The Oldest Unsolved Problem in Math
Рет қаралды 7,361,055
Күн бұрынDo odd perfect numbers exist? Head to brilliant.org/veritasium to start your free 30-day trial, and the first 200 people get 20% off an annual premium subscription.
Special thanks to our Patreon supporters! Join this list to help us keep our videos free, forever:
ve42.co/PatreonDEB
A massive thank you to Prof. Pace Nielsen for all his time and help with this video.
A big thank you to Dr. Asaf Karagila, Pascal Ochem, Prof. Tianxin Cai, and Prof. William Dunham for their expertise and help.
To try GIMPS out yourself: ve42.co/GIMPS
These sources were particularly helpful:
Perfect numbers via MacTutor - ve42.co/MTPerfect
Cai, T. (2022). Perfect numbers and fibonacci sequences. World Scientific. - ve42.co/Cai2022
Dunham, W. (2022). Euler: The master of us all (Vol. 22). American Mathematical Society. - ve42.co/Dunham2022
▀▀▀
References:
• Perfect Numbers and Me...
• Perfect Number Proof -...
Dickson, L. E. (1919). History of the Theory of Numbers.. (Vol. 1). Carnegie Institution of Washington.
Knill, O. (2007). The oldest open problem in mathematics. NEU Math Circle, December2. - ve42.co/Knill2007
Perfect number via Wikipedia - ve42.co/WikiPerfect
Introduction to Arithmetic via HalthiTrust - ve42.co/IntroArithmetic
Nicomachus of Gerasa via MacTutor - ve42.co/MTNicomachus
Sonja, B. (1988). The First Perfect Numbers and Three Types of Amicable Numbers in a Manuscript on Elementary Number Theory by Ibn Fellûs. Erdem, c. IV, 11. - ve42.co/Sonja1988
Ibn Fallus via Wikipedia - ve42.co/WikiFallus
Mersenne prime via Wikipedia - ve42.co/WikiMP
List of Known Mersenne Prime Numbers - ve42.co/ListOfMP
Marin Mersenne via MacTutor - ve42.co/MTMersenne
Leonhard Euler via Wikipedia - ve42.co/WikiEuler
Frank Nelson Cole via Wikipedia - ve42.co/WikiFNCole
GIMPS History via Mersenne.org - ve42.co/GIMPSHistory
EFF Cooperative Computing Awards via EFF - ve42.co/EFFAwards
Jonathan Pace via Primewiki - ve42.co/PWikiPace
Book with just one number sells out in Japan via BastillePost - ve42.co/PrimeBook
Predicted distribution of Mersenne primes via John D. Cook - ve42.co/JDCookMP
Euler’s Odd Perfect Numbers Theorem via Cantor's Paradise - ve42.co/EulerOPN
A Perfect (Math) Mystery via Medium - ve42.co/Machado2024
Brent, R. P., Cohen, G. L., & te Riele, H. J. (1991). Improved techniques for lower bounds for odd perfect numbers. Mathematics of Computation, 57(196), 857-868. - ve42.co/Brent1991
Ochem, P., & Rao, M. (2012). Odd perfect numbers are greater than 10¹⁵⁰⁰. Mathematics of Computation, 81(279), 1869-1877. - ve42.co/Ochem2012
Mathematicians Open a New Front on an Ancient Number Problem via Quantamagazine - ve42.co/QuantaSpoofs
Descartes number via Wikipedia - ve42.co/WikiDescartesNumber
Andersen, N., Durham, S., Griffin, M. J., Hales, J., Jenkins, P., Keck, R., ... & Wu, D. (2022). Odd, spoof perfect factorizations. Journal of Number Theory, 234, 31-47. - ve42.co/Andersen2022
Pomerance’s Heuristic that Odd Perfect Numbers are Unlikely via OddPerfect.org - ve42.co/Heuristic
Images & Video:
Clip of Piergiorgio Odifreddi - • Odifreddi da Gramellin...
Euclid’s Elements 1 via Claymath - ve42.co/CM1
Euclid’s Elements 2 via Claymath - ve42.co/CM2
Euclid’s Elements 3 via Claymath - ve42.co/CM3
Diophanti - ve42.co/Diophanti
Gauss book - ve42.co/GaussDis
Euler’s Archive 1 - ve42.co/Euler1
Euler’s Archive 2 - ve42.co/Euler2
▀▀▀
Special thanks to our Patreon supporters:
Anton Ragin, Balkrishna Heroor, Bertrand Serlet, Bill Linder, Blake Byers, Burt Humburg, Chris Harper, Dave Kircher, David Johnston, Diffbot, Evgeny Skvortsov, Garrett Mueller, Gnare, I.H., John H. Austin, Jr., john kiehl, Josh Hibschman, Juan Benet, KeyWestr, Lee Redden, Marinus Kuivenhoven, Matthias Wrobel, Max Paladino, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Stephen Wilcox, Tj Steyn, TTST, Ubiquity Ventures, wolfee
▀▀▀
Directed by Casper Mebius
Written by Casper Mebius and Derek Muller
Edited by Peter Nelson
Illustrated by Jakub Misiek
Animated by Fabio Albertelli, Ivy Tello, David Szakaly, Alondra Vitae, Alex Drakoulis, and Leigh Williamson
Filmed by Derek Muller, Raquel Nuno, and Peter Nelson
Additional research by Aaron Santos, Camilla Machado, and Gregor Čavlović
Produced by Casper Mebius, Gregor Čavlović, Han Evans, and Derek Muller
Thumbnail by Ren Hurley
Additional video/photos supplied by Getty Images and Pond5
Music from Epidemic Sound
@cupostuff9929 Ай бұрын
>walks up to blackboard >multiplies 2 numbers >walks away >round of applause Frank Nelson Cole was unfathomably based
@jacobe280 Ай бұрын
Am I the only one bothered that he says AND between all the millions, billions, trillions, etc... couldn't help but mention
@adriantcullysover4640 Ай бұрын
@@jacobe280 Yes. You are.
@herobrine1847 Ай бұрын
@@jacobe280no you’re not
@AMPProf Ай бұрын
Fish
@Bruzzzio Ай бұрын
@@AMPProfSquid
@madjson1429 Ай бұрын
When Euler says "it's most difficult", it's gotta be impossible.
@BixbyConsequence Ай бұрын
"I have discovered a truly marvelous proof of this, which this margin is too narrow to contain."
@TheXuism Ай бұрын
this guy is the biggest bragger in human history.@@BixbyConsequence
@funtastic1297 Ай бұрын
No it’s a joke reference to fermats last theorem lol
@melodyecho4156 Ай бұрын
@@BixbyConsequenceThat was Fermat
@MathSMR42 Ай бұрын
@@TheXuism how much do you know about Fermat? He was anything but a bragger in my Opinion. He never published any of his genious ideas, his son did it. He became one of the most famous mathematicians, but was an actually a lawyer. So mathematic was only his hobby. And you call him a bragger?
@MattDoesNothing 3 күн бұрын
Normal people would say “There’s no way” Some other people would say “The chance is low, but never zero” And then comes the mathematician: “The chance is never zero, but how low is it?”
@Osamabonjovi 18 сағат бұрын
*vsauce theme plays*
@Ferrohh Ай бұрын
Math is a hell of a drug
@oliverthomas3134 Ай бұрын
It will mad u
@WaddieJoe Ай бұрын
68th like
@RAGHAV4882 28 күн бұрын
@@WaddieJoe you mean (n-1)?
@LucasLiang-fi9cf 23 күн бұрын
@@oliverthomas3134you sound like your on drugs
@lucienli4553 22 күн бұрын
@@RAGHAV4882a-s-s
@thomasrinschler6783 Ай бұрын
13:25 "But Euler wasn't finished yet." I think this sentence appears in most histories of mathematical concepts.
