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A huge thank you to Alex Kontorovich, Andrew Granville, James Maynard, Roger Heath-Brown, Dimitris Koukoulopoulos, Debmalya Basak & George Shakan for their invaluable expertise and contributions to this video!

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0:00 What are twin primes?

3:08 How To Find Prime Numbers

6:11 The Sieve of Eratosthenes

11:26 The Closest We’ve Come To Proving Twin Primes

15:54 Searching For A Bounded Gap

18:47 How A Subway Worker Changed The Game

29:20 Finding An Upper Bound

32:04 Maynard and Polymath

36:42 Will we solve the twin prime conjecture?

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References can be found here: https://ve42.co/TwinPrimesRefs

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Writers: Vibhor Pandey, Casper Mebius and Alex Kontorovich

Producer & Director: Vibhor Pandey

Presenters: Derek Muller & Casper Mebius

Editors: George Reynolds & Trenton Oliver

Camera Operators: Casper Mebius & Derek Muller

Animators: Emma Wright, Andrew Neet, Alex Drakoulis, Domonkos Józsa & Fabio Albertelli

Illustrators: Jakub Misiek

Additional Editor: James Stuart

Researchers: Darius Garewal, Gabe Strong, Sophia Rose

Thumbnail Designers: Abdallah Rabah, Ben Powell, Daniel Ellacott & Patryk Ziolkowski

Production Team: Jess Bishop-Laggett, Matthew Cavanagh, Anna Milkovich & Josh Pitt

Executive Producers: Derek Muller, Casper Mebius & Emily Zhang

Additional video/photos supplied by Getty Images & Storyblocks

Music from Epidemic Sound