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There is this image on 9gag, with description: "Comparison between 5,000 and 50,000 prime numbers plotted in polar coordinates"

I thought it might have something to do with Ulam spiral, but something looks wrong in picture (but I'm not sure, of course).

I think this white spiral you can track on left image is too "proper", and then filled in second image?

And what would it mean to represent prime in polar coordinates, and how to do it?

Glorfindel
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Meow
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    Prime $p$ gets a point at coordinates $\varphi=\frac{p}{100}2\pi$, $r=\lceil\frac{p}{100}\rceil$ or something like that. – Ragnar Dec 28 '13 at 13:33
  • The very nice video by 3Blue1Brown, linked to in my comment below Jay V. Goyel's answer, makes it clear that what's being plotted are points in the complex plane of the form $pe^{ip}$ for primes $p$. – Barry Cipra Nov 18 '20 at 12:16
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    https://math.stackexchange.com/questions/885879/meaning-of-rays-in-polar-plot-of-prime-numbers/885894#885894 – Greg Martin Mar 13 '21 at 01:38

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As 3Blue1Brown explains, all you need to do is to make sure that the x and y coordinates in the polar plane (also represented by r (radius) and theta (angle between the line joining the point to the origin and the X-Axis) respectively).

In the second image, the Primes occur at a 'periodic' frequency which forms those straight arms, while the non-Primes are also somewhat periodic and hence form the white arms.

The non-Primes do occur a lot but because the scale is so huge, they are not seen properly.

Jay V. Goyel
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    It will be nice if you link the video too, for those users who are unaware of 3b1b – Anindya Prithvi Nov 18 '20 at 10:55
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    @AnindyaPrithvi, the link is https://www.3blue1brown.com/videos-blog/6ufkz2hkmu1xcx5u5d2nuvmhvimrpq -- I was able to track it down by googling on "3Blue1Brown" and "prime spiral" (and actually Google autofilled "spiral" while I was typing "prime"). I do wish posters would provide links when they're easily available, though it's possible new contributors are not allowed to. – Barry Cipra Nov 18 '20 at 12:08
  • @BarryCipra I think they are allowed to. I have observed SmokeDetector logs for quite sometime and spammers usually post links to promote products.Also, here is the youtube link for the prime spiral. – Anindya Prithvi Nov 18 '20 at 12:15
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    @AnindyaPrithvi, thanks. And, for the convenience of others, here's a link to the MSE post that was 3Blue1Brown's point of departure: https://math.stackexchange.com/questions/885879/meaning-of-rays-in-polar-plot-of-prime-numbers/885894 (though the OP here predates that post!). – Barry Cipra Nov 18 '20 at 12:25
  • Thank you. Will take care in the future. – Jay V. Goyel Dec 28 '20 at 11:10