Confession, I would not have clicked on the video if it said "Highly Composite Numbers" I wanted to know what the anti-prime was

@kelvinubaechu

8 жыл бұрын

same

@tiberiuswolf8259

8 жыл бұрын

I was waiting for some Da Vinci code thing, I'll be honest. plus, I wanted to see what a numberphile was >.

@MrDannyDetail

8 жыл бұрын

Phile=Lover in Greek. Numberphile= Lover of Numbers, Audiophile= Lover of Sound (usually music), Bibliophile= Lover of Books and Paedophile= Lover of Children (though used these days almost exclusively to mean inappropriate love).

@szymonsabat5195

7 жыл бұрын

instead, you know what Highly Composite Numbers are, as there is no such things as Anti-Prime Numbers. This way, the video title is misleading, even more for someone who already knew what HCNs are. ;c

@nmarbletoe8210

7 жыл бұрын

I suppose we can bestow the name 'anti-prime' as long as that is not already taken. They can have two names, why not? M-31 is also known as the Andromeda Galaxy...

Fun Fact: 5039- Prime 5040- Anti Prime 5041- Square I wonder if there is any other combination of three consecutive numbers with these properties!

@thefreekinscientist

4 жыл бұрын

Well that would be 2- Anti Prime 3- Prime 4- Square but that's boring. Next one is 4,5,6. A group that isn't completely obvious is, for example, 47 prime, 48 anti-prime, 49 square. I've taken a bit of time and ran through the highly composite numbers listed on the wiki page, and found that there is no square within a margin of 2 near a highly composite number above 5040 and below at least 720720, meaning no such trios exist there. It would be interesting to see if they exist beyond that, though.

@Sea_bear_42

4 жыл бұрын

Kind of weird how many coincidences there are in math

@briangeer1024

4 жыл бұрын

Any number that's one above an anti-prime has a pretty high chance of being prime. EDIT: or one below

@Spreehox

4 жыл бұрын

There's infinite trios

@AltoSnow

4 жыл бұрын

@@thefreekinscientist 2 is prime tho.

Wikipedia "A highly composite number (or anti-prime)" ITS OFFICIAL!!!!!!!!

@gabewrsewell

6 жыл бұрын

Timfoolery

@Achillionable

6 жыл бұрын

"Wikipedia official"

@SuckMyAqua

6 жыл бұрын

You know anyone can edit wikipedia right? 😂

@modernkennnern

6 жыл бұрын

LitAquah, and there are a lot of people who edit Wikipedia, so in the end, it 'converges' to fact

@cptaincrunch4438

5 жыл бұрын

Can we get to anti-prime likes

I love how 2, a literal PRIME number is also a highly COMPOSITE number.

@GeekProdigyGuy

9 ай бұрын

for lack of competition. :)

@meccevil321

5 ай бұрын

also, there are infinite prim numbers. only one of them is even.

@HeavyMetalini

Ай бұрын

My thought exactly

Yet *every* time I make a batch of 12 cookies, there's *always* 5 people to share with. Time to make 5040 cookies.

@toadstar1004

8 жыл бұрын

***** You're right! I meant 5 people total. My mistake.

@groszak1

7 жыл бұрын

You only need 60 (augmenting "12" with "5" ability, still highly composite)

@fgvcosmic6752

6 жыл бұрын

ToadStar100 what if you eat 2 extras?

@beargrills3508

6 жыл бұрын

ToadStar100 there is going to be 5039 people then. Sorry it's the rules.

@jakebasmati

6 жыл бұрын

12×5=60, 60÷12=5, so make 5÷nnnnnn... cookies.

Last year, at age 59, I was at the prime of my life. I am in the composite (anti-prime) of my life now. On my birthday, I will start another prime year.

@numbermathematics4137

6 жыл бұрын

Child of age 2 is both prime and anti prime

@theleftuprightatsoldierfield

6 жыл бұрын

friendofbeaver when I was 12, it was the same thing

@colonelstriker2519

6 жыл бұрын

You just took that chance

@vysionone8692

6 жыл бұрын

friendofbeaver Happy birthday!

@adhamhalabi7472

5 жыл бұрын

@Number mathematics so that's why children are lovable but confusing

2 is both prime and anti prime.

@AlgaeGaming

6 жыл бұрын

SporeZy the only number with that characteristic, since most people don't count 1 as prime!

@SYFTV1

4 жыл бұрын

@@AlgaeGaming 1 is not prime

@hay0099

4 жыл бұрын

@@AlgaeGaming one is not a prime

@derekwheeler4299

4 жыл бұрын

@@SYFTV1 one used to be a prime soooooo I don't think this is an argument worth having. One is just not a useful prime

@SYFTV1

4 жыл бұрын

@@derekwheeler4299 You say it as if any of the entire maths was useful at all

The prefix 'Anti-' Makes every word more interesting!

@grabern

6 жыл бұрын

Yeah like the word "semitic".

@RahulMaru3507

5 жыл бұрын

Anti-interesting?

@macleadg

5 жыл бұрын

... or anti-boring...😜

@yrden99

4 жыл бұрын

So... How about being meta... Let's talk about anti-words !

@vikram03

4 жыл бұрын

@@grabern That's dark

5040=7! btw. Just if anyone was wondering why so many factors.

@jacob042

8 жыл бұрын

Well that explains it.

@coloripple

8 жыл бұрын

Nice observation. So are 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. But 8!=40320 which is not highly compatible... (Not visible at 4:33)

@phiefer3

8 жыл бұрын

8! also meets all 3 requirements listed for "anti-primes": it's factorization would be 2^7 x 3^2 x 5 x 7, consecutive primes with decreasing powers and ends with a power of 1. However, the list is correct, 8! is NOT a highly composite number. The thing is, the 3 requirements are simply properties that all "anti-primes" have, but it is NOT a definitive test, there are false-positives, such as this one. To weed out false-positives you have to consider different ways we can manipulate the powers+1, though I'm not sure there's a simple way of describing it. For example, if we calculate the number of factors of 8!, we get 8x3x2x2=96. But we can rearrange this calculation to get 96 a different way, for example we can split that 8 into a 4x2 and move the 2 to the end: 4x3x2x2x2=96. Now let's reverse engineer this into a prime factorization (decrease each number by 1 and use it as a power of consecutive primes) we get 2^3 x 3^2 x 5 x 7 x 11, which is the factorization of 27720, which is smaller than 8! but has the same number of factors (96). Now, doing this does not always make the number smaller, for example if we split that 4 we get 3x2x2x2x2x2=96, but applying this to a prime factorization gives us 60060. Basically it has to do with the way you rearrange the factors of the number of factors (in this case 96), can result in making the prime factorization larger or smaller depending on how long the factorization winds up vs how big their powers get. (ie when went from 8! to 27720 the new factorization introduced a factor of 11, but the reduction in 2's exponent removed a factor of 16, so the overall effect made it smaller. But doing it again in this case introduces a 13, while the changes in exponents only removed a factor of 2 and a factor of 3 (total factor of 6), so the overall effect was an increase).

@dermaniac5205

8 жыл бұрын

Yeah, my first reaction when mentioned numbers with many factors was that I thought "Wouldn't I just take a factorial for that?"

@TyDreacon

8 жыл бұрын

Out of curiosity, and because I can only hope to be as smart or well-educated: do false positives still occur if 'anti-primes' are numbers with a number of factors greater than _or equal to_ the largest number of factors for numbers less than it, rather than strictly greater than? Is there even a way to check that?

James grime : probably the most enthusiastic mathematician alive

@abcd-yc8lz

8 жыл бұрын

have you watched the kleinbottle videos?

@stanfordfeynman2796

8 жыл бұрын

Well if I had his job, I would be too!

@if3660

8 жыл бұрын

Matt Parker. Known for the Parker Square.

@kiefac

8 жыл бұрын

did you see the klein bottle guy?

@JLConawayII

8 жыл бұрын

The most enthusiastic mathematician I've ever met puts him to shame. We're fairly convinced the guy consumes a colossal amount of methamphetamines for breakfast every day.

"The third thing that you may have noticed..." You flatter me, thricely.

I'm a fan of the highly composite number 720,720 as the smallest number divisible by everything from 1 to 16 (since it's 720 x 1001, and 1001 is 7 x 11 x 13 - with 720 taking care of all the other factors) - plus it also looks pretty neat with the repeated digits.

@reubenmanzo2054

Жыл бұрын

Actually, it's not the smallest. Try 360,360.

@Pseudify

Жыл бұрын

@@reubenmanzo2054. 360,360 is not divisible by 16.

@reubenmanzo2054

Жыл бұрын

@@Pseudify I stand corrected.

So 2 is prime, but also anti-prime...

@numberphile

8 жыл бұрын

nice!

@100najaja

8 жыл бұрын

14 min late :

@jaruqe

8 жыл бұрын

Oh my...

@spinvalve

8 жыл бұрын

hence it's bipolar

@umbreon8527

8 жыл бұрын

= mutual annihilation LOL

I will refer to highly composite numbers as anti primes from now on

@numberphile

8 жыл бұрын

+aragonaut thank you :)

@Jacob-uy1gk

8 жыл бұрын

1 is not Prime.

@piperboy98

8 жыл бұрын

So 2 is both prime and antiprime... Sounds a little contradictory, but I suppose '2 is both prime and highly composite' sounds equally strange

@Plystire

8 жыл бұрын

1 is the Mother Number

@gabemerritt3139

8 жыл бұрын

pretty much

I love watching this guy talk. His energy is infectious!

@maxj433

3 жыл бұрын

@@greatestgameofall That is incredibly unfortunate! 😢

@manuupadhyay1944

3 жыл бұрын

@@greatestgameofall Why are you spreading wrong information?

@xCorvus7x

2 жыл бұрын

@@manuupadhyay1944 what did they say?

12 is incredibly useful for web design, where you might want very flexible column layouts. If you have a grid of 12 columns, you could lay out a website into 1, 2, 3, 4, 6 or 12 parts or any combination thereof very easily. Just a little non-math tidbit. :P

@iconsworld9

2 жыл бұрын

Nice man. Now that's the world of software engineer and web developer, programmer. Awesome

@ronumpleby3517

Жыл бұрын

That's also why there are 12 inches to a foot

Numberphile has taught me that if anything cool happened in math, Ramanujan had something to do with it

@numberphile

8 жыл бұрын

and Gauss and Euler!

@mercronniel3122

8 жыл бұрын

and Riemann and Pascal!

@justthink124

8 жыл бұрын

to be fair I think James just knows a lot about him as well, Euler was messing with this stuff long before and came up with the Euler Phi Function which gives us that total number of divisors. I think Ramanujan just found more patterns in it like he describes

@andrewsauer2729

8 жыл бұрын

Ramanujan made vastly bigger contributions to mathematics than this interesting tidbit.

@NoriMori1992

8 жыл бұрын

I was just thinking something similar.

I bet they all look nice when written in base 12, too.

@fgvcosmic6752

6 жыл бұрын

Michael how did i not know this!!

@kandrid3362

6 жыл бұрын

Michael How could it end in E if it is base 12

@kandrid3362

6 жыл бұрын

Michael 11 is B

@D1nomite1

6 жыл бұрын

no for people that use base 12, they count 1 2 3 4 5 6 7 8 9 X E. they arent actually the letters, but new numbers that were made. but the new numbers look like an X and an E, so when typing we use those. numberphile did a video on it on 12/12/12.

@lararys7765

6 жыл бұрын

and 0 too

The first thing i thought when he said its an antiprime is: 2 is the only prime and antiprime at the same time

@achtsekundenfurz7876

3 жыл бұрын

Another quote about 2: "All primes are odd. 2 is VERY odd."

"A highly composite number, sometimes called an antiprime number, is a positive integer with more divisors than any smaller positive integer has. The term was coined by Ramanujan (1915). However, Jean-Pierre Kahane has suggested that the concept might have been known to Plato, who set 5040 as the ideal number of citizens in a city as 5040 has more divisors than any numbers less than it." this is from wikipedia and its official this is anti-prime

@countOfHenneberg

7 ай бұрын

But do we know when the line, "sometimes called an antiprime number" was added; before or after this video was released?

@genericgoat

6 ай бұрын

@@countOfHenneberg Just checked on internet archive, antiprime was not included in the wikipedia before this video

I learned about highly composite numbers the hard way. In 4th grade we played a dice game where you're on a number N, you roll the number D, then the number of steps you move is the remainder of N/D. First one to 100 wins. I landed on 60, and it took me a few turns to realize I lost.

@ragnkja

6 жыл бұрын

The choice of die had doomed you to lose.

@peterstangl8295

5 жыл бұрын

i don't get it

@oseremenuduehi4361

5 жыл бұрын

​@@peterstangl8295 60 (which is a highly composite number) is exactly divisible by all the numbers on the die (1 through 6). Therefore, the remainder when 60 is divided by the die outcome would always be zero, and you'll be stuck forever on the position 60 since you will only be able to move 0 step irrespective of the die outcome.

@alexwang982

5 жыл бұрын

Nillie *number theorist has entered the chat*

@mattdamutt

4 жыл бұрын

🤣🤣😂👍🏼

Video duration: leet

@petter9824

8 жыл бұрын

Holy shit

@Apfelloch

8 жыл бұрын

19 minutes late..

@dichidichi

8 жыл бұрын

In the thumbnails it says 13:38

@axelarthuro123

8 жыл бұрын

Only a Doctor in Mathematics can have this much swag

@Xeverous

8 жыл бұрын

Damn I am too late

Perfect structure in this. I love how he came out with something confusing, then broke it down with excellent examples that kept me asking questions until he had it fully explained. Perfect pacing and video structure.

(6:00) Prime factorisation is useful when you want to find the smallest number that can divide into two numbers. For sports, they wanted a framerate that could evenly split into 50 and 60 Hertz. 50 = 2×5² and 60 = 2²×3×5 Therefore we need a number that can make the fabrications for these two numbers above. That is 2²×3×5² = 300. That's why sports is recorded in 300 fps so it can air internationally. It also allows for slowmotion too.

@darksecret6050

2 жыл бұрын

LCM

@OhhCrapGuy

5 ай бұрын

3 years later, but whatever. Relatedly, the sampling rate on CDs is 44100, or 2*2*3*3*5*5*7*7, making subsampling by any product of two of its factors exceptionally easy. It's not a highly composite number, but that's because they didn't want it to be that exactly, they wanted it to have many small factors.

@Liggliluff

5 ай бұрын

@@OhhCrapGuy And video seem to go with 48000, which is 2*2*2*2*2*2*2*3*5*5*5, if you really want to divide by 2.

@Liggliluff

5 ай бұрын

This also means that if you want to support both 44100 Hz and 48000 Hz, you need 2^7 * 3^2 * 5^3 * 7^2, which is 7056000 Hz or 7056 kHz.

You still titled the video anti-prime numbers haha love your sense of humor! :D

@meunomejaestavaemuso

8 жыл бұрын

It's Brady idea, let him have it. I think it's a better term than Highly Composite Number.

@MichaelDerryGameitect

8 жыл бұрын

Finding out what an anti-prime is made me click on the video in the first place. I occasionally check out Numberphile videos but I probably would have missed this one under another title.

@rayh966

8 жыл бұрын

It's just Imperial English. Counterclockwise is anticlockwise in the Commonwealth as well. They prefer it, it just sounds weird to Americans, who don't use it as much.

@Ruminations09

8 жыл бұрын

Ray Harper Well, the joke obviously went over your head. Or you didn't even watch the video.

@jollygiants4645

6 жыл бұрын

its not going to catch on. stop trying to make it a thing

Cool! Let's all count in base 5040 for a much more practical everyday life! :D

@phlimy

8 жыл бұрын

***** Of course, why would you not? It's not that much!

@louisng114

8 жыл бұрын

*many

@Nukestarmaster

8 жыл бұрын

So we have to remember 5040 different symbols in order to do simple arithmetic?

@DaaOtt

8 жыл бұрын

We already do, with time and degrees and a 12 month year.

@snowfloofcathug

8 жыл бұрын

+Ott no, we use 10 symbols for all of them :)

I like how the first two properties sound interesting when you first hear them but have really obvious proofs. Anti-primes are nice to human brains.

The runtime of 13:37 is also special, not just because they are primes, but because 1337 is how Leetspeak writes the word "LEET" (1337) which means "elite".

@Perririri

2 жыл бұрын

OK, Boomer!

5040=7! btw

@myrus5722

6 жыл бұрын

You know one thing at least Jon Snow

@rahulsbhatt

5 жыл бұрын

And this is why 7 is a magical number in the wizardry , Harry.

@anirudhsilai5790

5 жыл бұрын

I think most factorials of prime numbers are highly composite

@TrickyTrickyFox

5 жыл бұрын

You're a factorial, Harry

@kmarasin

5 жыл бұрын

Or 10!/6!

So if I multiply a prime by an anti-prime will they annihilate?

@Reydriel

8 жыл бұрын

Nope, just makes a new number. A bit anti-climactic, don't you think? XD

@e1eventeen148

8 жыл бұрын

It resets the universe

@carmattsgp8404

8 жыл бұрын

More like anti-primactic

@robertr7923

8 жыл бұрын

+Reydriel 2 is prime AND anti prine. 2x2=4 which is also antiprime. 1 is antiprime and 2 is. 2*1=2 which is prime so you can get both

@simonvetter2420

8 жыл бұрын

I think if the prime is high enough (i.e. higher than the highest prime factor of the anti-prime) you will get a new anti-prime.

I love how two is both a prime and an anti prime

In High School Algebra, I always struggled with Prime Factorization. I just didn't get it. Later I flunked out of College Algebra one of the things I remember running up against was factoring and struggling again Now I'm going through college again, and learning Prime Factors, and I remembered this video, and Dr James Grime explaining the Fundamental Theorem of Arithmetic and it just clicked. Its as easy as adding or subtracting for me now. I wish someone had explained it that way to me 20 years ago. Thank you Dr. Grime and Numberphile for making Math fun, interesting, and accessible for all of us.

That's why 2 is my most favourite number; first prime number, the only number sharing both the traits of prime and anti-prime, and the only even prime number! Moreover, no number would show this pattern n+n=n*n=n^n!

@redswap

6 жыл бұрын

1+1=1*1=1^1

@lyrimetacurl0

6 жыл бұрын

The highest number that divides 100% of the numbers from 1 to itself.

@doommaker4000

6 жыл бұрын

Redswap Ummm 1+1=2 1*1=1 1^1=1 Whoops

@TheEternalPheonix

6 жыл бұрын

Lyri Metacurl That number would be 1. The only number that divides evenly into 1 is 1.

@hubert6943

6 жыл бұрын

=n!

Fun fact: if the number of divisors is odd, the number is a square!

@Gadget622

5 жыл бұрын

Makes sense. For any number m, every nth factor multiplied by the nth to the last factor gives you m. But if m is a square, the square root is the only factor that is both the nth factor and the nth to the last factor. Making the total amount of factors odd.

@teodoradragomir5008

5 жыл бұрын

@@Gadget622 well, everything makes sense now. Thank you.

@estebson

4 жыл бұрын

It's the same thing

@sanjj_1

4 жыл бұрын

@Ar'Khan _ Khizarkhajul those are prime factors

@tonyhakston536

4 жыл бұрын

Ar'Khan _ Khizarkhajul 525 has 12 unique factors.

James making a Mean Girls reference is something none of us knew we needed but that has nonetheless completed our existence.

4:05 All highly composite numbers above 3, can be reduced to 3, 6, 9 if you sum their digits. 5+0+4+0=9.

Wait, so 2 is both a Prime and an Anti-Prime? So ist annihilates itself?

@Janders3000

8 жыл бұрын

Just noticed someone else was a lot earlier.

@Janders3000

8 жыл бұрын

+Pahckle I know, I just like the name and made a joke out of it.

@RandallHayter

8 жыл бұрын

Highly composite and prime at the same time still sounds odd.

@gabemerritt3139

8 жыл бұрын

+Pahckle clearly antiprime is the superior term

@andymcl92

8 жыл бұрын

+Jan Wanders oops, I just commented that too!

Highly composite numbers are some of my favorite numbers but I didn't know exactly what they were called til now. There's so many ways to split 'em!

@numberphile

8 жыл бұрын

+Brandon Shaffer they're cool'

@gabemerritt3139

8 жыл бұрын

antiprimes are great numbers

@conejo093

7 жыл бұрын

is there a way to easily factor large numbers? like for example 20 digits up....?

@Isitar09

7 жыл бұрын

conejo093 no, but 20 digits is nothing for your computer ;) factoring is one of the milennia problems btw.

@SchemeTintFocus

6 жыл бұрын

6 is still the best

I love this channel. I think in numbers -- it's so difficult to block out, I can't even go on a car trip without seeing something crazy in every license plate I see. These sorts of videos help me try to explain to my mom how I see the world.

If I'm ever feeling too smart I watch Numberphile videos.

Can we talk about the length of the video?

@karlmuster263

8 жыл бұрын

I checked to see if it was highly composite or a prime or a perfect square before seeing it mentioned in another comment.

@you_just

8 жыл бұрын

Karl Muster ha

@ffggddss

7 жыл бұрын

+ You_just: What, the 13:37, you mean? That's sexagesimal for 13·60 + 37 = 817 = 19·43. What *did* you want to say about it?

@you_just

7 жыл бұрын

ffggddss obviously you don't understand the meme

@ffggddss

7 жыл бұрын

+ You_just Yes, that is, I didn't. I've since picked up on it, from looking at other comments. BTW, 1337 even looks a lot like "Leet" when you turn it upside-down!

12 is really interesting. (1^3)(2^2)(3^1) All base values increasing in consecutive order. All exponents decreasing in consecutive order. Sum of all the digits is 12. 6 factors, which is also highly composite. We really should be using base 12.

@skunkpirates

7 жыл бұрын

Vladimir Melnik your factorisation is also palindromic! But 1^3 is redundant, you could have chosen any power of 1 so it's not very special.

@havocmaverick

6 жыл бұрын

I would like a base 12 system

@steffen5121

6 жыл бұрын

count me in

@Cr8Tron

6 жыл бұрын

12 has also become the most highly standardized number for equally dividing the octave. So, right there is another thing that what you're saying is applicable to.

@Cr8Tron

6 жыл бұрын

+Vandreren Well, yes and no. 1 is arguably just as unique as the primes above it, being that it isn't a product of any positive integers that are between 1 and itself. Any integer x is only unique until we reach 2x and above. However, we only concern ourselves with what's below a given integer, when deciding whether or not to label an integer as "unique". There's nothing below 1; so, unlike the integers above 1, there's nothing to judge it from. Not exactly a fair game. However, if we DID consider all integers above any prime integer x, we could no longer simply say it is unique, but rather that it has MORE uniqueness than the primes below, and LESS uniqueness than the primes above. 1 is arguably not un-unique, but just the prime with the least amount of uniqueness.

Brady you are amazing ! love your enthusiasm for the word anti-prime.:-) James is amazing.

This is a *prime* contender for the most fascinating topic I have watched being explained on your channel in my taste.

I'm so glad to see you guys made a video on this topic. In school I often considered the number 60 and how many factors it has, especially the first six consecutively. I wondered for quite some time about the properties of 60 and whether there are other numbers like it, but never knew there was a name for the phenomena. Thanks again, Numberphiles!

There goes Brady again with the naming of things that already have names and insisting that people use them.... 😂💜💜

@numberphile

8 жыл бұрын

Wolfram Mathworld diverts "anticrime" to highly composite numbers - I was not the first to think it unfortunately.

@BoboDoboRobo

8 жыл бұрын

Batman does anticrime

@numberphile

8 жыл бұрын

yes

@massimopisati7922

8 жыл бұрын

anticrime numbers for the win

@DaveBarrack

8 жыл бұрын

Antiprime is far catchier than "Highly Composite Number"

This guy is so excited to share the cool bits about numbers and it makes me happy.

It's awesome to see you so enthusiastic and passionate about numbers

I like Numberphile videos so much. I must confess that I don't understand it all, but every now and then, I get something that makes my day and life greater. Thanks guys.

The Babylonians after jumping into a time machine and having a look at us: "Ok cool, you kept the 360 degrees in a circle, that's good ... 24 hour day, very nice, very nice .... the hours themselves still have 60 minutes at 60 seconds each, I see, never change a good thing .... and as a base for your number system you ... you _what_?!" Yep, we totally blew it there. Probably lost all respect in that moment.

@ThomasNimmesgern

8 жыл бұрын

So let's use Pi instead as the base of our number system. ;-)

@diabl2master

8 жыл бұрын

Yes... base ten :/ We have the fingers on our hands to thank for that. Base 12 would be much better. We could represent 1/6, 1/3, 1/4, 1/2 by 0.2, 0.4, 0.3, 0.6 respectively.... If only... ps. There were civilisations who used sexagesimal - base 60

@unvergebeneid

8 жыл бұрын

Davy Ker Yeah and you know who that civilization was? The Babylonians. Boom! ;)

@Malachiore

8 жыл бұрын

+Davy Ker I usually count to twelve on my fingers. I count the sections or joints on the inside of four of my fingers and use my thumb to point out which section. If you use both hands you can count up to 144 using one hand as the twelves and one as the ones. Come to think of it, I think one of Brady's channels talked about this.

@unvergebeneid

8 жыл бұрын

Malachiore Point is, you're a couple millennia late with all those tricks.

Was reading Plato's Laws, decided to look up the number 5040 on the internets, this video popped up in search. I love you guys.

Looking at the title, I guess it "caught on". Fascinating stuff as always. Thank you!

video length is 13:37 dank

@DatShepTho

8 жыл бұрын

Elite!!!

@xxnotmuchxx

8 жыл бұрын

What is leet and why is this video dank?

