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The Oldest Unsolved Problem in Math

  • เผยแพร่เมื่อ 24 ก.ค. 2024
  • Do 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:
    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
    • 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

ความคิดเห็น • 12K

  • @cupostuff9929
    @cupostuff9929 4 หลายเดือนก่อน +13822

    >walks up to blackboard
    >multiplies 2 numbers
    >walks away
    >round of applause
    Frank Nelson Cole was unfathomably based

    • @jacobe280
      @jacobe280 4 หลายเดือนก่อน +230

      Am I the only one bothered that he says AND between all the millions, billions, trillions, etc... couldn't help but mention

    • @adriantcullysover4640
      @adriantcullysover4640 4 หลายเดือนก่อน +299

      ​@@jacobe280 Yes. You are.

    • @herobrine1847
      @herobrine1847 4 หลายเดือนก่อน +78

      @@jacobe280no you’re not

    • @AMPProf
      @AMPProf 4 หลายเดือนก่อน +20


    • @Bruzzzio
      @Bruzzzio 4 หลายเดือนก่อน +16


  • @thomasrinschler6783
    @thomasrinschler6783 4 หลายเดือนก่อน +5815

    13:25 "But Euler wasn't finished yet." I think this sentence appears in most histories of mathematical concepts.

    • @brettgoldsmith9971
      @brettgoldsmith9971 4 หลายเดือนก่อน +579

      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
      @nananou1687 4 หลายเดือนก่อน +37

      Number theory concepts*

    • @ab3040
      @ab3040 4 หลายเดือนก่อน +176

      Possibly the most important mathematician in history

    • @rogerszmodis
      @rogerszmodis 4 หลายเดือนก่อน +79

      @@ab3040either him or Gauss

    • @ab3040
      @ab3040 4 หลายเดือนก่อน +167

      @@rogerszmodis 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

  • @MattDoesNothing
    @MattDoesNothing 2 หลายเดือนก่อน +956

    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
      @Osamabonjovi 2 หลายเดือนก่อน +40

      *vsauce theme plays*

    • @hunterofendermen367
      @hunterofendermen367 2 หลายเดือนก่อน


    • @themirrorbeauty
      @themirrorbeauty 2 หลายเดือนก่อน +3

      Lol, that's so true, that's what we say... 😄

    • @qibc2wi
      @qibc2wi 2 หลายเดือนก่อน +3

      Well aren't you motivational

    • @diniaadil6154
      @diniaadil6154 2 หลายเดือนก่อน +1

      The mathematician : "Theres something called a heuristic argument"

  • @socrunchyy1146
    @socrunchyy1146 2 หลายเดือนก่อน +433

    Did anyone else notice that in the number at 24:10 198,585,576,189, every set of three digits adds to 18?

    • @jimdecamp7204
      @jimdecamp7204 หลายเดือนก่อน +84

      I know that at least one person did.

    • @user-jz3qb5zv4e
      @user-jz3qb5zv4e หลายเดือนก่อน +5

      @@jimdecamp7204 same

    • @farthermoney2620
      @farthermoney2620 หลายเดือนก่อน +11

      Finally a person that knows this fact!

    • @1991dmj
      @1991dmj หลายเดือนก่อน +15

      I didn't, but you made me check what all perfect numbers' digits sum up to. And they all sum up to 1 (except the first one, being 6). That's actually something I didn't see anywhere while reading about perfect numbers.

    • @jimdecamp7204
      @jimdecamp7204 หลายเดือนก่อน +10

      @@1991dmj More succinctly, all perfect numbers modulo 9 equal 1, except 6. The properties of perfect numbers, the sum of its factors equal to the number itself is true independent of number base, as is my restatement of your interesting observation.

  • @BarryBarrington-zc6lz
    @BarryBarrington-zc6lz 4 หลายเดือนก่อน +1481

    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!

    • @1stlullaby484
      @1stlullaby484 4 หลายเดือนก่อน +19

      I saw this exact comment at least 24 hours ago, does that mean i time traveled?? Or did you delete your prev post and reposted

    • @1stlullaby484
      @1stlullaby484 4 หลายเดือนก่อน +7

      I have an important question
      Somebody said that The reason Gödel was able to show that math is incomplete [ that is there are true statements which can never be proven] is because he assumed that math is consistent (Meaning he assumed it's free of contradictions,
      So what the hell is happening!!??
      If this other guy is right, then Gödel's proof of incompleteness seems completely flawed

    • @ivoryas1696
      @ivoryas1696 4 หลายเดือนก่อน

      As someone's who's 21... sounds _surreal!_ I even feel like congratulating you, lol. 🫱🏻‍🫲🏾

