Tag: integer factorization

My Integer Factorization Study – Breakthrough! (If Not Precisely Eureka!)
Advertisements I believe now that I can completely characterize a relationship between the quantities m (number to be factored), s (least perfect square > m), r (the difference between s2 and m) and a reduced set of candidate values for c1, which will also give c2, n, p, and q. The details are in my…

My Integer Factorization Study: Woof?
Advertisements The latest revelations, which came almost unbidden despite my expressed desire to take a break from this study, turned out to be exciting ones, and I am trying to remain calm. I have found relationships between the value of r (which is the difference between the square of s (the integer ceiling of the…

My Integer Factorization Study: An Extended Pause
Advertisements I am pausing in my study of these numbers and their behaviors for a while, for two good reasons: The seeming chaos of some of the relationships between numbers was just too much for my brain to handle. I need to concentrate on the extensive cleaning tasks I need to complete in order to…

My Integer Factorization Study: A Mathematical Report
Advertisements I have begun writing a mathematical report, in my Google Docs shareable files, summarizing the basic principles I am examining and the work I have done, with discoveries I have made, so far. The report is here. (clickable link)

My Integer Factorization Study: This Isn’t Finished.
Advertisements After my Tiny Eureka yesterday led to nothing new in the way of mathematical discoveries – led, in fact, to a tautology, a sort of uninformative a=a result – I took a breather. I had already scheduled myself a break after “Tiny Eureka,” and it felt strange to pull away from the study on…

My Integer Factorization Study: May 7 2022 4:29pm Eastern Update
Advertisements This morning’s Tiny Eureka demonstrates itself right now to be a trivial finding, and therefore unlikely to lead me to a Big Eureka.

My Integer Factorization Study: Tiny Eureka! (or Should I Say “Woof!”?)
Advertisements I am finally barking up the correct tree, so to speak, and I have found the little squirrel I sought. From the beginning, with gusto! (By the way, the relationship I am about to describe took a while to hammer out on paper, and a great deal longer to get right in Perl code.)…

My Integer Factorization Study: Discouraged, but Then Renewed in Hope
Advertisements UPDATE: the sometimes triangular tables of values I have been building over the last several days have borne fruit, so to speak. I do not know where this will lead me, or how much easier it will make the task of integer factorization, but I have found a relationship between the product m of…