Tag: integer factorization

Some Math Notes
Advertisements These are from studies ancillary to my integer factorization explorations. Let m = 2n be an even positive integer corresponding to positive integer n, which may or may not be even. Let s be the Ceiling Root of m, the integer ceiling of m’s square root. s squared is the Ceiling Square of m, […]

Integer Factorization: Update, 14 November 2022
Advertisements Bimp’s Decreasingly Frequent Progress Report I am still working daily on my mathematics study, but want to get better at dropping a word now and then about my progress. Below is a text file created (without Perl script help, except in running my “gimme the next prime” wrapper routine) in just the past couple […]

Integer Factorization: Looking Again at the Data
Advertisements Research report follows, the first after a bit of silence, by way of a current example. Consider the integers m1=3317, m2=4061, m3=5461, and m4=6077. They all have adjusted ceiling squares – the least perfect square with oddness/evenness the same as one half of one more than their value that is greater than each of […]

Today’s Mathematical Visualization
Advertisements This is an artistically arranged gridbased drawing of the first 24 odd integers greater than 1, expressed as differences of squares – to include the first odd positive integer to have two different “nontrivial” factorizations, and thus two different squaredifference representations.

Adjusted Scatter Plot for Integer Factorization Study
Advertisements The plot below is similar to the one I put in my previous post. However, the data points are, I think, a better set for exposing properties, since I am using the concept of Adjusted Ceiling Square as follows: Let m be an odd positive integer. Define the Adjusted Ceiling Square of m as […]

My Integer Factorization Study: Hahaha!!
Advertisements I am laughing at the sheer trickiness, almost by design, of the mathematical relationships I am uncovering in my number study, and the most recent one in particular. I shared yesterday the VERY SMOOT GRAPH, suggesting to me a parabola, charting out the plot of odd integer m vs. the difference between (m+1)/2 and […]

Integer Factorization: Update, 10/12/2022
Advertisements Lately, I’ve just been switching back and forth between a kind of macrovision and microvision in examining properties related to my factorization study. I’ve gone back to my table of large (but not very large) discrete semiprimes, and I’ve also looked at, and added information to, my table of the smallest discrete semiprimes, all […]

Integer Factorization: Reestablishing Some Basic Steps
Advertisements I wrote this in an effort to restate some recent basic observations plainly. I am confident that this is no newlydiscovered set of mathematical truths, but I am enjoying making these derivations piece by piece and seeing what may follow from each successive one. Perhaps someday I will end up somewhere new. Right now, […]

Mathematical Explorations: Maximally Composite
Advertisements It’s time for some fun and games with some squarefree “maximally composite” odd numbers and all their representations as the difference of perfect squares. It’s kind of like following a growing pristine wave with patterns I didn’t expect to encounter, until it smashes into foam and chaos against a rocky shore.