Extra footage from this interview is here: ruclips.net/video/7D-YKPMWULA/видео.html New Numberphile buttons/badges and a Parker Square Mug: store.dftba.com/collections/numberphile
in case you didn't see my twitter comment you can also restate it as every number after a certain point is equidistant from two primes ( technically if you count distance=0 that's from 2 on, for distance>0 that's 4 on.)
+Numberphile The Goldbach's Conjecture and the solution to the Collatz Conjecture are intimately related. I will give you one week to prove it, if you fail in proving it I will prove it myself and post the solution in the comment section.
Again. The Collatz Conjecture If a number is even, divide by 2. If a number is odd, multiply by 3 and add 1. The Collatz Conjecture states that all numbers converge to 1. Due to the fact that all even numbers are contained within the power of 2 numberline, we have: n/2 = 2^s, where s are all positive integers. n = (2^s)(2) n = 2^(s + 1) Due to the fact that in order to make a number even we need to multiply it by 3 and add 1, we equal 3n + 1 to 2^(s + 1); we have: 3n + 1 = 2^(s + 1) 3n = 2^(s + 1) - 1 We equal s to the first strictly positive integer, that is, 1; we have: 3n = 2^((1) + 1) - 1 3n = 2^(1 + 1) - 1 3n = 2^(2) - 1 3n = 4 - 1 3n = 3 n = 3/3 n = 1 All numbers converge to 1.
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?"
snepNL yeah, the video isn't actually exactly 9:59 or 9:58 minutes, so if you watch it on phone or tablet, most of the time they'll lower it by 1 second, it's hard to explain it really
@@DreckbobBratpfanne That's the problem with modern academia: everyone is too concerned of their reputation as everything is built on the phd system. But in the past people like Einstein and Galois published research that is fundemental to physics and math today, and they were working outside a university environment. I swear if we didn't have this concern of reputation, the millenium problems would have been solved and we would've had a unified field theory long ago.
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.
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
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.
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.
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!
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.
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 always greatly enjoy Prof. Eisenbud's videos (still remember the Gauss - heptadodecahedron one, and specially, the proof of the Fundamental Theorem of Algebra...
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.
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.
And for every Numberphile video posted about a conjecture there will be at least two comments that say "I have proved this conjecture, but the comments are too small to contain it."
Real treat for us germans that someone who is not a native speaker pronoumces the "ch" correctly. Nomally they will pronounce it like "k" but you did nicely.
Goldbach's Conjecture is, in many ways, the arithmetic equivalent of Noether'sTheorem in Physics. It involves the conservation of bilateral symmetry as the numberline continuously translates permutatively into infinity. As the foundational level, the primes are the numbers whose distribution maintains this continuity. In an infinite space or line, every point is a potential midpoint. Midpoint is perpetually arbitrary, which is what makes the mathematics/geometrics universally applicable. (Mathematics as a Universal Language.) This means that the system is necessarily always in an evenly bisected state, i.e., a balanced state, no matter how continuously the system is bisected. There is a law that every integer has an additive inverse and distances are equivalent as measured from either equidistant endpoint to midpoint. In order for this to be universally true, the most foundational layers, i.e., the primes, must always maintain this same balance throughout and must therefore be positioned equidistant at each consecutive bisection as midpoint moves arbitrarily through the system. The system maintains balance through the primes as composites are stripped away. The distribution of the primes, and therefore basic Peano arithmetic, is thusly just like an infinitely successful Jenga Tower. Therefore, the strong Goldbach Conjecture is necessarily true simply as a matter of a design built upon the principle of maintaining perpetual system balance. When the mathematical purists finally admit to themselves that they only speak the common language of physics and engineering, perhaps they will see the simplicity of both the Goldbach and Riemann phenomena. Mathematics and Logic begin with the notion of a Standard Unit determined by the equivalence provided through actual or theoretical bisection of a space. The Goldbach Conjecture is Architectural Engineering 101 and is equivalent to the most primitive axioms of arithmetic.
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.
Push drag lift as a curve of pi in all dimension. Change the shape of pi by stretch lifting and twist In The center of al planes then give it direction equal to time
I've wondered that too for a while. Apparently you need to start off by reading (booking up) all the relevant stuff that has been discovered already and the various methods that have been used/papers that have been published. Then you probably start by working on a smaller problem within one of the already established ideas. I don't think one would just immediately have a groundbreaking idea out of nowhere.
JiaMing Lim , In my experience, throw things at the wall, see what sticks, read what other people have tried, try those yourself, read what people have tried for vaguely related problems, try those too. Repeat the above until something seems to not be there when it should, or be there when it shouldn't. That's the first grapple point. Keep working from that foothold until another is found, and just maybe, the climb proper can begin.
