How about 101+131+151=383? That’s 3 different Palindromic Prime Numbers added up to give you another Palindromic Prime Number.

@julian_ossuna

5 жыл бұрын

and I here thinking 42 was the most special number...

@Emile.gorgonZola

5 жыл бұрын

Nice

@Emile.gorgonZola

5 жыл бұрын

Are there infinite palindromic prime numbers

@ipudisciple

5 жыл бұрын

Are there infinitely many (you meant to say) palindromic prime numbers? There are about c*10^n/n primes of length n (where 1/c is log 10). There are about c*10^(n/2)/n palindromic primes of length n. So yes, but that's not a proof.

@bulgaria9003

3 жыл бұрын

OH NOOOO

Mad Maths Beyond Palindrome Three numbers enter. One number leaves.

@chenyanhao676

5 жыл бұрын

James Jumper this is one of the best puns I seen in a long while

@alephnull4044

5 жыл бұрын

I actually don't get it :(

@Jzphh

5 жыл бұрын

Mad Max Beyond Thunderdome the film

@JJ-kl7eq

5 жыл бұрын

Trust me Aleph. One of the memorable lines in the movie is about Thunderdome itself. “Two men enter. One man leaves.”

@alephnull4044

5 жыл бұрын

Ah, never heard of that movie but it seems many people have.

I got into a fight with 1, 3, 5, 7 and 9. The odds were against me.

@sebastianelytron8450

5 жыл бұрын

So funny I forgot to laugh

@egilsandnes9637

5 жыл бұрын

Even against those odds ... You should be OK.

@Nothing_serious

5 жыл бұрын

If it was with pi, e, and square root of 2, then that'd be an irrational fight.

@iangorix3557

5 жыл бұрын

i would back you up, but you don't believe in the imaginary. If only 3, 5, 7, and 9 left, then your opponent would be back at square one. Try to be careful, though, I think 3, 5, and 7 are in their prime. Here's a tip, you might be able to create a division between 9 and 3.

@manimax3

5 жыл бұрын

I think this is getting pretty complex.

Could be a module in "keep talking and nobody explodes"

@SimonDoer

5 жыл бұрын

Increases the Manual by 40 pages, just for one module. lol

@thomasthetankengine2653

5 жыл бұрын

Yesss

@nymalous3428

5 жыл бұрын

One might have to rename that: Call your loved ones, because you're going to explode.

@TheSweBoo

5 жыл бұрын

I played that game yesterday, that'd be insane hahaha

@zoranhacker

5 жыл бұрын

Maybe just have a few different types of numbers so it's not as extensive

So, if every number is sum of 3 palindromes, every palindrome is sum of 3 palindromes too...

@unreal-the-ethan

5 жыл бұрын

Palindrome + 0 + 0 = Palindrome. Yes, I know it's disappointing.

@SimonDoer

5 жыл бұрын

I believe every single-digit number counts as a palindrome. So it would just be 0+0+number

@mrmimeisfunny

5 жыл бұрын

It is less cool than it sounds. n+0+0

@pulykamell

5 жыл бұрын

Actually, a lot of the palindromic numbers do reduce to another three palindromes. Pretty much all the ones I randomly tried did, until I got to three-digit ones.

@Septimus_ii

5 жыл бұрын

Aside from the trivial ones in the other comments, if the first digit is more than 2 you can split each digit eg 5639365 = 1111111 + 2222222 + 2306032

Any quality math/logic content: * exists * Brilliant: *IT'S FREE REAL ESTATE*

@tofast4ya

5 жыл бұрын

So, kinda like... Gödels incompletenes Theorem?

@farisakmal2722

5 жыл бұрын

I KNOW RIGHT? I THOUGHT I WAS THE ONLY ONE GETTING ANNOYED

@DevilSpider_

5 жыл бұрын

I am annoyed by the sponsorship.

@thatoneguy9582

5 жыл бұрын

Marek Šťastný *any quality -math/logic- content

@whatisthis2809

5 жыл бұрын

*Super large numbers exist* Yeah i don't think so

Every night I wake in a cold sweat assaulted by my thoughts asking me “how, how did somebody discover this”

@BaddeJimme

5 жыл бұрын

And how many nights have you known this? The video is 1 day old.

