The guy just got the Field’s Medal! Congratulations sir 👏🏻
@aqeel6842
2 жыл бұрын
Exactly. He's so much smarter than he seems, since he's trying to explain math in a way us mere mortals can understand.
@aj_they
4 жыл бұрын
I hear 'all 7s' and immediately go 7 * 111111...111 etc. *Edit for a few people:* I'm not saying anything negative about anyone in this video, just bringing to light an error that was made for viewers. I understand completely that it was an on-the-spot discussion and that errors can and will be made, and in no way was I trying to be disparaging. I didn't in any way expect this to get as many likes as it did, so thanks, I guess?
@mycelialgoddess
4 жыл бұрын
Got eem
@CaturDe
4 жыл бұрын
yea, they didn't really think about it on the spot, if given a few seconds they would have probably realized.
@randomdude9135
4 жыл бұрын
Proof that not always the brightest of the minds can detect the obvious
@peter_castle
4 жыл бұрын
Maynard was focused on the main video explanation, obviously he knows that.
@bunderbah
4 жыл бұрын
@@randomdude9135 Brightest minds will always detect more obvious stuff than others in the long term.
@pragyan394
4 жыл бұрын
Feels like a recreational problem... Writes out a proof spanning 70 pages. Absolute mad lad
@roggendorf1685
4 жыл бұрын
Well it helps optimazing the search for primes ... At least it Shows a way that is Not usefull for optimizing the search
@markmandel6487
4 жыл бұрын
Hey, that makes sense to me. "Recreational" there means HE finds it fun. I'm a linguist, and I have fun with languages in ways that probably make no sense to most people.
@andrewmccauley6262
4 жыл бұрын
So many number theory proofs turn out to be really important. Large prime numbers are super important for cryptography.
@xeno4162
4 жыл бұрын
@@ESL1984 The monster?
@tomrush95
3 жыл бұрын
What makes something a recreational problem? Pretty much all of research level maths is recreational in that it has no obvious uses. It's a pretty natural question to ask. Also, proving anything original about the primes is a huge achievement
@ImCovino
4 жыл бұрын
I'm really glad you showed the clip at the start of the largest known prime and how evenly the digits are distrubuted within it. Really puts into perspective how uncommon a prime with absolutley zero 7s in it would be, and yet there are still infinitley many of them.
@evgiz0r
4 жыл бұрын
The somewhat hard proof might mean that its not so obvious this should be the case. If the probability goes to down to infinity to get a prime number with some property, but you have infinite "random" numbers still to go, is it guaranteed you will always have infinite numbers such as these? Maybe Trump knows
@JorgetePanete
4 жыл бұрын
absolutely*
@vidartraeland1424
4 жыл бұрын
Take any number, and remove all the 7`s. You will get a new number without any 7`s 😆
@rosiefay7283
4 жыл бұрын
I'm surprised that anyone bothered to find the digits and count occurrences of each digit-value. And print and bind the thing!
@Imthefake
4 жыл бұрын
@@rosiefay7283 that' what computers are for
@cwaddle
4 жыл бұрын
For a serious mathematician, i like that this guys always got a cheeky smile hiding
@pvic6959
4 жыл бұрын
he always knows something you dont :P
@michaelhendriks9006
4 жыл бұрын
It´s not a cheeky smile. It´s a lack of conversation skill. He is very insecure. You even see it off camera. But he is a cool dude.
@ihsahnakerfeldt9280
4 жыл бұрын
@@michaelhendriks9006 Doesn't sound insecure to me
@azap12
4 жыл бұрын
@@ihsahnakerfeldt9280 His body is dancing while talking.
@ihsahnakerfeldt9280
4 жыл бұрын
@@azap12 So? How does that show he's insecure?
@vincentpelletier57
4 жыл бұрын
All sevens: it is divisible by 7 and the number made all of 1s with the same number of digits, so definitely not prime! Only works with only 1s to get (possibly) a prime.
@arcanics1971
4 жыл бұрын
I'm trying to think of a reason why you are wrong and getting nowhere. Well spotted, Vincent.
@vincentpelletier57
4 жыл бұрын
@@smrusselkabirroomey7396 It is easy to miss that when you get asked it on the spot. I know I have done it many times, thinking about something later and realizing I missed the obvious! Prof. Maynard had a lot to think about, making sure he got all the bits he wanted to talk about, in a decent order, clear and concise, etc.
