Goldbach Conjecture - Numberphile 

Extra footage from this interview is here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-7D-YKPMWULA.html New Numberphile buttons/badges and a Parker Square Mug: store.dftba.com/collections/numberphile

"Prime numbers are mostly odd numbers." That's an understatement if ever I heard one.

Late at night, you're on your computer, lights out, hunched over the bright monitor, staring intently at what's on screen. Suddenly, your mom walks in unannounced and stares horrified at what she sees. "Oh my God! Are you trying to prove Goldbach's Conjecture?"

*video starts* ok I've forgotten English *panic*

Numberphile, the only youtube channel doing 9minutes and 59seconds long videos in 2017

I loved this video. I hope we can see Professor Eisenbud more often on the channel, I very much enjoy his calm way of talking.

Hang on a second, I've got this.

9:31 This guy definitely works on Goldbach’s Conjecture in his attic.

David Eisenbud is, hands down, my favorite guest on Numberphile. If I had him as a professor for Differential Equations, I might have actually retained that knowledge.

One time I got robbed and I said Hey I want my Goldbach

I appreciate his voice and calm talking Would love to sit in his lectures

He speaks about trying to solve Goldbach's conjecture as if it were smoking marijuana or something, haha. "I swear I've never done it!"

For some reason these mathematicians seem really pleasant people. This is one of the things I wish I had appreciated when I was young.

Starts video in a foreign language and I think I had a stroke.

I keep coming back to this one. Clear, concise, deeply fascinating, and Eisenbud is quite charasmatic.

Looks like Goldbach's Comet contains something like Sloane's Gap.

i emailed and asked for a video about this conjencure a few years ago and i am very happy to see one! hopefully there is material for another video about this crazy and beautiful theory that seems so intuitive and unintuitive at the same time! thank you for the amazing content, i have been a fan for many many years

These conjecture videos are really fascinating. Nice work numberphile.

I've been waiting this video for a long time. I'm glad it finally came up.

Uncle Peter and Goldbach's Conjecture

Another banging video, Numberphile. I first encountered the conjecture in one of Ian Stewart's books, and I must say it must be the easiest to understand maths question that still can't be solved. I couldn't wait for you to do a vid on it. Great job.

Me in the first seconds of the video: "Wow I should improve my English, I'm starting not to get some things..."

About time you guys make a video on Goldbach Conjecture. Enjoyed it. Thanks Numphile

You should seriously interview Prof. Eisenbud more often. He's one of the most eloquent mathematicians on your amazing channel.

Understatement of the century: "Prime numbers are mostly odd" is that an open question? Finally found a proof I could tackle!

I always greatly enjoy Prof. Eisenbud's videos (still remember the Gauss - heptadodecahedron one, and specially, the proof of the Fundamental Theorem of Algebra...

this conjecture helped me won the Qatar math quiz competition! Will never forget this as this changed my life!!!

Wow ths conjecture seems so logical when you see how the number of possible ways to express even number is growing steadily. It is rather interesting no one knows how to actually prove something so obvious.

Every even integer nn can be expressed as the point of intersection of two lines using linear functions: f(x)=2p1, f(y)=-0.5x-p2 where x

Man, besides the math, that dude has really nice handwriting skills...

My God, I love this guy. The voice, the enthusiasm. It gets to me.

I prefer Douglass Hofstadter's variation of the Goldbach Conjecture: "every even prime is the sum of two odd numbers". Much easier to prove!

This guess can be expressed in a more beautiful way. Each number is located in the middle of two prime numbers. For example 15 is located between 13 and 17. 12 is located between 11 and 13.

Videos like these make me realize how minimally I use my brain on a daily basis. A small part of me wants to be a number theorist and really become a mathematician.

i think you need an extremely optimistic mindset to think "Euler couldn't do it, but i'll give it a try"... :D

his voice talking about math is the most relaxing thing

The way professor writes the letter q is so cute :D

I've written a wonderful proof of the Goldbach Conjecture, however there is not enough space in the youtube comments section to write it here.

Wow 9:58-9:59 mins Brady your a beautiful human being

FINALLY YOU GUYS DID IT

Really nice video and video quality

I proved that any odd integer greater than 4 is the sum of a prime number and a positive even number. Now give me my fields medal !

Thank you Prof. Eisenbud.

David has the most soothing voice on earth.