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.
Halosty Yes, this boils down to: Every number greater than 1 has two primes equidistant from it. Given that the Goldbach conjecture has been tested extensively, this is also true as far as that's been tested. it's an interesting insight/way of restating the problem.
I also got to the "all numbers have a pair of primes equidistant" stage and thought I was making great progress. Nearly 40 years later and I am no further on :(
Might that be due to the symmetry of adding two numbers, such as when Gauss summed the numbers from 1 to 100? Each prime is odd and either one more or one less than an even number. When you sum two primes, the difference from an even number is either 0, +2 or -2. So one gets into the definition of primes and multiplication by 2 in terms of addition.The density of primes is related to the increased number of possible permutations of primes created by adding 1 to the highest composite number formed by all of the previous primes. (2x2), (2x3), (2x5), (2^2 x 3),(2^4), (2x3^2).
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?
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.
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.
Goldbach’s conjecture isn’t of any use in finding large primes. If you take a googolplex it obviously can be written as (googolplex-97) + 97. It’s easy to show 97 is prime but there’s no easy way to show (googolplex-97) is prime.
The CC at the beginning says "(Speaking Latin)", but the main part of the text is German. The fact that the technical terms are Latin borrowings doesn't alter the underlying basic language.
If the divisor is even then it's just a special case of Goldbach's conjecture. Who knows - there might be some special case that's more readily provable than the general case, but I don't know of it. If the divisor is odd then it's false. Multiples of an odd number will include the cases where the multiplier is also odd, giving an odd result, so to be the sum of two primes one of the primes would have to be 2. Whatever your divisor, eventually the primes will get too far apart for all odd multiples of it to be two greater than a prime.
Bonjour, Pour ceux que ça intéresse, je propose une résolution de la conjecture de Goldbach publiée sur RUclips 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
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
“I don’t know if there’s any lower bound known or guessed.” If there was a lower bound known on the number of ways to express an even number as the sum a two primes, that would constitute a proof of the conjecture.
il suffit d'utiliser la fonction asymptotique pour toute limite N > = 3 qui donne une estimation du nombre de couples p+q = 2N : pi(N) qui est le nombre de nombre premiers
Following my estimation the probability of the Goldbach conjecture being true nowadays is: The infinite product from m=4*10^8 to infinite of [1-(1-log(m/2)/(log(2m)*log^2(m))^m] But even Wolfram gets stack estimating this product
Extra footage from this interview is here: ruclips.net/video/7D-YKPMWULA/видео.html
New Numberphile buttons/badges and a Parker Square Mug: store.dftba.com/collections/numberphile
Numberphile could you do sublime numbers?
we only know of 2 of them
in case you didn't see my twitter comment you can also restate it as every number after a certain point is equidistant from two primes ( technically if you count distance=0 that's from 2 on, for distance>0 that's 4 on.)
+Numberphile The Goldbach's Conjecture and the solution to the Collatz Conjecture are intimately related. I will give you one week to prove it, if you fail in proving it I will prove it myself and post the solution in the comment section.
Again.
The Collatz Conjecture
If a number is even, divide by 2.
If a number is odd, multiply by 3 and add 1.
The Collatz Conjecture states that all numbers converge to 1.
Due to the fact that all even numbers are contained within the power of 2 numberline, we have:
n/2 = 2^s, where s are all positive integers.
n = (2^s)(2)
n = 2^(s + 1)
Due to the fact that in order to make a number even we need to multiply it by 3 and add 1, we equal 3n + 1 to 2^(s + 1); we have:
3n + 1 = 2^(s + 1)
3n = 2^(s + 1) - 1
We equal s to the first strictly positive integer, that is, 1; we have:
3n = 2^((1) + 1) - 1
3n = 2^(1 + 1) - 1
3n = 2^(2) - 1
3n = 4 - 1
3n = 3
n = 3/3
n = 1
All numbers converge to 1.
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?"
whiz 85 😂😂
Yo that is pretty horrifying
Haha nice 💯
You look up, realize that you are 47 and probably shouldn't be living in your parent's basement any longer.
are you winning son?
"Prime numbers are mostly odd numbers." That's an understatement if ever I heard one.
"MOSTLY"
AAAAND, 2
And 2 is an even integer that can’t be written as a sum of 2 primes.