@OrangeC7
4 жыл бұрын
I wonder if there's an infinite number of primes made up of repeating 1s. (Or, to put it more rigorously, are there an infinite number of primes that can be defined as the sum from 0 to n of 10^n?) edit: im dum dum who didnt watch the video through
@ducktectivewhitewings9276
4 жыл бұрын
I think he meant to say a number with only 1 and 7
@fahimp3
4 жыл бұрын
@@ducktectivewhitewings9276 7:47
@leeprice133
4 жыл бұрын
What's striking about the prime that Matt printed out is how uniform the frequency distribution of the digits is. It's perhaps not all that unexpected, but it's interesting to see it explicitly displayed.
@KohuGaly
4 жыл бұрын
If you think about it, digits of a number are remainders after division by powers of the base. If the number is susficiently large, the frequency of any given digit approaches 1/base.
@jujumw5918
4 жыл бұрын
@@palmomki i don't think you understand what he was saying, and your example is a really small number which he had excluded from his hypothesis.
@lukashora5993
4 жыл бұрын
@@palmomki But they are remainders after dividing by base to some power. 1234 mod 10 is 4, you have your last digit. You divide by ten ignoring the remainder, so now you have 123. 123 mod 10 is 3. Your second to last digit and so on. This is how you can convert numbers to other bases. Pretty simple honestly. As for the second statement. For a random number that statement is true. You have a 1/base chance for each digit to be put in the number. Sure if you pick 111111 it doesnt apply but for big enough random numbers I"m pretty sure it does.
@jujumw5918
4 жыл бұрын
@@palmomki ok, i get what you are saying. But, you get the intuition from what he was saying, right ? I understand it that way : Let k be a natural number, X a random number : X ~ Unif{1,..,10^k-1} We define Xi such as : X = X0 + 10*X1 +... + 10^(k)*Xk Xi ~Unif{0,...9} let a be a number in {0,..,9}: Frequency of a in X in mean 1/k*E[sum(1[Xi=a])] = 1/k *k*1/10=1/10 And this holds for any k, so The frequency of a digit appearing in a whole random number (defined above) is 1/10 (Generalization give 1/b)
@cryme5
4 жыл бұрын
@@jujumw5918 But are primes random?
@mastersasori01
4 жыл бұрын
Hey, he's one of the solvers of Duffin- Schaeffer Conjecture.. crazy smart dude
@MrBarryyoung
4 жыл бұрын
Some people talk with their hands; James talks with his head.
@deplorableneanderthal1265
4 жыл бұрын
He reminds me of Sir David Attenborough.
@tombiby5892
4 жыл бұрын
@@deplorableneanderthal1265 Sir Attenbobble?
@factsverse9957
4 жыл бұрын
Huh yeaa
@izayus11
4 жыл бұрын
Perhaps I had 1too many glasses of wine (4)... but for the first time of my life I got motion sickness from watching someone bob their head.
@Real_Tower_Pizza
3 жыл бұрын
They were wrong. You can't have a prime number only made of the digits 7 (exept for the prime 7). Because: 77 divides into 11 777 divises into 111 7777 divides into 1111 And so on. A number made of only the digit 7 would be able to be divided into 7*111111111... So you cant have a prime number only made of 7's (except for the prime 7 of course). This means you: - can't have a prime only made of 0's. - could have a prime only made of 1's (as far as I am concerned) - can't have a prime only made of 2's and/or 4's and/or 6's and/or 8's because they would divide into 2. (except for the prime number 2) - can't have a prime only made of 3's and/or 9's beacuse it would divide into 3 (except for the prime number 3) - can't have a prime only made of 7's. Because of the proof over. Conclusion: If you want a prime number only made of 1 type of digit, the digit must be 1. (Excluding the primes 2, 3, 5 and 7).
@negin1812
4 жыл бұрын
Professor's looking like he's really fascinated by his discovery. He can't sit on his chair calmly 😊
@bensonprice4027
4 жыл бұрын
I looks like he's a marionette controlled by a puppet master who bounces his puppet to show that it's speaking.
@neonblack88
4 жыл бұрын
hes dancing
@geekjokes8458
4 жыл бұрын
heads be bopping
@theseeker7194
4 жыл бұрын
Because he's very buoyant about his discovery.