Such a fascinating conjecture.

You do have a really relaxing voice...! :D

I've been working on the Goldbach Conjecture for a little while now, and before I even watched this video, I had discovered or realized a lot of properties of numbers that I didn't know before, just through my own exploration of numbers. And it's startling how similar that triangle graph looks to something I was using (that I came up with totally independently) for a little while. And earlier today I happened to formulate a hypothesis which is basically Hardy and Littlewood's conjecture (any odd number is the sum of a prime and twice a prime). Kinda scary to see it in a video just hours after wondering about the problem myself.... Even though I may or may not be any closer to coming up with something (it's actually pretty hard to tell; so many ostensibly false leads), I still have found many interesting properties about numbers through my own research and logical exploration. Very fun project for a Numberphile :)

I like him. He reminds me of a professor I had in college for an intro proof class and then differential equations.

2 and 3 are only consecutive prime numbers. We can generate all numbers using two and there as basis. For rest of prime numbers minimum distance is 2 (twin primes) we can generate all even numbers minimum distance of 2 using twin primes as basis.

0:33 the subtle additions drifting away gave away the conjecture (and yes I glossed over the intro)

From this conjecture an intesting fact follows. For every n there exist prime p and q for which p-n = n-q....

Anyone else notice that he puts the numbers of Goldbach’s birthday in a pair of primes?

Loved it!

Emil's Conjecture for (n) numberphile videos uploaded, at least 334.4 comments containing "first" will be posted during the first x*10 minutes

Since there is no certain way to find primes I'd say, Goldbach's conjecture is the closest to one. If you take a number significantly larger than the largest known prime, you should always find a prime bigger than the largest prime known.

Nice touch showing it for the numbers of his birth and death dates!

wow, Numberphile doesn't often do proofs like this, but this is a great, clear video on the application of Probability in Number Theory

For the prime + twice a prime, instead of writing it a+2b, write it (a+b) + c. If we prove that any even number can be written as a+b and we prove that any prime is an even + a prime, would that be proof that a+2b would be a way to write any number with primes a and b?

You missed 5+5...

Your videos taught me more than university

Huge Thank you old man

How does a mathematician even work on a conjecture? Like where do you start?

His german is lit.

Thank you Professor David Eisenbud. ... Wow! thanks for that clear and concise explanation. My pet wacky Prime number conjecture involves the "Ratio" between two Cousin Primes, e.g. 3 & 7, 7 & 11, 13 & 17, 19 & 23, etc. I call them Grandfather Primes. OK start trivial, 7 & 11 is roughly to the ratio 2/3 and 2 * 11 = 22, and 3 * 7 = 21, we know that the square root of any even number is never going to end .9999, it may end .49999... So we multiply the product 21 & 22 by four :- 21 * 22 *4 = 1848 and 43 * 43 = 1849. So 43 is the Grandfather Prime. So lets go a bit larger 307 & 311 are cousin primes, their ratio is roughly 76:77 and (76 * 77 * 4) + 1 = 153 *153, but 153 is NOT a prime , quite a lot of close ratios do not deliver a Grandfather Prime but one of them always does, even when tested with very large cousin primes. There are no Prime tests for the larger of the cousin primes so we are forced to resort to the trusty old sieve of Eratosthenes. That takes ages with a fast laptop. So we are limited to quite small cousin primes. I loved your Stochastic Explanation. Our Amateur Sophomore Conjecture, reminds us of G.H. Hardy. "Any damn fool can come up with a Prime Number Conjecture, and I am fed up with receiving them from undergraduate students! " Stochastically those suitable ratios grow exponentially as the cousin primes increase in size. We have statistics working in our favour, but out there may be a counter-example? ( OK 76:77 does not work, but 75:76 does. 151 is the Grandfather prime also a sexy Grandmother Prime, (78 * 79 * 4) +1 = 157 *157. ) Oops! ediit (307 * 311 * 4 * 80 "81 ) + 13^2 = 49,747 ^2 but careful about factoring RSA-256 the Ron Rivest - Adi Shamir -David Wagner DOS Attack Time Lock Hash-Cash Puzzle. Mining Ten Bitcoins with a Laptop every hour is naughty.

Numberphile is so cool. Which math channel has so much content that something as big as the Goldberg Conjecture gets its video after so many years?