@brettgoldsmith9971 Ай бұрын
Right? It feels like if we had found a way to keep the guy alive he would be responsible for the majority of all mathematical discoveries
@nananou1687 Ай бұрын
Number theory concepts*
@ab3040 Ай бұрын
Possibly the most important mathematician in history
@rogerszmodis6913 Ай бұрын
@@ab3040either him or Gauss
@ab3040 Ай бұрын
@@rogerszmodis6913 Gauss was equal in math and science, so overall he was probably more important, but as far as just math goes I gotta give it to Euler
@ZenZooZoo Ай бұрын
Not me watching thinking I’m gonna try to solve this while eating hot cheetos
@zhixinhuang4084 Ай бұрын
Ghost pepper, Cheeteeeeeeeaeeeaeaeaeaeaeaeaeaeaeaeæéêēêåeeeaeaeaeaeaea
@matt88townsend Ай бұрын
this comment just blew my mind🤯 doing this exact thing while high
@jin_cotl Ай бұрын
Nah it’s alright. Better an attempt at solving it, than not trying at all ❤
@CananaMan Ай бұрын
Even if you're not a mathematician, you should give it a go if you're interested! Math problems that stump the masters get solved by a novice perspective all the time, but even if you end up retreading existing ground, you'll end up learning something cool along the way :)
@joshuagoodsell9330 Ай бұрын
That's so inspiring haha thanks@CananaMan
@denverbeek 9 күн бұрын
I'd like to thank you for making me aware of GIMPS. I'm donating some of my cpu power overnight now.
@akoskiss2065 Күн бұрын
You might want to think about it, if you want to not fry your computer. It can be really straining on your processor and greatly shorten its life. But hey, someone got to solve this
@denverbeek Күн бұрын
@akoskiss2065 Just finished my first prime number last night. It was over 2 million digits long. My computer is nearing the end of its lifespan anyways, and I have the money to afford a new one. Thank you for the heads up though :)
@denverbeek Күн бұрын
@akoskiss2065 Just finished my first prime number last night. It was over 2 million digits long. My computer is nearing the end of its lifespan anyways, and I've saved up the money to afford a new one. Thank you for the heads up though :)
@Rob_BBX 20 күн бұрын
These mathematic equations make me and my autism feel happy to watch, but I can't help noticing that the guy presenting looks like a mixture of Ryan Reynolds and Paul Hollywood.
@fartherout.1046 Күн бұрын
litteraly omg 💀
@nathanaelhahn4795 Ай бұрын
4:03 "Euclid was actually thinking along similar lines" Euclid: calculates perfect numbers with actual lines
@idontkownhowiam2424 Ай бұрын
Euclid god of math
@supremelordoftheuniverse5449 Ай бұрын
I disagree
@pressaltf4forfreevbucks179 Ай бұрын
Foreal?
@isaachester8475 Ай бұрын
Beautiful pun
@shay_playz Ай бұрын
@@supremelordoftheuniverse5449why?
@logician1234 Ай бұрын
There is something so bizarre about Euclid and Euler having a collaboration. If the history of mathematics was a book of fiction, I would call this a fan service 😂
@ObjectsInMotion Ай бұрын
Eu(clid x ler)
@Xezlec Ай бұрын
Imagine the noises the readers would make if Gauss joined in!
@logician1234 Ай бұрын
@@Xezlec Math : No Way Home
@johnchessant3012 Ай бұрын
Oiclid and Yooler
@cefcephatus Ай бұрын
Maybe, "I reincarnated into math genius, Euler, and continue my own legacy. Yes, I was Euclid."
@Captainzentdx Ай бұрын
This show how dumb i am
@GhostieTheML Ай бұрын
omg exactly 37 likes !1!1
@Captainzentdx Ай бұрын
@GhostieTheML what it mean sir
@satriorukito Ай бұрын
@@GhostieTheML37…
@lilericinnacut Ай бұрын
@@GhostieTheMLwell it’s at 69 now
@khanhdmd Ай бұрын
I am not smart but I still ended up watching the entire video
@LoBoToM81 Ай бұрын
This channel is absolutely THE BEST science channel. Not only on YT but in general. I'm a primary school teacher from Poland and the amount of facts and curiosities I get from here and transfer into teaching physics, chemistry and even English is astonishing. Thank you.
@xninja2369 Ай бұрын
I absolutely recommend you Real engineering , Mustard , Vsause , Kirzguat in nuteshell ( Idk perfect name ) , But why , SciencePhileAI , Kosmo .. there are many more who provide valuable information with the proof and good details and you can learn something new that's worth your time instead of spending time on tiktk..
@deanrinehart Ай бұрын
Watching a math related video strictly out of curiosity and having your general math professor Bill Dunham from 25 years ago pop up is a surprise…and finding out he’s now a well respected mathematics historian and not just some guy who endlessly suffered non-math students struggles with train problems is absolutely fantastic. Go Mules!
@ArawnOfAnnwn Ай бұрын
Mules?
@Armageddon613 Ай бұрын
I would assume whatever institution his professor whom he recognized in the video taught at had a Mule as their mascot. Either that or this guy really just likes Moscow Mules, which I wouldnt blame him for.@@ArawnOfAnnwn
@LedionZogaj Ай бұрын
@ArawnOfAnnwn yea mules horses sheep lol....
@sumdumbmick Ай бұрын
did you have a stroke at some point, or have you always been illiterate?
@deanrinehart Ай бұрын
(He’s a prof emeritus at Muhlenberg College…mascot is the Mule…Go Mules)
@jonahmishaga1995 Ай бұрын
As a physics undergrad. I’ve come to realize that Euler is a Titan alongside Einstein and Newton. Every single bit of modern physics has Euler to thank for providing the mathematical Tools to construct a vivid picture of the universe and its underlying principles. Absolute legend.
@happmacdonald Ай бұрын
Penrose, Euler, and Archimedes of Syracuse try and fail to walk into a bar due to the exponential volume of proofs they collectively produce by accident on their journey from the parking lot
@Greyhawksci Ай бұрын
I will never not be disappointed that MIT's hockey team isn't the Eulers.
@FCHenchy Ай бұрын
The Age of Unreason series clued me into how awesome Euler is (though he's a secondary character), and I've been stanning ever since.
@rogerszmodis6913 Ай бұрын
@@Greyhawksci only like 1% of people would get it. I would bet the vast majority of people read and pronounce Euler phonetically.
@NStripleseven Ай бұрын
There’s the old joke that so many random bits of math are named after the guy, we may as well just start calling numbers Euler letters.
@CinemaDemocratica Ай бұрын
This channel is one of the most unfettered, beautifully conceived, brilliantly executed channels on this platform.
@cafemolido5459 5 күн бұрын
Take number 1, double it, repeat, create a series (1,2,4,8,16,32,8192,...) on the series, number ending in 2 (ex 32), subtract square root of previous number (ex 16) (32-4=28) 28 is potential perfect number (test it) REPEAT... (8192-64=8128).... Computer program can process easy
@joshuazelinsky5213 5 күн бұрын
Yes, this is easy. Good for recognizing that you can do this. This is also much less efficient than our best process for finding these which involves using what is called the Lucas-Lehmer test for Mersenne primes.
@VintageBlacklist Ай бұрын
I have a research project due tomorrow and I was really looking for something distracting. My procrastination thanks you.
@jakewolf3561 Ай бұрын
lol
@S4M3350 Ай бұрын
Same
@jin_cotl Ай бұрын
I’m actually early to a Veritasium video
@liambohl Ай бұрын
This comment hurts
@BOTthelesser Ай бұрын
Same although it’s project about a book
@theyreMineralsMarie Ай бұрын
Finding perfect numbers is one of the first algorithm assignments you get in a computer Science degree. I never knew it was such an old idea.
@Dranzer_Panzer Ай бұрын
Clearly you didn't watch the video, it's an even idea.
@Actrl51 Ай бұрын
@@Dranzer_Panzerthat’s a prime quality comment
@xuaalbito8303 Ай бұрын
When my professor asked us to write a program to find perfect number I was like wth is that then he gave us the formula so it was easy but never understood what it actually was until now I found only 2 6 and 28
@theyreMineralsMarie Ай бұрын
@@lucashershberger623 wonder away.