    • @michaellinner7772
      @michaellinner7772 4 หลายเดือนก่อน

      You forgot to end your parentheses. 😉​@@1stlullaby484

    • @blargghkip
      @blargghkip 4 หลายเดือนก่อน +19

      ​​@@1stlullaby484it's a form of mathematical proof known as proof by contradiction. Gödel showed that if you assume math is consistent and all true statements can be proven, obviously false statements (contradictions) arise.
      A simple example is a proof for the non-existence of a largest integer. We assume two things:
      1. You can increment any integer to create a larger integer.
      2. There exists a largest integer.
      If you apply assumption 1 to assumption 2, you end up with an integer that is larger than the supposed "largest integer". Therefore, one of the assumptions is false.

  • @VintageBlacklist
    @VintageBlacklist 4 หลายเดือนก่อน +1695

    I have a research project due tomorrow and I was really looking for something distracting.
    My procrastination thanks you.

    • @jakewolf3561
      @jakewolf3561 4 หลายเดือนก่อน +8


    • @S4M3350
      @S4M3350 4 หลายเดือนก่อน +5


    • @jin_cotl
      @jin_cotl 4 หลายเดือนก่อน +11

      I’m actually early to a Veritasium video

    • @liambohl
      @liambohl 4 หลายเดือนก่อน +24

      This comment hurts

    • @BOTthelesser
      @BOTthelesser 4 หลายเดือนก่อน

      Same although it’s project about a book

  • @matthewlloyd3255
    @matthewlloyd3255 หลายเดือนก่อน +21

    It's very rare I can sit through an informational video of more than a few minutes....I watched this all the way through in a single sitting, you're doing something right I guess!

  • @denverbeek
    @denverbeek 2 หลายเดือนก่อน +278

    I'd like to thank you for making me aware of GIMPS. I'm donating some of my cpu power overnight now.

    • @akoskiss2065
      @akoskiss2065 2 หลายเดือนก่อน +13

      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
      @denverbeek 2 หลายเดือนก่อน +51

      @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 :)

    • @usn9324
      @usn9324 2 หลายเดือนก่อน +3

      What are you doing here ordis

    • @Voidkitty_
      @Voidkitty_ 2 หลายเดือนก่อน +5

      As long as you have good cooling, and you aren't throwing in any unreasonable voltages, you should be fine, i personally would undervolt down to like 1.25 and whatever clocks that can stably sustain for any 24/7 long term stressing

    • @ME0WMERE
      @ME0WMERE หลายเดือนก่อน +4

      @@akoskiss2065 apparently, the thing that shortens processors' lifespan is temperature _changes,_ not a high temperature in itself (because of the induced stress due to expansion/contraction). So if the processor is at a constant temperature for a long time, it won't shorten its lifespan, unless the temperature is above what the manufacturer specified.

  • @madjson1429
    @madjson1429 4 หลายเดือนก่อน +6724

    When Euler says "it's most difficult", it's gotta be impossible.

    • @BixbyConsequence
      @BixbyConsequence 4 หลายเดือนก่อน +462

      "I have discovered a truly marvelous proof of this, which this margin is too narrow to contain."

    • @TheXuism
      @TheXuism 4 หลายเดือนก่อน +66

      this guy is the biggest bragger in human history.@@BixbyConsequence

    • @funtastic1297
      @funtastic1297 4 หลายเดือนก่อน +153

      No it’s a joke reference to fermats last theorem lol

    • @melodyecho4156
      @melodyecho4156 4 หลายเดือนก่อน +44

      ​@@BixbyConsequenceThat was Fermat

    • @MathSMR42
      @MathSMR42 4 หลายเดือนก่อน +84

      ​@@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?

  • @marcusscience23
    @marcusscience23 2 หลายเดือนก่อน +49

    Either odd perfect numbers exist, or they don’t. If they don’t, that would mean all perfect numbers are even and elegantly fit the form N = (2^p -1)*2^(p-1) with (2^p -1) prime. If they do, that means there’s some gargantuan odd perfect number somewhere out there just waiting to be discovered. And both possibilities are equally fascinating!

    • @RichardHennigan
      @RichardHennigan หลายเดือนก่อน +1

      Third possibility: it's indeterminate

    • @marcusscience23
      @marcusscience23 หลายเดือนก่อน

      @@RichardHennigan Indeterminate how? There either is or isn't.

