The Simplest Thing We Can't Prove

Goldbach's Conjecture states that every even whole number greater than 2 is the sum of two prime numbers. So, 28 is 11 + 17... 62 is 43 + 19... and it goes up. WAY up.
We've calculated every value up to 4 x 10^18, so it's got to be provable, right? WRONG. One guy tried it by hand; now we crunch the numbers with supercomputers and we're still not there. Confirming the Goldbach Conjecture's veracity has been just out of reach since Euler and Goldbach first communicated about it in 1742, and although we don't have any information or analysis to disprove it, we can't say with absolute certainty that Goldbach's Conjecture holds for every even whole number through infinity.
#shorts

[@karenkhudaverdyan9197]

Prime numbers are literally the most mysterious thing in math

[@snowsanta7]

I'd say the inclusion of imaginary numbers in physics and math is pretty up there

[@RGC_animation]

The SIMPLEST most mysterious thing in matg

[@Matt23488]

They are like the abstract building blocks of all of mathematics, but there is no way to write a definition to give you an arbitrary prime number.

[@maksymisaiev1828]

@@patfre what is the problem with complex numbers? The point that you can't pinpoint imaginary part to exact physical instance? Quantum physics use a lot of imaginary numbers, so we can indirectly describe complex number in real world. Also it is good in description some physical objects, which you cannot see on the real part. Mandelbrot set is built in complex system, but it is related to the real fractals. Feigenbaum constants relates to the real instances, but in complex plane it is related to Mandelbrot set. So yeah, complex number is investigated much better than prime number.

[@skallos_]

I say the sporadic finite simple groups are more mysterious.

[@fluffydragon1525]

Godammit it’s another one of those conjectures that we can’t prove simply because we don’t have a pattern for primes

[@kami_fps]

@@cameronbigley7483 It might be proven in our lifetime with quantum computing.

[@akirakato1293]

@@kami_fps why is that? Do you mean to find a zero that is not on the critical line? Cuz that hasn’t worked out well for decades. Also Riemann hypothesis is already assumed to be true. I’m not sure how quantum computer can help with Riemann hypothesis if you could help me understand.

[@Gqtor]

@@kami_fps Unless the quantum computer can come up with a proof for why it's true (if so, that would be terrifyingly awesome), it wouldn't be able to do any more than classical computers. Unless testing every number until infinity was possible, there's no point.

[@akirakato1293]

@@Gqtor I guess he was throwing buzzwords like a clueless journalist

[@namankumar1677]

@@cameronbigley7483 The Riemann Hypothesis in its present form does not imply any results about cybersecurity whatsoever. A proof or disproof is likely to result in new ideas related to prime numbers which may include better factorisation methods but the computational problem of prime factorisation would still remain. What's important is that there is no polynomial-time prime factorisation algorithm, and even then it would only affect a small amount of cryptosystems (a polynomial-time algorithm still doesn't mean fast, it just means not exponentially slow). We have already begun shifting to more secure cryptosystems than RSA and results about post-quantum cryptography have been staple for decades. Sure, the ideas covered in a proof of Riemann will have huge ramifications for analytic number theory as we know it, but it will have negligible impact on cryptography, which contrary to popular opinion relies on much stronger and realistic assumptions than the average person suspects.

[@zaydabbas1609]

(I think) the problem is we can't define prime numbers like we can with other numbers, for example we know an even number is 2n and an odd is 2n+1 where n is a whole number, so we can do those proofs algebraically. Not so much for primes.

[@robins437]

True but there is also the 3*n+1 thing that hasn't been proven, which is not connected to primes (i think). But in general I stand your point

[@somerandomweeb4836]

You're talking about the collatz conjecture Yeah you're kinda right, the problem is not algebra itself though but more so the fact that those 2 simple rules can be applied 1 after the other and literally generate an infinite number of equations. Since we can't just solve infinite equations we have to find another way

[@luciengrondin5802]

Do we even know if there is an algebraic way to sort primes? Somehow I doubt there is.

[@illused]

Does one ever truly come out of grade school or does the information just bounce around seeking application?

