Unlocking the Mystery of Prime Numbers: Patterns & Theories Revealed 🔍

In this video, we explore the "pattern" to prime numbers. I go over the Euler product formula, the prime number theorem and the connection between the Riemann zeta function and primes.

Here's a video on a similar topic by Numberphile if you're interested: https://youtu.be/uvMGZb0Suyc

There are a few mistakes in this video, so I clarified them in a pinned comment. Sorry about that!

This video adapted several concepts and ideas from this article: https://medium.com/cantors-paradise/the-riemann-hypothesis-explained-fa01c1f75d3f

More sources: https://docs.google.com/document/d/1_lFWtsuPfWNq0VFAiqknsSeAOa-Oy2MDrmH6d-EOiBg/edit?usp=sharing

Riemann Hypothesis by 3b1b: https://youtu.be/sD0NjbwqlYw

Complex Exponents by 3b1b: https://youtu.be/v0YEaeIClKY

Harmonic Series Divergence: https://web.williams.edu/Mathematics/lg5/harmonic.pdf

P-Series Convergence: https://www.khanacademy.org/math/ap-calculus-bc/bc-series-new/bc-10-5/a/proof-of-p-series-convergence-criteria

This video was animated using manim: https://github.com/3b1b/manim
Source code for the animations: https://github.com/vivek3141/videos

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Music by ChillHop

#primes #zeta #math