@corpsiecorpsie_the_original

4 жыл бұрын

@@BaddeJimme - the paper was published more than a day before this video

Every now and then I find a new video on this channel that takes a simple concept and uses it to blow my mind in the most satisfying way. Today is one of those days.

0:00 "I've got a cute little mathematical fact for you" - instant like :D

Love the Gaussian blur at 1:10... wonder how many others caught that reference!

"It's like a Sir Dooku!" Excuse me, it's _count_ Dooku.

@arnavj.3927

4 жыл бұрын

Very underrated

@Robi2009

3 жыл бұрын

Sudoku, not Sir Dooku... Don't laugh at Dr Grime's accent :/

@valthiriansunstrider2540

3 жыл бұрын

@@arnavj.3927 Agreed

“...But your gonna have to memorize 40 pages of algorithms...” Matt Parker can be heard distantly screaming

@fisch37

2 жыл бұрын

Meanwhile Speedcubers: So I did that

@rsyvbh

3 ай бұрын

​@@fisch37 57 oll and 21 pll is just the start

I never comment, but here is my first exception on KZread, with the hope that James or the other guy reads it. In Spanish we have a special word for PALINDROME NUMBERS. It is called CAPICÚA. We don't say "números palíndromos" ("palíndromo" being the word for, of course, your guessed, "palindrome"), but we are mathematically conscious. We say: ¡capicúa! I think it's a nice word that everyone should learn because it saves time. So: "todo número es la suma de tres capicúas." I hope it catches up.

@chrisg3030

5 жыл бұрын

I read somewhere that "capicúa" is originally Catalan. It literally means "head and tail" and was coined specifically for palindromic lottery numbers, which were believed to be lucky.

@Iulius4

5 жыл бұрын

@@chrisg3030 Yes cap i cua

Was ready to ask "Does this work outside of base 10?" and 3:17 comes around and smacks me. Great work to whoever discovered this.

@bvbinsane1vanity

Жыл бұрын

Maybe should watch the entire video before asking questions that you think will make you sound smarter then those in the video.

@lietz13

Жыл бұрын

@@bvbinsane1vanity projecting much?

A new episode with James... what a treat!

As interesting as this is... I'm curious as to how many unique solutions of 3 palindromes you can have for certain numbers.

@mrshr3d

Жыл бұрын

Did some mucking around in Excel using Gaussian's birthday, and found another solution: 30041777 = 29955992 + 85058 + 727 I would expect that the larger a number is, the more solutions it has.

I am impressed again and again in how people come op with that kind of theorem

@bernardfinucane2061

5 жыл бұрын

They actually get paid for it!

@jaakkonyh

5 жыл бұрын

High

@shelbyg.8553

5 жыл бұрын

Must've been really bored

@ahuman6546

3 жыл бұрын

@@jaakkonyh gold

@chriswebster24

2 жыл бұрын

They are nerds. I’m man enough to admit that I’m jealous of their superior intellect, though.

I am having an existential crisis right now because of VSauce and Numberphile.

I'm very glad you put links in for the original paper and also for the website (for when I lose patience with the paper). I'm going to have to try this at work if it gets slow...

@nymalous3428

5 жыл бұрын

By the way, I went to the website that does it for you and entered 1 000 000 006 (that is, a billion six... I did not put the spaces in, those are just for the reader's convenience). It actually came up with a nifty set of palindromes!

Great stuff hear! Thanks for the video, I could watch this all day!

I liked how the carry line in the Pi example was also palindromic, but was a bit sad to see that this isn't always the case.

7:40 "ashume"

@JeeCistion

5 жыл бұрын

???

@tamt332

5 жыл бұрын

Smerg the Dargon You’re right, that is the correct pronunciation of “assume”

@TiaKatt

5 жыл бұрын

Pretty sure that's perfectly correct for Brits. Plenty of words are correctly pronounced differently in different countries.

@willman85

4 жыл бұрын

It's a regional dialect. It's not very common in the UK.