Yeah
yeah, because 2 its a prime number but also an even one dumbass
Numberphile, the only youtube channel doing 9minutes and 59seconds long videos in 2017
Miche Delarue 9:58
Miche Delarue this is weird. before i click the vid it says 9:59. when im watching it says 9:58
snepNL yeah, the video isn't actually exactly 9:59 or 9:58 minutes, so if you watch it on phone or tablet, most of the time they'll lower it by 1 second, it's hard to explain it really
I posted a video that is exactly 3 minutes and 2 seconds long, and sometimes it rings up as 3 minutes and 3 seconds.
It's not the length...it's the substance.
*video starts*
ok I've forgotten English
*panic*
Stargazer hahahahaha lol
Stargazer same
I'm not a native english speaker so it took me some time to understant it's german.
Stargazer Yes!
It looks like some weird cross between Latin and German to me, not that I can speak either!
Hang on a second, I've got this.
+
"hold my beer"
Srinivasa Ramanujan jokes apart, we need people of that calibre to crack down stuff like this
Asther Phoenix It truly is a shame that Ramanujan died young. With some formal training, he could've rivaled even Euler himself.
So happy to see you are still alive! I thought you died, lol! :D
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.
He's like the Bob Ross of math? :) Except usually mistakes in math remain mistakes, and not happy accidents
Yeah, he’s got this really cal in chill avuncular vibe.
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!"
This is the same with the Riemann hypothesis, some may think you're crazy for trying, it can even destroy your reputation sometimes.
Somebody solved the mystery, while they were high 🍀 marijuana 🍀
marinujan.
@@pe3akpe3et99 that was a golden comment lol
@@DreckbobBratpfanne That's the problem with modern academia: everyone is too concerned of their reputation as everything is built on the phd system. But in the past people like Einstein and Galois published research that is fundemental to physics and math today, and they were working outside a university environment.
I swear if we didn't have this concern of reputation, the millenium problems would have been solved and we would've had a unified field theory long ago.
I appreciate his voice and calm talking
Would love to sit in his lectures
9:31 This guy definitely works on Goldbach’s Conjecture in his attic.
Yes
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.
For some reason these mathematicians seem really pleasant people. This is one of the things I wish I had appreciated when I was young.
I keep coming back to this one. Clear, concise, deeply fascinating, and Eisenbud is quite charasmatic.
One time I got robbed and I said Hey I want my Goldbach
Mike H Once my friend asked me what bread I'd like to eat, I said "I want Riemann and also a beer man."
It does when the German pronunciation of "ch" as in bach is very similar to the English pronunciation of "ck".
except it isn't similar at all
The ship's diesel engine was making a loud squeaking noise so I called in the Euler to fix it.
oh yeah? prove it
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
Incomplete proof
Starts video in a foreign language and I think I had a stroke.
😂😂Underrated comment
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
Uncle Peter and Goldbach's Conjecture
My God, I love this guy. The voice, the enthusiasm. It gets to me.
These conjecture videos are really fascinating. Nice work numberphile.
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.
You should seriously interview Prof. Eisenbud more often. He's one of the most eloquent mathematicians on your amazing channel.
I'm certain that he's quite busy, being the director of MSRI and all.
Haha fair enough. He is brilliant though.
his voice talking about math is the most relaxing thing
this conjecture helped me won the Qatar math quiz competition! Will never forget this as this changed my life!!!
Akul Sharma Congrats! How exactly?
Molka Ben It just did
there was a question as to how many conjecture a student knows and how you derive it!
Martin Stu Ignoring the fact that for many centuries the Middle East was the center of the scientific world. (It isn't anymore, but still)
Why are you using Arabic numerals until now butthead?
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.
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!
Understatement of the century: "Prime numbers are mostly odd" is that an open question? Finally found a proof I could tackle!
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.
David has the most soothing voice on earth.
Me in the first seconds of the video: "Wow I should improve my English, I'm starting not to get some things..."
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 :)
Hi
I always greatly enjoy Prof. Eisenbud's videos (still remember the Gauss - heptadodecahedron one, and specially, the proof of the Fundamental Theorem of Algebra...
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.
Looks like Goldbach's Comet contains something like Sloane's Gap.
0:33 the subtle additions drifting away gave away the conjecture (and yes I glossed over the intro)
Wow 9:58-9:59 mins Brady your a beautiful human being
san kitty "You"re"
I've been waiting this video for a long time. I'm glad it finally came up.
Man, besides the math, that dude has really nice handwriting skills...
i just think that FOR 2m=p+q, 0
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.
Pierre de Fermat I was looking for this comment xD
And now here it is again. This is getting old.
so is pierre
badman jones - Combat moi.
Pierre de Fermat - Imposteur!