@rosstuddenham2473
4 жыл бұрын
How still would you be sitting if you were being interviewed about something meaningful that you had discovered?
@user-kh5tv9rb6y
4 жыл бұрын
I really liked the exposition at the beginning! It helped put this whole thing into perspective.
@markkennedy9767
2 жыл бұрын
For a guy who won a Fields medal he seems remarkably relatable and down to earth. That combination of intelligence and ability to communicate his work is admirable
oh, that's true, i didn't notice until i saw your comment xD
@arcanics1971
4 жыл бұрын
I think you're tight. I wish I'd spotted that.
@pruusnhanna4422
4 жыл бұрын
Whenever primes are involved, mathematicians go ever so slightly bonkers.
@xario2007
4 жыл бұрын
That's because primes are like glances at the base code of the universe.
@codycast
4 жыл бұрын
Xario Withoutalastname how so? At its root level, why is a number that isn’t divisible by any other # special?
@xario2007
4 жыл бұрын
@@codycast Not the single primes themselves, but the complete set. It is completely deterministic but has MOST of the characteristics of a random distribution. Most of the he few (non-trivial) patterns that we now of, are still a mystery to us. In the vid, it was shown that the sum of the inverse prime numbers diverges, but JUST barely. Prime factorization is the base for contemporary cryptography, the Zeta function, which is basically prime factorization in the complex plane, contains one of the biggest unsolved problems in current math. Primes pop up in every area of math and are so fundamental that even natural evolution has stumbled upon them several times as a solutions to different problems.
@codycast
4 жыл бұрын
Xario Withoutalastname fair enough. I guess I just don’t know enough to have a proper appreciation. I wonder why the video didn’t show the largest prime number known without a 7
@xario2007
4 жыл бұрын
@@codycast Probably because it's not very large and thus not very impressive.
@harrymoschops
4 жыл бұрын
Pioneering mathematical discoveries are often attributed to the courage and inventiveness of youth, James Maynard we salute you!
@somgesomgedus9313
2 жыл бұрын
Congratulations for winning the fields medal! You certainly deserved it!
@jimisommer6585
Жыл бұрын
I think there was a mistake here. The only repdigit prime possible is all 1s, repunit numbers. A repdigit number with all 7s is always divisible by 7. Still, proving there is infinitely many repunit primes would be super cool.
@caio-jl6qw
4 жыл бұрын
Legend has it that James is still shaking his head.
@FrankHarwald
4 жыл бұрын
He sure got the groove! B)
@sebbe4717
4 жыл бұрын
I feel discomfort when watching him move this way
@djamckechan
4 жыл бұрын
@@sebbe4717 I usually watch at 1.25x but it was too shakey
@sp10sn
4 жыл бұрын
Bobbing to the beat of a different drummer 👍
@Triantalex
9 ай бұрын
??.
@hewhomustnotbenamed5912
4 жыл бұрын
He's back! This guy is an actual legend.
@chirayu_jain
4 жыл бұрын
Yes, he is actually a legend
@hewhomustnotbenamed5912
4 жыл бұрын
@@akshaj7011 let's hope no one likes my comment until yours gets 7 likes.
@lonestarr1490
3 жыл бұрын
@@hewhomustnotbenamed5912 His comment actually has 7 likes now. But I can't possibly deduce if that happened before your original comment exceeded 77 likes or not.
@hewhomustnotbenamed5912
3 жыл бұрын
@@lonestarr1490 I can but don't want to. The wayback machine is an online archive of millions of internet pages at different times, but I'm too lazy to check this KZitem video at different times. You could try it if you want.
@j.vonhogen9650
4 жыл бұрын
6:21 - That's the first question I wanted to ask in the comments! You guys are amazing!
@nHans
2 жыл бұрын
Hey James, congratulations for winning the Fields Medal for 2022 for your contributions to Number Theory! I was wondering why old Numberphile videos that I've already watched are showing up in my KZitem feed all over again ... and now I know! Nevertheless, I'm gonna re-watch them all over again.
@Kapin05
4 жыл бұрын
I like the little prelude at the beginning, it's nice to see style changes every now and then.
@gatg111ggrecords7
4 жыл бұрын
I see the title and i immediatly think "ah 13 right?"
