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/