From this conjecture an intesting fact follows. For every n there exist prime p and q for which p-n = n-q....
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 !
You can even set the prime number to three!
1 is not a prime, skhuksle :Ü™
yep, and so what?
@@Darker7 Yes it is. One and two are both primes.
@@ezioauditore4944 1 is definitely not a prime...
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.
Emil's Conjecture
for (n) numberphile videos uploaded, at least 334.4 comments containing "first" will be posted during the first x*10 minutes
if there are "n" firsts then how many of them will actually be not first? Let's call that The Kingbach conjecture.
Define x.
between n-1 and n.
And for every Numberphile video posted about a conjecture there will be at least two comments that say "I have proved this conjecture, but the comments are too small to contain it."
Emil Macko Completely unrelated to math, but by any chance, are you the guy who created Five nights at Candy's?
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.
About time you guys make a video on Goldbach Conjecture. Enjoyed it. Thanks Numphile
David is a legend - I love his approach
Thank you Prof. Eisenbud.
Your videos taught me more than university
I prefer Douglass Hofstadter's variation of the Goldbach Conjecture: "every even prime is the sum of two odd numbers". Much easier to prove!
Nordic Exile 1+1=2 lol
Real treat for us germans that someone who is not a native speaker pronoumces the "ch" correctly. Nomally they will pronounce it like "k" but you did nicely.
The way professor writes the letter q is so cute :D
It may be even qute, the very highest form of cuteness. 😁😁
FINALLY YOU GUYS DID IT
Goldbach's Conjecture is, in many ways, the arithmetic equivalent of Noether'sTheorem in Physics. It involves the conservation of bilateral symmetry as the numberline continuously translates permutatively into infinity. As the foundational level, the primes are the numbers whose distribution maintains this continuity.
In an infinite space or line, every point is a potential midpoint. Midpoint is perpetually arbitrary, which is what makes the mathematics/geometrics universally applicable. (Mathematics as a Universal Language.) This means that the system is necessarily always in an evenly bisected state, i.e., a balanced state, no matter how continuously the system is bisected. There is a law that every integer has an additive inverse and distances are equivalent as measured from either equidistant endpoint to midpoint. In order for this to be universally true, the most foundational layers, i.e., the primes, must always maintain this same balance throughout and must therefore be positioned equidistant at each consecutive bisection as midpoint moves arbitrarily through the system. The system maintains balance through the primes as composites are stripped away.
The distribution of the primes, and therefore basic Peano arithmetic, is thusly just like an infinitely successful Jenga Tower. Therefore, the strong Goldbach Conjecture is necessarily true simply as a matter of a design built upon the principle of maintaining perpetual system balance.
When the mathematical purists finally admit to themselves that they only speak the common language of physics and engineering, perhaps they will see the simplicity of both the Goldbach and Riemann phenomena. Mathematics and Logic begin with the notion of a Standard Unit determined by the equivalence provided through actual or theoretical bisection of a space.
The Goldbach Conjecture is Architectural Engineering 101 and is equivalent to the most primitive axioms of arithmetic.
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.
Push drag lift as a curve of pi in all dimension. Change the shape of pi by stretch lifting and twist In The center of al planes then give it direction equal to time
That miscalculation 3:25
oh boi
Egzolinas Gamer almost thoght i was the only one to ser it
Well, to be fair he did SAY it right... He just followed the wrong line.
Thank you! It was a simple mistake but it gave me such anxiety. lol
I like him. He reminds me of a professor I had in college for an intro proof class and then differential equations.
How does a mathematician even work on a conjecture? Like where do you start?
With an idea at the pub where your mate says "you're full of crap" and so you spend weeks, months or even years to keep your dignity
I've wondered that too for a while. Apparently you need to start off by reading (booking up) all the relevant stuff that has been discovered already and the various methods that have been used/papers that have been published. Then you probably start by working on a smaller problem within one of the already established ideas. I don't think one would just immediately have a groundbreaking idea out of nowhere.
Beer is powerful
JiaMing Lim , In my experience, throw things at the wall, see what sticks, read what other people have tried, try those yourself, read what people have tried for vaguely related problems, try those too. Repeat the above until something seems to not be there when it should, or be there when it shouldn't. That's the first grapple point. Keep working from that foothold until another is found, and just maybe, the climb proper can begin.
Notice a pattern. Check a lot of cases. Seems to be true? Done!
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.
Halosty Yes, this boils down to: Every number greater than 1 has two primes equidistant from it. Given that the Goldbach conjecture has been tested extensively, this is also true as far as that's been tested. it's an interesting insight/way of restating the problem.
