Make your own 'prime factorization' diagram

The Prime Factorization Sweater is a lovely idea and I thought it would be fun to reproduce the same idea electronically so that I could print out a poster version for home.

Enter Processing.

With it I've developed a small program that produces a diagram of the first 100 numbers and for each number there's a circle broken up into arcs.  Each arc is a prime factor.  As in the original sweater each factor gets a unique color (assigning unique colors is rather complex and I ended up using the color difference method based on CMC l:c and a nice online tool that does the work for you).

Here's the finished product.  The top left corner is the number 1 and the numbers read right to left.  So the first red circle is a prime number (2), the second the next number (3, which is prime) and so on.

There's also an option to print the numbers involved.

The source code is in the pfd repository on GitHub and licensed under GPLv2. Processing is a really nice environment for this sort of rapid hacking of anything graphical. See, for example, how I used it to visualize Ikea Lillabo Train Set layouts.

PS After encouragement in the comments from the person who had the original idea for the prime factorization sweater I've made a CafePress store in which you can buy men's and women's T-shirts printed with the prime factorization diagram.

Sondy said…
WOW! Since I was knitting, I never once thought about using circles! I totally love this. Now put it on a t-shirt!
Sondy said…
WOW! I totally love this! Since I was knitting, I never once thought about using circles. For printing the charts, this is totally cool! (Think about making a t-shirt!)
Unknown said…
Nice. One small point, the numbers read right to left is the wrong way around.
å±±çŒ« said…
This is the best idea about integer factorization, written here is to let more people know and participate.
A New Way of the integer factorization
1+2+3+4+……+k=Ny,(k<N/2),"k" and "y" are unknown integer,"N" is known Large integer.
True gold fears fire, you can test 1+2+3+...+k=Ny(k<N/2).
How do I know "k" and "y"?
"P" is a factor of "N",GCD(k,N)=P.

Two Special Presentation:
N=5287
1+2+3+...k=Ny
Using the dichotomy
1+2+3+...k=Nrm
"r" are parameter(1;1.25;1.5;1.75;2;2.25;2.5;2.75;3;3.25;3.5;3.75)
"m" is Square
(K^2+k)/(2*4)=5287*1.75 k=271.5629(Error)
(K^2+k)/(2*16)=5287*1.75 k=543.6252(Error)
(K^2+k)/(2*64)=5287*1.75 k=1087.7500(Error)
(K^2+k)/(2*256)=5287*1.75 k=2176(OK)
K=2176,y=448
GCD(2176,5287)=17
5287=17*311

N=13717421
1+2+3+...+k=13717421y
K=4689099,y=801450
GCD(4689099,13717421)=3803
13717421=3803*3607

The idea may be a more simple way faster than Fermat's factorization method(x^2-N=y^2)!
True gold fears fire, you can test 1+2+3+...+k=Ny(k<N/2).
More details of the process in my G+ and BLOG.

Email:[email protected]
Unknown said…
Great job, John! I like it a lot:)

One simple modification would really make the primes visually easy to identify: reduce the radius, maybe even by as much as 1/2.

Again, nice visualization. I will be sharing it with my weekly math/philosophy group, the Wing Circle, as the meeting topic is "Prime Numbers". Feel free to check out our facebook page here http://tinyurl.com/WC-EventHistoryList.

Sincerely,

swami_mathtraveler
Daniel said…
This has gained a lot of interest on G+ through a post by Richard Green:

I have really gotten a kick out of it and made a few modifications to the code to change the modulus with a single setting. I submitted a pull request on GitHub for you to review.

Thanks for creating something so cool!

Your last name contains invalid characters

My last name is "Graham-Cumming". But here's a typical form response when I enter it:

Does the web site have any idea how rude it is to claim that my last name contains invalid characters? Clearly not. What they actually meant is: our web site will not accept that hyphen in your last name. But do they say that? No, of course not. They decide to shove in my face the claim that there's something wrong with my name.

There's nothing wrong with my name, just as there's nothing wrong with someone whose first name is Jean-Marie, or someone whose last name is O'Reilly.

What is wrong is that way this is being handled. If the system can't cope with non-letters and spaces it needs to say that. How about the following error message:

Our system is unable to process last names that contain non-letters, please replace them with spaces.

Don't blame me for having a last name that your system doesn't like, whose fault is that? Saying "Your last name …

Importing an existing SSL key/certificate pair into a Java keystore

I'm writing this blog post in case anyone else has to Google that. In Java 6 keytool has been improved so that it now becomes possible to import an existing key and certificate (say one you generated outside of the Java world) into a keystore.

You need: Java 6 and openssl.

1. Suppose you have a certificate and key in PEM format. The key is named host.key and the certificate host.crt.

2. The first step is to convert them into a single PKCS12 file using the command: openssl pkcs12 -export -in host.crt -inkey host.key > host.p12. You will be asked for various passwords (the password to access the key (if set) and then the password for the PKCS12 file being created).

3. Then import the PKCS12 file into a keystore using the command: keytool -importkeystore -srckeystore host.p12 -destkeystore host.jks -srcstoretype pkcs12. You now have a keystore named host.jks containing the certificate/key you need.

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More fun with toys: the Ikea LILLABO Train Set

As further proof of my unsuitability to be a child minder (see previous post) I found myself playing with an Ikea LILLABO 20-piece basic set train.

The train set has 16 pieces of track (12 curves, two straight pieces and a two part bridge) and 4 pieces of train. What I wondered was... how many possible looping train tracks can be made using all 16 pieces?

The answer is... 9. Here's a picture of the 9 different layouts.

The picture was generated using a little program written in Processing. The bridge is red, the straight pieces are green and the curves are blue or magenta depending on whether they are oriented clockwise or anticlockwise. The curved pieces can be oriented in either way.

To generate those layouts I wrote a small program which runs through all the possible layouts and determines which form a loop. The program eliminates duplicate layouts (such as those that are mirror images of each other).

It outputs a list of instructions for building loops. These instructions con…