Uploaded February 2022 | Updated September 2026, 1 week ago

---

💻 Code: thecodingtrain.com/challenges/167-prime-spiral
✨ Watch the uncut version on Nebula! nebula.tv/videos/codingtrain-the-prime-spiral-uncut-version-coding-challenge-167
✨ Watch this video ad-free on Nebula! nebula.tv/videos/codingtrain-the-prime-spiral-coding-challenge-167

Why do prime numbers show up as diagonals in a spiral? In this video, I create a visualization in JavaScript (p5.js) of the Ulam Spiral (aka Prime Spiral) named for Polish Mathematician Stanislav Ulan.

p5.js Web Editor Sketches:
🕹️ Prime (Ulam) Spiral: editor.p5js.org/codingtrain/sketches/0Ud-XsaYb
🕹️ Number Spiral: editor.p5js.org/codingtrain/sketches/Zs65bV-Al
🕹️ Prime vs Random Spiral: editor.p5js.org/codingtrain/sketches/3np1hBlXD
🕹️ Shapes & Color: editor.p5js.org/codingtrain/sketches/mCvvSKpZ5
🕹️ Incorporating 3D: editor.p5js.org/codingtrain/sketches/-eX078HZ5

🎥 Previous video: youtu.be/55iwMYv8tGI?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH
🎥 Next video: youtu.be/NJCiUVGiNyA?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH
🎥 All videos: youtube.com/playlist?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH

References:
📺 CodingTrainChooChoo on Twitch: twitch.tv/codingtrainchoochoo
2️⃣ Mathematical Games: The remarkable lore of the prime numbers (1964): scientificamerican.com/article/mathematical-games-1964-03
📓 An Observation on the Distribution of Primes, M. Stein and S. M. Ulam: doi.org/10.2307/2314055
🗄 Prime Numbers (Wikipedia): en.wikipedia.org/wiki/Prime_number
🗄 List of Prime Numbers: en.wikipedia.org/wiki/List_of_prime_numbers
🔗 Download Processing 4: processing.org/download

Videos:
🎥 Prime Spirals: youtube.com/watch?v=iFuR97YcSLM

🎶 Processing Theme Selector music by twitter.com/WillFromAmerica

Timestamps:
0:00 Welcome! Choo choo!
0:23 History of the Ulam Spiral
1:16 Diagramming the Spiral
2:18 Starting to Code
3:25 How and when do I rotate?
4:25 Coding the number spiral
7:00 Debugging!
9:40 Visualizing the spiral
12:22 What is a prime number?
14:31 Code to check if a number is prime.
18:57 Marking primes in the spiral
19:40 Porting to Processing (Java)
22:46 More references & examples

Editing by Mathieu Blanchette
Animations by Jason Heglund
Music from Epidemic Sound

🚂 Website: thecodingtrain.com
👾 Share Your Creation! thecodingtrain.com/guides/passenger-showcase-guide
🚩 Suggest Topics: github.com/CodingTrain/Suggestion-Box
💡 GitHub: github.com/CodingTrain
💬 Discord: thecodingtrain.com/discord
💖 Membership: youtube.com/thecodingtrain/join
🛒 Store: standard.tv/codingtrain
🖋️ Twitter: twitter.com/thecodingtrain
📸 Instagram: instagram.com/the.coding.train

🎥 Coding Challenges: youtube.com/playlist?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH
🎥 Intro to Programming: youtube.com/playlist?list=PLRqwX-V7Uu6Zy51Q-x9tMWIv9cueOFTFA

🔗 p5.js: p5js.org
🔗 p5.js Web Editor: editor.p5js.org
🔗 Processing: processing.org

📄 Code of Conduct: github.com/CodingTrain/Code-of-Conduct

This description was auto-generated. If you see a problem, please open an issue: github.com/CodingTrain/thecodingtrain.com/issues/new

#primenumbers #p5js #javascript