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

3Blue1Brown · explainer · Watch on YouTube

Recreational & visual mathPure mathematics

What it is

3Blue1Brown explains why plotting primes in polar coordinates produces spiral patterns, using modular arithmetic, Dirichlet's theorem and rational approximations of pi.

Why Hacker News recommends it

Frequently recommended as the clearest explanation of prime spirals and the Ulam spiral.

  • 7 people recommended it
  • 5 different months
  • 1 strong recommendations
  • first 2019, last 2024

What HN commenters said

  1. “Here is one of the most enlightening explanations for these kinds of spirals I have seen by 3blue1brown”

    Enlightening explanation of prime spirals

    shezi, 2021-08 · Strong recommendation · in “Ulam Spiral”

  2. “after watching the following video, I think it just says something about modular arithmetic and rational approximations of 2 Pi.”

    Spirals reflect modular arithmetic and approximations of 2 Pi

    excessive, 2019-11 · Recommendation · in “Unexpected Beauty in Primes”

  3. “I really enjoyed 1brown3blue breaking down why prime numbers form patterns when graphed in polar coordinates.”

    Breaks down why primes form patterns in polar coordinates

    hinkley, 2020-07 · Recommendation · in “Why do electron shells have set limits? (1999)”

  4. “3B1B has a semi related video”

    Related video on properties of primes

    lupire, 2021-03 · Recommendation · in “The Prime Hexagon”

  5. “this video by 3Blue1Brown explains why primes plotted as (p, p) in polar coordinates produce interesting patterns.”

    Explains why primes plotted in polar coordinates form patterns

    andrewflnr, 2021-03 · Recommendation · in “The Prime Hexagon”

  6. “3b1b[2] (with a particularly good explanation of why it happens)”

    Particularly good explanation of why prime spiral happens

    zimpenfish, 2024-08 · Recommendation · in “Breakthrough a step toward revealing hidden structure of prime numbers”

  7. “Grant's teaching style is so good you might even convince yourself of the thing he is disproving”

    Shows how visualizations can trick us into seeing patterns

    godelski, 2024-08 · Recommendation · in “Ask HN: What is the best software to visualize a graph with a billion nodes?”

Excerpts from Hacker News comments, linked to the originals. Summaries and labels were written by a language model from those comments.

Topics: primes, ulam spiral, modular arithmetic, pi approximation, 3blue1brown

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