Euler's Proof of the Infinitude of Primes

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Join the channel to get exclusive and early videos, original music, lecture videos, and more! https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 🛍 Check out my math fashion brand: https://mathshion.com/ More Math Chats: https://www.youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO Business Inquiries: [email protected] Around 300 BC Euclid proved the infinitude of primes using a simple argument typically presented as a contradiction proof. In the 1700s the singularly prolific mathematician Leonhard Euler proved the infinitude of primes essentially as a corollary of a deeper result concerning the equality of the Riemann Zeta function with a product of prime-related factors. In this video we go over Euler's classic proof of this ancient result. #maths #primenumber #mathematics Likelihood of Picking Two Integers with No Common Factors: https://youtu.be/Cbkyarr7QRc Textbooks I Like! Graph Theory: https://amzn.to/3JHQtZj Real Analysis: https://amzn.to/3CMdgjI Abstract Algebra: https://amzn.to/3IjoZaO Linear Algebra: https://amzn.to/43xAWEz Calculus: https://amzn.to/3PieD1M Proofs and Set Theory: https://amzn.to/367VBXP (available for free online) Statistics: https://amzn.to/4d5HbUQ Discrete Math: https://amzn.to/3qfhoUn Number Theory: https://amzn.to/3JqpOQd ★DONATE★ ◆ Support Wrath of Math on Patreon: https://www.patreon.com/join/wrathofmathlessons ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● TikTok: https://www.tiktok.com/@wrathofmathedu ● X: https://x.com/wrathofmathedu 0:00 Intro 1:40 Setting the Stage 4:06 Start Proof 7:41 Identifying Pattern 9:53 Key Division Step 10:55 When s=1 13:00 Harmonic Series 16:22 The Final Step