@zeke1220 Ай бұрын
@@lucashershberger623 Circumstantial evidence, maybe
@shanielle3777 Ай бұрын
What's also really cool is that if you divide the perfect number (at least the first four) by the last number in the line of numbers that make it then divide the perfect number by it, the result keeps doubling. To explain: 6 is 1+2+3, 6/3 is 2 or 2^1. 28 is 1+2+3+4+5+6+7, 28/7 is 4 or 2^2. 496 is 1+2++3...30+31, 496/31 is 16 or 2^4 or 4^2. 8128 is 1+2+3+...127+127, 8128/127 is 64 or 2^6 or 8^2. I don't know if the other perfect numbers fit that, but the first four do and I think that's funky
@devanshgupta794 Ай бұрын
Bro its literally told in the video... Altho slightly differently, but its there... Cuz 1+...+127 is 127*182/2 and that the euclids representation too
@LawlFrank Ай бұрын
Let's say P is a perfect number. Any series 1+2+3+4+... +n is n terms long and on average (n + 1)/2, so the sum is n * (n + 1) / 2. So P = n * (n + 1) / 2. Another thing we notice, is that all the series are (3, 7, 31, 127) in length. Those are powers of 2, minus 1, so let's say n = 2^m - 1. Now, you say you divide the perfect number by the last number in the series, that would be n. So, divide P by n simply gives: P / n = n * (n + 1) / 2 / n = (n + 1) / 2 = (2^m - 1 + 1) / 2 = 2^m / 2 = 2^(m-1). In other words, the power of 2 you end up with after dividing by that last number, is m - 1. Let's look at 6 again. It it the sum of 3 numbers, n = 3, m = 2 (2^2 - 1 = 3). So P / n is 2^(m - 1) = 2^(2 - 1) = 2^1 = 2. For 28 n is 7, m is 3, so P / n = 2^2 = 4. For 496 n is 31, m is 5, so P / n = 2^4 = 16. For 828 n is 127, m is 7, so P / n = 2^6 = 64. There is not even really a pattern there. And it doesn't work anymore for the next one: P = 33550336.
@fionakelleghan3267 5 күн бұрын
I'm an English major, and I just subscribed to Veritasium because I enjoyed this so much. Thank you! I can't wait to chase down every last video!
@rayrwyr 4 күн бұрын
Add math as your second major
@fionakelleghan3267 3 күн бұрын
@@rayrwyr I had over a decade of university studies, but it's tempting. 😊
@lifthras11r Ай бұрын
One big application of Mersenne primes, that came from studying perfect numbers, is a good random number generator. RNGs had been historically very bad, until the introduction of Mersenne Twister in 1997, which uses a property of Mersenne primes to prove a good randomness. The most popular version uses a Mersenne prime 2^19937 - 1 for example, hence the name MT19937. There exist much more performant RNGs than Mersenne Twister now, but Mersenne Twister is still widely used thanks to its initial impact.
@lpc9929 Ай бұрын
The
@Inuzika Ай бұрын
That actually helps a lot with understanding why RNG is multiplicative in most video games.
@till8413 Ай бұрын
omg i was using that in programming, never knew why it was called MT19937 😮 my mind is blown away
@kphaxx Ай бұрын
@@lpc9929well said
@helpiminabox Ай бұрын
Got any keywords to recommend for searching for information on these PRNGs? If there's something more performant that I can guarantee generates the same sequence regardless of platform that would give me something fun to do for a game engine I'm writing as a hobby.
@AudreyRoberts-jl4yg Ай бұрын
Your videos are always so crisp, clean, and educational
@djakfkanfnanfajfiajdjajdjd6719 Ай бұрын
There's something heartwarming about seeing the quote at 9:26 and knowing how far we've come since then. I feel like past nerds would be so happy for and jealous of us for the technology we have to use for our own pursuits of knowledge haha Edit: Not just that quote but this WHOLE VIDEO goes to show how computers were an absolute game changer. And a game changer built on the accomplishments of every genius before them 😭
@Tritone_b5 Ай бұрын
As a computer and math enthusiast I'm so disappointed I didn't know what Prime 95 was for, other than a OC stress test tool.
@leksitarmik4636 Ай бұрын
I knew Prime95 was to find Primes in addition to a stress test, but I had no idea of the depth of the GIMPS project. Considering the program is both so simple yet computationally intensive, to be known as one of the most intense stress tests for a computer, really speaks to the sheer computing power we have needed to go this far.
@jonasplayedthat2220 Ай бұрын
@irradiatedturtle Ай бұрын
Read this as “as a computer who is also a math enthusiast” at first and had to think for a second lmao
@simon6071 Ай бұрын
26:17 "Carl Pomerance predicts that between 10 to 2,200 and infinity, there are no more than 10 to the (power of) negative 540 perfect numbers." I'm not good at math. Can anyone tell me why that number is to the negative power instead of positive power? As far as I know, 10 ^-1 = 1/10^1 = 1/10 = 0.1 10^-2 = 1/10^2 = 1/100 = 0.01 Therefore, 10^-540 = 1/10^540) = 1/ (1 followed by 540 zeros) = 0. (539 zeros)1 10^-540 is less than 1. However, 51 perfect numbers have already been discovered, so how can the there be no more than 0. (539 zeros)1 perfect numbers in Carl Pomerance's prediction? Is there an error somewhere?
@Nereus74 Ай бұрын
@@simon6071 10^-540 perfect numbers of the form N=pM^2 An odd perfect number must have the form N=pM^2, so there are very close to zero odd perfect numbers expected in the range 10^2200 to infinity.
@martafixarcoolt5993 Ай бұрын
I love when people have made up their mind on something, like there is a heuristic argument for that there is no odd perfect numbers, and then faced with a reasonable counter argument, imidiately recognize that their original argument is flawed. Just listening to reason and take that logic in, it is beautiful
@ThisHandleIsAlreadyTaken839 Ай бұрын
I love when people spell immediately correctly
@rishabhchauhan8948 Ай бұрын
Absolutely😊
@hanu6158 Ай бұрын
@@ThisHandleIsAlreadyTaken839 I love when people realize that not everyone knows how to spell or read, some didn’t go to a fancy uni, check your privilege 😠
@gavinathling Ай бұрын
@@hanu6158 115 have thumbsed up their message, so this is one person getting their jollies from being petty. But a spell checker is not privilege - all computers, cellphones, etc. have one.
@RH-ro3sg Ай бұрын
Well, he does add that there are additional arguments that make the original heuristic argument stronger, he just doesn't specify what these arguments are (possibly implossible to explain to laymen in the space of a few minutes?)
@chrisanderson687 Ай бұрын
Veritasium is an unbelievable treasure to humanity, thank you for your curiosity, your humility, and your obvious love and passion for crafting such incredibly high quality videos, they have enriched my life, and countless others around the world.
@Amor_24 16 күн бұрын
I had a fun watch, definitely amazing to think about! I've been fascinated with numbers and problems since grade school and has been thinking about problems with patterns like this ever since. Not that I am any good at it nor am I sure when trying to come up with formulas based on these patterns. And sometimes, I tend to simplify these kind of problems based on what they look at. With that, I also think there is no odd perfect number for the fact that these perfect numbers we currently have all have the factor "2" which obviously makes it divisible by 2.
@patinho5589 Ай бұрын
I clicked on the video and immediately solved it. But my solution is too long to fit into this comment.
@balloonboy5212 13 күн бұрын
r/iamverysmart
@billboll 13 күн бұрын
Thanks, Fermat!
@mina-qf3wd 13 күн бұрын
yeah, sure.
@No-kw2os 13 күн бұрын
Same
@sangminjung9454 12 күн бұрын
ㅋㅋㅋㅋ
@Kari-Bond Ай бұрын
I loved the last note here. So many people get bogged down with the “why”. Sometimes “I want to” is enough of a reason.
@tristanmoller9498 Ай бұрын
Why is the only irrelevant question in math.
@steamer72 Ай бұрын
Sisyphus
@ItsJustKaya Ай бұрын
Most sukkuna quote ever. They ask me why and if. But i do it when i like to kinda message ( admittedly finnished it few hours ago yet cant recall its quote)
@GodplayGamerZulul Ай бұрын
@@ItsJustKaya Why are you writing like this?
