Why Do Prime Numbers Make These Spirals? - Dirichlet’s Theorem, Pi Approximations, and More
3Blue1Brown via YouTube
Overview
Syllabus
- The spiral mystery
- Non-prime spirals
- Residue classes
- Why the galactic spirals
- Euler’s totient function
- The larger scale
- Dirichlet’s theorem
- Why care?
: 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 the sum of the reciprocals of all primes in a given allowable residue class diverges, which proves that there are infinitely many primes in such a sequence.
Taught by
3Blue1Brown