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

What people said

Strong rec Oren Milman · 2019-10 · Mathematics Stack Exchange · on “Meaning of Rays in Polar Plot of Prime Numbers”

For anyone who doesn't know 3Blue1Brown (who created the video that MCCCS linked to [this video] ), but is interested in the beauty of math, please do yourself a favor and check out his legendary YouTube channel [LINK] .

Strong rec shezi · 2021-08 · Hacker News · on “Ulam Spiral”

Here is one of the most enlightening explanations for these kinds of spirals I have seen by 3blue1brown: [this video] Note that the setup is slightly different,since in that video they plot numbers along their polar coordinates. The results are very similar, since both create spirals with predictable angular offsets.

Recommends Secret · 2019-10 · Mathematics Stack Exchange · on “Is there known ways to pick a way of presenting a problem such that it emphasise mathematical coincidences that illuminate a deeper theory?”

[this video] This cool video explains how coordinate artifacts in the polar coordinate system, just happened to single out residual classes that demonstrate Dirichlet theorem. Having experience of both recreational mathematics and formal mathematics, seeing things like how one can construct certain n roots if you have another tool besides compass and straightedge, as well how visualisations sometimes make the problem easier to approach, I am wondering about a more general question that is implicitly raised in this video: It is clear that the mere act of drawing a picture of a given mathematical problem $q$ actually imposes the constraint of the paper (basically $\Bbb{R}^2$ with continuous curves

Recommends excessive · 2019-11 · Hacker News · on “Unexpected Beauty in Primes”

The first time I saw these, I thought it hinted at some deep insight into the nature of primes. However, after watching the following video, I think it just says something about modular arithmetic and rational approximations of 2 Pi. [this video] The video is only about Archimedian spirals, but I suspect a similar analysis would apply to Ulam spirals too. We really like to find patterns.

Recommends jerrymouse · 2019-11 · Mathematics Stack Exchange · on “Meaning of Rays in Polar Plot of Prime Numbers”

$3$ Blue $1$ Brown has given a beautiful explanation to the spiral and ray patterns. Please watch his video titled " Why do prime numbers make these spirals? [this video] "

Recommends hinkley · 2020-07 · Hacker News · on “Why do electron shells have set limits? (1999)”

In this vein, I really enjoyed 1brown3blue breaking down why prime numbers form patterns when graphed in polar coordinates. [this video]

Recommends Théophile · 2020-12 · Mathematics Stack Exchange · on “Why do prime gaps tend to make these weird spirals?”

It probably doesn't tell us much except that it's fun to make pictures. :) You might be interested in this video, though: [this video] (related to this question: [LINK] )

Recommends lupire · 2021-03 · Hacker News · on “The Prime Hexagon”

3B1B has a semi related video on how working with prime numbers can help you see properties that are also found in composite numbers, since the sequence of primes overlaps with many other sequences. [this video]

Recommends andrewflnr · 2021-03 · Hacker News · on “The Prime Hexagon”

For IMO a more meaningful phenomenon, this video by 3Blue1Brown explains why primes plotted as (p, p) in polar coordinates produce interesting patterns. [this video]

Recommends user17592432 · 2024-04 · Stack Overflow · on “Need large integers and floats. Trouble with long long int and long double”

@gregspears A great "prime number" video from 3b1b [this video] ... Consider the storage requirements (or how much _iterative probing_) was needed to make these _pretty pictures_ (elucidating the wonders of math...)... Answer: Lots and Lots!!!