[@dqrksun]

I'll try to define prime numbers. Heres how: let all the prime numbers be a set, call it p. Let non prime positive integers be a set call it q (n*m=q, n and m ∈ positive integers). When p union q it is equal to the set of positive integers and when p intersect q it is equal to 0. Symbolically: n*m∈q , {n,m}∈ℤ^+ . p∪q=ℤ^+ , p∩q={∅}

[@ValentineC137]

1 billion seconds is 32 years, so that guy wasn’t very good at using pencils lol

[@yudoball]

Maybe he used 3 pencils simultaneously

[@olyseth]

Maybe he had anger issues

[@Tommuli_Haudankaivaja]

Perhaps he ate pencils in frustration.

[@moderndayvampire1469]

never said he used the pencils to write.

[@joshuakevinserdan9331]

​@@Tommuli_HaudankaivajaIf you can eat a pencil in a second... I'd give you a billion pencil a second for 32 years

[@LazlosPlane]

Mathemeticians discover yet ANOTHER cure for insomnia.

[@X8hnc]

i was expecting 3x+1

[@cadespaulding3837]

same

[@itismethatguy]

Same

[@youngmathematician9154]

same

[@hotpotato5587]

Collatz Conjecture

[@Nateguana]

same

[@1oddentity]

What stimulant is Kevin on? I need some of that

[@chrismanuel9768]

ADHD and excitement

[@sir_fapalot]

He's smoking math

[@_the_Necromancer]

​@@sir_fapalot beat me to it!!! FUARK

[@neiljohnson7914]

Math, my man. Pure math.

[@stolensentience]

Prime Mathamphetamine

[@riddlersroad3802]

This dude is succeeding in making me excited for math where school failed

[@havardmj]

Selection bias

[@Austin-hm6qq]

Without your school teachings you wouldn’t understand the fun stuff on KZbin. School didn’t fail

[@riddlersroad3802]

@@Austin-hm6qq i literally had to teach myself algebra because my teachers bullied me

[@giovannicabrini8457]

​@@Austin-hm6qq Aaaaand on this episode of "shut up with your entitlement over things you don't know":

[@Austin-hm6qq]

@@giovannicabrini8457I'm entitled because you didn't pay attention in school? bet

[@boium.]

0:11 that's not Goldbach. That's Hermann Grassmann.

[@boium.]

How can you even have a photograph of Goldbach if the camera wasn't even invented yet. You said it yourself: ''He wrote to Eurler.'' Do you not even question why we don't got a photograph of Euler but do have one for Goldbach???

[@sollec9279]

@@boium. I know this reply is over year old but how did no one notice this guy replied to himself?

[@danialrafid]

​@@sollec9279 He was adding onto his original comment. Is replying to your own comment illegal?

[@sollec9279]

@@danialrafid Well if he were really adding to his comment, he could have edited his original comment. Also, I didn't say that replying to your own comment is illegal.

[@danialrafid]

@@sollec9279 Yes, he could've, but it makes no real difference. Then what's your problem with him replying to himself?

[@Mayur7Garg]

Another way to look at it is that for every number greater than 1, there exists at least one pair of prime numbers equidistant from that number. If that number itself is prime, the solution is trivial at distance of 0. For example, two prime numbers equidistant to 2 are (2, 2) at distance of 0 each. Other examples: For 4 -> (3, 5) at distance of 1. For 5 -> (5, 5) at distance of 0 and (3, 7) at distance of 2.

[@Arceaus98]

I don't think that's at all the same idea

[@pbandme24]

​@@Arceaus98 It's the same idea because the sum of those two prime numbers is 2 * the number their equidistant from. It's always (x +y) + (x - y) = 2x, where x is a whole number and y is the distance. The Goldbach Conjecture talks about even whole numbers (greater than 2), and 2x covers that.

[@Arceaus98]

@@pbandme24 That makes sense, thank you

[@LOLinsultan]

how do u mathematically prove this: "there exists at least one pair of prime numbers equidistant from that number". or is this the issue?

[@Mayur7Garg]

@@LOLinsultan What I am saying is that this is another way to look at the Goldbach conjecture. If you prove the conjecture, you prove this as well. Both are same.

[@OsirisMalkovich]

a billion pencils? Not literally _a billion_ pencils, though, right?

[@marcusscience23]

No, only a trillion lol

[@castleanthrax1833]

No. His dog ate one of them.

[@immort4730]

I doubt those pencils are the pencils you are thinking of. Pencils in geometry are families of lines or conics fixed by a set of points, usually n-1 points that define a specific singleton object.