Gotta hand it to them, I'm super impressed! Top demonstration too, as always on this channel.

I love it when the video really is just about numbers. Classic style!

Mathematical proof of Brady's conversion

Random uncivilized animal: "This is useless" Us: "Shut up this is art"

@davidtrindle6473

5 жыл бұрын

Psykopate Both statements are true. Why attack others and call them names? Take a break from math for a while and consider the most important question for you to ask, “What is the payoff to me of putting others down? Comfort? Safety? Stability? Importance? Getting laid?...you get the idea.”

@55Marvin55

5 жыл бұрын

Why don't you take a break from internet, take a deep breath and re-read my comment with some distance and not literally ? PS: i like how you subtly attack me and call me names while calling me on attacking others and calling them names

@davidtrindle6473

5 жыл бұрын

Psykopate Sure.

@Triantalex

7 ай бұрын

false.

The site by Chritian Lawson is just .. ...AMAZING

One of the more amazing videos.

The completely crazy (and potentially coincidental) thing is that the carry row contains a palindrome number as well for the first digits of π: 101101

@lucanina8221

11 ай бұрын

I guess if you sum palindrome numbers and the result is palindrome you have this behaviour

Nice video!

For some reason, this felt really natural fir me. Cheerio, James!

I just studied maths for an hour and thought I needed to relax a little, and what did I do? Started to watch a Numberphile video.

Sooo... if this works in every base, does this mean you could encrypt a binary file into 3 palyndromes that can be stored separately, and that you would need all three parts to reconstitute the message? Also, because they are palyndromes, you can also compress the information by a flat 50% per number of palyndromes (multiplicatively) before standard compression, since you only need to store half of it. In addition to all this the message can be reconstructed by two or three simple additions! This is pretty significant cutting edge maths! I'm gonna try to do this in C# with BigInteger type or a bitmap...

@sumdumbmick

Жыл бұрын

the palindromes are all close in size to the original number, so this compression will actually take more room than the original number.

@abigailcooling6604

Жыл бұрын

@@sumdumbmick Although it won't make the file smaller, it might make it more secure as you have to have all three palindromes before being able to tell what the original file is.

@TheEternalVortex42

11 ай бұрын

For binary it actually takes 4 palindromes. That means it's no better than the trivial algorithm of writing it as an XOR of two things (i.e. a "one time pad"), which is already optimally secure.

Even with the algorithm, it's like solving Minesweeper

James Jumper took my word... this was MAD! Felt like doing soduko or solving the Rubik's cube...

Fascinating!

I was flabbergasted when I learnt that its true for all bases...😯😯

@torlumnitor8230

5 жыл бұрын

Why did it upset you? It's amazing.

@stevethecatcouch6532

5 жыл бұрын

Aaron Cruz It isn't true for all bases. Dr. Grimes misspoke. The authors give 10110000 as an example of a binary number that requires 4 palindromes. The problem is that, with the exception of 0, all binary palindromes are odd. An even binary number is the sum of three palindromes only if it is the sum of two palindromes.

@arcuesfanatic

5 жыл бұрын

No, he said it was proven to work for all bases 5 or greater, and that someone else worked on the base 2, 3, 4 numbers.

@Kyrelel

5 жыл бұрын

Did you not read the first Abstract he showed? It is only valid for bases >= 5

@Rhovanion85

5 жыл бұрын

I am not a native English speaker so I had to look up Flabbergast. I thought it meant "loud farting" or something.

S U D O O K O O

@schizophrenicenthusiast

5 жыл бұрын

Count Dooku

@stephanosioannou1825

5 жыл бұрын

@@schizophrenicenthusiast hello there

@OrangeC7

5 жыл бұрын

my old friend

@gcp-starchump

5 жыл бұрын

it *is* a bit like a sudookoo, yeah!

@gcp-starchump

5 жыл бұрын

also, *ASHOOM.* the paper tells you to ashoom.

Amazing, Thank you sir!

3:19 "You can do this in any base" That's what I was waiting to hear! Before 3:19, I was thinking "You do know that base 10 decimal form is not the One And Only True Form of a number, right?"