    • @Gorabora
      @Gorabora หลายเดือนก่อน +1

      @@marcusscience23it could be one of those that can never be proved or disproved
      the incompleteness trap card

    • @user-iv4dh7zp7s
      @user-iv4dh7zp7s 26 วันที่ผ่านมา +1

      ​@@marcusscience23 There is undecidableness. When running Conway's game of life there is no algorithm that guarantees predicting it's outcome in a limited number of time. So it's kind of selecting "or" from "yes or no".

    • @thoughtricity4296
      @thoughtricity4296 8 วันที่ผ่านมา +1

      Similar to problems like the Riemann hypothesis and 3n+1, if it's unprovable then it must be true, since it being false means there exists a counterexample. It can't be unprovable and false because there exists a defeater. If ZFC isn't strong enough to prove a result then you can keep adding axioms until it is, but it is impossible to know if any system at ZF's strength or stronger is consistent (you can prove it from stronger systems but this just pushes around the problem). Which leads right into Veritasium's video about the hole at the bottom of mathematics.

  • @neverid02
    @neverid02 2 หลายเดือนก่อน +62

    kids nowadays gonna go crazy over sigma function 💀

    • @DefenderoftheOctoberists
      @DefenderoftheOctoberists หลายเดือนก่อน +2


    • @elitegames6969
      @elitegames6969 หลายเดือนก่อน +5

      i can imagine some kid saying "what the sigma?" after reading it in their textbook💀💀💀💀

  • @nathanaelhahn4795
    @nathanaelhahn4795 4 หลายเดือนก่อน +3685

    4:03 "Euclid was actually thinking along similar lines"
    Euclid: calculates perfect numbers with actual lines

  • @lifthras11r
    @lifthras11r 4 หลายเดือนก่อน +1004

    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
      @lpc9929 4 หลายเดือนก่อน +17


    • @Inuzika
      @Inuzika 4 หลายเดือนก่อน +52

      That actually helps a lot with understanding why RNG is multiplicative in most video games.

    • @till8413
      @till8413 4 หลายเดือนก่อน +59

      omg i was using that in programming, never knew why it was called MT19937 😮 my mind is blown away

    • @kphaxx
      @kphaxx 4 หลายเดือนก่อน

      @@lpc9929well said

    • @helpiminabox
      @helpiminabox 4 หลายเดือนก่อน +4

      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.

  • @Haokai8328
    @Haokai8328 18 วันที่ผ่านมา +4

    27:49 I just love that classic veritaserum music * applause *

  • @simonbasilico6713
    @simonbasilico6713 วันที่ผ่านมา

    Hello, I am grateful with the video and its dubbed version in Spanish, it has helped me understand the problem and above all it has inspired me to solve one of the two undeciphered Nicomano conjectures, and understand that if there are odd perfect numbers, these cannot be an infinite set. I would be delighted if we could solve this last problem as a community.

  • @logician1234
    @logician1234 4 หลายเดือนก่อน +2499

    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
      @ObjectsInMotion 4 หลายเดือนก่อน +301

      Eu(clid x ler)

    • @Xezlec
      @Xezlec 4 หลายเดือนก่อน +162

      Imagine the noises the readers would make if Gauss joined in!

    • @logician1234
      @logician1234 4 หลายเดือนก่อน +192

      @@Xezlec Math : No Way Home

    • @johnchessant3012
      @johnchessant3012 4 หลายเดือนก่อน +71

      Oiclid and Yooler

    • @cefcephatus
      @cefcephatus 4 หลายเดือนก่อน +65

      Maybe, "I reincarnated into math genius, Euler, and continue my own legacy. Yes, I was Euclid."

  • @user-sl5zm9ih8c
    @user-sl5zm9ih8c 4 หลายเดือนก่อน +666

    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.

    • @dannya951
      @dannya951 4 หลายเดือนก่อน +12

      He was one of my favorites!

    • @JLchevz
      @JLchevz 4 หลายเดือนก่อน +2

      lol that's cool

    • @RazgrizAce67
      @RazgrizAce67 4 หลายเดือนก่อน +9

      He also likes Magic the Gathering based on all the cards on his desk in the background. My kind of guy!

    • @17jtl
      @17jtl 4 หลายเดือนก่อน +5

      He seems to like playing Magic and has a Chuck Norris fact hanging on his wall, sounds like a cool guy indeed.

    • @wesleyrm76
      @wesleyrm76 4 หลายเดือนก่อน +2

      He was such a great professor, and I was surprised when he explained his research. It sounded pretty useless. But at least he's now a leader in that field, haha.

  • @jl8217
    @jl8217 หลายเดือนก่อน +2

    This is a fascinating topic, thanks!

