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Plotting Prime Numbers (2021)
- mikhailfranco 2y agoUlam Spiral (and see ref to Martin Gardner's famous SciAm article): https://en.wikipedia.org/wiki/Ulam_spiral 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 https://www.youtube.com/watch?v=EK32jo7i5LQ
- block_dagger 2y agoI’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.
- saurik 2y agoThe 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).
- fecal_henge 2y agoNot 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.
- tess0r 2y agoyou 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/ https://tessi.github.io/walking-the-ulam-spiral/
- y42 2y agoshameless 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/ https://primes.nickyreinert.de/
- classic959 2y agoIf 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.