Goldbach Conjecture - Numberphile

Professor David Eisenbud on the famed Goldbach Conjecture.
More links & stuff in full description below ↓↓↓
Catch David on the Numberphile podcast: • A Proof in the Drawer ...
Extra footage from this interview: • Goldbach Conjecture (e...
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Prime Number Theorem: • Primes are like Weeds ...
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Professor Eisenbud is director at MSRI... See some of his favourite Numberphile videos: • Director's Cut on Numb...
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[@numberphile]

Extra footage from this interview is here: kzbin.info/www/bejne/bXWQin6GgryIgqM New Numberphile buttons/badges and a Parker Square Mug: store.dftba.com/collections/numberphile

[@intelligentshitpastinginc]

Numberphile could you do sublime numbers?

[@intelligentshitpastinginc]

we only know of 2 of them

[@htmlguy88]

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.)

[@FisicoNuclearCuantico]

+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.

[@FisicoNuclearCuantico]

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.

[@iAmTheSquidThing]

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

[@devrim-oguz]

"MOSTLY"

[@effectz_end]

AAAAND, 2

[@Freedom-js4th]

And 2 is an even integer that can’t be written as a sum of 2 primes.

[@effectz_end]

Yeah

[@pulatpulet7202]

yeah, because 2 its a prime number but also an even one dumbass

[@whiz8569]

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?"

[@zerosubs5422]

whiz 85 😂😂

[@arpitdas4263]

Yo that is pretty horrifying

[@ultraviolet.catastrophe]

Haha nice 💯

[@aktosweden]

You look up, realize that you are 47 and probably shouldn't be living in your parent's basement any longer.

[@tipitossj]

are you winning son?

[@StarryNightGazing]

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

[@LucasRodmo]

Stargazer hahahahaha lol

[@CerealGirl]

Stargazer same

[@youtubeforme7735]

I'm not a native english speaker so it took me some time to understant it's german.

[@lesliematynia9484]

Stargazer Yes!

[@chriswilson1853]

It looks like some weird cross between Latin and German to me, not that I can speak either!

[@srinivasaramanujan5209]

Hang on a second, I've got this.

[@fossilfighters101]

+

[@TheRealEvab]

"hold my beer"

[@astherphoenix9648]

Srinivasa Ramanujan jokes apart, we need people of that calibre to crack down stuff like this

[@axemenace6637]

Asther Phoenix It truly is a shame that Ramanujan died young. With some formal training, he could've rivaled even Euler himself.

[@isthattrue]

So happy to see you are still alive! I thought you died, lol! :D

[@michedelarue2872]

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

[@snepNL]

Miche Delarue 9:58

[@snepNL]

Miche Delarue this is weird. before i click the vid it says 9:59. when im watching it says 9:58

[@user-uu5fc5ek7o]

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

[@E1craZ4life]

I posted a video that is exactly 3 minutes and 2 seconds long, and sometimes it rings up as 3 minutes and 3 seconds.

[@markinnes4264]

It's not the length...it's the substance.

[@JG-zs8tr]

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

[@alejotassile6441]

Yes

[@icheckedavailability]

He definitely thinks about it while taking a dump

[@Liliou]

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.

[@michaelbauers8800]

He's like the Bob Ross of math? :) Except usually mistakes in math remain mistakes, and not happy accidents

[@NousSpeak]

Yeah, he’s got this really cal in chill avuncular vibe.

[@brandonthesteele]

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!"

[@DreckbobBratpfanne]

This is the same with the Riemann hypothesis, some may think you're crazy for trying, it can even destroy your reputation sometimes.

[@robertruschak7083]

Somebody solved the mystery, while they were high 🍀 marijuana 🍀

[@pe3akpe3et99]

marinujan.

[@jingalls9142]

@@pe3akpe3et99 that was a golden comment lol

[@JohannaMueller57]

🎵 _i was about to prove the conjecture.. but then i got hiiigh_

[@mikeh3035]

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

[@Nothing_serious]

Mike H Once my friend asked me what bread I'd like to eat, I said "I want Riemann and also a beer man."

[@Hootkins.]

It does when the German pronunciation of "ch" as in bach is very similar to the English pronunciation of "ck".

[@huawafabe]

except it isn't similar at all

[@1959Edsel]

The ship's diesel engine was making a loud squeaking noise so I called in the Euler to fix it.

[@badmanjones179]

oh yeah? prove it

[@roderickwhitehead]

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.

