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

A curious pattern, approximations for pi, and prime distributions. Help fund future projects: An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: Based on this Math Stack Exchange post: Want to learn more about rational approximations? See this Mathologer video. Also, if you haven’t heard of Ulam Spirals, you may enjoy this Numberphile video: Dirichlet’s paper: Timestamps: 0:00 - The spiral mystery 3:35 - Non-prime spirals 6:10 - Residue classes 7:20 - Why the galactic spirals 9:30 - Euler’s totient function 10:28 - The larger scale 14:45 - Dirichlet’s theorem 20:26 - Why care? Corrections: 18:30: