No video :(

The Six Triperfect Numbers - Numberphile

Подписаться 4,5 млн

Просмотров 421 тыс.

50% 1

Check out Brilliant (and get 20% off their premium service): brilliant.org/... (sponsor)
More links & stuff in full description below ↓↓↓
This video features Dr James Grime - singingbanana.com
Catch James in a recent Objectivity video with Brady: • Squaring The Circle (f...
More James Grime videos on Numberphile: bit.ly/grimevideos
More videos on Perfect Numbers: bit.ly/PerfectN...
Triperfect T-Shirt...
US: teespring.com/...
EU: teespring.com/...
Discuss this video on Brady's subreddit: redd.it/8ursq4
Extra links for Brilliant...
Number Theory course: brilliant.org/...
Problem of the Week (always good fun): brilliant.org/...
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumb...
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. www.simonsfoun...
And support from Math For America - www.mathforame...
NUMBERPHILE
Website: www.numberphile...
Numberphile on Facebook: / numberphile
Numberphile tweets: / numberphile
Subscribe: bit.ly/Numberph...
Videos by Brady Haran
Patreon: / numberphile
Numberphile T-Shirts: teespring.com/...
Brady's videos subreddit: / bradyharan
Brady's latest videos across all channels: www.bradyharanb...
Sign up for (occasional) emails: eepurl.com/YdjL9

Опубликовано:

28 июн 2018

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 1 тыс.

@numberphile 6 лет назад

Triperfect T-Shirt... US: teespring.com/en-GB/triperfect-numbers EU: teespring.com/en-GB/triperfect-numbers-EU

@timeaesnyx 6 лет назад

Numberphile use semicolons to separate the numbers 😝

@victormarinho6858 6 лет назад

I found 2 sistems of formulas that describes all the primes except 2 and 3, could you help me to publish it ?

@Superman37891 6 лет назад

Gamer_ Obscuro make a blog and put it there. Maybe send it to a journal as well, and once it’s published maybe numberphile will do a video on you

@victormarinho6858 6 лет назад

This is not secure, can be stolen from me...

@Superman37891 6 лет назад

Gamer_ Obscuro I know don’t put here. I said get it in a journal or sonething

@usami_ruku 6 лет назад

It's really nice how the number of triperfect numbers is a perfect number.

@chickeyy1792 6 лет назад

Gle fakat

@schaubooyoavgrin6795 4 года назад

Its just perfect

@Ny0s 3 года назад

Thanks, I did not even notice :o

@Catman_321 3 года назад

It would be better though if all the other numbers of x-perfect numbers were a y-perfect number as well though

@dialecticalmonist3405 3 года назад

And it is also the smallest perfect number.

@SpeakShibboleth 6 лет назад

"The largest one we've found is 46 million..." That's not so bad. I could check larger numbers than that easily. "Digits long." Nevermind

@fss1704 6 лет назад

hey, depending on the calculus you want to make 46million can mean a lot...

@fss1704 6 лет назад

especially with degrees of recursion

@Elizhium 6 лет назад

I had the exact same feeling

@MrMebigfatguy 5 лет назад

Just because thats the last they found, doesn't mean they haven't looked waaaaaaaaaaaaaaaaay bigger.

@bradensorensen966 5 лет назад

People, the joke is that there is a big difference between 46,000,000 and Nx10^46,000,000

@trevorarashiro2155 6 лет назад

“And it would be really weird if there was some massive massive gap and then some tri-perfect number”. What about the sequence 1,3,tree(3)

@smiley_1000 4 года назад

I think you mean TREE(3), tree and TREE are different functions

@hewhomustnotbenamed5912 4 года назад

@@waftingcloud it's a function involving coloured nodes that grows stupidly fast. TREE(1)=1 TREE(2)=3 TREE(3)>Graham's number The exact size of TREE(3) is not known, only lower limits and that it is finite. Numberphile actually has videos on the TREE function that you can watch for an explanation of what the function does.

@ivanjones6957 4 года назад

i like trees.

@whatno5090 3 года назад

@@hewhomustnotbenamed5912 The exact size of TREE(3) is just one more than TREE(3) - 1

@bammam5988 3 года назад

To be fair, TREE is based on a totally different problem, involving different objects than integers. And my (layman) understanding is that most functions in the Fast-Growing Hierarchy have boring values for x=1 and x=2, just due to the way they are constructed, so you always expect things to get interesting starting at 3. Tri-perfect numbers, on the other hand, grow at a regular pace for a while, with 6 values that steadily grow into the billions, then they just stop indefinitely.