@MoosesValley
4 жыл бұрын
James is exploring what he loves, on the frontier of human knowledge, with such humour and enthusiasm, and who knows where this research or the techniques being developed could lead. Great video, thanks !!
@chriswebster24
2 жыл бұрын
Wow, keep your shirt on.
@financeexplainedgraphics
2 жыл бұрын
Hey mate, congrats on the Fields Medal!
@nymalous3428
4 жыл бұрын
The very end made me smile, when he was talking about the random number he gives when asked. I'll have to do that myself from now on.
@johnchessant3012
2 жыл бұрын
2022 Fields medalist!!
@abcjme
4 жыл бұрын
12:20 ~ 7 is salient because of the exotic effect ~ it's the only single digit number that has 2 syllables (excluding glottal stops) ~ 37 is salient because of the law of least effort, because of the recency effect, and because of the exotic effect ~ we generally remember recent (end) objects better than initial (start) or middle objects ~ thus, when giving a list, people are inclined to think of the end object (7) more than the other objects ~ and 3 (thirty) is the least effort initial object to get to the exotic (7) end object ~ on a side note: ~~ “the” is, by far, the most common morpheme and english word ~~ the consonant [θ] “th” requires little effort to produce relative to most other consonants
@axrmtech
2 жыл бұрын
Fast forward in 2022, James Maynard WON the 2022 Fields Medal
@area51xi
2 жыл бұрын
Seeing a number that large printed out like that gave me goosebumps. It's obvious but at the same time absolutely mind blowing to see it like that. It's like staring into the abyss.
@oz_jones
Жыл бұрын
What is wild to me is that there are infinitely many primes larger than that prime.
@RibusPQR
4 жыл бұрын
"They disproportionately choose 37." In a row? Hey, try not to choose any two-digit numbers on your way out to the parking lot!
@SmegEdmoOn
4 жыл бұрын
They say Matt Gray is the bounciest man on the Internet but James could give him a run for his money!
@shalcueva4074
2 жыл бұрын
Heartiest congratulations to James on his Fields Medal 2022
@AlgyCuber
4 жыл бұрын
7 is the only prime with only 7’s bc all other ones will be divisible by 7
@maximilianlorosch936
4 жыл бұрын
Or 11 or 111...
@underslash898
4 жыл бұрын
@@maximilianlorosch936 Assuming 111 had no other factors, it doesn't follow the same pattern as 7 because 1 isn't a prime factor. And if you take 11, then it still doesn't work.
@wierdalien1
4 жыл бұрын
@@underslash898 no he means 77 or 7777 or 7777777 is divisable by 7 OR 11, 111, 1111 etc
@underslash898
4 жыл бұрын
@@wierdalien1 Ah, that makes sense
@Rougarou99
4 жыл бұрын
The same can be said with 2, 3, and 5.
@richardnorris9256
26 күн бұрын
Numberphile videos, I always get lost almost immediately, but nonetheless find them utterly compelling from start to finish.
@danielortega2441
2 жыл бұрын
Nice to see him win fields medal and we need an interview of him.
@uladzislaushulha1994
4 жыл бұрын
I kind of loved the postpunk vibe of Brady's apartment and even more the dancy-wavy vibe of James as he talks what he's passionate about.
@koenth2359
4 жыл бұрын
7:00 As for the repunit 1, it is not only that multiples of 3 don't go. It can only be a prime if its number of digits is a prime. For example if n=(10^14-1)/9=11111111111111 consisting of 14 digits, you can write n=11×1010101010101=1111111×100000001=11111111111111, because 14=2×7.
@Crokto
Жыл бұрын
idk if i misunderstood this, but he also said that only 1 and 7 are possible to use for repunit primes, but won't any number with all 7s be divisible by 7? or do you exclude the number itself when considering whether its a repunit prime
@Xonatron
4 жыл бұрын
All single digit numbers can be divided by that digit. One way to see this is consider they all can be multiplied by 10, or 100, or 1,000, etc. Numbers composed of only the digit 1 can potentially be prime because dividing by the digit in question (1) doesn’t count.
@JorgetePanete
4 жыл бұрын
I wanna listen to the imaginary disco music that he is jamming to
@peepzorz
4 жыл бұрын
7:50 A number consisting of all 1's is a "repunit" (1 == unit), but with all 7's would be a slightly more generalized "repdigit". BTW, repunits or repdigits can be specified for any base. For example Mersenne numbers are base-2 repunits.
@highlewelt9471
4 жыл бұрын
I love this guy, more of him please!
@Lortagreb
Жыл бұрын
This guy is so sweet. The way he's passionate shows in his body language and tone, makes it really enjoyable to listen to him.
@princesstrevor3277
4 жыл бұрын
Loving the intro to give some extra context. Great addition.
@justadamazing
2 жыл бұрын
Congratulations James on your Fields medal!
@MusicFanatical1
4 жыл бұрын
5:06 Holy moly a quadruple integral! *Needs a lie down in a quiet room*
@_ilsegugio_
2 жыл бұрын
Congratulations Doctor Maynard!! 🎊)
@omargaber3122
4 жыл бұрын
We want a detailed explanation of Hodge's conjecture, the British Dyer conjecture, and Clay Institute problems
@vishaltripathy3620
4 жыл бұрын
I had never thought that I will ever see an interview of James Maynard. So happy
@cougar2013
Жыл бұрын
A number of any length will all 7s will always be divisible by 7
@anshusingh1493
4 жыл бұрын
JamesMaynard seems like he is rapping ,the way he is enjoying while delivering the whole idea, maths seems to be like music😍😍😍
@shruggzdastr8-facedclown
4 жыл бұрын
Gotta love how he used the non-number "gazillion" in this video!!
@seancooper4058
3 жыл бұрын
How many south americans does it take to change a lightbulb? A brazillion.
@Vacuon
Жыл бұрын
Brady is amazing, contagious enthusiasm and genuine curiosity! It makes those videos so fun to watch
@DiscoPickle102
4 жыл бұрын
So what you're saying is that the treasure was the techniques we made along the way?
@Furiends
4 жыл бұрын
When you do programming this exact principal applies. You might be making a "fun" project but what you learn along the way can be applied to many fields.
@psteknyo
4 жыл бұрын
7:50 Certainly a prime number cannot consist of only sevens, because such numbers are obviously divisible by seven.
@Kaczankuku
4 жыл бұрын
They thought about one and then sevens.
@unbekannter_Nutzer
4 жыл бұрын
That's wrong. Example: 7.
@TimothyReeves
4 жыл бұрын
Stefan Wagner that’s THE example. As in, the only one.
@ChicagoJon2016
2 жыл бұрын
Great intro Brady -- and great video as always
@madhavan_raja
4 жыл бұрын
James Maynard, lead singer of the band LOOT.
@xjdfghashzkj
4 жыл бұрын
I'd listen to LOOT
@brunoalejandroandrades354
4 жыл бұрын
I'm a simple man; I see James Maynard; I click
@krishnagc3260
4 жыл бұрын
Are there infinite number of primes with their all digits being prime?
@carltonleboss
4 жыл бұрын
Do you mean just those containing 3, 5 or 7, or do you consider 1 to also be prime?
@MrMctastics
4 жыл бұрын
Probably. Not proven though
@markzero8291
4 жыл бұрын
@@carltonleboss You forgot 2 😜
@carltonleboss
4 жыл бұрын
@@markzero8291 oh yeah
@Brainsucker92
4 жыл бұрын
@@carltonleboss 1 is certainly not a prime number.
@martinepstein9826
4 жыл бұрын
Wow, so base 10 actually came out of the problem naturally. Wasn't expecting that at all. Also, I spot Artin's 'Algebra' on the shelf! Great book.
@zoz4864
4 жыл бұрын
Ok, but here's an idea: if we can similarly prove that there are infinitely many primes whose binary expansion has no zero, that would mean there are infinite primes as strings of ones in binary, which are always 1 less than a power of two, which are Mersenne numbers, which are linked to the perfect numbers... So it would function as a proof of infinite perfect numbers!
@SquirrelASMR
2 жыл бұрын
Coool, even though idk what a perfrct number is Is there already a proof for infinite mersene primes? Bc maybe that part is already proved
@ethanyap8680
2 жыл бұрын
Unfortunately I think the proof that there are infinitely many mersenne primes is still unsolved meaning it's probably harder than this
@power-l5z
2 жыл бұрын
You can't have all 7s because it's divisible by 7; specifically a number that's 7 repeated n times is equal to 7 * 1 repeated n times (responding to the discussion @ 7:30 )
@Guderian0617
4 жыл бұрын
Surely all 7's would be divisible by 7??