@Borednesss

8 жыл бұрын

1337 pwnz0rz

@nal8503

8 жыл бұрын

In the older Counter-Strike games one of the choices for picking "Terror" was the 1337/Elite Crew. Kind of turned into a meme before memes were a thing.

@maltager5106

8 жыл бұрын

Leet is where you replace letters with numbers, e.g. you might say "n00b" instead of "noob". If you try to replate 'leet' with numbers, you get 1337.

lets make antiprime a thing!

@hannovb5379

8 жыл бұрын

no.

@U014B

8 жыл бұрын

Stop trying to make antiprime happen!

@FreeER

8 жыл бұрын

I actually do like anti-prime better than "Highly composite number", it's shorter and reuses the same word (just with a prefix) xD

@qazedctgb19

8 жыл бұрын

+Noel Goetowski so you are anti antiprime?

@homelab-student

8 жыл бұрын

Wolfram Mathworld already recognises "Antiprime" as a synonym of "Highly composite number", so to some it extent it already is "a thing"

Learning the divisor thing was extremely useful, thank you!

I can't stop wondering about this room from Dr Grime, what is that??? Great video as every one in your channel!

the video has 5040 views at the time of writing this... damn.

@bt4670

8 жыл бұрын

Should have taken a screenshot.

@GraveUypo

8 жыл бұрын

thank you for not saying "should of". it's sad the you're the exception.

@rparl

8 жыл бұрын

+GraveUypo Arguably, that could be written "should 've" so it's ok in conversation.

@craftminerCZ

8 жыл бұрын

And the video is kinda leet-long

@virgulewouldthat6009

8 жыл бұрын

+Ross Parlette this is not Grammarphile

Did the phrase anti-prime come off the cuff? Surely it can't have, it's too perfect!

@numberphile

8 жыл бұрын

totally - as he described it I just thought that must be its name... others have thought so too, I have since discovered.

@LukePalmer

4 жыл бұрын

How else are perfect things made?

@basilforth

4 жыл бұрын

It's from a Star Trek episode. ;) j/k

I love it.. learn so much from this channel :D

Loved his ‘anti-prime’! 😂😃🤣👍🏾TFS! Happy Holidays to you both! 🎄❄️☃️🤘🏾💫

I remember having to solve for and write out the answer to 100P20 and I spent an hour multiplying by hand and checking my work in the end it was correct, but I wondered how I could write the same number in less space, and I didn't know it at the time, but I wrote it in prime factorization format. I love how I can watch these videos and relate them to things I've done that I didn't know were special.

Maybe do an episode on 1337, huh?

@alfonsorico7167

8 жыл бұрын

What is special about it?

@TrixxyFlash

8 жыл бұрын

It is the length of this episode. Besides another fact...

@eventseen7317

8 жыл бұрын

the video length is 13:37

@Nightstalker314

8 жыл бұрын

not a prime. 1337 = 7 x 191. you should be ashamed.

@Ruminations09

8 жыл бұрын

+thststth Skaries never claimed it was a prime...

These videos are great. Thank you.

I used to hate math in school, but I can't get enough of these videos. I've seen the video on the quaternions, I would like to see one on the octonions and how much we currently understand them. 🤓

13:37 that's pretty 1337

@pianoss4376

4 жыл бұрын

One thousand three hundred thirty seven is my number

@Jivvi

4 жыл бұрын

0m9 1h4t'5 4m42in9

@natebit7167

4 жыл бұрын

Pianoss lol I was born 13/37 actually

@moose200

4 жыл бұрын

WashiestDrop198 wait wha-

@danedickerson

4 жыл бұрын

What is the significance of 1337????

A teacher like you back in school and I would have been a mathematician today! Keep it up!! :D

@stefanozurich

8 жыл бұрын

This is not the stuff you learn in a maths degree.

@sheg5910

8 жыл бұрын

It's less what he's teaching, and more the passion he has.

@MajesticSkywhale

8 жыл бұрын

no but he means anything he was teaching would be made into fun easy-to-understand examples instead of the usual maths teacher with monotonous voice saying "that's just how it's done" and "you just have to learn it." when you ask questions :P

@KaelynWillingham

8 жыл бұрын

+stefanozurich Not unless you take number theory. And do math in your spare time.

@mdsharfuddinmd5710

Жыл бұрын

Thank you sir

Calling highly composite numbers “antiprimes” is like calling complex molecules “anti-atoms”.

@py10playz82

3 жыл бұрын

Lol

10:36 the number magically becomes 540

@pianoss4376

4 жыл бұрын

Five hundred forty

Where can I buy used Numberphile brown paper?

@numberphile

8 жыл бұрын

I occasionally ebay one or send them to Patreon patrons... follow Numberphile on Twitter/Facebook/Patreon etc and I would usually let people know there!

@tijojose7966

8 жыл бұрын

+Numberphile Thanks!

@ApexHerbivore

8 жыл бұрын

Strange. I can't see Numberphile's reply. Can someone enlighten me?

@TheIchigo1324

8 жыл бұрын

+BobSkiz1 He said "I occasionally ebay one or send them to Patreon patrons... follow Numberphile on Twitter/Facebook/Patreon etc and I would usually let people know there!"

@ApexHerbivore

8 жыл бұрын

TheIchigo1324 TY :)

1:42 "I don't think it's going to catch on..." Haaaaave you met Brady?

Actually, the only highly composite number is 0, because that has infinite factors, because it obviously has itself, and any number times 0 is 0.