@someguydudeGAME 6 лет назад

I love these old school "pure" Numberphile videos where it really is just talking about some numbers. It's like fun mathematical trivia.

@whitherwhence 6 лет назад

"As for how many we should sell in each pack, how do you like the number 6?" "It's perfect"

@Rudxain 2 года назад

Hexagons are the bestagons

@maxaafbackname5562 2 месяца назад

@@Rudxainpacks of 7 cans? That can save a lot of space during transport and storage...

@Rudxain 2 месяца назад

@@maxaafbackname5562 6 around and 1 in the center? yeah!

@PC_Simo Месяц назад

The origin-story of 6-packs 👍🏻.

@PC_Simo Месяц назад

⁠@@maxaafbackname5562 @Rudxain True 💡😃.

@dmatuzo 6 лет назад

I love when James is featured in a video! He makes everything he explains sound twice as interesting

@JDLupus 6 лет назад

"We think there are infinitely many of them but we've found fifty." I love maths so much XD

@Catman_321 3 года назад

This is basically the same thing with mersenne primes though right

@Pfisiar22 3 года назад

@@Catman_321 perfect numbers and mersenne primes are linked. Each even perfect number has a mersenne prime in its factors.

@MrCyanGaming 6 лет назад

so perfect numbers are actually biperfect numbers and the closest thing we have to perfect numbers are primes. They're themselves +1 or you could just say that 1 is the only perfect number...

@tyab87 6 лет назад

CyanGaming | ᴹᶦᶰᵉᶜʳᵃᶠᵗ ⁻ ᴳᵃᵐᵉᴾᶫᵃʸ Lim(P→+inf)(P+1) = P

@SpencerTwiddy 6 лет назад

tyab87 yet for all reals, p =/= p + 1

@gastrobot 6 лет назад

No, there's exactly one perfect number: The number 1. -1 also, if negatives are allowed.

@richardlinsley-hood7149 6 лет назад

-1 is a vector, not a number. 1 'pace' in the negative direction. So the number/quantity/magnitude is still 1 :)

@vglocus 5 лет назад

Yes, this inconsistency annoyed me :)

@robotate1 6 лет назад

Fascinating! But I think there is a logic error around 5 minutes: "Either we'll find an odd perfect and therefore the list of triperfects is not complete, or the list is complete and there are no triperfects". There is still one remaining option on your truth table, there could be no odd perfects but still be more triperfects. Unless there is a proof you didn't mention that any new triperfects have to be related to an odd perfect.

@Tulanir1 5 лет назад

Thank you! I was surprised no one else mentioned this.

@angelmendez-rivera351 4 года назад

Tulanir1 Because there was little need to mention it.

@PotatoMcWhiskey 6 лет назад

Dr James Grimes has a triperfect smile :)

@PotatoMcWhiskey 6 лет назад

@thezebraherd8275 4 года назад

Bro Its cool to see you here

@fernandossmm 4 года назад

It's not him, his RU-vid channel is singingbanana

@Triantalex 9 месяцев назад

false.

@darreljones8645 6 лет назад

For the record, the prime factorizations of the six triperefect numbers: 120 = (2^3) * 3 * 5 672 = (2^4) * 3 * 7 523,776 = (2^9) * 3 * 11 * 31 459,818,240 = (2^8) * 5 * 7 * 19 * 37 * 73 1,476,304,896 = (2^13) * 3 * 11 * 43 * 127 51,001,180,160 = (2^14) * 5 * 7 * 19 * 31 * 151

@zenotfun9759 6 лет назад

The perfect number doesn't exs......

@Magnus_Deus 5 лет назад

*f o u r t y s i x m i l l i o n*

@thehiddenninja3428 5 лет назад

@@Magnus_Deus Digits long*

@anandsuralkar2947 5 лет назад

@Triantalex 9 месяцев назад

@ick567 8 месяцев назад

@vari1535 6 лет назад

Perfect numbers should be called biperfect numbers then.

@angelmendez-rivera351 4 года назад

Variety of Everything Or, better yet, tri-perfect numbers should be called bi-perfect numbers, so that way, we do not deal with the shenanigan that there would only be one mono-perfect number.

@matthijshebly 3 года назад

Or purrfect, purrrfect, purrrrfect, etc

@anawesomepet 3 года назад

@@matthijshebly 120 is a purrrfect number, but not a purrfect number. Say that.

@KasabianFan44 3 года назад

@@anawesomepet This might lead to some confusion between rhotic and non-rhotic accents lol

@lonestarr1490 2 года назад

@@anawesomepet Try to tell Isaac Arthur to say that.

