Gaps between Primes (extra footage) - Numberphile

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Featuring Ed Copeland and Tony Padilla (with a very non-expert intro by Brady).

NUMBERPHILE

Videos by Brady Haran

[andrewxc]

Prof. Zhang was my basic proofs teacher. I ended up missing a lot of classes due to mono. I regret not working with him more. Very unsurprising, though, that his paper is "crystal clear."

[branominal]

Massive props to the editor for realising it was a paper worth reviewing quickly

[MoosesValley]

Really appreciate this extra footage. It's astounding to me that even on the edge of infinity the largest gap between primes can be bounded. 70 million seemd such a small gap (in an infinite number system). But as others have reported here, and this quote from inyen1 "Terence Tao and later joined by James Maynard who had found additional new methods, they got the bound down from 70, 000, 000 to 246 (and if the Elliott–Halberstam conjecture is true down to 16)." For me, 246 is just such an unexpected and insanely small gap between massive primes on the edge of infinity. Incredible work by Dr Yitang "Tom" Zhang and others who have lowered the gap and followed on from his work.

[gyorgy]

Eratosthenes not Aristophanes, he was a playwright. The Sieve of Eratosthenes is a miracle of elegance.

[tgwnn]

Apparently the limit is now at 246 (down from 70 million).

[grandexandi]

Damn, Brady. I'm translating the subtitles into Portuguese, but the word for 'prime' is the same word for 'cousin', so I get to this 'cousin prime' thing and I'm like "os primos primos"... LOL

[feliciabarker]

This and the Goldbach paper coming out so close together leads me to propose the twin papers conjecture

[chattyw]

Should've added 2 seconds to the video to get 19:01 1901 is a prime or added 12 seconds to get 1151 seconds total which is a twin prime with 1153.

[fournya]

As soon as you said "You know that's what I would have done, " I looked down to see the length of the video. I love your attention to detail!

[Maddolis]

I find it hard enough to wrap my head around any number over 10000 being a prime number. This is just mind-blowing.

[NoriMori]

I love how this video is a prime number of minutes long.

[natejc]

At UNH, I was taught by Zhang, he is a funny dude. No one pronounces his name correctly so he said at the very first day of class that is name is Tom (affectionately). I took multi-d calc with him and it was easy:P I mean its unh ya know?

[kevinohare]

Watching this 10 years later, it seems that the proposed proof of the weakened Goldbach Conjecture, which Tony mentions around 14:48, still hasn't been confirmed. Bummer.

[Ljk]

Can we get a follow-up? I would *love* to hear how this proof has been evolved by mathematicians!

[PTNLemay]

Thanks for taking the extra time to explain this further. I had to watch the first video a few times before I finally grasped what it was trying to say. And now that I do get it, I agree it's pretty cool.

[Makajezi]

i absolutely loved what he said at the end of the video.

[heyandy]

Brady is really nerding out in the beginning. Usually he lets the talent do the talking, but you can tell he is a worthy candidate for the title of Numberphile.

[wreckim]

What appeals to me about a subject like this, like Fermat's Last Theorem etc...is that it is so easy to understand the problem, and even picture how difficult it is to prove it--yet I KNOW I can't keep up with the math, but I imagine I can with proper explanation. It's a lot like watching a chess analysis of a a Carlsen in the World Championships...I imagine I too would make that move. Dreamers...I am one.

[InfamousBLT]

Brady, do you always have this much extra footage? This stuff is fascinating...you should publish extra footage more often. It's great stuff!

[EmyllSomar]

The spark can also go into it. It also goes into the first one. Genius!