@zushyartold
Жыл бұрын
0:48 The digit counts are roughly equal.
@TheRealGuywithoutaMustache
4 жыл бұрын
Infinity in and of itself is quite an interesting concept
@natalyawoop4263
2 жыл бұрын
And the primes are like a way to "probe" infinity. That might be one of the reasons mathematicians like them so much.
@tongqiustb847
3 жыл бұрын
guys plsss stop pointing out the same mistake of the 77....77 being divisible by 7 and 11....11. It's already pointed out so many times that I cannot enjoy reading the comment section
@patavinity1262
4 жыл бұрын
He's so young to have done something so cool in the field of mathematics.
@renniwful
4 жыл бұрын
I like the way he casually said notwithstanding like it's a word that's used all the time
@letstalksciencewithshashwa9527
2 жыл бұрын
WHOS HERE AFTER HE GOT FIELDS MEDAL?
@MarcoRoepers
4 жыл бұрын
I never thought that that print of the big prime Matt made would be useful again
@Willy-nu3oc
2 жыл бұрын
Here comes the Fields Medalist
@theman4884
4 жыл бұрын
What about numbers that begin and end with 1 and all the other digits are zero? 101 is prime but the next several 1001, 10001, 100001... all seem to be composite.
@ethanmartin2781
4 жыл бұрын
i love how every math professor ever has like 30 yellow GTM books lined up on their bookshelves xd
@Einyen
4 жыл бұрын
2 Mersenne primes larger than the 2^74,207,281 - 1 in his 3 printed books have already been found: 2^77,232,917 - 1 and 2^82,589,933 - 1.
@joshuamitchell5530
2 жыл бұрын
Here after he won the Field’s medal
@HasekuraIsuna
4 жыл бұрын
The happiness when you find a Numberphile video you somehow missed to watch!
@dataunknown
4 жыл бұрын
What's the biggest prime discovered so far that doesn't have a 7?
@pullt
2 жыл бұрын
7777.... will always be divisible by 7 You'd think that would already be considered, and dismissed when you're already having the 1111.... issue that you've considered.
@imdartt
Жыл бұрын
7:40 all 7s doesnt work becaus a number made up of n 7s will always be divisible by n 1s
@danielbranscombe6662
2 жыл бұрын
as for numbers made of a single digit, you can quickly eliminate any digit>1 because any digit made entirely of the digit N>1 would have N as a divisor for example 777=7*111. Better question would be can we have infinitely primes made only of the digits N and zero.
@jerry3790
4 жыл бұрын
Simple: just find a prime in binary. No sevens
@alonjudkovsky
4 жыл бұрын
He stresses it being in decimal.
@gobyg-major2057
4 жыл бұрын
Jerry Rupprecht actually base 2 to 6 work because they don’t have a 7
@kjyhh
4 жыл бұрын
base 7 has no 7
@アヤミ
4 жыл бұрын
You can redefine the base 10 numbers so that 7 doesnt exist anymore
@ciangrant3042
4 жыл бұрын
@MATTHEW GOH CHIN LIN (Student) it's not a whoosh stop using that at every possible opportunity
@mythbusterman8541
4 жыл бұрын
One of the great KZitem channels
@IMadeOfClay
4 жыл бұрын
This maths dude be trippin'. My man can't keep his head from bobbin'.
@IsabinMarius
4 ай бұрын
He made a fundamental oversight in mentioning something about numbers made of only one type of digit, sy all 1's or all 8's, etc. He says likely you can have a prime consisting of just sevens (aside from a lone 7 itself). that is clearly false since any number consisting of only sevens are absolutely devisible by 1, 7, and the number consisting of as many ones as the number in question contains 7's, as well as the number itself. so the only multi-digit single digit type numbers that could ever be prime will consist of only 1's of a quantity that's not a multiple of 3.
@tadperry1817
4 жыл бұрын
Also, why did these guys agree that there might be infinitely many primes that are made up of all 7's? Wouldn't it be divisible by 7???
@JorgetePanete
4 жыл бұрын
7s*
@frankcl1
4 жыл бұрын
Indeed, the only digit which could work is 1.
@sarvesh_soni
2 жыл бұрын
james maynard got the field medal ! 2022
@kevsterking
4 жыл бұрын
What's the largest known prime with a missing digit?