In school, I learnt something about factor sums and the names for numbers with certain factor sums.

And I clicked on this because I am a bell ringer, and we love us some 5040 action! (5040 is the number of changes in a peal of seven bells or less, where the goal is to ring all of the permutations of seven without repeating a row anywhere. And who said the bell ringing couldn't be mathematical?)

@Rudxain

3 жыл бұрын

*7!* = 5040 sqrt(5041) = *71* sqrt(7! + 1) = 7*10+1 7! + 1 = (1+7*10)^2

Looks like Brady did a Parker square of naming these numbers

Another great video!

ugh once again i’m reminded how much i love numbers

I still think 2520 is neat. It only has 59 factors, but it's the first number that all numbers 1 through 10 divide into.

@Tweakimp

8 жыл бұрын

The factor to number ratio is much higher with this number. This should be the winner.

@tilnation14

8 жыл бұрын

so 1 should be the winner because the ratio is exactly 1:1?

@Plystire

8 жыл бұрын

1 is the mother number. It represents the essence of being (which is naturally 100%), while 0 represents the essence of nothing. All numbers thereafter are birth'd through 1 and each other.

@georgegoulding8451

8 жыл бұрын

+Tiln TheModerator 2 is also 1 to 1 with 2 factors

@donathartyan2566

8 жыл бұрын

100% off topic here, but you made me think about the Intel i5 2520M

Screen resolutions are often composed of those numbers apparently. Makes total sense actually. :)

Excellent video thanks ☺️ ❤

Recursive definition of antiprimes: 1) A given antiprime has more divisors than the last antiprime. 2) The first antiprime is 2.

'Uploaded 7 sec ago' damn that's early. And I'm not even subbed :(

@hijnaziox

8 жыл бұрын

You should subscribe!

@pythor2

8 жыл бұрын

Not subbed. Pffft PFFFT

@dichidichi

8 жыл бұрын

Subbed as in subtitle or subscribe?

@Mati-le1ko

8 жыл бұрын

+Rizky Andyno Ramadhan subcribed Why would he not be subtitled?

@DongenShoreGaming

8 жыл бұрын

subscribed...> I'm not kinda a math person. Sorry! But he makes quality vids tho

7!

@shotguntornado

8 жыл бұрын

I get excited about it too

@liliesandtulips91210

8 жыл бұрын

HAHAHA

@redbeam_

8 жыл бұрын

7?

@BeatPeet

8 жыл бұрын

7! (7 factorial = 7x6x5x4x3x2x1) is 5040.

@SpartanA5213

8 жыл бұрын

Thats actually really cool

I worked a lot with prime factorization when I was doing my mathematics thesis about group theory (with a focus on dihedral groups). I did a lot of combinatorics without realizing that was what I was doing. I understand this topic.

...a personal favorite from childhood was 55,440. (equals LCM of 1 thru 10, times 22) A current favorite is the tautonymic, easy-to-decompose-into-factors 360,360.

It seems that our clocks and calendar systems use quite a few of these anti-prime numbers. I'm guessing this is intentional.

@pauljs75

8 жыл бұрын

Circles, electricity standards in U.S., probably some other things.

@gabemerritt3139

8 жыл бұрын

Definitely, they are very useful

@IONATVS

8 жыл бұрын

They're mostly artifacts of older cultures that used non-decimal counting systems (mesopotamian numerals, for example, used base 60 and the greeks got their first astronomical tables from them), but yes, the greeks and romans did specifically keep the using the nonnative system because they liked being able to divide them in so many ways.

@pauljs75

8 жыл бұрын

Even with decimals, repeating ones are often a total pain when it comes to quick calculations. (Possible to get deviations adding or multiplying them back together.) So these types of values may be handier than you'd think in modern applications.

@jakebrodskype

8 жыл бұрын

At last! A reason I can give to my friends on the other side of the Atlantic as to why 60 Hz is better! (actually, it matters if you're building synchronous motors...)

After reading comments on KZread for a while I was under the impression that the whole world had suddenly become stupid. However, the comments on this video have restored my faith in humanity. Thanks, guys/girls.

@zombiesalad2722

5 жыл бұрын

Then stop lurking on the wrong side of KZread

as a computer nerd, I go for 45045 which has all odd divisors through 15. Its binary is sweet - 1010 1111 1111 0101. Then can just bit shift to pick up even divisors.

Brady’s response to 1:45 is “**** you I can call the video what I want” 😂

Didn't realize prime factorization would be something that I'd ever watch about on youtube XD

A million dollar challenge: find a highly composite number "n" such that: sigma(n) > ln(harmonic(n)) * exp(harmonic(n)) + harmonic(n) If such a number exists, it will disprove Riemann's hypothesis. On the other hand, if you can show that no such number exists, then the Riemann's hypothesis will be marked as "proved" and you will win a million dollars.

