October 8, 2019

Wow, so much has happened in my life since my last update. I have been playing the violin again, moved to a new place, and played with some electronics. I never finished the snail story, or any other story, but I'm still chugging at it.

For a few days, I thought I had solved Oppermann's conjecture, but I hadn't. However, I have now written up a few pages of the mathematics that I used. Maybe it will be useful in the future.

A few days ago, I connected the NodeMCU chip to a Waveshare EPD. The NodeMCU is a Wifi capable board with a microcontroller on it. It is programmable and can be used to connect to other devices. The Waveshare EPD is an e-ink display system.

I was able to connect the NodeMCU to the Waveshare EPD by disabling the watchdog reset, following a few tutorials, testing the Waveshare EPD with an Arduino to ensure correct Waveshare EPD connections, and then using those connections to connect with the NodeMCU. When things didn't work out, I used an oscilloscope to figure out what I had misconnected. I also had to change some of the pins to make the Arduino sample code work on the NodeMCU. I also spent a lot of time understanding what I was supposed to do, how to read the pin mappings on the Waveshare schematics, and about general electronics stuff.

In the end, everything worked, and here is a link to a video showing that it worked: Proof of working EPD to NodeMCU connection..

Here's a link to another project I completed: Temperature sensor project.

January 27, 2019

Today, I added a favicon to my site and changed some of the styling. Then, I made the menu click and area become an actual parallelogram instead of a rectangle. I used xlinks, but the end result was worse than what I had before, so I kept it on my blog(there's now dead space between the buttons on the menu).

I also figured out that on the first level to Prince of Persia, you can get past the guard by luring him to the end of his screen, and then doing a fast jump right into him. You end up behind him.

I use a NodeJS static file server for local development now for this blog. I find it more convenient to set up than using other webservers.

I am analyzing Legendre's conjecture again. I am trying a bit of analysis with pronic numbers.

These past few weeks, I've been writing a short story about snails. I couldn't finish the story, but at least I wrote a few good paragraphs.

I bought a licence to the Sublime text editor and regret it. I should have used the trial period better. I don't like how Sublime opens up folders, and I don't like some of the automatic space settings, and I don't like how I have to research how to use on the command line. I ended up still chained to vi, which I bought Sublime to replace. The lesson here is to not buy into the hype. Just because lots of other people like something doesn't mean you will.

Strangely, I use the default note-taking application that comes with the Mac, Notes. It just seems friendlier to use than Sublime, whose icon is right next to it. When I use Notes, I feel happy. It would be cool if I could use Notes for coding.

VS Code is the editor I think is best right now. I will not go back to eclipse. I just don't like it. VI and gvim, I keep for convenience and use on big files, but I prefer to not use them when possible.

January 7, 2019

This past week was very pleasant. Here are some of the things that I did:

1. I installed StudioTax on Linux using the Wine emulator. At first, I used a 64 bit version of Wine, and that caused me many headaches. I only succeeded at installing Studio Tax after switching to the 32 bit version. After that, I had to install dotnet45 several times until I succeeded. To install dotnet45, I had to install winetricks. I followed a slightly faulty instruction manual for installing StudioTax2017 to install Studio Tax 2018. It wasn't a bad manual, but the commands did not work 100% on my setup, and being new to Wine, I didn't know what the error was for a long time, so I made some guesses, and when I had finished guessing wrong, I guessed right and was able to run Studio Tax 2018.
2. I beat Prince of Persia 1. I didn't want to spend so much time on the game when I could have been doing other things, but I did. I like games.
3. I watched more Murdoch Mysteries. I enjoy most of the series' episodes, but I realize I should be doing other stuff, like finding work.
4. For a couple of days, I thought I was close to solving Legendre's conjecture again, but I couldn't do it. However, for the first time in a long while, I changed my focus and approach on the issue. I used to focus on the size of the prime gap, but now, I have abandoned that approach and am trying to look for a different approach.

January 1, 2019

Today I sat in quiet reflection.

Last night, I wrote a Python program that counts up from 1 to infinity, and as it does so, it also continually calculates the average number of prime factors from 1 to n.

So, for example, the number 1 has 0 prime factors. Therefore, the average number of prime factors is 0/1 = 0.

The number 2 has 1 prime factor, and the number 1 has 0 prime factors. The weighted number of prime factors from 1 to 2 is 1*1 + 0*0 = 1. 1/2 = 0.5.

The number 4 has 2 prime factors, the number 3 has 1 prime factor, the number 2 has 1 prime factor, the number 1 has 0 prime factors. The weighted number of prime factors from 1 to 4 is calculated as follows: There is one number with two prime factors(4). There are two numbers with 1 prime factor(2,3). There is one number with 0 prime factors(1). Multiplying the number of prime factors by the number of numbers that have that number of prime factors, you can calculate the weighted number of prime factors from 1 to 4. (#of numbers with 2 prime factors) * 2 + (#of numbers with 1 prime factor) * 1 + (#of numbers with 0 prime factors) * 0 = 1*2 + 2 * 1 + 1 * = 4 (The weighted number of prime factors from 1 to 4.) Therefore, the average number of prime factors from 1 to 4 is 4/4 = 1.

I tried to look for some patterns based on this experiment. Assuming that the number of prime factors tends to increase without bound, I listed the first number such that the average number of prime factors from 1 to n had greater than or equal to 1 prime factor, 2 prime factors, 3 prime factors, 4 prime factors, etc. The numbers I found were:

1. 4
2. 32
3. 2178

I had been hoping that all the numbers would be powers of 2, but that was not the case. Here is a screenshot:

Here is some source code: Average number of prime factors source files. (Use python3 averagenumberofprimefactors.py)