The sound of primes

A little animated journey that builds the bridge between the prime counting function and the zeta-function.

For me it was very fascinating and not at all obvious, when I understood the connection between the primes and the zeta-function. I hope that I can share some of this fascination with you.

Let me know what you think in the comments.

Content:
0:00 Intro
0:56 Overview
1:42 Part I: Fourier decomposition of the step function
3:25 Part I: Audio experiment
5:40 Part II: The zeta-function
8:43 Part III: The bridge between the prime counting and the zeta function
12:30 Part IV: Riemann 1859

Corrections:
1:56 should read: - sum_x^p/p
4:54 p relates to x^(1/n), or simpler put p^n = x. The logarithm disappears by the exponentiation

#primes #zetafunction #complexfunctions
#primecountingfunction #zerosofzeta #nontrivialzeros #primedistribution

The material is created with
manim: https://www.manim.community/
blender: https://www.blender.org/
audacity: https://www.audacityteam.org/