@marttielvisto3519

7 жыл бұрын

Daniel Șuteu please explain the challenge. I don't understand the operations

@anarcho.pacifist

7 жыл бұрын

1) sigma(n) is the sum of the positive divisors of n. For example, the positive divisors of 12, are [1, 2, 3, 4, 6, 12], therefore sigma(12) = 28. 2) harmonic(n) is the nth-harmonic number, which is the sum of reciprocals of the first n natural numbers (1/1 + 1/2 + 1/3 + ... + 1/n). 3) ln(x) is the natural logarithm of x. 4) exp(x) is e^x, where e is 2.71828... Highly composite numbers have lots of divisors, therefore sigma(n) is at its maximum (this special group of highly composite numbers, are called "colossally abundant numbers". See: oeis.org/A004490 ). In 2001, Jeffrey Lagarias (building on the work of Grönwall from 1913), showed that the Riemann hypothesis is equivalent with the statement that I wrote in my original comment (see Lagarias' paper here: arxiv.org/pdf/math/0008177v2.pdf ). Just for illustration, when n=5040: a) sigma(5040) = 19344 b) ln(harmonic(5040)) * exp(harmonic(5040)) + harmonic(5040) = 19836.31... In this specific case, a 1, then the Riemann's hypothesis would be proved correct. On the other hand, if anyone can find a counter-example, the Riemann's hypothesis would be disproved (very unlikely).

@AA-100

6 жыл бұрын

Yes I think I figured it out. The number is 92934939291874748381929399485848388881829922828881209993884777775811002939948585766788289919293984857675848838929199193994998819992992948472810298485757488291919293847575673719393948885888281919199399192929394858675747382819191203050012947365810294858488289191776528593999108876632819298192938884757575748382919192929384857575838.

@witherblaze

6 жыл бұрын

1?

@blue9139

6 жыл бұрын

It is... Not 99999999999999999999999999999999999999999p99999 Or 5000000000 Or 200000000600000000

Seems to me that every “anti-prime” is a valid number of divisors for another anti-prime. (2 has 2 divisors, 6 has 4, 12 has 6, 60 has 12, 360 has 24, 1260 has 36, 2520 has 48, 5040 has 60, etc.)

Anti-primes helped me to understand primes better. Thank You.

In fact some of what he's discussing simplifies a bit if for your prime factorization you include the entire set of prime numbers and have zeroes as the powers of primes that aren't in the factorization. For example 12 = 2^2 * 3^1 * 5^0 * 7^0 * 9^0 * ... . Note that you still get exactly one unique prime factorization for every counting number, it's just that you are instead looking at infinite sequences of exponents most of which are zero. When you do this then the first two rules of highly composite numbers can be condensed to just say that the sequence of exponents must be weakly decreasing. For instance, if you are "missing a prime factor" then that means you have a zero as an exponent which is followed by a non-zero exponent which means the sequence isn't decreasing. Also notice that the formula to calculate the number of factors still works, since if the exponent is zero that translates into multiplying the formula by one for that factor.

@hannovb5379

8 жыл бұрын

infinite sequences are mathematically difficult to deal with.

@thenorup

8 жыл бұрын

Lot's of problems become easier when you use infinite series, just look at Fourier analysis.

@Justin-dk9rl

8 жыл бұрын

Good idea, this way every integer can be unambiguously defined only by the sequence of its exponents

@Bodyknock

8 жыл бұрын

Jabberwocky I'm not sure what you're getting at saying "a^0 = 1 which isn't prime". 2^3 = 8 isn't prime either but it is part of the prime factorization of 40 = 2^3 * 5^1 = 2^3 * 3^0 * 5^1 * 7^0 * 11^0 *....

@Bodyknock

8 жыл бұрын

Justin Right, it's similar to how a decimal expansion is the infinite sum of a sequence of numbers of the form k*10^(-n) where k is an integer from 0 to 9 and n is a counting number. (Except that numbers can have more than one decimal expansion such as 0.500... = 0.4999... while all counting numbers only have one unique prime factorization.)

There are 5040 ways in which you can arrange days of a week!

@mackycabangon8945

5 жыл бұрын

Ashish Jog Write all permutations

@KanishkMalkan

5 жыл бұрын

you just meant 7 factorial indirectly ;)

@blue9139

5 жыл бұрын

Yea because 7! ="5040

@bigfoot722

5 жыл бұрын

This is kinda true: because days of the week are cyclical, {M, T, W, R, F, Sa, Su} is equivalent to {T, W, R, F, Sa, Su, M} and therefore these aren't *really* unique. Truly unique arrangements are 7!/7, or generally (n-1)!

@blue9139

5 жыл бұрын

@@bigfoot722 :D

Its very interesting to point that every single anti-prime is either a multiple or divisor of 12. Put on my list of reasons of why 12 is my third favorite number

i understood most of this. that makes me happy. i got 800 on my math sat, but i was always aware that i was at the low end of 800, with other people at the high end like you.

I'm glad you mentioned it was the 'ancient Greek philosopher' Plato, otherwise I'd be confusing him with all the other renowned Platos around.

5,040 is also 7! (! means factorial.)

@GothicKin

4 жыл бұрын

First time reading this I though, wow how excited for a wrong statement, then I read you meant factorial xD

@Rudxain

3 жыл бұрын

sqrt(5041) = *71* *7!* = 5040 sqrt(7! + 1) = 7*10+1 7! + 1 = (1+7*10)^2

@ViratKohli-jj3wj

3 жыл бұрын

@@Rudxain wow

@debblez

3 жыл бұрын

Any askers?

@austinlincoln3414

3 жыл бұрын

yes hes in the movie called nobody

I really don't like math, but I really like your channel, a lot.

And here I just always called them "factor-licious" numbers.