@matthewstuckenbruck5834
4 жыл бұрын
4621
@kevsterking
4 жыл бұрын
@@matthewstuckenbruck5834 Not sure if I was clear enough. Perhaps I meant. The largest prime known that doesn't contain all digits.
@matthewstuckenbruck5834
4 жыл бұрын
@@kevsterking it's a joke, I'm not sure that anyone is looking for those. They would be really hard to find
@andrewkepert923
4 жыл бұрын
You can start finding some, but they’re pretty common amongst numbers that are easy to work with, and even for numbers that are beyond that. Put “next prime after 111111111111111111111111111111” into wolfram alpha [that’s (10³⁰ -1)/9] and you’ll find that 111111111111111111111191 is prime. This is not surprising due to density of primes: all n-digit numbers whose first n-8 digits are 1 and whose other 8 digits are anything have a missing digit (pigeonhole principle with negative pigeons). Then due to the prime number theorem, for numbers with n digits, the density is approx 1/ln(10ⁿ) = 1/(n ln(10)) = 1/(2.3n). For this to be less than 10⁻⁸ (suggesting none of the numbers 1111...1111abcdfegh are prime) requires n>10⁸/ln(10)=43 million. A similar probability argument would apply if you chose some other set of 8 places to differ from 1 or some digit other than 1 (excluding obvious cases where last digit is 2,4,5,6,8,0). That is, we would expect missing-digit primes to be common enough for primes with 43 million digits. (For comparison, current largest known prime has 24 million or so digits)
@andrewkepert923
4 жыл бұрын
Oh fun - maple has “prevprime” so 7777...7771 (1067 digits) is prime.
@evgiz0r
4 жыл бұрын
cool reduction between the 2^n-1 and binary primes without zero. The second one sounds slightly easier :)
@vandanaasthana1216
4 жыл бұрын
U cant have a prime no with all 7 beacuse the no. Will be divisible by 7.
@Kaczankuku
4 жыл бұрын
1777777... - this is they thought about.
@soulstealingginger3612
4 жыл бұрын
well 7 is prime and all 7's
@vandanaasthana1216
4 жыл бұрын
@@soulstealingginger3612 oo
@Aquaras3141
4 жыл бұрын
Wouldn't an all 7's number be divisible by 7? And, same for anything besides 1?
@friedchickenUSA
4 жыл бұрын
but any number made out of all 7s is divisible by 7 1 is rhe only digit that allows primes with a single digit
@JorgetePanete
4 жыл бұрын
the*
@keithwilson6060
2 жыл бұрын
“Base 100” Head explodes.
@henryginn7490
4 жыл бұрын
He's going to be lecturing the first years linear algebra 2 next term, I'm pretty jealous
@tlocto
4 жыл бұрын
Lucky!
@rahowherox1177
4 жыл бұрын
Try just going to lecture anyways.
@henryginn7490
4 жыл бұрын
rahowhero X yeh I could do, there’s nothing stopping me. You can just walk into the maths institute and into a lecture, don’t have a register and you don’t need to scan your card at the door or anything.
@rahowherox1177
4 жыл бұрын
@@henryginn7490 lol. You dont at any uni where I live, nor uk or oz. Usa?
@henryginn7490
4 жыл бұрын
rahowhero X James Maynard is at Oxford which is in the UK
@pretzelbob1640
4 жыл бұрын
This makes me think about the James Grime video "3 is everywhere" I think also on your channel
@kimothefungenuis
4 жыл бұрын
Next video Something in math that seems random but actually has a pattern
@elbaecc
4 жыл бұрын
That has been done. aka Mandelbrot sequence.
@kimothefungenuis
4 жыл бұрын
@@elbaecc another one
@ceruchi2084
4 жыл бұрын
Lol, or just rewatch that video where Neil Sloane holds up graphs that look like things.
@brentonverlo7419
4 жыл бұрын
Are there an infinitely many prime with no chains of the same digit? (11,22,33,44...111,222,333. Etc.)
@grandmask
4 жыл бұрын
....i didnt even realize this was uploaded 24 seconds ago...until i noticed the view count was 0
@MatesMonchis
11 ай бұрын
In base 2, writing the numbers for the prime number in the intro would've taken approximately 10 volumes instead of 3. And all of the digits would be 1.
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