Teenager Solves Three-Decade-Old Conjecture

Listen to 100s of Science Documentaries on Turing for Free. Check out the App at iOS: https://apps.apple.com/in/app/the-turing-app/id6752724106 Android: https://play.google.com/store/apps/details?id=com.theturingapp.turing&hl=en or listen at https://theturingapp.com ----------- TIMESTAMPS: 00:00 - A 17-Year-Old Sends a Proof Into the Adult World 02:11 - The Child Who Asked About Infinity 05:47 - Yitang Zhang and the Romance of Prime Gaps 09:07 - Finding the Sweet Spot: Prime Impostors & Carmichael Numbers 13:23 - How Daniel Larsen Solved the 30-Year-Old Carmichael Problem 16:50 - Recognition, Regeneron, and the Future of Number Theory ----------- In this video, you'll learn how high school senior Daniel Larsen proved Bertrand’s postulate for Carmichael numbers, solving a 30-year-old math problem. We cover the fascinating history of prime impostors and the advanced sieve methods used to map them to help you understand how breakthrough discoveries happen in modern number theory. This detailed overview breaks down the inspiring story of Daniel Larsen's mathematical breakthrough. We explore how he adapted techniques from Fields Medalist research on prime gaps—developed by mathematicians like James Maynard, Terence Tao, and Yitang Zhang—and applied them to pseudoprimes. Whether you are a math student or a science enthusiast looking to understand complex number theory concepts, this guide breaks down the technical details into accessible ideas. We discuss related concepts like primality testing, Fermat’s Little Theorem, Carmichael numbers, and analytic number theory. ----------- Turing is a leading publisher of popular science books. Check out our collection on Amazon: https://www.amazon.com/stores/Turing-Editorial-Team/author/B0GVXKMGGJ/allbooks?ccs_id=4637a82d-44e3-49b7-92d6-ed1aec5fe06b Apple Books: https://books.apple.com/us/author/turing-editorial-team/id1895369034?see-all=books ---------------- Check out our Series of Weekly Podcasts On Wonders of Science Adventures into Chemistry Spotify: https://open.spotify.com/show/0kqIbkcrhuzFPf5rgRDPkQ?si=88693d8c97934fc6 Apple Podcasts: https://podcasts.apple.com/us/podcast/adventures-into-chemistry/id1801975450 Beyond Proof: Stories in Maths Spotify: https://open.spotify.com/show/0EJXj5CF6wqE79WTwpYKGr?si=a429edd3979b4429 Apple Podcasts: https://podcasts.apple.com/us/podcast/beyond-proof-stories-in-mathematics/id1881693625 Mavericks of Science: Meet the most influential and groundbreaking contemporary researchers Spotify: https://open.spotify.com/show/48c6VqsI8vtH9D2W5MYXfG?si=acc3565470d246ef Apple Podcasts: https://podcasts.apple.com/us/podcast/mavericks-of-science/id1875688838 Million Dollar Problems of Mathematics: Legendary, unsolved puzzles that have baffled the world's sharpest minds, using Everyday Language Spotify: https://open.spotify.com/show/1dHIDxANHtjJtVzITrOwYM?si=8e7b302f198548ac Apple Podcasts: https://podcasts.apple.com/us/podcast/million-dollar-problems-of-mathematics/id1796668358 Mysteries of the Universe: Questions that keep astrophysicists awake at night Spotify: https://open.spotify.com/show/53cFFxbShCGjYBKFFUayNq?si=d47ed62f389c4f8b Apple Podcasts: https://podcasts.apple.com/us/podcast/what-would-worlds-largest-telescope-find/id1796678795?i=1000768443430 Planet Earth: Science of Climate and Earth Spotify: https://open.spotify.com/show/4HRLQiQJ6GUgJs6wotO3xn?si=b99ce74037534f28 Apple Podcasts: https://podcasts.apple.com/us/podcast/planet-earth/id1886256155 Quarks to Cosmos: Journey Inside the Atom to the Far End of Cosmos Spotify: https://open.spotify.com/show/0OtvBwq0GA0SGijgF2GZYv?si=4a2d444aadd94121 Apple Podcasts: https://podcasts.apple.com/us/podcast/quarks-to-cosmos/id1809992176 Realm of Quantum Mechanics Spotify: https://open.spotify.com/show/3ESCY4B2HB03ZpZJB5J6Y9?si=462d90847a4a4077 Apple Podcasts: https://podcasts.apple.com/us/podcast/realm-of-quantum-mechanics/id1796673349 The Future of Medicine Spotify: https://open.spotify.com/show/7ioXdgkNuHThPc8p1DRHxk?si=ebcbfe9b417f48bb Apple Podcasts: https://podcasts.apple.com/us/podcast/the-future-of-medicine/id1793412323 The Science of Us: Biology, neuroscience, and psychology to unpack the machinery behind our daily experiences Spotify: https://open.spotify.com/show/28qepKUu83gGzPXtst5MeT?si=2c2a7aec570d4a54 Apple Podcasts: https://podcasts.apple.com/us/podcast/the-science-of-us/id1887044303 What the Tech: Foundational math and engineering underneath The Frontier Tech Spotify: https://open.spotify.com/show/41I3bea5v66iKTZdOglG0R?si=279f4848e6bd46eb Apple Podcasts: https://podcasts.apple.com/us/podcast/what-the-tech/id1887925458 Wild Origins: Nature, Animals and Us Spotify: https://open.spotify.com/show/0sdLh1dp4jT7WgGNSvzyVG?si=aa15e34f827446ab Apple Podcasts: https://podcasts.apple.com/us/podcast/wild-origins/id1881725041