@petergibson2318 Ай бұрын
When Boolean Algebra was invented in the 1840s it was purely theoretical without any possible practical use. Today it is the way the circuits in digital computers work.
@BoolFalse 25 күн бұрын
i'm becoming more respectful to my teachers, when i realize i can now understand and enjoy these kind of videos.. even 15 years later after the school..
@snowflake5219 Ай бұрын
At 7:00 - what the guy says - "400 years later" The video - *300 BC to 100 BC*
@Xanthe_Cat Ай бұрын
Nicomachus is not BCE.
@kanishkjaiswal7260 24 күн бұрын
Its only 100, theres no bc
@BronsonMWhite Ай бұрын
WOAH! Dr. Pace Nielsen was my professor for intro to proofs. I was NOT expecting him to show up in the video. He's a fantastic guy, exceptional professor, and brilliant number theorist.
@ES-54321 Ай бұрын
A brilliant number theorist, sure, but would you say he's a perfect number theorist?
@ashraf5151 Ай бұрын
@@ES-54321 good one
@puchacz199 Ай бұрын
@@ES-54321 even then.. would he be considered a brilliant perfect number theorist or even a perfect perfect number theorist or maybe a perfect even perfect number theorist?..
@theslothwithin Ай бұрын
@@ES-54321da dum dun tssss
@fratco1896 Ай бұрын
@@ES-54321 😂😂
@lifeisfakenews Ай бұрын
17:37 ish "he gave a talk" "without saying a word" thats a new level of genius
@LuisSierra42 Ай бұрын
Based genius
@maddawgzzzz Ай бұрын
Based AF braa
@djangosouthwest6043 Ай бұрын
Actions speak louder than words
@edwinkjobi Ай бұрын
Nelson Cole is the main Character!
@CrimsonA1 Ай бұрын
*Drops chalk and walks off stage
@annaefraimidou5726 Ай бұрын
Congrats on making such a topic so enjoyable and interesting throughout the whole video. Wow!
@CountessBathory418 28 күн бұрын
28 years later you single handedly taught me how formulas are made!!!!
@joshuazelinsky5213 Ай бұрын
Video is well done. I'm a mathematician some of whose work has been on this topic (some of the results you put on at 23:51 are mine, and one is due to a joint paper of me with Sean Bibby and Pieter Vyncke). My apologies also for the length of this comment. I do have some quibbles about some of the history details but they are minor. (And it is possible that I'm getting some of the details wrong myself.) Descartes's construction of a spoof perfect number, shows he had a pretty good understanding of how sigma behaves. Descartes's spoof shows he had a pretty good understanding of sigma(n). Also, Descartes likely did prove that an odd perfect number must be of the form he suggested. What Euler did was a bit stronger. Euler showed that if n is an odd perfect number n= p^e m^2 where p is a prime , p does not divide m, and p and e are both 1 (mod 4). Notice that this implies Descartes's result. Regarding the Lenstra-Pomerance-Wagstaff conjecture, while it gives a specific estimate for how large the nth Mersenne prime is, there is some degree of doubt of if it is correct. We're much more confident that the conjecture is correct up to a multiplicative constant near 1. And we are much much confident that there are infinitely many Mersenne primes, even if LPW turns out to be wrong even on the order of growth of Mersenne primes. Regarding Pace's comment to high school students, I want to expand on that slightly. No one should be working on this problem with any hope of solving it any time soon. The problem is genuinely very difficult. The spoofs are in many respects a major obstruction to proving that no odd perfect numbers exist. In particular, many of the things we can prove about odd perfect numbers, also apply to spoofs. So if they were enough to prove that no odd perfect numbers existed, we would have proven that no spoofs exist, which is obvious nonsense. To use an analogy that my spouse suggested a while ago: If we are trying to convince ourselves that Bigfoot doesn't exist, but all we've done is list properties that all mammals have, we can't hope to show Bigfoot isn't real. There are few other big obstructions, one of which has a very similar flavor. But, Pace correctly notes that not that many people are working on the problem, so there may be more low hanging fruit than one would otherwise expect for aspects of the problem. For most really famous open math problems, like say the Riemann Hypothesis, or P ?= NP, lots of people have spent a lot of time thinking about aspects of it. So most mathematicians have a general attitude of not trying to bash their head against problems that a lot of other people have thought about. But in the odd perfect number situation, to some extent, the community may have overcorrected, and thus spent less time on it than they might otherwise. However, this may also be due in part to the odd perfect number problem being famous, but not by itself being very enlightening in terms of what it implies. Hundreds of papers prove theorems of the form "If the Riemann Hypothesis is true then " . And those papers are themselves very broad and varied in what follows after the then. In contrast, I'm aware of only a handful of papers with results of the form "If there are no odd perfect numbers then" and what follows after the then is always something involving divisors of a number in a somewhat straightforward fashion.
@jamesknapp64 Ай бұрын
The end of your comment reminds me of my Mentor saying one time that part of him hopes someone disproves the Riemann Hypothesis just because of all the papers hes read on "if the Riemann Hypothesis is true then X" and how they'll all have to be withdrawn. He thinks its true fyi. I wouldnt call myself an odd prime "truther" but I see no reason infinitely many couldnt exist just the first one being say > 50th Fermat Number would put it out of search range for the forseeable future. Then one about every billion more digits.
@Featherless1 Ай бұрын
1×1=2
@asheep7797 Ай бұрын
Do you know any papers that rely on the existence of odd perfect numbers?
@daniels8625 Ай бұрын
@@Featherless1keep going...
@justusimperator537 Ай бұрын
2x2=4=2+2
@utabrandenburger5547 4 күн бұрын
Mersenne primes are always a G (C=tonic=0) in the third octave . Perfect numbers relate to perfect intervals in a tone circle of 5 octaves.
@Thystan2000 Ай бұрын
The calculation itself is the application. In IT we use prime95 to stress test a machine, for example for overclocking or checking if the hardware is faulty.
@jasoncheng3303 Ай бұрын
17:48 Something about this quote just hit me hard, we are in the age of computers that started just a few decades ago and we often ignore how seriously revolutionary computer advancements are, something that could take years can now be done by a child with an iPad.
@DJFracus Ай бұрын
No doubt, this age will be remembered in history as the beginning of the computer age. It has completely transformed society in a way few technologies have before.
@dorianguerrazzi5040 Ай бұрын
Same, I literally shed a tear.
@rogerszmodis6913 Ай бұрын
I remember when a computer beating a human at chess was newsworthy.
@elLooto Ай бұрын
Now realize that LLMs dont even come close to representing that increase in the efficiency of labour....
@FLPhotoCatcher Ай бұрын
I just had a thought about primes. Has anyone figured 'primes' for fractions? What I mean is, instead of using whole numbers, try using a small fraction, such as 1/1298ths as your potential prime, and figure out if any two larger normal fractions multiplied together can make the smaller one. Or some other scheme using fractions to find fractional 'primes'. I'm thinking some cool new mathematical knowledge could be found, or a cool pattern.
@periodictable118 Ай бұрын
The absurdity of that 1000 page book containing that one number is that in paper form it is essentially useless, but the symbolism is so profound that people were scrambling to get a hold of a physical copy, that it sold out within days. I think this has something to do with human nature in that there is some spiritual value in having a physical copy of something, even if it is practically useless and infinitely more useful to just have a text file containing that number.
@PTfan54 Ай бұрын
A book containing the largest known prime and a text file containing the largest known prime are actually equally useless.
@falconerd343 Ай бұрын
It makes a fairly decent random number generator. Flip to a page and stab your finger at a number. Just skip the first and last numbers (the first is more likely to be 1 (I think, I might be thinking of something else), and the last is odd). It's also kinda like a code pad, but less secure since there's lots of copies of it out there. To be truly secure there should only be 2 copies of a code pad. It's unbreakable though since the data is completely masked by randomness. Assuming the pad is created in a truly random manner.
@BishopStars Ай бұрын
@@falconerd343Benford's Law. One Time Pad.
@ES-54321 Ай бұрын
I assumed they were all just scrambling to buy gag gifts for their mathematician loved ones
@jamesmnguyen Ай бұрын
Imagine how much energy and computation went into making that book.