[@Galundor01]

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

[@adymode]

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

[@lornenix2243]

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

[@jacobadams8757]

😂😂Underrated comment

[@Robinsonero]

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

[@azaas]

Uncle Peter and Goldbach's Conjecture

[@Gooberpatrol66]

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

[@kevingil1817]

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

[@AgglomeratiProduzioni]

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

[@numberphile]

Catch David on the Numberphile podcast: kzbin.info/www/bejne/b6qUc3qso7msh6M

[@jazzsoul69]

his voice talking about math is the most relaxing thing

[@mirrimiau]

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

[@dreamscapeai7]

These conjecture videos are really fascinating. Nice work numberphile.

[@mosbate]

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.

[@MrAkashvj96]

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

[@MuffinsAPlenty]

I'm certain that he's quite busy, being the director of MSRI and all.

[@MrAkashvj96]

Haha fair enough. He is brilliant though.

[@daryladriano3435]

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.

[@sebastianportalatin5658]

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

[@nordicexile7378]

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

[@megamutant4539]

Nordic Exile 1+1=2 lol

[@NetAndyCz]

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.

[@akulsharma3164]

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

[@molkabenmarzouk6502]

Akul Sharma Congrats! How exactly?

[@johnox2226]

Molka Ben It just did

[@akulsharma3164]

there was a question as to how many conjecture a student knows and how you derive it!

[@catradummy_ytp]

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)

[@treelight1707]

Why are you using Arabic numerals until now butthead?

[@manueldelrio7147]

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

[@Eyes_On_America]

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

[@renatoherren4217]

It may be even qute, the very highest form of cuteness. 😁😁

[@bensonzhang7331]

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

[@guardingdark2860]

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 :)

[@MathematicsClasses7004]

Hi

[@KaisarasAR]

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

[@JohannaMueller57]

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

[@casacara]

If it weren’t for those who tried to build on the shoulders of giants, we’d never get anywhere

[@just_a_random_person9910]

@@casacara true bro without our prediseser's rigourus maths we would ve no where

[@MuffinsAPlenty]

Euler was certainly a brilliant mathematician, but Euler had a tiny sliver of the mathematical machinery we have today. There are, undoubtedly, many problems Euler couldn't solve that undergraduate math majors today could solve. The difference between those problems and Goldbach's conjecture is that those other problems have already been solved by newer mathematical machinery, whereas Goldbach's conjecture has not. So I don't think it's incredibly optimistic to think that someone today could solve a problem that Euler couldn't. Any time a new mathematical idea or tool is developed, it could be the spark of inspiration or the missing piece to approach a solution. Eh, on second thought, I think the general sentiment I described in the above paragraph is rather optimistic after all :P

[@mberg1974]

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

[@thedoctorate]

Thank you Prof. Eisenbud.

[@Gorvinhagen]

David has the most soothing voice on earth.

[@ritz9243]

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.

[@questafinia6980]

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

[@grasianofau8771]

Incomplete proof

[@StreuB1]

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.

[@adiginist]

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

[@osamaghaedy1869]

Your videos taught me more than university

[@sansamman4619]

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

[@phant0mknlght869]

san kitty "You"re"

[@heliocentric1756]

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 !

[@skhuksle]

You can even set the prime number to three!

[@Darker7]

1 is not a prime, skhuksle :Ü™

[@skhuksle]

yep, and so what?

[@ezioauditore4944]

@@Darker7 Yes it is. One and two are both primes.

[@alexanderjnaazeer]

@@ezioauditore4944 1 is definitely not a prime...

[@cristiandelvillar3121]

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

[@sergejnekrasov7688]

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!

[@MarkWaner]

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

[@Joker9586]

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.

[@MrPABLOplay]

Pierre de Fermat I was looking for this comment xD

[@nelsonemerson6690]

And now here it is again. This is getting old.

[@badmanjones179]

so is pierre

[@silphaertheperson7638]

badman jones - Combat moi.

[@silphaertheperson7638]

Pierre de Fermat - Imposteur!

[@freewilliam93]

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....

[@olbluelips]

Such a fascinating conjecture.

[@anthonycannet1305]

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?

[@EmilMacko]

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

[@johnvonhorn2942]

if there are "n" firsts then how many of them will actually be not first? Let's call that The Kingbach conjecture.

[@kendram90]

Define x.

[@Padarom]

between n-1 and n.

[@nelsonemerson6690]

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."

[@poissonsumac7922]

Emil Macko Completely unrelated to math, but by any chance, are you the guy who created Five nights at Candy's?

[@Seth4All]

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

[@na-ve9cp]

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

[@jumpander]

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

[@jiaming5269]

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

[@Lord_Hendy]

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

[@alephnull4044]

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.

[@Lord_Hendy]

Beer is powerful

[@timh.6872]

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.

[@eac-ox2ly]

Notice a pattern. Check a lot of cases. Seems to be true? Done!

[@saschb]

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

[@ygalel]

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.

[@deenell9039]

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.

[@JohnSmith-nx7zj]

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.

[@andrewxc1335]

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.

