73939133 - Probably the Most Interesting Prime Number [Part 1]

[@NPCooking69]

Hey you there! :D Thanks for watching! Make sure to watch the other part of the video too kzbin.info/www/bejne/nGPPdnVqo7Kgr6s and to subscribe to this channel as well as Flammable Maths Two if you haven't done so already and enjoyed what you've witnessed here today! :D

[@guill3978]

How do you proove that is number is a truly prime number?

[@integralboi2900]

Guille Check whether it’s divisible by any primes that are smaller than it. If it is divisible, then it’s not prime.

[@integralboi2900]

Adam Romanov You were complaining on 3b1b’s vid and you’re doing it here. If these videos are too easy for you, then go to some of his older videos, which contain complex analysis and other stuff or you could watch Michael Penn’s videos. He was explaining how numbers work, so he could transition into the summation formula.

[@integralboi2900]

I find 57 as the most interesting prime number.

[@integralboi2900]

It’s right and left truncatable.

[@guill3978]

No, it's not prime. You can decompose it as 3 times 19.

[@hemandy94]

@@guill3978 r/woosh

[@sudhansh6998]

@@guill3978 Someone just disrespected Grothendick smh

[@noether9447]

@@guill3978 the "smartest" mathematician said that it's prime. I know whose word I will take.

[@dradenmerenox7172]

0:08 can someone redefine our boi to be a 1 dimensional Hilbert Space? He wouldn't be lonely, he would have the dual space.

[@Luebbi97]

1-d vector space also has a dual space (though not a dual space of continuous functionals as it doesn't have a topology), so there is no need to be lonely ;)

[@abramthiessen8749]

In binary the largest right truncatable prime is 7 (111).

[@elliottsampson1454]

but 1 isn't prime, so there aren't any. in base 3 though, the biggest is 2

[@abramthiessen8749]

@@elliottsampson1454 You are correct. I had to extend the definition of primes in order to get anything to work in binary. Which is clearly cheating.

[@EngMorvan]

@@elliottsampson1454 in base 3, 212 is prime and right truncatable. Also, it is left truncatable and a perfume brand. 😁

[@elliottsampson1454]

@@EngMorvan in retrospect I don't know how I got that wrong

[@reubenadams7054]

I liked the technique you used to generate them! It perhaps could have been explained a bit simpler: 1) The first digit must be prime (obviously). 2) Each time you add a digit, it cannot be 0, 2, 4, 5, 6, or 8, because numbers ending with one of these digits are not prime. 3) I assume you did the decimal expansions to get the formula p_n = 10p_{n-1} + d_n, which can then be used for the python code. But I imagine most viewers would find this more direct explanation of the formula easier: To append a digit to the end of a number, you need to shift all the other digits one place to the left, which is the same as multiplying by 10. This leaves a zero at the end, and replacing the zero with your digit is the same as just adding the digit.

[@cougar2013]

My thoughts exactly. No need to go into so much detail about digit decomposition will all the notation etc. I couldn’t bring myself to watch it, so I fast forwarded through everything. Then I read the video description lol. This was a very confusing way to explain something very simple.

[@PapaFlammy69]

No, it's just the mathematically right way.

[@gibson362]

@@PapaFlammy69 yeeeee guys u need mathematical rigor!!!

[@noshadb.e3111]

if you told the teen me "you would procrastinate with Math in future" I would say "get out of here" but.. here I am and I am enjoying it

[@CoyMcBob]

Nice video. Does anyone else think he used a super roundabout way to show the possible values of dn? I mean he could have just said that prime numbers greater than 1 digit long cannot be even or be divisible by 5, so they could only end with 1, 3, 7, or 9. That seems much more straightforward haha

[@JoseFernandes-js7ep]

He had to prove it with rigor. Afterall he is a mathematician.

[@CoyMcBob]

@@JoseFernandes-js7ep Hahaha I guess. I mean what I said above can be said just as rigorously and in a tenth the time

[@Ashbakhaaz]

But the trunkable number property is base dependant. Meaning that, unless it also has other interesting properties not mentioned in the video, 73939133 is only interesting in base 10. But some mega numbers are interesting in every base; so 73939133 must not be the most interesting mega number.