@captnmaico6776 Ай бұрын
Such a great video! I love your animations, its so easy to follow.
@user-hu2qb9ih6c Ай бұрын
HELP! I need some conversions. I need all of the following each into Exatons and Kilotons!! 30 Megatons 3 Gigatons 22 Gigatons 48 Gigatons 15 Teratons 4 Petatons 8 Petatons 60 Exatons 400 Exatons
@DoShiAcademy 2 күн бұрын
Congrats on making such a topic so enjoyable and interesting throughout the whole video. Wow
@wfaction Ай бұрын
wow this is crazy. prime95 is widely used for cpu benchmarks during overclocking to check temperatures and crashes. But up until today I didn't know it was calculating mersenne prime numbers. I thought it was just trying to find prime numbers for cpu stress test. great video as always
@zeevtarantov Ай бұрын
It is used for stress testing overclocks because it is sensitive to mistakes in the calculation caused by overclocking too much.
@isthismyfinalform169 Ай бұрын
Damn thats interesting
@fulgerion Ай бұрын
It says this during the test.
@ViliamF. Ай бұрын
Finding primes was (and still is) its original purpose. It just so turns out that finding primes takes a lot of computation power and it is so well optimized that it can squeeze out every drop from a CPU. And if there is a fault anywhere in the CPU, it will show.
@tauzN Ай бұрын
@@fulgerion you probably also read EULA’s 💀
@Art_Vandelay_Industries Ай бұрын
As someone that was never good at math it blows my mind how people could and can think in ways that can actually make sense of math so abstract. And without having computers to do the crunch for them back in the days.
@IdOnThAvEaUsE69 Ай бұрын
Crazy how humans are capable of all this, but still can't stop using plastic for everything lol. We're too intelligent for our own good xd.
@tincanblower Ай бұрын
@@Believe5inJesusChristYou may be barking up the wrong tree. This video is about people setting out to prove or disprove claims with evidence - the exact opposite of religion which asserts a claim and then uses the claim itself as evidence. "I believe that a god exists, as claimed in the Bible." "Where's your evidence?" "Look at this from the Bible..."
@Argoon1981 Ай бұрын
@@tincanblower Not only that but also "Where's your evidence?" "Look at this book written and rewritten by humans for millennia before the printing press, humans so propense to make mistakes, lie, cheat and push some ideology into the paper if that suits them" This is why the old testament God, is so different from the new testament God, they were invented and imagined by humans that add very different ideologies, about what is right and wrong.
@BlueSparxLPs Ай бұрын
@@tincanblower It's a bot. There's a lot of them on KZfaq that exist just to quote verses.
@stompthedragon4010 Ай бұрын
@@Argoon1981As Sabine Hossenfelder has said, " The existence of God is not a scientific question. It can neither be proven or disproven by science. It is a philosophical question "
@fredericbachelier1620 6 күн бұрын
Incredible and fascinating! Even though I am fond of maths, I never heard of this problem... Besides, happily surprised to see how many times this video was viewed... :-) Excellent job that did this KZfaqr! Congrats!!
@SirThanksalott Ай бұрын
To add to your question on the use for discovering these numbers. They will be eventually be used to quantify the compression and decompression mechanics of energy and matter in this Universe
@Wunba Ай бұрын
They lowkey tricked me with the outro at 16:25 I was so disappointed for a second 😂
@The7Shadows. Ай бұрын
I was so relieved it was finnally over. BUT IT WASNT
@PriggarGaming Ай бұрын
What da faq you doing here ?
@ruskcoder Ай бұрын
Fr Minecraft KZfaqr on math 😮
@parthhooda3713 Ай бұрын
@@ruskcoderso what? Everyone enjoys Veritasium whether they like maths or not
@aamirkhan_ Ай бұрын
I was looking for this comment..
@wendeltenebroso9324 Ай бұрын
It's good to know that there are more and more vloger balancing the traditional media thanks.
@Snarffu 5 күн бұрын
I am not a math person. I see the beauty in it for sure but it is abstract and I need to touch stuff to understand it well. That said, this was one of my favorite videos made by these guys. The published book of massive primes made me unreasonably happy!
@Rabcup Ай бұрын
I thought it was weird for this to be uploaded at night for EST but then I remembered he just moved to Australia, so it’s still technically a normal morning upload for him
@TheSuperiorQuickscoper Ай бұрын
When did he move from LA?
@Lapse-a-lot Ай бұрын
Can confirm. It's midday here in 🌏
@jin_cotl Ай бұрын
Fr I’m about to sleep soon
@augisterman3685 Ай бұрын
It's evening for me
@THICCTHICCTHICC Ай бұрын
Honestly it feels weird to be awake when a big channel releases a video lmao Australia's timezone is hilariously inconvenient if you watch US or Euro stuff
@ytmadpoo Ай бұрын
I've been involved with GIMPS for about 27 years now and it's great to see us mentioned in the video. It was one of the earliest examples of using distributed computing to work on these enormous tasks, and it's been fun to learn more about the math behind it along the way and talk with all kinds of really smart people around the world in the process.
@Filo127 Ай бұрын
you've been involved with gimps ? 🤨
@LeVasTiaN Ай бұрын
@@Filo127you haven't watched the video?
@nivyan Ай бұрын
I have a micro super computer, because I both do software development, video editing and play around with AI with huge models and video games. I've just started contributing to the project; since my demands are high, I usually replace parts before it's reasonable to do so. Now I can actually put my CPU and excessive cooling to good use when I'm just watching youtube and not waiting for something to encode or data to parse. I'm already 1.2% into my first assignment.
@SamuelRamirez-js5rb Ай бұрын
Do you know what a gimp suit is? If not look it up lol.@@LeVasTiaN
@drunkredninja Ай бұрын
OG distributed computing projects were the best way to stress test overclocks back in the day. did alot of gimps, fah and seti myself.
@The90DegreeOfficial Ай бұрын
Me: > starts watching video > gets engrossed > gets the motivation to find the odd perfect number > forgets what a perfect number is > refuses to elaborate > leaves
@muesliriegel7306 Ай бұрын
If I view this search for the odd perfect number in a transcendental way, it seems oddly aesthetic and meaningful to me, but I can't exactly say why. Is it that some of the greatest minds in history play the ball to each other over the course of centuries? Is it because we are really protruding deeper into the mysteries of the universe, getting closer to it's very fabric? Is it because we can? Is it because people try to solve the problem despite the fact that it is seemingly impossible? It might not have a real life application (which is also highly uncertain, there might be useful new techniques discovered in the process) but it certainly makes as much sense as meditating, dancing or creating art.
@sophiejones3554 Ай бұрын
It's a question so difficult to answer that the attempts to do so have shown people the limits of their technology, which humans have nevertheless persisted in trying to answer for almost the entirety of recorded history: despite there being no obvious use for the answer to this question. So yes, I think it's fair to say it is aesthetic. The fact that we do this, says more about us humans than it does about numbers or the universe. For all we know, the concept of a perfect number has no meaning in nature at all.
@MarkArandjus Ай бұрын
17:41 I choose to believe he dropped the chalk like it was a mic and just walked out, dapping up a few mathematicians on the way.
@periodictable118 Ай бұрын
Imagine he just wrote some random ass numbers and it didn't even multiply to the original
@cloudyblueskye Ай бұрын
😅u
@jmwmusic5665 Ай бұрын
That point at the end, about the value in doing math, felt like the thesis statement every veritasium math problem video. Hats off.
@Fire_Axus Ай бұрын
your feelings are irrational
@mcpr5971 Ай бұрын
I was also thinking it's a fallacy to think because someone is working on "something that matters" that they are necessarily accomplishing anything. Given the amount of academic research fraud going on, it's hard to know whether someone got published because they found something interesting, or they are milking the system for more grant money or to get on the tenure track.
@CCCompiler Ай бұрын
@@Fire_Axus your comment is perfectly odd
@FuncleChuck Ай бұрын
Where’s the proof
@johnchessant3012 8 күн бұрын
One thing I'm curious about is how Descartes was able to guess the correct form for odd perfect numbers, when he of course didn't have any examples to work with, and he didn't have the language of the sigma function and its multiplicative property.
@joshuazelinsky5213 8 күн бұрын
Very likely Descartes was aware that sigma was multiplicative. His spoof example doesn't make a lot of sense without it. One could try to do something similar just by thinking about pretending what is prime and counting things, as well as thinking about what is happening in terms of parity without that, but that would be tough.
@Iliketrains446 4 күн бұрын
what the sigma
@joshuazelinsky5213 4 күн бұрын
@@Iliketrains446 Please watch the video. They explain what the Sigma function is.
@prosimion 9 күн бұрын
this video makes me want to solve some paradoxes I was knot going to tangle with ...that just came out of know where
@sil1235 Ай бұрын
Very nice video! Just a small thing, the reason why the largest known prime is almost always a Mersenne number is not because it grows so quickly (for example numbers of form 2*3^n-1 would grow quicker...), the real reason is because we have efficient test for numbers of that form so we can test them much faster (the Lucas-Lehmer primality test).
@mehrabnikoofaraz233 Ай бұрын
I must mention that 3^n -1 is always even so none of those are prime. But about the test I think you are right.
@sil1235 Ай бұрын
@@mehrabnikoofaraz233Thanks for correction, I've changed it to different example to avoid confusion.
@TruthNerds Ай бұрын
Ironically, the test is so efficient that someone skilled at arithmetic could perform it using pen and paper in some hours or days, for 15-20 digit numbers. Mersenne's "all time would not suffice" claim was likely based on trial division … the oldest and least efficient primality test. The test goes like this: Let n be an odd prime. (NOTE: a prime exponent is necessary anyway, so other than ruling out 3 = 2^2 - 1 this is w.l.o.g.) Construct a sequence S(i) with: S(1) := 4 S(k + 1) := S(k)² - 2 p := 2^n - 1 is prime if and only if S(n - 1) is divisible by p. E.g. n=3 is an odd prime, p=2^3 - 1 = 7, S(3 - 1) = S(2) = 14 = 2 * 7, therefore 7 is a Mersenne prime. Crucially, because only divisibility matters in the end, it suffices to calculate the remainders of the S(k) modulo p, which prevents the intermediate results from growing very large.
@HeadOnAStick Ай бұрын
@@TruthNerdsClear and informative. Thank you.
@ragnkja Ай бұрын
It’s because it’s both: it’s fast-growing but _also_ easy relatively to check.
@saswatachakraborty4937 Ай бұрын
This channel is one of the greatest argument in favour of KZfaq as a wonderful medium of learning.
@colepeterson5392 Ай бұрын
channels like these are why I love KZfaq in general
@MikkoRantalainen Ай бұрын
I agree, Veritasium, Vsauce, SmarterEveryDay and Sabine Hossenfelder are prime examples of channels that make KZfaq worth using even if you wouldn't like all the ads and random stuff.
@farmertree8 Ай бұрын
@@MikkoRantalainen "prime" examples
@james6401 Ай бұрын
Asianometry
@talosgak1236 Ай бұрын
You didn’t really learn anything You just watched a video for entertainment and will forget everything the moment you click on a different video
@ThePrinceVegeta7 Ай бұрын
Love how this guy at the end has a cabinet full of commander decks on top.
@hasantao 15 күн бұрын
Euler surprises me every single time. He has been an absolute genius.
@wenaolong Ай бұрын
One thing that is helpful about solving (or attempting to solve) such problems is that a lot of methodology is developed in the process, and methodology is always useful.
@nachoijp Ай бұрын
Another great thing is that it's fun to try. And that fun is a great motivation to learn the more tedious parts of mathematics. It's like when we used to say "why would I learn the multiplication tables if I have a calculator", and we had a point: what's interesting about something that's already solved? But every person I've talked about mysteries like this one are suddenly enthralled by the idea of maybe finding the answer, and that motivation to learn is priceless.
@RUHappyATM Ай бұрын
I sometimes wonder what else could be invented or discovered if the productivity is redirected to some other endeavours.
@marinmarinhola Ай бұрын
Exactly, this whole quest spawned Prime95, which has helped me overclock PCs for years now.
@happmacdonald Ай бұрын
29:08 - "If you're a high schooler and you just love mathematics and you think 'I want a problem to think about', this one's a great problem to think about. And you can make progress, you can figure out new things. Yeah, don't be scared" Instructions unclear, and now I am caught in the steely grip of the Collatz Conjecture. Gee, thanks Professor Nielsen! 😂
@harshrajveermaran5792 Ай бұрын
Hey after 8128 is the next perfect number 41,328?
@Grizzly01-vr4pn Ай бұрын
@@harshrajveermaran5792 No. The next perfect number is with p = 13, so 2¹²(2¹³ - 1) = 33550336
@minerscale Ай бұрын
@@harshrajveermaran5792no it's 33,550,336.
@KiLLJoYYouTube Ай бұрын
Veritasium already did a video on Collatz 🫡
@Felipe-sw8wp Ай бұрын
What if there is only one odd perfect number, and it's the only number at which Collatz Conjecture fails? 😳
@samburgess7924 3 күн бұрын
I noticed the powers of 2 being (2^p - 1)x2^(p-1) at the binary part, you can see there is always one extra 1 vs the 0s. 110, P is 2, it represents the number of 1s then p-1 is the 0s.
@wise_alchemist 13 сағат бұрын
"The number must be greater than 10^2200." Meanwhile, the number "1": "Hello, I am a perfect odd number." It was also not entirely correct that the possible number of divisors of such a potential number “>=10” was indicated. A quantity cannot be an even number, since the sum of an even number of odd numbers will always be even, and the divisors of an odd number are, by definition, all odd.
@joshuazelinsky5213 12 сағат бұрын
> Meanwhile, the number "1": "Hello, I am a perfect odd number." No. This is incorrect. Recall, for a number to be perfect, it must be equal the sum of its positive divisors which are less than the number. Notice that 1 does not have any positive divisors which are less than 1. So the relevant sum is zero. Since zero is not equal to 1, 1 is not perfect. > It was also not entirely correct that the possible number of divisors of such a potential number “>=10” was indicated. A quantity cannot be an even number, since the sum of an even number of odd numbers will always be even, and the divisors of an odd number are, by definition, all odd. You misheard or misunderstood what was said there. The statement was that the number of *distinct prime divisors* had to be at least 10 for an odd perfect number. That's not a statement about the number of possible divisors. You are correct that that the total number of divisors of an odd perfect number which are less than itself must be odd.
@Soken50 Ай бұрын
My favorite bit of "useless" math at the time of its discovery are quaternions, they were discovered/invented a century before we needed it for avionics, orbital dynamics and computer graphics, yet they are integral to our civilisation now, allowing us to compute spatial rotations effortlessly. I hope this leads to a great discovery that enables even more awesome technology in the future.
@marcosmith6613 Ай бұрын
Thanks for sharing this 😊
@glennllewellyn7369 Ай бұрын
Toilet flow direction is important.
@Whiterioot Ай бұрын
You sound really smart. Sincerely.
@Soken50 Ай бұрын
@@Whiterioot Thanks, I try my best.
@g..h..o..s..t Ай бұрын
@@Soken50 congratulations on trying your best to sound really smart, which is what you just agreed with @Whiterioot about. 👍
@Tamonduando Ай бұрын
10:45 I feel that calling Euler a "prodigy" is a bit of an understatement.
@jamesknapp64 Ай бұрын
Yeah Magnus Carlson was just good at Chess at 20 pales to the understatement that 20 year old Euler was just a prodigy
@cf-yg4bd Ай бұрын
Even though I'm pretty sure there's no better single word that could be applied, I agree.
@folkrav Ай бұрын
@@cf-yg4bd I was about to throw one back at you then realized I legitimately can’t think of one either. Well said.
@PlayerSlotAvailable Ай бұрын
What is special about them? It is my first time seeing their name.
@timothyobaob3624 Ай бұрын
@@PlayerSlotAvailablehe’s a revolutionary in math-you can look him up on your own time, but for example, he’s the one who came up with the modern notation for functions, and also came up with the most beautiful math equation (Euler’s identity).
@PlasmaDoesGames 5 күн бұрын
sigma function
@masonleppala8757 4 күн бұрын
ong
@user-sw8nx1nd3w 15 сағат бұрын
😗😌😗😃😄
@calatcryptomathicdotcomyea8751 Ай бұрын
I'm sure there's one lurking out there silently chuckling to itself; then again- I think we'll make contact with an alien species before we find it.
@tokenr7414 Ай бұрын
As the co-discoverer of the first GIMPS prime (the 35th), I wasn't even aware of this unsolved problem...! -Joel Armengaud
@kitfifty Ай бұрын
whgats a GIMPS prime
@PaulDeanBumgarner Ай бұрын
What a waste of time. Look… There isn’t an odd one. This is now officially solved.
@DasAntiNaziBroetchen Ай бұрын
@@PaulDeanBumgarner Is the joke that you pretend to be a boomer? Cuz "Bumgarner" surely can't be a real name.
@TheCommentor- Ай бұрын
Bro is real
@N4SCARfaN Ай бұрын
@@DasAntiNaziBroetchenI've seen both Bumgardner and Baumgartner, I'm sure Bumgarner exists somewhere
@vigilantcosmicpenguin8721 Ай бұрын
I love the bit at 21:02 that says "If we ever lost all the prime numbers, someone could find this book, and be like, here's a big one." I just think it's hilarious to imagine some archaeologist coming across a book and going, "Is this just a bunch of numbers? no, wait. IT'S THE ONE WE'VE BEEN SEARCHING FOR!"
@Larkian Ай бұрын
After all this years, I have all of them.
@dliratx 27 күн бұрын
I want my name in history, I already have 4 servers in the GIMPS project, great video.
@eloncole5702 18 күн бұрын
This is the reason why i love this channel ❤
@NoraOlson-ct7nr Ай бұрын
almost cried at the end. "the only way to know for sure is to try" has always, always made so much sense to me. and i just found another one. I'm so glad to just be alive at times like these.
@annoy4nce648 Ай бұрын
bro, that's literally part of the foundation of all of science and mathematics.
@glacialis3329 Ай бұрын
@@annoy4nce648 Damn the takeaway from this video though - now I have a burning desire to actually go try something that might be a dud XP
@PotionsMaster666 Ай бұрын
🫂 we brothers should make our own country
@DasAntiNaziBroetchen Ай бұрын
These comments are extremely weird.
@rabbr2sdsd799 Ай бұрын
@@DasAntiNaziBroetchenyou aint lie my boy 😂😂😂
@user-pw6sy2sq7y Ай бұрын
Terrific video. However, the part about Edouard Lucas could have been much stronger. He did not merely show M_67 was not prime, he was able to show M_127 was prime. This is the largest prime ever found without the aid of a computer. He did so using novel methods that did not rely on trial factorization, but rather exploited properties of the Fibonacci numbers. Using his methods he could test M_n for primality for all n equivalent to 3 modulo 4. These methods were further refined by D. H. Lehmer (who also should have been mentioned) so that all M_n could be tested; giving us the Lucas-Lehmer test for Mersenne primes. It is this test that makes GIMPS possible. For more informations see "Edouard Lucas and Primality Testing" by Hugh. C. Williams.
@tensor131 Ай бұрын
a very important observation - good
@JBG-AjaxzeMedia Ай бұрын
love me some gimps
@zarki-games Ай бұрын
I was half expecting the end of this to be one of those "For more information, Google 'Two Girls One Cup'." Sort of jokes.
@warrior4christ777 Ай бұрын
Ooo ah....your so smart.but are you wise?
@WarthogDoctor Ай бұрын
😂@@warrior4christ777
@JustSomeGuyInHisOwnWorld Ай бұрын
I just solved this problem... The question was, "is there any odd perfect numbers" the answer is no. If the equation is taking one, doubling it and you keep doubling it, and you're multiplying prime numbers to the last number in the sequence you'll always get an even number. Think about it, when you add an odd number to itself you'll always get an even number, if you multiply odd numbers by even numbers it will always result in an even number.
@joshuazelinsky5213 Ай бұрын
The formula you are referencing, that a perfect number is of the form 2^(p-1)(2^p -1) has only been proven for even perfect numbers. Using it to prove there are no odd perfect numbers is circular.
@leniorrb 2 күн бұрын
Great video! Just need an update in the Portuguese-Audio, it seems that you upload the Pi audio into this video.
@Oriol-oo7jl Ай бұрын
I admire this guy enough to know that when he says "WHAT BLOWS MY MIND IS" and after saying the thing he does the BOOM gesture... if I stay impassive, it means that i have missed an important chunk somewhere
@vigilantcosmicpenguin8721 Ай бұрын
When Derek's mind is blown, everybody's mind is blown!
@Xelianow Ай бұрын
The real benefit of solving those kinds of problems is usually not the solved problem itself, but the insight you gained while solving it and the kinds of techniques and methods developed beeing useful in other areas where you didn't expect them to be useful. Noone knows whether the tool you invented to solve this kind of problem will suddenly crack open other problems as well in (at first glance) unrelated fields of mathmatics. Edit: Thats also the reason why proving something simply by checking all possible cases with a computer isn't very well respected by mathematicians. Sure, you may have the proof that something does/doesn't exist, but it tells you absolutly nothing about *why* it does/doesn't exist. Your understanding of the topic is still the same as befor....
@November8888 Ай бұрын
its the journey as they say
@rishikeshwagh Ай бұрын
'The real treasure is the friends you made along the way'
@Ne_Ne_Vova_UA Ай бұрын
Well, i don't think knowing if there is an odd perfect number would help anywhere
@Ne_Ne_Vova_UA Ай бұрын
@@rishikeshwaghyes, especially the friends from 2000 years ago who wrote about perfect numbers
@stxnw Ай бұрын
mathematicians should be banned from using computers
@stianlarsson6625 Ай бұрын
It makes me unreasonably happy to think about a typo in that prime number book.
@LithiumProductions Ай бұрын
Almost EVERY Veritasium video has me for the first half....then totally loses me!
@robincharles7057 Ай бұрын
16:57 Idc how nerdy this makes me, but for me this feels like the mathematical version of walking away from a house while it explodes and not looking back and I love it. 😍
@slooptrooperunlimitedofthe1772 Ай бұрын
Yeah, while I was watching this I started thinking about all the mathematicians he mentioned as badass celebrities/superstars in some kind of drama or thriller.
@Ceelvain Ай бұрын
The story is likely romanticised.
@zes3813 Ай бұрын
wrg, some tech, math etc s k , write that s k, doesn tmatter, no nerx etc nmw
@zenmkultra Ай бұрын
heh, nerd
@mothgirl326 Ай бұрын
@zenmkultra are you... are you new here? This is the Veritasium youtube channel
@arbalist5 Ай бұрын
11:10 Euler named the function after himself
@barneyronnie Ай бұрын
The Euler Totient Function...😮
@lgachaboyyt Ай бұрын
look up how many things are named after Euler
@romyojitpaul2200 Ай бұрын
Sigma Eular 😅
@theunknowman12 Ай бұрын
Well if you discover new function i think you earned the right to named it after yourself
@abdurrezzakefe5308 Ай бұрын
he meant sigma guys, chill :)
@camellkachour4112 Ай бұрын
I am mathematician, and I learn this from you ! Thank you !
@maxmonroe9461 25 күн бұрын
You can subtract consecutive square numbers by adding their square roots
@kshitizmalviya6909 Ай бұрын
16:17 Peter Barlow's statement awakened the mathematician in me until this transition
@samuraichicken9248 Ай бұрын
All I can think is how mathematicians throughout history would be absolutely blown away by modern computer technology. I think they would be so proud to know that people picked up and carried their legacy and continued work on this problem. Just imagine what could have happened if Euler got his hands on Matlab or Wolfram alpha
@grissee Ай бұрын
on the contrary, matlab or wolfram alpha might not exist without Euler discoveries
@mikeinjapan2004 Ай бұрын
@@grissee very true, it's because of these number theory why supercomputer turned out to be super... math is the foundation of everything 🎉
@miloradmilutinovic7691 Ай бұрын
US would be bombimg mars by now.