[@mathyland4632]

One reason is so difficult is that it’s a problem bridging the properties of multiplication and addition. Primes have to do with multiplication and factorization, and we’re asking about the sums of these. Plus Number Theory is just hard.

[@conanobrien1]

What is the point of limiting yourself with 9781??

[@IVIr_Smith]

Asking the real questions here. My guess is it happens to be the largest 4 digit prime number that exists, so maybe that's why it was chosen.

[@TechN9cian01]

Makes no sense. 4 is the smallest number we can't write as two primes if one is smaller than 2. Think that's fascinating? 8 is the smallest number we can't write as two primes if one is smaller than 5. Talk about a mind blow. What a silly pointless limitation.

[@user-ro1db3xv9r]

@@TechN9cian01 Can you not write 4 as 2 + 2? I think the 9781 limit is only because people were lazy to check further because the calculations just took too long. Not sure though..

[@adamgalloy9371]

I think that is just a statement about how far mathematicians have been able to check with computer programs and there is nothing inherently "special" about these numbers. Limiting to 9781 just allows for faster searches (otherwise they would have to check a large number of primes for each number they want to test). I suppose it's also kind of interesting and counter-intuitive that you can get up to 19 digit numbers while limiting one of the primes to four digits or less.

[@Spika94]

@@TechN9cian01 I don't even know what that means.

[@sasukesuite1]

Well yeah, going to space is just geometry. Trying to numerically solve for an infinite amount of numbers is going to take a LOT longer with our current computing power lol

[@sujimayne]

Going to space is just geometry? Yeah, please don't discuss physics, engineering or math, you clearly know nothing about either subject.

[@sasukesuite1]

@@sujimayne I guess I have to give my astronautical engineering degree back to my university lol. But every orbit is a conic section, so yeah it really is just geometry.

[@shelk37]

@@sujimayne imagine trying to judge someone's entire knowledge about a subject because of a vague sentence they said

[@benjioffdsv]

@@sujimayne and what are physics, maths and engineering ? Geometry.

[@RacTac]

You can‘t prove by computing, that‘s the issue

[@kjellgunnartrimbo-forthun6052]

I remember this. For a computer class I had to write a program that would do this

[@reginaldmustardbacon5866]

Ahh classic proffs making you do stuff way over your pay grade

[@soheil5710]

​@@reginaldmustardbacon5866 Spoken like a true web-dev

[@foreverbroken98]

You finally pop into my FYP once again after years and finally, get a video of this 😂

[@gchtrivs7897]

The picture you showed is not Goldbach, it's Grassmann

[@HaydenTheEeeeeeeeevilEukaryote]

woah, that’s strange, “grassmann” brings up only the photo he used, but “goldbach” brings up like a ton of different people

[@stolensentience]

I doubt he would ever touch grass man

[@BlaxkEdits]

My god that handwriting will make the docters jealous

[@jordansean18]

This one might be easier to *disprove*, if only we can find an acceptable way to prove that these sums aren't even rare.

[@jerma984]

It will be very hard to disprove if it is true

[@youtubeisstupid1952]

@@jerma984 well if jts true you can't disprove it

[@HagenvonEitzen]

Interestingly, whether Goldbach is true or false *may* even depend on what model of the natural numbers you are talking about. Perhaps even more surprisingly, *if* it is the case that the truth of Goldbach depends on the model of natural numbers, then it is actually *true* for "the" natural numbers, but *cannot* be proved with the standard proof methods for theorems about natural numbers. D'oh

[@Brien831]

@@HagenvonEitzen I am not sure, wahr a different model of natural numbers would be

[@danielyuan9862]

​@@HagenvonEitzenWho said that? The even natural numbers and prime numbers is well-defined, and this definition either creates an even number that is impossible to create with the sum of two primes, or not.

[@JediWreith]

This intuitively feels related to the fibonacci sequence. I don't know what to do with that idea, but it's the first thing I thought.

[@uforob5601]

When i read the title I thought it was Goldbach Conjecture, so maybe it's really simplest thing we cannot prove (or disprove)

[@ComDenox]

This is one of those theorems for which would be very easy to prove it's false (just find one single number for which it doesn't work), but it's very probably true, so you actually can't.

[@paulborst4724]

You're right on multiple levels. Easier to prove something false than true and the conjecture sounds reasonable two odd prime numbers summed are going to give an even value. Primes are infinite ... so it's reasonable to assume all evens would be countably covered due to the fact that primes grow faster than evens, thus evens could never overcome the primes which would be required to create a falsicity.

[@isaacbruner65]

Well just because something is seemingly impossible to falsify doesn't mean it can't be proven true. Lots of things have been proven in math that nobody ever thought could be. You just have to think outside the box.

[@dontreadmyprofilepicture.5418]

Maybe the easier approach would be to prove Riemann's hypothesis first.

[@shockbladezed2352]

Furthermore: for every natural number n>1, every multiple of n, greater than it, can be expressed as the sum of n primes.

[@LastTalon]

What about the Collatz conjecture?

[@codycast]

What about your mom

[@DrSardonicus]

‘Surprise anal’ camera angle. Well done, Kevin. You’re a filmmaker.

[@rmt3589]

If it's probably true, assume it's true until it's disproven.

[@shanggosteen9804]

"We dont know if aliens exist, they most likely do, so lets assume they exist until proven otherwise." You see, thats a sort of fallacy in logic. If you provide a claim or any sort of evidence, you have the burden of proof on your shoulders, meaning you need to prove it or else it isnt considered legitimate. Thats why its a conjecture, not a theorem. We cant assume something is true based on intuition and not from concrete evidence. But specifically with the goldbach conjecture, the most interesting about it is the proof for the problem, assume its simply true wont change anything in mathematics.

[@codyx8273]

That was a very specific restriction on that huge number.

[@drmadjdsadjadi]

But we can disprove it with one counterexample. Still have not found a counterexample but it could still be out there. We just don’t know (and might never know because if brute force is the only way to disprove it, it would be impossible to prove and the number that will disprove it could always be so large that it is always bigger than any we have been able or would be able to try.

[@TheAcidicMolotov]

You wrote nonsense. Good job!

[@TheAcidicMolotov]

@@wibbuffey8485 it makes sense but it is pointless to write since he is just writing definitions

[@bm-br3go]

Heuristics show that the goldbach conjecture is very likely true. There's a somewhat naive probabilistic argument which concludes that the average number of ways a given even integer can be written as the sum of two primes increases without bound as the integers get large. Even though it's a bit inaccurate, empirically it seems to hold pretty well.

[@reynoldskynaston9529]

I’ve actually did a study on the goldbach conjecture for one of my classes in college. Didn’t find a proof though…

[@kami_fps]

Have you tried all the numbers till 100,000 maybe that will help?

[@reynoldskynaston9529]

@@kami_fps numbers have been tested much further than 100,000. The amount officially tested is actually 4,000,000,000,000,000,000. Also as the numbers get bigger it takes longer to test. I did find some interesting patterns but no proof haha.

[@TheAcidicMolotov]

Mans wrote a paper on someone elses work

[@reynoldskynaston9529]

@@TheAcidicMolotov isn’t that what most research papers are?

[@TheAcidicMolotov]

@@reynoldskynaston9529 not math research papers

[@beefykenny]

His camera angle reminds me of Armin pinned by Mikasa on the table.

[@wolfmanhcc]

Numbers that large weren't even comprehensible back then.

[@EpoxyCircus]

Prime content ❗️‼️

[@strings1984]

Primes proves infinity to our numbers, but it also makes me feel like we are doing numbers wrong...

[@bm-br3go]

Primes prove infinity?? What does that mean?

[@findichwitzig1118]

nice video man

[@rubiks6]

As a math hobbyist, I think this is hilarious.

[@frenchertoast]

The colatz conjuncture is even simpler, if you'll tell a five year old about the goldbach conjuncture- he'd ask you what's a prime. If you'd tell him about the colatz conjuncture- he'll immediately try playing with the numbers.

[@kevindavidson8281]

Absolutely vile of you to not say what the conjecture is

[@daveinacave]

Here’s the thing: prime numbers MUST be odd- by definition they can’t be dovisible by 2, which even numbers are. As such, EVERY even number is the sun of two odd numbers. THAT part is easy- it’s the idea that who of those numbers can be prime that’s the problem. So our head accepts what feels like 90-95% of the theory easily, which makes not being able to 100% prove it so frustrating.

