Why do prime numbers make these spirals?

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by Super User, 5 years ago
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A story of the value in mathematical play.
Brought to you by you: http://3b1b.co/spiral-thanks

Based on this Math Stack Exchange post:
https://math.stackexchange.com/questions/885879/meaning-of-rays-in-polar-plot-of-prime-numbers/885894

https://youtu.be/CaasbfdJdJg

Also, if you haven't heard of Ulam Spirals, you may enjoy this Numberphile video:
https://youtu.be/iFuR97YcSLM

Dirichlet's paper:
https://arxiv.org/pdf/0808.1408.pdf

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These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim

If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.

Music by Vincent Rubinetti.
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.

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