[@chrisg3030]

I agree it's base dependent. I think I just found a longer one in base 26: 511773N939F5 (but please check if you're interested). The bigger the base the easier they must be to find. Say you already found a suitable prime of so many digits in a given base, then tacking another single digit onto the right is more likely to result in yet another prime if there are a lot of single digits to choose from, that is, a big base. In general, I'm a bit surprised that KZbin vids about interesting numbers so often ignore the base dimension and just stick to base 10. Some deeper patterns are being missed out on.

[@maehmaehmaeh9560]

"Most efficient algorithm i can think of in python" hearing "efficient" and "python" in one sentence kinda hurts my brain

[@jt....]

Python is not *_that_* bad. It is efficient enough generally speaking, and if used properly it can be faster than what one would write in C for example, because of things like generators and certain optimizations one wouldn't implement in C generally. Of course if one reimplements all optimizations Python has, C will be faster, but still. Python code *can* be quite efficient

[@thinboxdictator6720]

@@jt.... I agree with you. but from what I saw in his video where he wrote program for this, his python skills are not that impressive. it could be that talking to audience and explaining what you are doing is taking some of his brain power, but .. even then ..

[@jt....]

@@thinboxdictator6720 I noticed that too, but still, that isn't the programming language's fault

[@scubasteve4971]

3B1B where you at???

[@user-en5vj6vr2u]

c++ gang

[@JBergmansson]

*Start with a good introduction of a cool concept. *Take 13 minutes to derive, in an excruciatingly pedantic way, the properties that each digit of a right-trunkatable prime has to have. (First digit needs to be a prime, the others can be chosen from {1, 3, 7, 9}.) *Explain the python script, which combines all the numbers according to the rules above, letting people know that it uses "an algorithm" to check if a generated number is prime. *Finally get to the most interesting fact about the number, and explain that since "the algorithm" has checked every combination we could come up with, we know that the highest number we got is the highest possible right truncatable prime.

[@richardslater677]

I’m no mathematician but isn’t it blindingly obvious that the digits of a right truncatable prime must only include 1 3 7 and 9, except the first digit which must be 2. 3, 5, and 7 only. The last digit of any prime number must contain these digits only or it’s not prime.

[@PapaFlammy69]

sure, but Mathematicians like to prove statements :)

[@roteruebe9919]

This is the first flammy video where I understood everything.

[@GammCheaNoo]

Cool video, and easy enough to follow (at least for me). But this is an interesting way to go about this. I might have thought to explain it in a more intuitive way like "Well, if you chop of the last digit you obviously can't get an even number, as it wouldn't be prime anymore" (and so on). This might have been how other chanels would have gone about this as well, but the way you tackled this seems more rigorous. You had the same ideas but put them into a more mathematical framework and worked with that, instead of just working with the gist of the idea. When taking a step back you can directly see how everything that you showed simply has to be true intuitively. Good stuff.

[@jebrooks]

Fascinating video

[@YellowBunny]

I don't really like number properties that rely on a certain base.

[@k_meleon]

I love your vids man!

[@KillianDefaoite]

I agree.

[@chrissekely]

Are there number properties that don't depend on the base?

[@Kram1032]

@@chrissekely Lots!

[@YellowBunny]

@@chrissekely Yes, a prime number for example is a prime number in any base. But when the property contains something like taking apart the digits of a number that usually means that the property depends on the base.

[@mattc3581]

Feels like we did two blackboards worth of maths to find out properties that were obvious from just looking at the question :( If you want to make a longer truncatable prime you have to have a shorter one and add a digit on the end, which would clearly make it 10 times bigger plus the digit on the end. What digits can you add on the end, well guessing we would rule out the ones that would make the number obviously even or a multiple of 5.

[@hemandy94]

The first few minutes in when you talked about right truncatable primes I noticed that all the digits were odd and I thought the reason being if there exists an even digit inside the number then it wouldn't be right truncatable anymore. It could even result in the new number being divisible by 3. Luckily, in the latter portion of the video you explained throughly the exact restrictions and limits the digits have .

[@HurricaneEmily]

Thanks for the video. I normally can’t keep up when people go really fast but I understood you perfectly. I wasn’t aware of these primes. Hadn’t thought about it. Off to watch your python video.

[@arturslunga3415]

Very fascinating! I am amazed that there is a finite number of right truncable primes, i would not have guessed that.

[@PapaFlammy69]

yup, quite surprising indeed! =)

[@franolich3]

How do you prove that the list of right-truncatable primes is finite? Surely the process of adding digits to generate new candidate right-truncatable primes can go on for ever. The algorithm you described never terminates. So there must be another step in the logic to prove that there are no right-truncatable primes beyond 73,939,133. Or did I miss something blindingly obvious.....

[@franolich3]

​@Dawid Garus Much appreciate you bothering to point out the blindingly obvious. I need more sleep!

[@darylewalker6862]

Francesco Tirimo, I thought he was going to show a formula that indicates where to stop. But here it’s just an exhaustive search where all the combinations of 739,391,33{1, 3, 7, 9} fail.

[@timmycasey]

@Dawid Garus Ahhhh, yes. Thanks - this is why I came searching through the comments!

[@Booskop.]

Prime numbers are great for prog rock or prog metal/math metal. Odd time signatures are the best when they're prime. 5/4, 7/8, 19/16, 23/32 etc. I love prime numbers.

[@sudhansh6998]

*coprime

[@devincetee5335]

9/8 8/8 7/8 Let's see who gets the reference.

[@kevin27966]

Is there a set of right-truncatable primes where instead of truncating off 1 digit at a time, you must truncate off 2 digits at a time? If so, what is the largest member of that set?

[@chrisg3030]

11031121072123030309671749 is as far as I got, but please check. Nevertheless it has 13 digit pairs compared to the 8 single digits in 73939133. It was fairly easy to get to by hand in the sense that though laborious, when appending a further 2 digits to an already truncatable prime I only twice had to backtrack and try a change to the current last 2 digits. So it wouldn't surprise me if the largest was pretty large.

[@tyrannism5648]

Those 9s make me want to cry

[@Kdd160]

This channel's name should change to flammablenumberphile 😂😂

[@MathIguess]

Dude I'm gonna record my mega fav number thingy today :P

[@MathIguess]

Lol when you said "it's a prime number, thank you guys for watching" xD I laughed out loud fr

[@PapaFlammy69]

:D Can't wait to see it! :)

[@jony7779]

wheeehhhLCAM back to anaahhhhhbideoo ;) love it every time

[@LittlePharma]

This feels like it should be a project Euler problem!

[@alcesmir]

It has at least one problem about truncatable primes already, e.g. projecteuler.net/problem=37

[@nathanielouzana]

Oh, look, a video I completely understood for once 🤪 I have hope! 😂

[@happygimp0]

Are there number systems which can produce truncatable primes with an infinity length?

[@chrisg3030]

Maybe If there was a maximum gap g between primes and if you had a number system b such that b-1> g, you could always find a single digit that would bring the current truncatable prime up to the next one. But if you go with Euclid's famous proof (which I must admit I've never quite grasped) that there's no maximum prime, then maybe there's no maximum prime gap either.

[@Nimasho2go]

Neat video. Cool number. But what are those sigmas? The only reason I figured out what it is is because you said it was a summation as you wrote it. It takes .5 seconds to make a Σ. You don't even need the serifs.

[@XayadSC]

very cool video ngl I'm a bit of a prime number nerd.

[@mastershooter64]

this video showed up in my notification and the full title didn't show up, it was like "73 963 133 probably the most interesting..." i thought the title was most interesting number or something and after that i seriously thought you were gonna say that this number was divisible by both 69 and 420. well lets be honest here the great flame math boi will definitely make a video about that. also i like the number 86940

[@amirbannouri4642]

that's my dad's phone number omg

[@pmcgee003]

Nice guy. He says "Call your mother".

[@joryjones6808]

4:43 I thought your most favorite number would be 169.

[@cicik57]

hey, can you solve that analytically, because eratosphene siege + check number is way too easy ...

[@bglfine7902]

Thanks papa flammy

[@simplicjusz]

thanks to #MegaFavNumbers I discovered a dark web of maths content on YT that will take several lifetimes to watch. I better get going now.

[@ErhardNeher]

two, free, fave and seven

[@muskyoxes]

I can't get behind a number that depends on base ten for its coolness. Its coolness should transcend base or, failing that, should be based on base 2.

