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Plotting Prime Numbers (2021)(jaketae.github.io)
38 points by aragonite 7 months ago | 7 comments
  • mikhailfranco7 months ago

    Ulam Spiral (and see ref to Martin Gardner's famous SciAm article):

    https://en.wikipedia.org/wiki/Ulam_spiral

    Why do prime numbers make these spirals? | Dirichlet’s theorem and pi approximations - 3Blue1Brown

    https://www.youtube.com/watch?v=EK32jo7i5LQ

  • tess0r7 months ago

    you can not only map prime numbers in a circle/spiral, but also in a triangle and get some nice knitting patterns :)

    https://tessi.github.io/walking-the-ulam-spiral/

  • classic9597 months ago

    If you're plotting primes, all the coordinates where you're not plotting are non-prime - so every 2nd coordinate will be blank. As will every 3rd and every 4th, 5th, 10th, 11th. etc etc.

    Surely that's where the pattern comes from.

  • block_dagger7 months ago

    I’m not a mathematician so correct me if I’m wrong, but the patterns that emerge or more the natural result of the plotting method vs revealing anything meaningful about the distribution of primes.

    • fecal_henge7 months ago |parent

      Not a mathematician either but I think some quadratics have a tendency to produce more primes than others. What you are seing is the characteristic of various quadratics when plotted in this way. I plotted something quite simmilar.

    • saurik7 months ago |parent

      The article explicitly says as much.

      > So what’s clear here is that the spirals themselves have nothing to do with prime numbers; a much cleaner and fuller pattern can be seen when we plot all positive integers (as well as zero).

  • y427 months ago

    shameless self promotion:

    i built an "animation framework" in JavaScript around it where you can control and animate several parameters and even record the animation

    https://primes.nickyreinert.de/