@dsblocks 6 лет назад

"The largest one we've found is the most recent one. It's 40 million.." -- "sounds big" -- "...digits long."

@stibar8050 6 лет назад

5:25 "I'm glad you asked" This has to be the best moment in Numberphile history

@centralprocessingunit2564 4 года назад

after the parker square

@miloandash 6 лет назад

Yay James is my favourite person on this channel! He's always so full of energy!

@OlbaidFractalium 6 лет назад

Minimum 11-perfect number seem to be is 2.518…E+1906. very very large!

@sebastianzaczek 6 лет назад

Olbaid Fractalium that's gonna be my next favorite number

@angelmendez-rivera351 5 лет назад

It'd be an interesting to define a sequence named R(n), such that R(n) is the smallest n-perfect number and then study this sequence.

@OrangeC7 3 года назад

@@angelmendez-rivera351 I was finding it interesting, that it seems like the number of n-perfect numbers is infinite when n=2, but then increases from six starting at n=3. I wonder why that is, and what it means about n=2, though I guess this is a number theorist's job lol

@d4slaimless 3 года назад

@@angelmendez-rivera351 it is also interesting if this sequence stop at some n. Or maybe just R(n) grows to infinitely big numbers.

@SG2048-meta 2 года назад

@@OrangeC7 pretty sure they meant the smallest n perfect number. They said it in their comment.

@adamkelly5478 6 лет назад

James needs to be on numberphile more often.

@curtiswfranks 6 лет назад

And 1-perfect numbers! (If you add up every factor of such a number, including itself, then you get itself). The list of which is, in total: 1. (0 is factored by everything, so it does not count).

@frogstereighteeng5499 5 лет назад

We don't talk about 0.

@quinn7894 3 года назад

0's factors are: 1,2,3,4,5,6,7... which add up to -1/12. Unless you don't count the number itself, in which case it's -1/12.

@debblez 3 года назад

@@quinn7894 this is the best comment I have read in a while

@rianderous8761 6 лет назад

Are there n-perfect numbers for every n?

@prithusharma2559 6 лет назад

lol wt

@letMeSayThatInIrish 6 лет назад

And what about fractional-perfects, like 3/2 perfect?

@ruben307 6 лет назад

well there is a 0-perfect number and a 1-perfect number.

@happy_labs 6 лет назад

I was hoping they'd finish the video with that point. Intuitively it feels to me like there shouldn't be, but the trend from 4-5-6-7 seemed to indicate there are more and more n-perfect numbers as n grows, but the numbers get larger and larger.

@SVP-uy9qb 6 лет назад

I think there are n-perfect numbers for every n as we can do the factors of n to find a n-perfect number based on m-perfect numbers with m

@nikonissinen6772 6 лет назад

I suck at math, but still, I watch every video and try to understand. Maybe some day it all opens to me. Thank you for these videos.

@rogermouton2273 6 лет назад

One of the few things that still deeply fascinate and excite me is the fact that, despite the combined brain power of many very clever people over centuries, many very simple maths questions (such as: is there an odd perfect number?) cannot be definitively answered. Amazing.

@carlyaeger5756 6 лет назад

Love the Mighty Nail and Gear in the background!

@md.sazzadhossain6680 6 лет назад

People wants to know why singing banana stopped singing.

@JorgetePanete 6 лет назад

Md. Sazzad Hossain want*

@md.sazzadhossain6680 6 лет назад

My bad😊

@iabervon 6 лет назад

We think he stopped singing, and it would be weird if there was more after a gap this size, but nobody's been able to prove the set is finite.

@md.sazzadhossain6680 6 лет назад

Why did he stop making videos on his own channel? --that's what I meant.

@centralprocessingunit2564 4 года назад

@@iabervon lol

@SlimThrull 6 лет назад

How about 1/2 perfect numbers? (Where all the factors (except the last) add up to 1/2 the original number.) Perhaps call the semi-perfect numbers?

@ruben307 6 лет назад

wouldn't that be the even numbers?

@MrCyanGaming 6 лет назад

impossible, in order to half a number it must be even: so straight away, any possible candidate can be ruled since when halfing a number, it must also have factors 2 and every number has a factor of 1. so for example: 14: 7+2+1=10

@manuc.260 6 лет назад

Would there be another one besides 2?

@rajdeepchakraborty6828 6 лет назад

2 is perhaps the only 'semi-perfect number'.

@MrCyanGaming 6 лет назад

2 is the only one

@vanhouten64 6 лет назад

I'd enjoy a video about perfect numbers, triperfect numbers, etc in other bases besides base10.

@sirk603 2 года назад

wouldn't it be the same?

@f424m0nd 6 лет назад

As Dr. Grime started listing the other N-perfect numbers (4-perfect, 5-perfect, 6-perfect and 7-perfect), and noticing that above N=2 (the perfect numbers), all of them are thought to be finite, I wondered if there's also a ceiling to N. But then again, there seems to be no pattern to the numbers of N-perfect numbers. Sorry, just throwing that thought out there. ------------------- EDIT: And just as I've suspected, there's already investigation along these lines. en.wikipedia.org/wiki/Multiply_perfect_number

@Pining_for_the_fjords 6 лет назад

Two questions: How do they know that a hypothetical odd perfect number x2 would be a triple perfect number? And what's the highest possible perfect number series? Can you have a 20-perfect number, a 100-perfect number? Where does it stop and why?

@axemenace6637 6 лет назад

Conway79 The answer to your first question is simple. If N is odd perfect, the sum of its factors including N equals 2N. But when we introduce a factor of 2, we have double of each of these factors also on the list. Therefore, the sum of the factors of 2N is 2N+(2*2N)=6N meaning 2N is triperfect. I suspect that the answer to your second question is not well-known.

@dg2903 6 лет назад

I love how their Gold and Silver RU-vid Play Buttons are jsut casually sitting against the wall on the ground like that =]

@IMortage 6 лет назад

Yay, I love it when a numberphile video pops up in my inbox.

@thomasmrf.brunner 3 года назад

3:21 - The Six Triperfect Numbers: 120 , 672 , 523776 , 459818240 , 1476304896 , 51001180160

@15schaa 6 лет назад

Yesterday was perfect number day: 28/6. Also tau day, but I'm a pi bro.

@-kat 4 года назад

15schaa 15schaa ew pi

@centralprocessingunit2564 4 года назад

I need to take note of this

@elfro1237 4 года назад

Americans writing 6/28 are very sad, luckily I’m from Australia.

@dabiskitt 5 лет назад

I wonder how it would look if you graphed all the triperfect numbers on a graph

@TakeWalker 6 лет назад

It's funny, you'd think as the 'order of perfection' increases, the counts would go down, but other than perfect->triperfect, it seems to keep going up.

@jamesknapp64 2 года назад

When you multiply a number the sum of factors gets bigger relative to the new number. Example Take 6. Sum of factors is 12 or double Now multiply 6 × 2 = 12 ; the sum of factors is 28 which is more than double 12. 6 × 5 = 30 and its sum of factors is 74 more than double 30 In this way it makes sense there are more 4 perfect then 3 perfect etc.

@MAP233224 6 лет назад

120 is the best number ever, no doubt. So many simple and elegant ways to write it :D

@rkpetry 6 лет назад

*_...not that it should be important but what-about 'sesquiperfect' (1.5×) and all the other 'rationally perfect' numbers..._*

@MrCubFan415 5 лет назад

2 is sesquiperfect

@angelmendez-rivera351 4 года назад

For any r = (p + 1)/p where p is prime, the only r-perfect number is p.

@Christoph1990 6 лет назад

I would really like to know the search algorithm for these perfect numbers. There certainly must be a clever twist to it, otherwise it would be impossible to check all numbers up to x* 10^30 and higher.

@craftyraf 6 лет назад

every even perfect number is represented in binary as p ONES followed by p − 1 ZEROS, e.g. 28 = 11100, 496 = 111110000, etc. Those are very easy to generate.

@Christoph1990 6 лет назад

Raf M. That‘s pretty cool

@axemenace6637 6 лет назад

Chr1z2 In fact, there is a specially fast algorithm used to find Mersenne primes (which is why all of the largest primes are Mersenne). Every Mersenne prime generates a perfect number, which is a more direct way of saying what a previous commentor was saying about binary.

@darreljones8645 6 лет назад

I also know that Mersenne primes don't have to be checked by looking for divisors. There's a simpler test, that involves dividing the potential Mersenne prime into a number in a "square the last number and subtract 2" series. If it divides the corresponding number evenly, it's prime; if it doesn't, it's not.

@anarcho.pacifist 5 лет назад

The known triperfect numbers are 151-smooth (all the prime factors are

@justinhoffman5339 6 лет назад

Uni-perfect numbers: where if you add up all the factors not including that number, you get 1.

@WiggysanWiggysan 6 лет назад

Congratulations Dr James. You have beaten your previous on confusing me to a level of 100% in less then 30 seconds. I doff my cap to you.

@rumikhuwaja8708 6 лет назад

Who instantly likes when they see Dr. James

@CultistO 6 лет назад

Then would you call 1 a (the) monoperfect number?

@toddbiesel4288 6 лет назад

CultistO Or uniperfect...

@angelmendez-rivera351 5 лет назад

Yes.

@tuzeds 5 лет назад

Do you mean a number where the sum of his divisors equals itself?

@tuzeds 5 лет назад

Because if you do, the only "monoperfect" number is 1

@angelmendez-rivera351 4 года назад

Tuzeds Yes, exactly.

@StickyLabel7 6 лет назад

I think 2 is a perfect number, it's nice and small, and has that cute curly flick, and makes me feel warm and fuzzy on the inside.

@william1729 5 лет назад

4-perfect should be tetraperfect, and 5-perfect should be pentaperfect, and 6- hexa, and 7- hepta, etc.

@pedroscoponi4905 6 лет назад

Couldn't help but notice that the larger the N for the n-perfect rule is, the more examples of it there are. Does that pattern hold up? And is there an obvious reason why that I didn't think of?

@adampaul2986 6 лет назад

There’s a pretty obvious explanation for that. If you don’t know it then you should ask somebody who does, because I have no idea. I hate math.

@lucasng4712 6 лет назад

That's not true..? There are 6 tri and 50 perfect

@Catishcat 6 лет назад

hey proto

@Jhopsssss 6 лет назад

The larger the number, the more factors there could potentially be.

@anandsuralkar2947 5 лет назад

Hmm

@eyflfla 6 лет назад

Good old school numberphile.

@brickandmortar1 6 лет назад

Numberphile: We don't know that this is a complete list, but it would be really weird if it wasn't a complete list. Math: Hold my beer.

@erikswanenberg8719 4 года назад

the enthusiasm of this gentleman is amazing! Keep posting

@SHASHANKRUSTAGII 6 лет назад

I can die, but cant miss any NUMBERPHILE video Love for Maths

@mighty8357 6 лет назад

A James Grime video *breathing intensifies*

@ARVash 6 лет назад

the fact that the total number of n-perfects are near to but not quite powers of two irks me in a way that I'll never fully describe or recover from.

@Motinu 6 лет назад

That Hello Internet Nail and Gear in the Background! :D

@moky1125 6 лет назад

That is just 2-perfect :0

@bonecanoe86 6 лет назад

Does 0 count? These are the factors of 0: 0. Let's add all those up: 0. 0 = 3 X 0. Mmmkay?

@jogiff 6 лет назад

Literally every natural number is a factor of zero. And, as we all know the sum of the natural numbers is -1/12 (it really isn't, but who's counting)

@joeshoesmith 6 лет назад

bonecanoe86 Factors of 0: 0, 1, 2, 3... add them all up then.

@michaelempeigne3519 6 лет назад

0 is not a natural number so then it would be : 0: 1, 2, 3, ,4 ,5 , 6, 7.........Now add them all up .

@EebstertheGreat 6 лет назад

And since -1/12 is ∞·0, zero is an ∞-perfect number.

@Leafsgobrrrrr 6 лет назад

If so, then zero is nth-perfect

@Lashb1ade 6 лет назад

I did a thing: For any N that is odd we see that: {factors(2N)}={factors(N), 2*factors(N)} Assume N is biPerfect. By definition: sum({factors(N)})=2*N Note that we also have: sum({2*factors(N)})=2*sum({factors(N)})=2*2*N so combining both above: sum({factors(2N)})=sum({factors(N),2*factors(N)} =sum({factors(N))+sum(2*{factors(N)}) =2*N + 2*2*N =6*N Thus: sum({factors(2N)})=3*2N Therefore 2N is triperfect.

@lyrimetacurl0 4 месяца назад

There's only one 1-perfect number, which is the number 1 (total sum of factors = n). Prime: total sum of factors = n+1 Perfect: total sum of factors = 2n Triperfect: total sum of factors = 3n etc.

@harshsharma5768 6 лет назад

Tri perfect number = 3*sum Di perfect/perfect number = 2*sum So does that mean we also have monoperfect number =1*sum ... I mean 1 can be a monoperfect number ...

@sadhlife 6 лет назад

well, it totally is.

@EchoHeo 6 лет назад

1½perfect number

@EchoHeo 6 лет назад

2 is a 1½perfect number

@tothm129 6 лет назад

1 is the only monoperfect. Primes have the lowest factors and they are all one too big

@ethan00016 6 лет назад

Two questions: 1. Is it true that James Grime is the brother of Frank Grimes, and only ditched the 's' so as to not arouse suspicion? and, 2. Like his brother, does he also like being called Grimey?

