, than it has been something spontaneously occurring, which is especially noticeable during my wife’s current extended absence from our residence (to help care for grandchildren), compared to how the Process seemed […]

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 […]