[@brandond2768]

2 is prime

[@mandi8345]

@@brandond2768 The conjecture expressly omits 2, likely because it is A) even, and yet B) prime, and C) 1 is neither prime nor composite thus falling into a whole other circlejerk of maths weirdness.

[@mandi8345]

I had to scroll FAR too far down the circlejerk of 'ERHMUHGURD PRIMES ARE SO MYSTERIOUS' vitriol to finally find someone who remembers their 3rd grade maths class involving the relationships of adding evens and odds. I remember this....and Ive done drugs, lots of drugs. What is everyone elses 'oh no i heard about someone saying the word lead I HAVE CANCER OF THE AUTISM NOW!!!' excuse for wasting all that STEM funding while cosplaying for the geek chic craze instead of ... actually learning something ... possibly ... le gasp ... getting smarter as more of humanities knowledge has become more accessible than ever? Friggin posers, man......

[@AaronCross760]

it's like someones holding a gun to his back 'do smart stuff'

[@SerifSansSerif]

This makes sense in a way. Any number can be represented as the sum of any number and a corresponding second number. So every number can be expressed as the sum of a prime number and another number. All primes are odd, so if your total is odd, the other number summed must be even and thus not prime. So now the hardest part is proving that the second number in the conjecture always has an option that is also prime.

[@chrismanuel9768]

Given that 2, 3, and 5 are primes, there becomes very few POSSIBILITIES that an even number could exist that wouldn't fit the bill, because there are incredibly small primes to bridge the gap.

[@YaamFel]

​@@chrismanuel9768that makes no sense. Primes get sparser as numbers get larger, so having small primes to "fill the gap" does not help at all

[@MrDjmaidi]

I miss the old vsauce… very much.

[@jordanburkert6208]

Wdym?

[@jan-lukas]

I like the collatz conjecture (3n+1) more but still nice

[@CORKPARK-]

when you put your head against the table,the way you see the cameras is the way I see bullies😭😭😭

[@zropper4397]

can we do 3 like that

[@colinallcars5239]

What's the point of the last info about 3,325,581,etc. ? Why is that info relevant?

[@heatshield]

I guess that's just as far as we've checked. Someone probably ran out of lab time on the big computer.

[@TheJaredtheJaredlong]

@@heatshield It's definitely an exponential problem. The higher number you check, the more primes there are that need to be analyzed. At some point there's so many possible combinations of primes there's not enough time in the universe to check them all.

[@danielyuan9862]

​@@TheJaredtheJaredlongThe number of primes you need to search only increases approximately logarithmicly

[@TheOrigamiGenius]

Primes numbers: *Gets all the fame* Composite numbers: What about me? I guess I'm a bunch of primes :(

[@hellydpsin]

Try playing with the percentages of prime numbers in the set

[@Runeite51]

bro pls leave a second at the end of the vid uncovered so i can pause to read or screenshot it

[@gavinrock2452]

My brain hurts

[@RGC_animation]

You could also write a lot of Odd numbers with 2 primes.

[@mcnole25]

Hint: Use the number 2 on one of the primes

[@XenicTheDurr]

All primes except 2 are odd, and 2 odds always sum to an even number, so this would only work for twin primes, where the smaller prime plus 2 equals the larger prime.

[@refrashed]

@@XenicTheDurr That is also true, but OP just said odd numbers, not primes. Any non-prime odd number that can be made from primes =2+p.

[@vibaj16]

only odd numbers that are 2 above a prime

[@harshitrawat811]

did anybody else see that the board literally faded as the video ended(except the heading)

[@davidhim3527]

That's when i look at it and say "Ehhh... Good enough lol"

[@georgegeorgia3856]

I would dedicate my lifetime trying to solve this isue aslong as it is relevant or in any way helpful to mankind.

[@TheAcidicMolotov]

I dont think you would either way. Plus you could never know it was useless.

[@HagenvonEitzen]

Is it relevant and helpful? Well, once proved (or disproved), this very video ought to be taken down, so ...

[@TheAcidicMolotov]

@@HagenvonEitzen nah, we should just burn all the wrong papers of the past? No need to take the video down bc we could not at this time prove it

[@thesphider8298]

👽: "such a primitive species! That's preschool math"

[@tufigeat1781]

Our maths teacher tried to make our test harder when explaining how to prove equations. Guess what…

[@non-binarynerd08]

Sending Captain Kirk to space is more important lol

[@nathan1sixteen]

The fact we made it to over 3 quintillion before running into problems shows that some nerds have waaayyy too much time on their hands

[@think3237]

no it just shows we have computers now

[@bertberw8653]

But it was a computer....