@johnallan8613 4 года назад

For perfect numbers 4perfect, 5 perfect, to n-perfect what is the biggest “n” we have found?

@Abhishek-Verma 6 лет назад

Hi Dr Grime

@LiveHedgehog 6 лет назад

Perfect numbers are perfect because all their factors EXCEPT themselves add up to themselves. So why are tri-perfect numbers not bi-perfect numbers? Why ignore the number itself for perfect numbers but not tri-perfect numbers? The only effect it would have would be shifting the number denoting the set down by one.

@ruben307 6 лет назад

because when they started they wanted a cool name. And now 1 would be the only perfect number and that is a lonely number.

@fee8422 6 лет назад

because normal perfect numbers aren't perfect, they're technically bi-perfect, but there are no real perfect numbers, because even a prime number n has a sum of factors of n+1, and it makes more sense this way than arbitrarily substracting the original number. perfect numbers are probably the first if this sort to be made up/ discovered, so they got the name. Edit: as someone mentioned below, there actually is one perfect perfect number: 1.

@JM-us3fr 6 лет назад

Because mathematicians don't always name or define things in the most elegant way

@z-beeblebrox 6 лет назад

Yeah it's kinda like how some genius decided that numbers off the number line should be called "imaginary", like as if numbers aren't imaginary already

@angelmendez-rivera351 5 лет назад

Jason Martin Not only do they not always do it, they rarely do.

@bytewav3341 6 лет назад

I'd like a video about Marko Rodin's vortex mathematics please. I think that would be super fun.

@MrSuperMarioB 6 лет назад

I found something interesting while watching. Read my thoughts, what do you think? TriPerfect numbers there are six. So 2 times 3. 6=2×3 4-perfect numbers there are 36. 36=4×9=2squared x 3squared 5-perfect numbers there are 65. 65=5x13=2+3×4+9 (the numbers used above) I just think that is an interesting coincidence. Someone will tell me the obvious connection, but I don't know it better.

@HasekuraIsuna 2 года назад

6-perfect numbers there are 245. 245=(2+3)×(4||9) Can't find anything clever for 7's 516 so I think it's just a coincidence.

@alexved692 6 лет назад

Hello, Numberphile. I know it's not in the subject, but I think I found a contradiction in your video: “ASTOUNDING: 1+2+3+4+5+…=-1/12” (Well, or I SSI). This video says that the sum of all natural numbers is -1/12, but it is also Alef0. So Alef0=-1 / 12. Alef0+1=Omega. Omega=11/12=121/144. Alef0*Alef0=Alef1. Alef1=1/144. Omega＞Alef1. Although, it may be that it is not, because the cardinals and ordinals are arranged in a certain order, but do not have a certain value. And sorry for my English, I'm just from Russia.

@ben1996123 6 лет назад

this is what happens when you think mathematics is about writing down meaningless symbols and shuffling them around. absolutely everything you wrote is nonsense

@angelmendez-rivera351 5 лет назад

No, the sum of all natural numbers is not Aleph(0). There is absolutely no proof of this, nor did you provide a source.

@KauanRMKlein 6 лет назад

It's weird, right? How that dude is so FREAKING AWESOME in a totally nonsexual way?

@alimostafa8193 6 лет назад

Absolutley! How?!

@chaserox5 6 лет назад

He's pretty awesome in a sexual way too. 😉 Talk dirty to me math daddi

@LowellMorgan 6 лет назад

Non-sexual? Speak for yourself.

@coloripple 6 лет назад

is he really unique in his nonsexualness combined with his freaking awesomeness to you? I know plenty of people that I find freaking awesome in a nonsexual way, since for me awesomeness and sexualness aren't all that connected

@Triantalex 9 месяцев назад

false.

@maxonmendel5757 5 лет назад

The factors of 496 are my faves. After 16, they're the nth binary number minus the (n-5)th binary number

@bernhardmelitamann6512 6 лет назад

How about assigning each number a value of perfection. The expected value for (bi)perfection for the number 5 would be 2x5=10. But 1+5=6. 6/10=0.6. So the number 5 is under performing. The number 12 on the other hand has an expected value of perfection of 24. The sum of factors is 1+2+3+4+6+12=28. 28/24=1.1666... So 12 is over performing. The expected value is always 2xn which is always even. The expected value divided by the actual sum of factors should be 1. And for triperfect numbers; 3xn. The expected value for perfection for 10 is 3x10=30. Sum of factors is 1+2+5+10=18. 18/30=0,6. 10 is under performing. Also interesting is the notation of perfect numbers in binary. The first ones as I could read in the wikipedia are written as p ones and p-1 zeros. I dont know if this is true for all perfect numbers.