@therealax6 Ай бұрын
@@grissee While this is true, it's interesting to imagine what would've happened if the development of the technology could've happen within their lifespan. Impossible, of course, but it's interesting to think about.
@XIIchiron78 Ай бұрын
I wonder if they would be even more shocked at how much we still can't solve...
@Green_Real 19 күн бұрын
5:04 I dont know if anyone noticed but 6 and 28 are the first 3 digits of tau, or pi*2, meaning that not only 6 and 28 are true numbers, but also digits of pi*2
@lindseyreyes983 10 күн бұрын
Does it hold true? If so, it could be an indication that there is an infinitely large amount of perfect numbers 🤔 I’m on my way to go look up tau and our known list of perfect numbers… Edited: it doesn’t hold true, but it’s still neat!
@thetrueslugman 17 күн бұрын
been using prime 95 for years for cpu stress testing and tuning, had no idea it was for this.
@hippynurd Ай бұрын
A couple hundred years ago, this Galois dude worked on this unsolvable geometry thing, he actually came up a solution (or whatever the appropriate expression is), and 200 years later it was found to be useful in designing cell phone antenna. Its a crazy story, and his short life should probably be made into a movie,just because its all so darn crazy
@alexismiller2349 Ай бұрын
This Galois dude 😅
@halgerson Ай бұрын
I was watching this on my TV, and I had to pause so I can come to mobile to say this: I love you. There are no traditional media companies who provide anything close to the same content that you do. Thank you, and thank you, and thank you for everything that you do.
@nikhilsharma32907 Ай бұрын
💯 agree
@Redmenace96 Ай бұрын
We all swim in the water of YT, and as fish say, "What is this 'water'-thing you speak of?" I watched all of Cosmos when I was a kid. Saw a few Burke's Connections in U.S.A. Just has to sink in that we are living in a golden age of science/math content. "Traditional media" don't care about math! Can't sell the soap, ha,ha!!!!
@uberipitangalobato2653 Күн бұрын
seems to be some technical problem with this video. It's only playing 3 minutes or so. the remainder is missing
@user-fs4kh4lt3j 17 күн бұрын
I also noticed that adding all the digits of each perfect number together to reduce to a single digit , they all result in 1. Except for 6, 28 as 2+ 8 = 10, 1 + 0 = 1. 496 as 4 + 9 + 6 = 13 + 6 = 4 + 6 = 10 = 1 + 0 = 1. 8128 as 8 + 1 + 2 + 8 is as 9 + 10 is as 9 + 1 = 10. 1 + 0 is 1. Reducing to a single digit always ends in 1. I noticed these patterns when studying 9. 9 times any number can be reduced by adding into single digits. 9 x 8 = 72. 7 and 2 is 9. Numerology is shifting the sequence to a single digit not a total sum.
@joshuazelinsky5213 17 күн бұрын
What you are seeing is due to what is called modular arithmetic where one does arithmetic just looking at the remainder when you divide by some number m. You've seen a version of this before on a clock. When it is 8 o'clock and you say "In 6 hours it will be 2 o'clock" you are doing modular arithmetic with m=12. (We often just abbreviate this as mod m for short.) Since every power of 10 leaves a remainder of 1 when divided by 9, the sum of the digits of a number always has the same remainder when divided by 9. So the modular arithmetic of mod 10 corresponds to roughly speaking repeatedly doing this digit sum until you have a single number. So for example, 193 leaves a remainder of 4 when divided by 9, and so does its digit sum which is 13, and so does its digit sum which is 4. The pattern for even perfect numbers takes a tiny bit more work but involves looking at Euclid's formula for even perfect numbers and thinking carefully about how it behaves mod 9. Unfortunately we cannot prove the same result for odd perfect numbers, although we know that if N is an odd perfect number, then the remainder when N is divided by 9 must be one of 0, 1, 4, or 7.
@ZeronimeYT Ай бұрын
Ancient Greek in their free time be like:
@CF3593 29 күн бұрын
🤣🤣💔
@JetBen555 Ай бұрын
I used Prime95 so many times to stress test my PC after overclocking it and I didn't even know what it was used for... until now 😅😅
@Subhit_Goswami 2 күн бұрын
Watching this video till last , I even forgot what is a perfect number , still kept watching .. So the fact that how much we are wasting our time watching these random videos and still be okay with that is more intimidating than being unable to find an odd perfect number..
@navidahmed1083 Ай бұрын
I first learned about GIMPS in a science magazine in Bangladesh, I think in around 2012-2013. I set up GIMPS in my dad's laptop (I did not own a laptop then), and then his work computer. Finally I installed it in my laptop in 2019 when I came to the States for higher studies. Currently my dad is retired and the program only runs in my laptop. I have donated computing power to show that more than 50 numbers are not prime, still looking for one. My wife pokes fun at me when around every two to three months the LL test (or now the PRP test) on a potential number nears completion as everytime the number has turned out to be not a prime and I have been sad, and my wife finds this ritual mildly amusing. I do not even shut down my laptop. 😅 it is always on and the program is always running
@jonathanberry1111 Ай бұрын
I think I earned about them from watching Pulp Fiction...
@user-Aaron- Ай бұрын
Nice 🤜🤛
@kakao1930 Ай бұрын
Awesome
@PFBM86 Ай бұрын
Thank you for your service
@randomblueberry5019 Ай бұрын
This sounds like crypto mining lol
@kumarnilay2598 Ай бұрын
26:47 Pace Nilsen shows an incredible sign of intelligence! Not only did he immediately agree with a contradictory statement and not let his own beliefs that "Odd Perfect Numbers don't exist" overpower him, but simultaneously, he also reexamined and concluded that he had a bias. The same theory that heuristically shows Odd Perfect Numbers don't exist also shows that large, even perfect numbers don't exist. This is a true sign of intelligence, not to let your ego get in the way and search for the truth. We all can have biases, but only intelligent people will be able to look past them.
@09NXN06 Ай бұрын
Exactly
@yasyasmarangoz3577 Ай бұрын
I thought he was joking with that assumption anyway.
@MrTuneslol Ай бұрын
Unfortunately the scientific community fails to do this _far_ too often. Especially if that bias is either profitable or gets more funding for their projects.
@kumarnilay2598 Ай бұрын
@@yasyasmarangoz3577 , haha, might be. But it did feel like he believes that they don't exist, which, probabilistically, might eventually turn out to be true.
@kumarnilay2598 Ай бұрын
@@MrTuneslol I think this happens everywhere, but at the same time, many people in the scientific community can look past it, and that is when truly wonderful things are discovered or invented.
@pieczarsonv2576 Ай бұрын
And what if we will look on this that way: This number cannot be square of other odd number, because it must have odd number of its dividers, because they need to sum up to odd. For example: 35 -> 1 + 5 + 7 = 13 69 -> 1 + 3 + 23 = 27 225 (15^2)-> 1 + 3 + 5 + 9 + 15 + 25 + 45 + 75 = 178 So, every dividers are in pairs, because they need to multiply to this number, except if divider is root of it number. So every number which doesn't have integer root, have a sum of its dividers (except itself) equal to an odd number. If it have an integer root, then it is only one divider, so sum of this must be even. I don't know if it's big hint, but it can help to solve this. (Sorry for mistakes, english isn't my native language)
@joshuazelinsky5213 Ай бұрын
Your observation that it cannot be an odd square is correct. Using this sort of logic and taking it further is what leads to the theorem of Euler mentioned in the video that an odd perfect number must be a prime times a perfect square.
@tidegoesoutskiinyd1179 9 күн бұрын
we can never know what knowledge will be used for its never a waste of time to solve problems. Shame more os society doesn't value themselves or others on achievement and problems solving rather than what they think or believe. Thanks for your video very interesting
Marat Oralgazin
Рет қаралды 1 МЛН
Scary Teacher Gaming
Рет қаралды 57 МЛН