Exploring the mysteries of the Prime (gaps!) Line.

From Standup Mathematician.

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Thanks to Kerry D. Wong who originally piqued my interest by sending me this:

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:

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.

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.

– 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
– At 23:43 I mentioned your ISP knowing what you are searching for but I forgot that https means the rest of the URL is hidden from your ISP. So they would only know you have visited google, but not see anything after the "?" in "https://www.google.com/search?q=giant+chalkboards+covered+in+maths". I should have used a website as the example. I’ll do that next time.
– 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.

As always: thanks to Jane Street who support my channel. They’re amazing.

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/
US book: https://www.penguinrandomhouse.com/books/610964/humble-pi-by-matt-parker/
UK book: https://mathsgear.co.uk/collections/books/products/humble-pi-signed-paperback