@DanielGonzalezL 6 лет назад

Cool! Does the amount of discovered n-perfect numbers increase as n increases? That seemed to be the case with these examples

@boumbh 6 лет назад

Daniel Gonzalez We should look at S(n) = the sum of factors of n Maybe take an average of it or the max and study the divergence

@DanielGonzalezL 6 лет назад

boumbh interesting, thanks!

@clickaccept 6 лет назад

You would need to remove the word "discovered" for there to be a hope of that being true.

@FrogSkull 6 лет назад

James!

@pipolwes000 4 года назад

As far as I know, 1 is the largest 1-perfect number.

@coloripple 6 лет назад

then couldn't you say 1 is the only monoperfect number, since it's the only number which adds up to itself if you add up all the factors (only 1). Then all other primes would be near monoperfect; monoperfect + 1 in fact.

@angelmendez-rivera351 5 лет назад

Kalkaanuslag Yes

@L4Vo5 6 лет назад

If you start looking for N-perfect numbers, and you don't limit N to being an integer, how big can it get?

@Trockenshampooleopard 6 лет назад

That doesn't make any sense, because that would turn any number into a N-perfect number. Take 42: it's a 16/7-perfect number.

@zoranhacker 6 лет назад

Infinitely big

@pR0stYp3 6 лет назад

Well of course it makes sense. Maybe you find out, that the sum of all factors of a number is bounded by some constant, say sumoffactors(n)

@lucaswatson5845 6 лет назад

Ah yes, the fabled sqrt(2)-perfect number... Yet to be found!

@benjaminprzybocki7391 6 лет назад

L4Vo5 N can be arbitrarily large. This is because the a abundancy index function is unbounded.

@meme6455 6 лет назад

46 million... Wow that's a big num- DIGITS long Oh

@daxvena 6 лет назад

Hmm I noticed that the total number of known n-perfect numbers are pretty close to powers of two: 3-perfect: 6-2^3 = -2 4-perfect: 36-2^5 = 4 5-perfect: 64-2^6 = 1 6-perfect: 245-2^8 = -11 7-perfect: 516-2^9 = 4 I wonder if it has any significance.

@mani1e 6 лет назад

I wonder if you could write up a program that would write up all the factors of any given number, let's call the given number A and add then add the factor the number itself included, let's call that B, then find out the X in the equation: B=A*X and see if X is a whole number then make an automated process of trying this for all A(going upwards with numbers from 1) and noting down all the A values that give you the same X value together in a category as long as X is a whole number

@steliostoulis1875 6 лет назад

You're so Precious When you *smile* ❤️

@steliostoulis1875 6 лет назад

EdinPlayZ stfu

@steliostoulis1875 6 лет назад

EdinPlayZ "oooooooooooollllllllllllldddddddd Meme" is surely intellectual

@johnox2226 6 лет назад

Stelios Toulis Surely EdinPlayZ is a cancerous 9 year old

@steliostoulis1875 6 лет назад

John Ox probably

@vitormelomedeiros 6 лет назад

EdinPlayZ i found it funny lol

@zacharieetienne5784 6 лет назад

Is there atleast 1 nth-perfect number for every n?

@idontwantanamethx 6 лет назад

Zacharie Etienne That means the sum of all factors of the number, including the number itself, is the number itself. Only one such number exists: 1

@015Fede 6 лет назад

Abishek Anil you misunderstood the question

@MisterAppleEsq 6 лет назад

+Abishek Anil They mean “is there some n-perfect number for every value of n”, rather than “is n n-perfect”.

@kedrak90 6 лет назад

If you think about it 0 is a all n perfect solution. But I don't think that's a satisfying answer.

@SpencerTwiddy 6 лет назад

Shardar 1 no, zero doesn't work for a single finite n.... And I don't think the people calling it "infinity-perfect" are correct either, because technically each positive factor would have a negative counterpart. So it COULD satisfy the criteria for a "0-perfect" number but that's just my intuition, likely there is no 0-perfect number and 0 is not any type of perfect number

@brightsideofmaths 6 лет назад

Why are the picture frames not hanging on the wall?

@adamt7413 2 года назад

I was hoping James would explain why if there is an odd perfect number then 2N would be triperfect

@SubhashMirasi 6 лет назад

How perfect are u sir?

@Food_india_smile 6 лет назад

Do tri perfect number exists...?? But my mom said "no one is perfect"😭😭

@apexlegendsindia 6 лет назад

Yeah but it only applies to human beings... Not on numbers 😉😉😂

@imanharrisidham8971 6 лет назад

Not one number is perfect, however an infinitely many of them are

@ragnkja 6 лет назад

Numbers only need to fit a single definition of "perfect", while humans are faced with lots of different, and often conflicting, definitions of "perfect".

