41:30If Prime Numbers Become Increasingly Rare, Then Why Do They Keep Showing Up In Pairs?
Veritasium tells the full story of the twin prime conjecture, the 2000 year old claim that prime pairs two apart like 11 and 13 never run out even as primes thin away. It walks both lines of attack: Viggo Brun adapting the sieve of Eratosthenes into a war of main term against error term, and the bounded gap program that hit a 'one half barrier' everyone believed was a wall. The hero is Yitang Zhang, a former Subway bookkeeper who in isolation pushed past that barrier by one part in 584 and proved infinitely many prime pairs sit within 70 million of each other. James Maynard and Terence Tao's Polymath collaboration then showed the half barrier was a mirage and drove the gap to 246, where it stands today.