That miscalculation 3:25 oh boi

Thanks. Never knew about this conjecture and it is pretty neato! Does this also apply to other divisors like 3, 4, 5, etc?

Wait-- I love this video and you method of teaching, the whole video I'm thinking; "when did the number 2 become a prime number?" Thanks for, sharing mate! - cheers

As a German, i was wondering as I started the video and prof. Eisenbud started speaking German, but just a compliment for prof. Eisenbud: His pronounciation is quite good!

is there any relation between discrete logarithm and integer factorization?

7:00 - There could be a unique way: look for the pair of primes with the smallest possible prime, or find the pair of primes with the smallest difference.

Thanks for the video.

I know people who like math are the rare ones, but watching this not being excited and thrilled, they are the ones missing out so much in life.

I wanna see Numberphile sit a GCSE maths paper

oh wow german has changed since this has been written

Working from outer to inner numbers you have the top 4 with bottom 26 equals 30....24 plus 5 29, 6 plus 22 is 28....

one of the most important video of numberphile

Bonjour, Pour ceux que ça intéresse, je propose une résolution de la conjecture de Goldbach publiée sur RU-vid en 5 épisodes sous le titre générique "Variations Goldbach". Comme elle s'adresse à tout public, pour ceux qui veulent entrer directement dans le vif du sujet, une formule donnant la proportion minimale de couples de premiers au sein de l'ensemble des couples d'impairs dont la somme vaut un nombre pair se trouve épisode 2 et l'essence de la démonstration épisode 5. Le commentaire de J ci-dessous est tout à fait exact, mais en fait, il y en a beaucoup plus. Entre plus ou moins 10.000 et 16.000 le nombre de minimum de couples de premiers monte à environ racine carrée du nombre pair, et ça continue d'augmenter comme je le démontrerai dans l'épisode 6, qui clôturera cette série. Berendans

Apparently a Filipino mathematics teacher claimed to have solved this problem

i just think that FOR 2m=p+q, 0

Best explanation

I love how taboo it is to try to discover a solution :P

*Sees video is 9 minutes and 58 seconds long* "Numberphile being edgy"

I live for this show

I also love Goldbach conjecture.. Assuming distinct primes are possible, which i guess is the case for even number greater that 8, we can prove that any prime is an average of two other primes. From that Bertrand postulate will follow..Not sure if any prime is average of two other primes is a valid theorem, but interesting that a valid theorem ( Bertrand Postulate) comes out of it.

An interesting thing is that this can sort of be extended: For every even number, there are two primes an equal magnitude from half of that even number, the sum of which is the original number. For example: 8/2=4, 3 and 5 are both 1 away from 4, and 3+5=8 76/2=38, 29 and 47 are 9 away, 29+47=76 88/2=44, 41 and 47 are 3 away, 41+47=88 1.I obviously can't prove this, or I would say it's more than "interesting" 2.I can't say I have put as much rigor into testing this as other people have with their theories... only up to around 100.

I bet James Grime works on this in secret and laughs maniacally whenever he makes progress!

Felt like I'm actually in a lesson 😂 very interesting topic

New Numberphile video with professor Eisenbud -> day made ■

I have an elegant proof for Goldbach Conjecture but I’m suffering from lack of space in the comment section

I wonder if anybody will ever prove the "Brady Conjecture": That Numberphile is the best channel on RU-vid :).

For easy visualization related to prime distro: GB - EVERY 'number' is the average of two primes.

David sounds like me when I'm imitating my history teacher

I have learned more maths from Numberphile than school.

Jaaa! Deutsch... Endlich verstehe ich etwas...! :D

More David please.

I would guess that 2 can't be written as the sum of 2 primes, since 1 isn't a prime, and I suspect 0 isn't a prime either. While some claim that -2 and -3 etc are also prime numbers, they are in general not considered primes. But if we exclude negative numbers as primes. Then 2 is an even number that can't be written as the sum of 2 primes.

goldbach is the new fermat I think.

This taboo about working on the conjecture seems to work against moving towards a proof. This realization seems obvious. So I keep treating the conjecture like that?

Goldbach's conjecture works because of the wildcard numbers 2 that go through every pair also the 5 that doubles itself 5.10.15.20.25...prime numbers are not doubled by the number 3 and 7 also perfect squares odd minus ending 5 example 3+3+3... to infinity and 7+7+7... to infinity and the perfect squares