@ITR 6 лет назад

no one is perfect, but some tri are

@imaginaryboy2000 6 лет назад

That's because one isn't a perfect number.

@dialecticalmonist3405 3 года назад

It's beginning to happen. I'm beginning to love numbers.

@MrJayPuff 6 лет назад

It’s nice to see james again

@thomasesr 6 лет назад

The answer for all is 42

@fabled. 6 лет назад

pft, that's not even a perfect number.

@sta89mit 6 лет назад

FabledDan I'm guessing you didn't get the reference. 42 is indeed the Answer to the Ultimate Question of Life, the Universe and Everything.

@fabled. 6 лет назад

Indeed I have watched Hitchhiker's Guide to the Galaxy, it was just a joke :)

@sta89mit 6 лет назад

FabledDan ahhh... missed it through text. My apologies!

@richardlinsley-hood7149 6 лет назад

It was really 41 but people will forget you can start from 0 as well as 1. Display error.

@krsnasameer 6 лет назад

Its Grime, horray!!!

@letartean 6 лет назад

Seems counterintuitive that the postulate for n-perfect numbers is that they are a finite set when n>2 but infinite when n=2. I wish this was talked about in the video... Still very interesting, as usual.

@jeffreyaustin6279 6 лет назад

This is why I subscribed. For my occasional fix of numbers. ❤

@Mr6Sinner 6 лет назад

If numbers are infinite, why /wouldn’t/ there be more examples?

@015Fede 6 лет назад

Well, not because the are infinite it means that there will be an infinite amount of them. A clear example is that there is one and only one number that is even and prime at the same time, and we know for sure that there isn't any other. Same thing may happen with these numbers.

@konstanty8094 6 лет назад

If numbers are infinite, why is there only one example of even prime?

@weeboogaijin 6 лет назад

Konstanty because the only even prime is 2 and all other even numbers have at least one more factor than 1 and itself which is 2

@SVP-uy9qb 6 лет назад

Lol this is nonsense

@Skyle42 6 лет назад

No, this is Maths. Get used to it.

@Marconius6 6 лет назад

The sequence of how many of each are kinda reminds me of the sequence of perfect polyhedra in higher dimensions... I wonder if there's a connection there.

@cougar2013 6 лет назад

This should have come out yesterday. 6/28 is the only perfect day on the calendar!

@quinn7894 3 года назад

Tau day!

@beamathematician2487 6 лет назад

What is another natural number, which shows following property, example-'231' addition with 1 up to 21 is 231 and additon of prime factor of 231 is 21. 231=3×7×11 or 3+7+11=21 or 1+2+3+…+21=231.

@jasmin7168 6 лет назад

I love you Dr. James Grime

@WillToWinvlog 6 лет назад

Aww yeah! This video really hits the spot! THIS is what I've been craving this week!!!!!!

@peterfireflylund 6 лет назад

You have a very nice fireplace, Brady!

@Tulanir1 5 лет назад

There's something I don't understand. James used the argument that because 2N is triperfect for any odd perfect N, and there probably aren't any odd perfect N, that means there probably aren't any large triperfect numbers. But that's invalid. Not only is it the -converse- inverse of modus ponens (false), it could also be used to show that there likely aren't any triperfect numbers at all, which clearly isn't the case. At 5:08 he basically said that there is either an odd perfect number *OR* there is no other triperfect number, which doesn't logically follow from the theorem.

@jlf_ 4 года назад

I love this guy

@rodwayworkor9202 5 лет назад

Dr. Grimmes, any Mersenne prime if is 2^k-1, then (2^k-1)(2^(k-1)) is a perfect number................... so.

@xjdfghashzkj 6 лет назад

Here's my question: for all integers n, does there exist at least one n-perfect number?

@michaelempeigne3519 3 года назад

formula for perfect number : ( - 1 + 2^n ) ( 2^( n -1 ) ) - 1 + 2^n is an odd number 2^( n - 1 ) is always even when you multiply these together : odd * even = even THerefore, there will never be an odd perfect number.

@shaungrace9164 5 лет назад

Might be related to tangent line angles moving along rough diameter of a circle. Eg. If there's finite lines and angles and assuming equal (not odd) top number of tangent lines, the angle between each tangent line reaches a limit where cannot find any more fitting numbers inside larger number. Might be a set angle where if go over obtuse? limit between tangent line corners/joins, you cannot find more. My maths rhetoric is terrible but hopefully it's understood.