5:52 "It's like you're doing a sudoku" lol

He's right, you do have a choice when it comes to the second digit of the second palindrome! He put 2, as per the algorithm, but I put 1 just to see, and it worked out to: 2210122 + 915519 + 15951. Then I tried it with 0, and I got 2220222 + 904409 + 16961. It doesn't work with 3, though. ...And then if you change the second digit of the first palindrome, you really open up the possibilities! 2159512 + 971179 + 10901 2163612 + 966669 + 11311 2143412 + 990099 + 18081 I'm sure you could get a dozen more possibilities as well. Once you have the first and last bit of each palindrome sorted, solving the rest really does have the same sort of feel as doing a sudoku. It's pretty fun, I high recommend it as a way to procrastinate from writing your master's thesis while still feeling smart.

This is amazing

Mind blown. Glad I wasn't the one who had to write the code that captured that algorithm. Lot of work.

I see james grime, *I CLICC*

For me the most remarkable piece of information from this video is that there exists someone whose name is Christian Lawson-Perfect

@Rithmy

5 жыл бұрын

for me its your username.

i can think of an easier way than the methods in the video: first you identify the type of the number and fill in the first and last digits, then you subtract the 3 numbers you get from this step. For example, for 3141592 in the video, you subtract it by 2000002, 900009 and 10001 and get 231580. you then delete the zero from the end and get 23158. this number will follow the same property as it can be put into 3 palindromes, which are the middle part of the answer for 3141592. then you can identify the type of number this is and carry on.

Yay, James Grime!

Amazing

It's also easily demonstrable that many numbers have more than one solution. 9 for example can be 9+0+0 or 8+1+0 or 7+1+1 or ...

@chrisg3030

5 жыл бұрын

Yes, I went on that website and easily found alternative solutions myself for 5-digit numbers even.

Thank you for providing me with a new and fun way to fill up my spare time, I'll just go print out those *40 pages*

WOW...... that's actually pretty cool =D. Really liked this video

at 7:40 there is no need to assume you have a carry you definitely do as the column to the right already has a value greater than the target i.e there is already a 4 so to reach a 1 a sum of 11 must be reached hence there is definitely a carry

@AzrgExplorers

5 жыл бұрын

He's following the algorithm exactly. Presumably the algorithm is simpler if you leave checks like that till the end.

@canis_lupus2220

5 жыл бұрын

Also there can be carries of 2 when adding 3 numbers...

@OrangeC7

5 жыл бұрын

Perhaps the paper calculates the numbers in a way that makes it only necessary to carry over one. Maybe that's what happens every time? Then again, there could just be twos and they happened to not be in the examples.

@Reubs1

5 жыл бұрын

That would work for this particular number but that may not always be the case. The algorithm James is using was designed to work for all numbers in any base, so it has to be made robust enough to deal with all cases.

@Flourish38

5 жыл бұрын

palp1880 Algorithms are designed to require no thinking at all when you are running them. You are correct, but it is either faster or simpler (probably both) to not think about it and correct it at the end using the algorithm.

cool, now I have something to do in my spare time, program this in python XD

@bonenintomatensaus

5 жыл бұрын

That's gonna be a loooong script judging by that paper they showed

@copperfield42

5 жыл бұрын

excellent, I'm going to have fun for days XD

@AndresFirte

5 жыл бұрын

Please share us your program when you complete it

@srirammusic4033

5 жыл бұрын

All the best

@copperfield42

5 жыл бұрын

Adrés Firte sure (o.o)b

What an amazing fact, any base too!

Thank you for video on my birthday :)

Anybody else’s spine hurt when he drags the sharpie across the rough paper?

@Kyrelel

5 жыл бұрын

because, like you, they are weirdoes

I want to see a 3 Parker palindrome.

@Jivvi

5 жыл бұрын

300=191+99+010 It's not technically right because 10 isn't a palindrome, but it works because of the leading zero.

Me starting to write: “ does this work in other bases?” at 3:07. James at 3:17: “...you can do this in any base...” I’ll just shut up and listen.

Love the slide rule on the table. Conversation piece?

Fark I love this stuff but got lost at 0:02

ASHume

@imveryangryitsnotbutter

5 жыл бұрын

Gesundheit.

Amazing - I didn't believe it to start with...😱👏

I just love how excited this guy is about math

Pure mathematics: fun with no foreseeable application

@neonKow

5 жыл бұрын

Number theory is used in cryptography

@thomasthetankengine2653

5 жыл бұрын

@@neonKow but that's such a small part of everything mathematicians do

@torlumnitor8230

5 жыл бұрын

It's not the solution, but the path to it, that furthers understanding.

@Hootkins.

5 жыл бұрын

The same used to be said about fractals.

@BaronVonTacocat

5 жыл бұрын

@Hootkins Fractals are used in computer animation. I think the only application for palindromic numbers is wizardry. ; D

I see lots of comments here wondering about how this holds for small numbers, but to me, the surprising thing is that it works for *large* numbers. Palindromes get sparser as numbers get larger, so I would've expected more palindromes to be required to make larger numbers.

@pierrestober3423

5 жыл бұрын

exactly my thoughts

@BaddeJimme

5 жыл бұрын

If you consider 1000 digit palindromes, there are about 10^500 of them, and roughly 10^1500 triplets of such palindromes. These triplets far outnumber the roughly 10^1000 numbers that they might add up to.

@AzrgExplorers

5 жыл бұрын

Yeah, that makes sense.

Fantastic. Thanks.

I found a glitch on the site: type the number (i.e.) 11021 and the site gives 4 numbers to add together, although one of them is zero ("00" actually) and can obviously be assumed to be unnecessary.

@jeffo9396

5 жыл бұрын

That's certainly an interesting glitch. It seems to be unique to that one site though, because I tried 11021 on a different site, and it didn't generate "00".

I can do better than that. Every positive integer is a sum of ONE palindrome. In base 1-higher-than-itself. Because it's a 1-digit number in that base, you see, so it's a palindrome.

@badgerb2172

5 жыл бұрын

Every positive integer n > 2 is a palindrome in base (n-1): 11 base (n-1) = 1(n-1) + 1

@greenwaldian

4 жыл бұрын

Congratulations youv'e just discovered how to count

@arthurthekyogre9155

4 жыл бұрын

Your profile picture is evil

@naverilllang

4 жыл бұрын

I was today years old when I realized that tally marks are base 1

So does that mean then that every palindrome number can be written as the sum of 3 palindrome numbers? 22+44+55 = 121 is all well and good, but of course all these can then be written as palindromes 9+7+6 = 22, 1+2+3 = 6, 1+0+0 = 1. From this we can determine that 0 is a palindrome, but if that's the case, suddenly it become quite easy to find these triplets for any palindrome number, simply by adding 0 twice to the original number.

@OrangeC7

5 жыл бұрын

If you require the two additional numbers to have more than one digit unless the beginning number is less than 19, then you could probably calculate the reduction of many numbers and graph it out into a tree to see if it forms any significant shape.

@kitty13kitty

5 жыл бұрын

entering any number of 3's into the algorithm seems to agree with you

@seededsoul

5 жыл бұрын

Great breakdown, you show that this theorem is not significant math.

@theignorantphilosopher4855

5 жыл бұрын

Assuming you are replying to me, I don't know that you're right, but I do think clarification is needed.

@namewarvergeben

5 жыл бұрын

Assuming that zero is a palindrome, then adding zero twice only works if the other number is a palindrome. The premise was that every positive integer can be written this way, in which case zero just doesn't work, and other single-digit "palindromes" are only useful up to maybe two- or three-digit numbers.

Would love to see a video where Cliff Stoll talks about sphericons!

@7:35 You don't need to assume the carry 1. because in the column right next to it you need to add something to a 4 to get 1. Obviously that's not possible without a carry over. So yeah....no guesswork or assumption needed. We HAVE to carry over 1 to make the next culumn work :)

Irrelevant but I’ll prove why my birthday is the best. 16/04/02 Every number is the square root of the one before it (other than 16 since there are no numbers before it)

@jeffo9396

5 жыл бұрын

Unless you were born on the 256th minute of that day.

@supermarc

5 жыл бұрын

Four days late, but congrats on your birthday.

Was it a car or a cat I saw?

@jacksainthill8974

5 жыл бұрын

+Sebastian Elytron. _Was it a car or a rat I saw?_ A rat. Tara!

@nymalous3428

5 жыл бұрын

Ask Schrodinger.

@OrangeC7

5 жыл бұрын

It was a racecar

@bonenintomatensaus

5 жыл бұрын

A man, a plan, a canal. Panama!

@X_Baron

5 жыл бұрын

Notable gel baton?

7:30 - in this case you know the carry is a 1 without assuming it, because you've got a 4 in the column that needs to end up with a 1, and you can't get a carry of 2 from that row, so it has to be 4 + 0 + (7 or 6 with a carry) = 11, carry the one.

Love the vintage microphone at the end.

Numberphile is meant to be about numbers :) Videos like these are refreshing. No magic tricks, no physics. Just number theory.

Are palindrome representations unique?

@Jaweissnich

5 жыл бұрын

No. 2=2+0+0=1+1+0 for example.

@alexanderf8451

5 жыл бұрын

T L Ak, I should have thought of that. Shame really. If they were unique representations palindromic numbers would suddenly be really mysterious.

@Jivvi

5 жыл бұрын

Also, palindromes like 999 have lots of different solutions. 333+333+333 616+232+151 787+111+101

That’s a really neat piece of math

I've stopped watching Numberphile videos, but when it's James Grime it's an insta-click for me

8:36 Anyone else notice that the carry is also a palindrome! :D

Lagerregal

@icesun_

5 жыл бұрын

Regallager

@OrangeC7

5 жыл бұрын

Reggerregger

@jeffirwin7862

5 жыл бұрын

Is it crazy how saying sentences backwards creates backwards sentences saying how crazy it is?

Gaussian blur on Gauss' portrait--subtle, but quite neat at 1:06

My favorite numberphile person!

Dude put your art up. It’s been there for like a year.

1. IS THE LONLIEST NUMBER THAT YOU'LL EVER DO.

@imveryangryitsnotbutter

5 жыл бұрын

Two can be as bad as one.

@blindleader42

5 жыл бұрын

It's the loneliest number since the number one.

Fascinating

At 6:20, does the algorithm specify a 2 (or just specify that there's no carry in that column, or something)? Or is it similar to later on when he says "You have a choice here and if it's wrong you'll correct it later?"

The carry numbers also formed a palindrome... coincidence?

@ErwinPommel

5 жыл бұрын

Or something more sinister?

@markorezic3131

5 жыл бұрын

the universe is a -hologram- *palindrome*

@Monotof1

5 жыл бұрын

I would assume so, otherwise this information would likely be used in finding the palindromes

@exod4

5 жыл бұрын

I THINK NOT

@OrangeC7

5 жыл бұрын

It's a coincidence, it doesn't happen for other numbers. Maybe it always happens if the beginning number is a palindrome as well? I wonder how you would prove that...

They found the algorithm and proved that it's always possible, I'm more interested in WHY you can do that.

At 7:40, you don't need to assume. You can see that the next column already has 4 and 0 and it should add up to 1 so obviously it would leave a remainder of 1.

YAY James!

Some guy: Man I with their was a way I could figure out the three palindromes that summed produce this number. Some other guy: there's an app for that... Also why?

In base 1, every sum is entirely made up of palindromes.

The videast Michael Launay, from the channel Micmaths (French), gave me the will to start watching your cool videos again :)

I don’t know if this was just coincidence, but I loved that the carry row was a palindrome as well

That is the most useless thing I learned all week.

And if you write that date *properly* the three palindrome numbers are 4001004 , 281182 , and 19591.

@vivafeverfifa2524

5 жыл бұрын

Well, not properly, it's just Americans write their dates backwards.

@jonathanallan5007

5 жыл бұрын

13311331 + 4404044 + 55055 would make a "proper" version of 17770430 - the digits of the ISO 8601 format. (Or 11022011 + 6360636 + 387783 if you use the algorithm)

Another James video :D

wow that is amazing! and i probably will forget this! :(