Ulam Spiral Visualization - The Pattern of Prime Numbers

The Ulam spiral is a way of visualizing the distribution of prime numbers (in blue). This pattern is one the great unsolved mysteries in mathematics and has important consequences in Cryptography.

[@therobotmaker]

I really appreciate the time you take to make the sound as engaging as the content. Really makes the whole package stand out.

[@ArtOfTheProblem]

thanks for the feedback, haven't had a comment on this video in a Looooong time.

[@Alonso6390]

This is the best Ulam spiral video on TH-cam, and the most cinematic. Most of the Ulam spiral videos are essentially just output from a math program, and the pattern of lines, divorced from the numerals, seems somewhat abstract. In my own video, I show the numerals, but this limits me to small numbers; once we get out into the millions showing the numerals is rather unwieldy. ArtOfTheProblem has in this video found the perfect compromise and done it with flair and elan.

[@RoyalPomegranate]

Prime number patterns are the most determinate yet chaotic things at the same time

[@wexer82]

Art of the Problem is one of my favorite channels on youtube. That being said, I was disappointed by this video. I really want to see the complete continuous zoom out from 0:20 to 0:21 instead of just displaying a new image. Small gripe among the high praise. Keep up the great work.

[@ArtOfTheProblem]

Thanks for the support! Interestingly, this was the first video I ever uploaded and was more of an experiment. Definitely cheated at the expense of time savings :-)

[@Michael-hf7vj]

This is so beautiful, I nearly cried. Thanks xD

[@ArtOfTheProblem]

I think this was my first ever video :)

[@ArtOfTheProblem]

@Alonso6390 Thank you kindly for the great feedback. It would be really cool to explore this further sometime and show the sound of primes by scanning the spiral with notes really fast (as you have done)

[@ArtOfTheProblem]

@Koseiku I agree, I especially like this pattern as it's simple to understand, yet has far reaching consequences. It is the root of a much longer episode I'm working on at the moment, should be finished by September

[@namelastname4077]

if you map a random sequence onto a spiral coordinate system the sequence is going to look like a spiral

[@joeprice2240]

Very nice visualization. How did you assign the radius of the circles in the last bit of the video?

[@McDaddyboy]

Thanks for a beautiful Ulam spiral video. How can I see more of your work!

[@juggleninjaguy]

Very nice video. What software did you use to make this visualization?

[@ronaldvonk]

What is the distinction between a large circle or a small circle?

[@ArtOfTheProblem]

@juggleninjaguy Thanks, I used a combination of After Effects, Photoshop & Final Cut Pro

[@Msn08512]

YOU SIR,
ARE A MASTER AT MATH.

[@DMgHalt]

What if our number system had a different base? Would it make any difference?

[@protonjinx]

No. Prime numbers represent quantities which cannot be split evenly (except splitting into 1-unit parts) without dividing into partial units.

[@davidponte5125]

This is beautifull😊

[@ArtOfTheProblem]

wow you found my first vid, I have a new one here: new vid! th-cam.com/video/OFS90-FX6pg/w-d-xo.html

[@janjohandealgenman]

It's not quite correct, the first part of the video highlights the primes themselves in blue. But then it cuts to a variation of ulams spiral where the size of the blue points corresponds to the number of prime factors the number has.

[@DisSsha]

True

[@sahebjotsingh6306]

How did you create this video?

[@Champignon1000]

probably programming

[@Ronny42]

Cool video

[@Jeeznofreenicks]

101 is also a primal number.

[@willwell9918]

Invest in Prime coin now XPM and people will be rewarded big time.