I also got to the "all numbers have a pair of primes equidistant" stage and thought I was making great progress. Nearly 40 years later and I am no further on :(
Might that be due to the symmetry of adding two numbers, such as when Gauss summed the numbers from 1 to 100? Each prime is odd and either one more or one less than an even number. When you sum two primes, the difference from an even number is either 0, +2 or -2. So one gets into the definition of primes and multiplication by 2 in terms of addition.The density of primes is related to the increased number of possible permutations of primes created by adding 1 to the highest composite number formed by all of the previous primes. (2x2), (2x3), (2x5), (2^2 x 3),(2^4), (2x3^2).
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....
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?
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.
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.
Goldbach’s conjecture isn’t of any use in finding large primes.
If you take a googolplex it obviously can be written as (googolplex-97) + 97. It’s easy to show 97 is prime but there’s no easy way to show (googolplex-97) is prime.
wow, Numberphile doesn't often do proofs like this, but this is a great, clear video on the application of Probability in Number Theory
I wonder if anybody will ever prove the "Brady Conjecture": That Numberphile is the best channel on RUclips :).
This is where the text book says : "The proof is left as an exercise to the reader" 😆
I have learned more maths from Numberphile than school.
I literally spent last night trying to prove it. I didn't know I was entering a Hall of Shame.
*Sees video is 9 minutes and 58 seconds long* "Numberphile being edgy"
+johnny dss
What is the significance of this?
He lost a lot of money by not making the video 2 seconds longer.
johnny dss they don't get paid extra for over 10 minutes anymore now btw
The CC at the beginning says "(Speaking Latin)", but the main part of the text is German. The fact that the technical terms are Latin borrowings doesn't alter the underlying basic language.
Apparently a Filipino mathematics teacher claimed to have solved this problem
Which is very embarrassing. This only reinforces the stereotype na bobo ang mga Pinoy.
Edit: I mean we have the PISA Studies, but it is what it is.
Huge Thank you old man
is there any relation between discrete logarithm and integer factorization?
I like prof eisenbud's voice. he's a great teacher.
Alicia Costello he sounds like he's constantly doing a mediocre dirty harry impression
His german is lit.
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?
Thanks. Never knew about this conjecture and it is pretty neato! Does this also apply to other divisors like 3, 4, 5, etc?
If the divisor is even then it's just a special case of Goldbach's conjecture. Who knows - there might be some special case that's more readily provable than the general case, but I don't know of it. If the divisor is odd then it's false. Multiples of an odd number will include the cases where the multiplier is also odd, giving an odd result, so to be the sum of two primes one of the primes would have to be 2. Whatever your divisor, eventually the primes will get too far apart for all odd multiples of it to be two greater than a prime.
Such a fascinating conjecture.
Bonjour,
Pour ceux que ça intéresse, je propose une résolution de la conjecture de Goldbach publiée sur RUclips 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
one of the most important video of numberphile
You missed 5+5...
Nice touch showing it for the numbers of his birth and death dates!
oh wow german has changed since this has been written
Half the German sentence is actually in Latin - so it's almost not understandable for Germans as well. ;)
"sey"
The picture was of Euler, are you sure it wasn't Dutch?
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
The first thing u should do when watching a numberphile video is to thumbs up
Anyone else notice that he puts the numbers of Goldbach’s birthday in a pair of primes?
Sino nandito dahil kay danny calcaben? Potcha mapapa aral ako ng wala sa oras😭
“I don’t know if there’s any lower bound known or guessed.”
If there was a lower bound known on the number of ways to express an even number as the sum a two primes, that would constitute a proof of the conjecture.
il suffit d'utiliser la fonction asymptotique pour toute limite N > = 3 qui donne une estimation du nombre de couples p+q = 2N : pi(N) qui est le nombre de nombre premiers
You do have a really relaxing voice...! :D
This is proof that geniuses have a healthy sense of humor
I have an elegant proof for Goldbach Conjecture but I’m suffering from lack of space in the comment section
He seems like one of the most pleasant people.
I wanna see Numberphile sit a GCSE maths paper
For easy visualization related to prime distro: GB - EVERY 'number' is the average of two primes.
And this, guys, is the voice you get after a life of shouting on poor students...
So you know him personally?
Following my estimation the probability of the Goldbach conjecture being true nowadays is:
The infinite product from m=4*10^8 to infinite of [1-(1-log(m/2)/(log(2m)*log^2(m))^m]
But even Wolfram gets stack estimating this product
I love how taboo it is to try to discover a solution :P
The sound of the marker on the paper gives me shivers.