[@danielyuan9862]

And it's nerds being nerds.

[@martinpat94]

I mean I feel like after getting to a number that high for most basic calculations smaller than like a million you could probably assume it to be true. Also what exactly would this help with when it comes to mathematics?

[@TheAcidicMolotov]

Assumptions were not used to send people to space. What do you think mathematics is?

[@SomethingSmellsMichy]

Maybe it can be used as a method to find prime numbers

[@gulgaffel]

That's not how mathematics is done. This conjecture probably doesnt help with much stuff. For alot of conjectures the conjecture itself isnt really that important, however the methods that are being developed to prove or falsify a conjecture is very important. It's a bit like the problems one solves when practicing maths, the problem itself is completely pointless, it's all about what's being learned from doing it. There are of course conjectures that are of great importance. I just dont think this is one of them.

[@Errenium]

math doesn't care about what humans find useful. it was here long before us, we get lost exploring it now, and it will be here long after there is no trace humanity ever existed.

[@gulgaffel]

@@Errenium Disagree, maths isnt explored, its defined. We create maths, it wasn't here before us. Sure 1+1=2 is true without our definitions but there is nothing intrinsic in the universe that say that 1 isnt prime, we just chose to define primes so that it wasn't.

[@matthewsanders6499]

Never knew Euler was Professor Quirrell

[@marlondowney4033]

I remember when I thought about the goldbach conjecture. I was like 12 was working on a proof with primes and my math teacher told me what I was working on was called the goldbach conjecture and that greater men than me have tried. I did about two years and then gave up.

[@ethicalcollective]

Congrats to everyone Who is early and who found this comment💕

[@_Insert_Username]

Yeah. I am so early

[@nothosaur]

What about sporadic finite simple groups? Those are pretty mysterious.

[@nekogod]

Feels like it would be related to the Fundamental Theorem of Arithmetic.

[@macnolds4145]

It's much, much harder to "unravel" the multiplicative properties of numbers than it is unravel the additive ones. That's because every number is either prime or a bunch of primes multiplied together (i.e. Fundamental Thm. of Arithmetic). When we deconstruct numbers by addition, we have a whole bunch of additive partitions, and none of these partitions "uniquely" identify numbers. For example, 4=2+2=3+1=1+1+1+1. None of these best capture the "essence" or uniqueness of 4. But 4, as a product of primes, is uniquely 2x2. That's it's "unique essence" (i.e. prime decomposition).

[@S8EdgyVA]

The worst part is that since you can any odd number is 2 more than another odd number, and every even number is 3 more than an odd number, that means any whole number can be represented as a sum of 3 primes

[@frankied.2828]

THATS NOT A PICTURE OF GOLDBACH, THAT FIRST PICTURE WAS HERMANN GRASSMAN

[@codeouter]

Yes, because even numbers are divisible by two, so YES😂

[@saltedslug7954]

The only good trend that came from TikTok is the speed up of shorts

[@RoderickEtheria]

Seems like we should be able to prove it by distance between primes. If the frequency of primes between p and 2p consistently increases, it should be more and more likely to be able to find two primes from subset p, which included each prime less than or equal to p, such that they sum to each even number upto 2p. If you then include the p+2p prime candidates to cover the evens up to 2p, the probability of finding an even number up to 2p that isn't covered becomes much less.

[@mandi8345]

Okay, now write the program and prove it....Ill call the Nobel committee and tell them to start shining.....

[@TimPortantno]

Wait, so what would it take to calculate for primes greater than 9,781?

[@DudeMcAwesome]

Its like a carnival barker of math

[@DanielleStarks]

When I was in the 4th grade I figured out the Goldbach conjecture on accident by adding prime numbers over and over again cuz it was fun at the time, and I thought I had discovered something new for math lmao😭😭😭

[@menteausenteprops]

For some reason I always get captions automatically in your shorts and it's very anoying to turn off, is it something yo do or my account?

[@Lemurai]

These are one of the topics in mathematics that even mathematicians ignore lol!

