Thanks to Kerry D. Wong who originally piqued my interest by sending me this:
http://www.kerrywong.com/2009/09/06/an-alternative-illustration-of-prime-number-distribution/
Here are the papers about finding arbitrarily large gaps between primes:
The first paper: https://arxiv.org/abs/1408.4505
The paper one day later: https://arxiv.org/abs/1408.5110
Watch the author of the second paper James Maynard talk about it on Numberphile:
https://www.youtube.com/watch?v=BH1GMGDYndo&ab_channel=Numberphile
The 'top dots' are called "Jumping Champions" and you can read more about them being primorials here: https://mathworld.wolfram.com/JumpingChampion.html
Here is loads about prime gaps with references if you want to see the original papers.
http://sweet.ua.pt/tos/gaps.html
That link was sent to me by my Patreon supporter Bruce Garner (who has also calculated the first trillion prime gaps using C++). That page is excellent; I wish I'd found it before I started writing the video.
CORRECTIONS:
- At 08:07 they should have been p_(n+1) - p_n ≥ 8. Or I guess p_n - p_(n-1) ≥ 8. But not what I put. What I put was wrong.
- Wow. At 15:33 I said "big zero" instead of "big O". I'm so adamant that I say "zero" instead of "oh" for the digit that I finally had a subconscious false-positive!
UPDATE: I actually spotted this one right before release and it looks like responses were pretty split on if I should have fixed that. I didn't. https://twitter.com/standupmaths/status/1379438185374171137
- Let me know if you spot any mistakes.
Thanks to my Patreons who are vital in keeping the videos coming. Future Matt has a very expensive rider.
https://www.patreon.com/standupmaths
As always: thanks to Jane Street who support my channel. They're amazing.
https://www.janestreet.com/
Filming editing by Alex Genn-Bash
Graphics by James Arthur and Matt Parker
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: http://standupmaths.com/
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