JCSBimp's Hexagonal Orthogonal

Advertisements Let odd positive m be the product of two unequal prime numbers p and q. Let the Ascent of m be the difference between (p+q)/2 and c, the Ceiling Root of m, which is the value of ceil(sqrt(m)) with 1 added, if necessary, to make c even or odd as (p+q)/2 is even or…

Advertisements I know better than to get too optimistic, but some of the numbers and relationships I am examining in my integer factorization study this week are seeming to show a possible way to compute smart, fast jumps to good candidates for factors using the Zone Grid. It’s not too easy a process to derive,…

Advertisements For brevity, this post presupposes familiarity with material from earlier posts, namely this one and this one. I have just derived the precise quantities for the following: The line on the Zone Grid for a Remainder Series that represents odd positive integer m=c2-r has a linear equation with slope 2c-2(ceil(sqrt(r))-1. This formula makes this…

Advertisements It occurred to me to articulate a simple relationship between odd composite integer m=ab, where a and b are odd positive integers, its Ceiling Square and Ceiling Root, and its Ascent, which is the least number n, always even, that one must add to the Ceiling Root c so that (c+n)2-m is a perfect…

Advertisements I am ironing out some new calculations that may come to nothing, but also may show me an advance into simplification. I was looking at the fact that a series of consecutive values of rn in any odd positive integer m’s Remainder Series will differ from a series of consecutive perfect squares by linearly-progressing…

Advertisements New revelations in my study of factorization, Ceiling Squares, and the Zone Grid have not been coming lately, but I have indeed been looking at the data and trying out new ways to visualize their relationships, every day, and my work is still underway, despite no evidence of these facts in this blog. Right…

Advertisements The most tantalizing current avenue in my study is to continue examining the relationships between m’s trivial factorization arising from its expression as ((m+1)/2)2-((m-1)/2)2, its remainder line on the Zone Grid, and the zone boundaries thereon. I am looking at 427 of the odd discrete semiprimes with the smallest prime factors in hopes of…