If Prime Numbers Become Increasingly Rare, Then Why Do They Keep Showing Up In Pairs?
Video Overview & Insights
Do twin primes go on forever? Sponsored by Brilliant - Head to https://brilliant.org/veritasium to try Brilliant’s tutor for free, plus receive 20% off an annual Premium subscription
Is this statement true?
"Every prime number can be written as a sum of (a positive integer)^(a prime number) and a prime number, If it fails, then it can be written as a sum of (a positive integer)^(a prime number) and (a positive)^(a prime number)"
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if you change the base number from base 10 to base 12 all these prime numbers are different. so who cares.
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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Are therr a finite number of numbers of which I am unaware?
0:00 What are twin primes?
3:08 How To Find Prime Numbers
wait....what? (Jack Sparrow face)...me after finishing the video...
6:11 The Sieve of Eratosthenes
11:26 The Closest We’ve Come To Proving Twin Primes
Prime numbers keep showing up in pairs because composite numbers are 'clumpy'. Precisely because each divisibility 'marches to its own tune' they will be out of sync with each other which precisely means that the density of composite and therefore prime numbers as well will fluctuate (taking into account necessary statistical results, of course). The only question is whether this fluctuation is 'big enough' to allow for infinitely many twin primes.
15:54 Searching For A Bounded Gap
18:47 How A Subway Worker Changed The Game
Fascinating video, but one thing I might have missed: Is there a practical usage for this? Encryption?
29:20 Finding An Upper Bound
32:04 Maynard and Polymath
Now random dudes will try to use AI to solve this conjecture for good… let’s see what happens…
36:42 Will we solve the twin prime conjecture?
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My Littlewood got Hardy
References can be found here: https://ve42.co/TwinPrimesRefs
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Ngl, I was lying down while watching this, and I remember all the parts Derek narrated and remember none of it which was narrated by others 😂
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Not to be a math curmudgeon, but have any of the "inventions" used to attempt this problem actually had any practical, real-world benefit?
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Writers: Vibhor Pandey, Casper Mebius and Alex Kontorovich
Producer & Director: Vibhor Pandey
Presenters: Derek Muller & Casper Mebius
Mind the gap
Editors: George Reynolds & Trenton Oliver
Camera Operators: Casper Mebius & Derek Muller
"Anals of Methamatics"
Animators: Emma Wright, Andrew Neet, Alex Drakoulis, Domonkos Józsa & Fabio Albertelli
Illustrators: Jakub Misiek
Title changed for the third time
Additional Editor: James Stuart
Researchers: Darius Garewal, Gabe Strong, Sophia Rose
Finished the video but understand none. But ill keep watching veritasium anyway.
Thumbnail Designers: Abdallah Rabah, Ben Powell, Daniel Ellacott & Patryk Ziolkowski
Production Team: Jess Bishop-Laggett, Matthew Cavanagh, Anna Milkovich & Josh Pitt
The adverts is uncool (And illegal). You should be ashamed of doing this kind of obfuscated, underhanded and sneaky stuff.
Executive Producers: Derek Muller, Casper Mebius & Emily Zhang
Additional video/photos supplied by Getty Images & Storyblocks
Music from Epidemic Sound
I just searched about professor zhang and found veritasium video😮
More User Perspectives
11,13,17 would have three primes according to the stencil
@mustafamahirdaiyan179Guys, I have feeling something weird on YouTube. I don’t even know what is this 0
@ishuuu_youtubeI’m too dumb for this one
@NicodemusTI have some weird feeling that prime numbers have a lot more to do with our universe than they seem. In a universe of infinite chaos, prime values leave an intriging framework for order to be seeded. Over time, values can can be broken down are, and those that cannot remain. Maybe the various forces or quantum fields are the physical emergence of prime values in some way.
@experyment42I didn't know that they were working on that, and nobody told me it was impossible. So I brought it down to 2.
@dark-secI swear they changed the thumbnail of this guide 3 times
@SophanGhatani-e8dbro is dropping bars "raer" "pair" hits hard
@ShineDang-x7lVery poor explanation at 12:07
@conseraziaI hate the changing thumbnail/title thing. Saw this video. Came back later to find it. Couldn't cause it's name changed. Realised it had a new name.
@adagioleopard6415THE POWERS OF TWO ARE SAME AS IF YOU KEEP DOUBLING THE NUMBER.
@DipakNGOEarthI wonder if this is still Derek... He said ln like lawn. Sketchy
@RikusNelMy guess is that we will solve the twin prime conjecture before we will get GTA VI.
@rfvtgbzhnAfter a long time, I can say that the quantity on this channel has increased, but the quality has decreased.
@husseinjafarinia224i feel as though this subway worker couldve been better represented on the thumbnail you made him look like jared fogle lmao
@shmelvingame20:38 is that... a bare lightbulb hanging from a car roof? I was hoping veritasium wouldn't be using AI for their assets but that's pretty hard to explain away
@flamshizDerek should do more on screen time & other guys do all other & background works , we love that.
@anshuman2187Shouldn’t the thumbnail show 1, 3 and 5, 7 as pairs? It shows 3, 5 then 5, 7. Using 5 twice
@BushyHippoThis is confusing
@MielKellens39:57 "World roundest object", the video that got me into Veritasium.
@diegofernandez4789previous title was better
@arcsss-c2iLove the video but hate the clickbait title
@divandrey-u3qCada vez que dicen Niagara, me recuerdo a que tengo que planchar jajaja
@adanrodriguezq24:46 67
@adolenko961224:47 6 7
@DevinPerkins19These math vids are way over my head
@xyzxyzxyzxyz'It always seems impossible until it's done' - Nelson Mandela
@ScienceSpider-sigmaI like the title better now
@Ash-ut1swWhat is with this changing video titles on YouTube?
@mahela1993The number of times this video changed titles in less than 24 hours is beyond me
@confusedusername