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

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: Important error correction: In the video, I say that Dirichlet showed that the primes are equally distributed among allowable residue classes, but this is not historically accurate. (By “allowable“, here, I mean a residue class whose elements are coprime to the modulus, as described in the video). What he actually showed is that t