[@jamesharmon4994]

This video is 2 years old. Has the "Smallest even number that isn't a sum of two prime numbers" changed? If not, what is the current condition imposed on that statement? Two years ago, it was "if one of the two primes is less than 9,781."

[@earlgrey3519]

It still works long enough for me! My personal use will not go beyond that number, so i am SET😂

[@kreuner11]

Sounds a lot like trying to prove the Collatz conjecture

[@danielkrcmar5395]

I've a feeling I know a guy who actually proved this but they used another equation that hasn't been solved to do it so they wouldn't allow it.

[@lightknightgames]

For a number to break the goldbach conjecture, each previous number will be need to be sum-able. Other than 2 For a number to be 1 larger than another, and be un-sum-able, with the constraints, then it is required to occur at a point where no prime number appears for greater than half of it's value. The only place this can occur is at 2. This is because any previous prime number +1 and -1 can be made in the goldbach conjecture, otherwise that number would be the answer, continue this logic forever and we get to 2

[@janpapai9205]

Germans: Goldbach Americans: gouldbaak

[@ucantSQ]

Wait wait wait We didn't REALLY send William Shatner to space did we?

[@reddcube]

That seems like an awfully small prime for a counter example limit.

[@suddenllybah]

... This involves mapping all prime numbers. No wonder we can't prove it.

[@Jamie_Pritchard]

I'd be curious to know if this has any real world application.

[@bloopsphere9291]

Meanwhile, Lu Zhou from Scholar's Advanced Technological System: Casually solves the Goldbach Conjecture in front of a bunch of people

[@Al_Pal111]

I see, a fellow novel reader. Just reading that story made me feel so much smarter until I search up half the things he solved. I don’t even know where to start with the navier stokes equation, but somehow it was always satisfying when he solved and you understand nothing except he used his cool L-Manifold thingo I think it was called.

[@trivikram4962]

When did fantano start teaching maths

[@Lolo5Boss]

What about 4 ? It can’t be express as 2 prime numbers because the only prime number before is 3 (one is not a prime number because it only has one number that divides it) and 3+3 is not equal to 4

[@nindohubermichael1354]

2 is also a prime number and 2 + 2 = 4

[@trappedcosmos]

2+2

[@Sentient.A.I.]

We can't disprove it either.

[@cubing7276]

We also proved the problem to 1+2 ie all even numbers can be expressed as the sum of a prime number and a number with 2 prime factors

[@buttonmasherbaberkins7490]

Can you make a video on what it would look like/ take to prove something like this?

[@JessePoage]

There are a ton of great videos on the subject, search for Polynomial, non polynomial, and NP-Hard questions

[@mandi8345]

It has already been answered. Its 42, obviously.

[@samuellerbet7990]

It would have been interesting to mention that the validity of Goldbach's conjecture is “known” for most even numbers in that the density of the set of even numbers that cannot be written as p+q with p and q prime is zero (in a sense as rigorous as can be expected of mathematics, almost no even number number disproves the Goldbach conjecture). In fact, there are explicit (asymptotic) bounds on the number of even integers less than N that disprove the Goldbach conjecture-this is work of Montgomery and Vaughan in the seventies if Wikipedia is to be believed. Of course, this is in no satisfying sense an answer to the question since even with Montgomery and Vaughan's result, there could still be infinitely many counterexamples while the conjecture predicts that there are none.

[@TypingHazard]

Isn't this just another expression of the Sieve of Erathosthenes though? It seems like it's implicit that if you're eliminating values which are divisible by other primes you're collating a set of numbers that are composed of primes

[@maroonmonkey7475]

Lol jus thanks for not being another “digital creator” twerkin on my screen lol… Good Content🔥🤙

[@imonkalyanbarua]

Is it necessary to have two distinct prime numbers? For instance 4 is an even number greater than 2 and can be written as only 2 + 2 and similarly 6 can be written only as 3 + 3. Are thse the only solutions?

[@martamielnaz2762]

I already thinked that when I was a kid, now I know I'm dumb as quack

[@user-fp1hw1yr7x]

you can, next question. you think I'm wrong? prove it.

[@polymath437]

that picture is not Goldbach it is Herman Grassman

[@Mikejones011990]

Have y'all tried asking Wolfram Alpha? Or ChatGPT?

[@jensenb6]

I think the better question is if you can disprove it

[@bakugou216]

I was too dum to understand 😅