# Tag: number theory

• ## AfterMath: Even Numbers Are Just Odd.

Advertisements The thoughts I still get in the early morning hours about numbers and factorization are not so imperative now that I have programmed and published that new, simple algorithm. Sometimes I can just smile at them and go back to sleep. And other times … they’re just WEIRD. This morning’s stay-awake-and-think-about-it notions concerned the…

• ## 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!

• ## 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…

• ## Some Number Theory

Advertisements Let prime number p be a factor of positive integer m. The integer m has an expression as the difference between two perfect squares s and t, with s greater than t, such that either s+t or s-t equals p. When m=p×1, this will be the only such s and t, and s=t+1. Define…

• ## Math Insight, After a Morning “Off”

Advertisements Early Tuesday morning, I popped awake, but no mathematical insight was waiting to compel me to stay awake. However, i did walk quietly downstairs to work on my mathematical study, as I have been doing every early morning since the insights started coming – about a week and change now, I think. I took…

• ## This Morning’s Math Realization

Advertisements Azarya’s Angels did not give me a realization as the result of a train of thought that seized me upon popping awake very early. However, I did pop awake early, and began studying data while enjoying coffee and a donut, and by about 7 a.m., the realization for which the Angels apparently awakened me…

• ## Math Study Progress

Advertisements I have added all the information I have figured out so far about splitting roots and ceiling discrepancy, as well as the colorful chart I shared here earlier, to the report on Telescoping the Integers. (link) So far, it contains nothing suggestive of new advances in integer factorization, but time and further study will…

• ## What Hath Eratosthenes Wrought?

Advertisements Numbers sieve us, this table and chart are something he hath wrought! Not bad for a nearly-2300-year-old dead man, eh? P.S. – Hey, Aleister Crowley! Did you know that the discrepancy between the ceiling root of 79 – which is one more than the number of cards in a tarot deck, a.k.a. The Book…

• ## Mathematical Thoughts: This Morning’s Gifts

Advertisements This morning’s gifts (which I could consider to be from the Queen of the Sciences Herself or from “Azarya’s Angels” who appear to serve as Her messengers to me), the mathematical insights it occurred to me in the early morning hours to ponder, relate to two concepts I have newly discovered: ceiling discrepancy and…

• ## New Math Paper in Progress

Advertisements The new report on Telescoping the Integers is in progress, and you can go see what’s there so far, if you wish. I shall be exploring and writing a good bit more on it as soon as tonight. https://docs.google.com/document/d/1jpcGfykv5sQl4OPAEx2k8On0oN17cmKGuCI_9xdUaqI/edit?usp=sharing