[@marcelweber7813]

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?

[@95rockanglez]

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

[@Dan1elAndrade]

His german is lit.

[@EgzolinasGamer]

That miscalculation 3:25 oh boi

[@raquelalmeida9002]

Egzolinas Gamer almost thoght i was the only one to ser it

[@bb2fiddler]

Well, to be fair he did SAY it right... He just followed the wrong line.

[@davidb5205]

Thank you! It was a simple mistake but it gave me such anxiety. lol

[@highlewelt9471]

New Numberphile video with professor Eisenbud -> day made ■

[@blabby102]

I love the way that this guy says the word "Billion". Sounds a little like Mr. Burns.

[@mohna.shenas3511]

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

[@thesavantart8480]

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

[@valhar2000]

+johnny dss What is the significance of this?

[@TheLeporad]

He lost a lot of money by not making the video 2 seconds longer.

[@dbsllama6042]

johnny dss they don't get paid extra for over 10 minutes anymore now btw

[@arnoldinho.mp4]

FINALLY YOU GUYS DID IT

[@prawtism]

Really nice video and video quality

[@samvandhapathak2167]

I have learned more maths from Numberphile than school.

[@chaoslab]

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

[@digitig]

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.

[@batmite3000]

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

[@divyanandvalsan5580]

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.

[@farnazkhoshnam3748]

is there any relation between discrete logarithm and integer factorization?

[@Halosty45]

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.

[@unexpectedTrajectory]

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.

[@malcolmbryant]

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 :(

[@BlueGiant69202]

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).

[@nyroysa]

one of the most important video of numberphile

[@rubenscabral2657]

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

[@anonymoususer9837]

You missed 5+5...

[@robertnake2448]

I wanna see Numberphile sit a GCSE maths paper

[@sanjayrohra9560]

Huge Thank you old man

[@NKLStone]

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.

[@maxdebeer4626]

Bonjour, Pour ceux que ça intéresse, je propose une résolution de la conjecture de Goldbach publiée sur KZbin 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

[@mashmax98]

oh wow german has changed since this has been written

[@moatl6945]

Half the German sentence is actually in Latin - so it's almost not understandable for Germans as well. ;)

[@tysonprice5058]

"sey"

[@Tasarran]

The picture was of Euler, are you sure it wasn't Dutch?

[@thewordshifter]

I like prof eisenbud's voice. he's a great teacher.

[@TedMan55]

Alicia Costello he sounds like he's constantly doing a mediocre dirty harry impression

[@BrianSmith-jl8qn]

Loved it!

[@LesIsMoreFilms]

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

[@althaz]

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

[@RodelIturalde]

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.

[@billyrussell7789]

it’s the only even number that cannot be expressed as the sum of two primes and negative numbers are not as they have at least a third factor or -1 so they’re generally excluded

[@jacksoncapper]

I literally spent last night trying to prove it. I didn't know I was entering a Hall of Shame.

[@SOLAR_WillToWin]

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

[@jumpander]

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

[@unvergebeneid]

Dann ist dein Latein aber auch nicht von schlechten Eltern!

[@moatl6945]

Was hab' ich gerade gelacht... :)

[@jumpander]

Und mein Chinesisch? und mein Japanisch...? 中國話也很好。 俺の英語も大好きですか？ sry... Autismus... :I

[@gonzalomorislara8858]

dein Japanisch, keine Ahnung, aber dein Chinesisch sieht als es von Google Translator genommen wäre aus ( auf Deutsch du hast gesagt:" Chinesisch er (ist) sehr gut" (Zhongguó yi ta hen háo) )

[@Andriak2]

何ですか。私の日本語はちさいです。

[@vadimvladimirov868]

Referring to log base 10 and writing (in the video animation) ln instead... As far as I can remember, it is actually ln that appears in all those prime numbers concerned theorems and conjectures Otherwise, cool video! Good job! I love what Brady and Co. does on this channel!

[@staceyburchette3276]

Vadim Vladimirov Mathematicians in practice work mostly with ln and typically mean ln when they say "log" though it is technically the natural log.

[@vadimvladimirov868]

Stacey Burchette yeah, I get it. Though, he mentioned that log of a million is 6. That's why I was like "wtf?". Anyway, we can always apply change of the base)))

[@WarzSchoolchild]

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.

[@7gaia8]

And this, guys, is the voice you get after a life of shouting on poor students...

[@TykoBrian7]

So you know him personally?

[@cpt_nordbart]

goldbach is the new fermat I think.

[@6JoJo6]

“Smithers, use the amnesia ray!” If you told me he was the voice actor for me burns on the Simpsons, I would believe you

[@GuilhermePereira-ph9xy]

appalus für deine worte. Mein herz geht auf wenn du lehren.