Wednesday, December 22, 2021

Primality Testing and Factoring Using Pascal's Triangle

An interesting if not impractical way of primality testing and factoring a number using Pascal’s Triangle.

Click here to read my paper.

Sunday, October 13, 2019

Collatz Conjecture

I've previously linked to Jason Davies website for another article. He has another JavaScript program for the Collatz Conjecture.

To pretty it up, remove the circle fill in collatz.css and modify the circle append (line 83) in collatz.js as follows:
          .attr("fill", function(d) {
            var cc;
            var i = parseInt(;
            if ((i && (i & (i - 1)) === 0) && (i <= 16)) {
              cc = "#0000ff";
            else if ((i % 3) === 0) {
              cc = "#c8c8c8";
            else if ((i % 6) === 1) {
              cc = "#ffff00";
            else if (((i % 2) === 1) || (((i % 3) === 2) && (((i / 2) % 2) === 0))) {
              cc = "#ffa500";
            else {
              cc = "#000000";
            return cc;
         .attr("r", 5);
I was only interested in the initial node for those in orange and yellow.

Thursday, October 10, 2019

Minimal Set for Powers of 2

The minimal set for powers of 2 is currently nondeterministic and can be shown to be more complex than previously proposed.

Click here for my analysis on it.

Monday, July 01, 2019

Mathematicians Discover the Perfect Way to Multiply

Four thousand years ago, the Babylonians invented multiplication. Last month, mathematicians perfected it.

On March 18, two researchers described the fastest method ever discovered for multiplying two very large numbers. The paper marks the culmination of a long-running search to find the most efficient procedure for performing one of the most basic operations in math.

“Everybody thinks basically that the method you learn in school is the best one, but in fact it’s an active area of research,” said Joris van der Hoeven, a mathematician at the French National Center for Scientific Research and one of the co-authors.

Click here and here for more information.

Tuesday, June 18, 2019

A 53-Year-Old Network Coloring Conjecture Is Disproved

A paper posted online last month has disproved a 53-year-old conjecture about the best way to assign colors to the nodes of a network. The paper shows, in a mere three pages, that there are better ways to color certain networks than many mathematicians had supposed possible.

Click here for more information.

Wednesday, April 03, 2019

Andrew Booker, a Mathematics Professor at the University of Bristol, Just Solved a Deceptively Simple Puzzle That Has Boggled Minds for 64 Years

A mathematician in England has cracked a math puzzle that's stumped computers and humans alike for 64 years: How can the number 33 be expressed as the sum of three cubed numbers?

While it might seem simple on its face, this question is part of an enduring number-theory conundrum that goes back to at least 1955 and may have been mulled over by Greek thinkers as early as the third century. The underlying equation to solve looks like this:

`x^3 + y^3 + z^3 = k`

That answer is:

`(8,866,128,975,287,528)^3 + (–8,778,405,442,862,239)^3 + (–2,736,111,468,807,040)^3 = 33`.

Click here for more information.

Friday, March 22, 2019

Karen Uhlenbeck is first woman to win prestigious maths Abel prize

Mathematician Karen Uhlenbeck has become the first woman to win the Abel prize, sometimes called the Nobel prize of mathematics. She has been awarded the 6 million Norwegian kroner ($700,000) prize for her work in the fields of gauge theory and geometric analysis, which have been credited with far-reaching impact in both mathematics and physics.

Click here for more information.