[@Jirayu.Kaewprateep]

That is why we always found these numbers in natural functions, 73 939 133 as they canno't digest more.

[@billclintonscomputer1408]

why do your sigmas look like 🗿's

I came to the comments just to see what people have to say about those sigma symbols... and the three dots that follow???

[@tandoril4253]

Yeah picking a list of primes I can generate a number with this property like 59393 but this is the biggest

[@parodysam]

That’s super close to my phone number which is also a prime.

[@rob876]

How about implementing the algorithm in a SQL script?

[@aldasundimer]

with recursive find(prime) as ( select * from (values (2), (3), (5), (7)) as initial(prime) union all select prime * 10 + digit as prime from (values (1), (3), (7), (9)) as next(digit), find where ( with recursive factors(v, factor) as ( select (sqrt(prime * 10 + digit)::int) + 1 as v, false as factor union all select v - 1 as v, (prime * 10 + digit) % (v - 1) = 0 as factor from factors where v > 2 ) select not exists (select * from factors where factor) ) ) select prime from find you are welcome :D

[@aldasundimer]

it is terribly inefficient, but I did not want to use functions, and did not find an easy way to precalculate the primes.

[@aldasundimer]

using postgresql btw

[@cosimobaldi03]

Now you got me really curious: why do you like 135? I mean it's not bad, it's 5 x 3^3... But what about you?

[@sthubbar]

Thanl you. I could follow.

[@HAL-oj4jb]

Both parts are equally long and i instantly thought this is another trolling video lol

[@cacostaangulo]

It is nice, well done, but the explanation can be done in 5 min instead of 15 min.

[@hoodedR]

Wow my guess was close.. I thought each substring would also be prime

[@redpepper74]

Ranjan Bhat that would be pretty crazy! But 3 * 3 = 9 so there goes that guess haha I wonder what the highest number with that property is?

[@redpepper74]

Ranjan Bhat I’ve just discovered some cool properties! You can find all of the numbers where each substring is prime using this process: *Start with all the single-digit prime numbers and join them together with each other. Of those numbers, remove the ones that aren’t prime. Then, take all those double-digit numbers and join them with each other. By “join them,” I mean to overlay them with an offset of one digit. All overlapping numbers must be identical. For example, joining 37 and 73 results in 373. Remove all numbers that aren’t prime. Repeat this process for the newly created 3-digit numbers, and so on.* A comprehensive list of all of these numbers: 2, 3, 5, 7, 23, 37, 53, 73, 373. I wonder this is on the On-Line Encyclopedia of Integer Sequences (OEIS)...

[@redpepper74]

Ranjan Bhat Oh, it’s already there: oeis.org/A085823 Their approach was slightly different though, interesting!

[@patrikkula7117]

isn't 99 the biggest number?

[@bjornthormann2]

Hearing a German speaking English always makes me mad because of.... well you guessed it: accent! :-D it´s hard to follow the content while listening. Apart from that, I would appreciate your work more if I wouldn´t have heard about this by the one ans only, James Grimes. No offence, man, you`ve done a great video!

[@txikitofandango]

What is the largest right-truncatable prime in seximal?

[@g.ashwinshiva6578]

This guy reminds me of big bang theory

[@academicalisthenics]

My favourite prime is 69 247 :)

Ohhh my god

[@RYANREFORMED]

n minus tooth power

[@elbrohermanito3496]

My favorite prime number is 73, is the 21th prime number, and it's reverse is 37(prime number too), wich is the 12th prime number, and 21 is the reverse of 12. And 7*3=21, 73 is the only prime number that satisfies this property :o

[@אביב-ת7ל]

73 also satisfies this property.

[@elbrohermanito3496]

@@אביב-ת7ל hahahahahahahhaha yeah but you know what i mean hahaaha

[@אביב-ת7ל]

@@elbrohermanito3496 2,3 and 7 also satisfies this.

[@elbrohermanito3496]

@@אביב-ת7ל ok that's not correct bro, i am talking about primes that have at least two digits

[@אביב-ת7ל]

@@elbrohermanito3496 you never said that lol

[@Ivan_1791]

For me 163 takes the cake.

[@juandiaz3651]

My favorite prime is 30,041,777 (30/04/1777) because it’s Gauss’s birthdate

[@leefisher6366]

Lemme guess before I watch this. Is the number continuously prime as you write it? 7, 73, 739... Yeah, I think it is.

[@diffusegd]

My favourite prime number is π

[@colkadome]

I thought this was a numberphile title 🐹

[@Invalid571]

Meanwhile on vsauce: kzbin.info/www/bejne/iaO4aox6pL14bpo Aleph null ain't shit.

[@banan9782]

69 is such a good number it's an honorary prime 69420 and 42069 are so great they actually bend number theory so much, such that they become primes. This is known as the Dankness Theorem

[@wkingston1248]

best prime number is 2 :), being small is cool.

[@geniusgamer8046]

11th

[@99Dragonborn]

First time i notoced his 9s looks like "g"s

[@Redditard]

Lol fact- prime no.s are always made up of prime no.s or their products example- 73939133: 7 a prime no., 3 a prime no., 9 product of 3*3 and 1 somewhat prime

[@Matrixician]

Aren't all numbers like that? (Assuming you're ignoring ones with zero)

[@Redditard]

@@Matrixician yes actually even ur username name (Don't tell anyone about 0)

[@shambosaha9727]

@@Matrixician Your username is the first 5 rows of Pascal's triangle!

[@hybmnzz2658]

@@Matrixician the first part of ur username is ur wifi password

[@angelmiranda-acosta6092]

So you are saying, is that all the digits are either prime or composite

[@h2_]

For the purposes of right truncation I would personally treat 1 as a prime, and then the result is bigger: 1979339339

[@Redditard]

GG

[@bastianfrom77]

Ther is No Most interesting Prime. If this ist the Most interesting, the next lower PN would be biggest Not Special PN below the Most Special PN which makes IT quite Special

[@heisenberg4703]

My favorite number below 1 Million is 69 Nice

[@lipamanka]

LET JAN MISALI IN

[@stephenamy9879]

Best watched at playback speed 0.75

[@happygimp0]

Pretty boring, it is only true in the decimal system which is a bad choice for a base.

[@Censeo]

Are there any other prime numbers over a million that has been proven to be the largest in a specific kind of primes? If not, this one is very interesting!

[@T3WI]

I like 1,000,001

[@AbiGail-ok7fc]

I gave up after 10 minutes. There might still be some viewers out there who are still stuck in using Roman Numerals, but most of us have gotten used to a positional numbering system by now.

[@GrifterMage]

The video boils down to "X is the largest member of {this list}. Here's how to generate that list in rigorous detail." Okay, sure. But what makes it *interesting?* Why is being right-truncatable interesting? Is what's interesting that there's a finite number of them? Is it that it's so high? Is there some interesting underlying mathematical pattern at play here? Is this technique useful in some unexpected way? Why should we care?

[@a.artbart3020]

Wait couldn’t one also be the first number?

[@maxwellsequation4887]

Nope there is no first number

[@AlexJones-ue1ll]

1 is not a prime number

[@plushbeery]

Cool.

[@NPCooking69]

[@mastershooter64]

@@NPCooking69 hey jens could you please make a video about the math section of the exams "jee mains and jee advanced" these are the exams that a high school student should write in order to get into a prestigious college in india. They're very famous for being very difficult. also they have negative marks like if you get a wrong answer you get -1 marks for that and 0 marks if you leave it edit: just a kind request

[@cougar2013]

There is no reason for this video to be so long

[@brendawilliams8062]

100000474

[@muesk3]

flemebel mefs

[@carlosdecabodelavega3660]

View 666,

[@natepolidoro4565]

Fahv

[@devanshsharma8638]

Please solve jee advanced paper 2019 paper 1 and 2

[@Matrixician]

Bruh not THIS again

[@sudhansh6998]

News flash: Papa flammy is not a JEE coach and will not solve those gimmicky piece of shit problems

[@torment808]

learn c++ tgank you. jk good video

[@anandsuralkar2947]

When i learned python.in pydroid i made 5-6 different codes for finding prime numbers under some number like 1million.. And it would make file with all primes upto million.s And compared speed of various algorithms i founded

[@tszhanglau5747]

4206969420

[@all462]

Too bad 42069 is less than a million.