  • @toffotin
    @toffotin 18 วันที่ผ่านมา +1

    I love that the universe just constantly does all this math without any lag.
    It "just happens".
    Or maybe there is lag, but we don't notice it.

  • @Tritone_b5
    @Tritone_b5 4 หลายเดือนก่อน +1202

    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
      @leksitarmik4636 4 หลายเดือนก่อน +156

      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
      @jonasplayedthat2220 4 หลายเดือนก่อน +2

    • @irradiatedturtle
      @irradiatedturtle 4 หลายเดือนก่อน +42

      Read this as “as a computer who is also a math enthusiast” at first and had to think for a second lmao

    • @simon6071
      @simon6071 4 หลายเดือนก่อน +7

      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
      @Nereus74 4 หลายเดือนก่อน +3

      @@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.

  • @Art_Vandelay_Industries
    @Art_Vandelay_Industries 4 หลายเดือนก่อน +680

    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
      @IdOnThAvEaUsE69 4 หลายเดือนก่อน +1

      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
      @tincanblower 4 หลายเดือนก่อน +32

      ​@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
      @Argoon1981 4 หลายเดือนก่อน +24

      @@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
      @BlueSparxLPs 4 หลายเดือนก่อน +15

      @@tincanblower It's a bot. There's a lot of them on TH-cam that exist just to quote verses.

    • @stompthedragon4010
      @stompthedragon4010 4 หลายเดือนก่อน +10

      ​@@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 "

  • @priyanshusharma1570
    @priyanshusharma1570 26 วันที่ผ่านมา

    It blew my mind... ❤️..... Nice explanation of the mystery of perfect number

  • @DoShiAcademy
    @DoShiAcademy 2 หลายเดือนก่อน +4

    Congrats on making such a topic so enjoyable and interesting throughout the whole video. Wow

  • @theyreMineralsMarie
    @theyreMineralsMarie 4 หลายเดือนก่อน +853

    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
      @Dranzer_Panzer 4 หลายเดือนก่อน +191

      Clearly you didn't watch the video, it's an even idea.

    • @Actrl51
      @Actrl51 4 หลายเดือนก่อน +104

      @@Dranzer_Panzerthat’s a prime quality comment

    • @xuaalbito8303
      @xuaalbito8303 4 หลายเดือนก่อน +22

      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
      @theyreMineralsMarie 4 หลายเดือนก่อน +13

      @lucashershberger623 wonder away.

    • @zeke1220
      @zeke1220 4 หลายเดือนก่อน +2

      @lucashershberger623 Circumstantial evidence, maybe

  • @PlatzHalter-j3i
    @PlatzHalter-j3i 9 วันที่ผ่านมา +1

    considering (6:33) you explain the way of representatoin of 2 ... that was shown before as binary equation. Means if you look at the exponent is the amount of 1 in binary and the second exponent of 0 is one less than for 1 so 110, 11100, .... where it should be easy to see the pattern goes - nice findings !!!

  • @FionaKelleghan3267
    @FionaKelleghan3267 2 หลายเดือนก่อน +26

    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
      @rayrwyr 2 หลายเดือนก่อน +3

      Add math as your second major

    • @FionaKelleghan3267
      @FionaKelleghan3267 2 หลายเดือนก่อน

      @@rayrwyr I had over a decade of university studies, but it's tempting. 😊

    • @LeonCoretz
      @LeonCoretz 2 หลายเดือนก่อน

      Now chase down that last perfect odd number! You only have to find one!

  • @jonahmishaga1995
    @jonahmishaga1995 4 หลายเดือนก่อน +2488

    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
      @happmacdonald 4 หลายเดือนก่อน

      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
      @Greyhawksci 4 หลายเดือนก่อน +179

      I will never not be disappointed that MIT's hockey team isn't the Eulers.

    • @FCHenchy
      @FCHenchy 4 หลายเดือนก่อน +30

      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.

    • @rogerszmodis
      @rogerszmodis 4 หลายเดือนก่อน +34

      @@Greyhawksci only like 1% of people would get it. I would bet the vast majority of people read and pronounce Euler phonetically.

    • @NStripleseven
      @NStripleseven 4 หลายเดือนก่อน +88

      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.

  • @ytmadpoo
    @ytmadpoo 4 หลายเดือนก่อน +814

    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
      @Filo127 4 หลายเดือนก่อน +49

      you've been involved with gimps ? 🤨

    • @LeVasTiaN
      @LeVasTiaN 4 หลายเดือนก่อน +21

      ​@@Filo127you haven't watched the video?

    • @nivyan
      @nivyan 4 หลายเดือนก่อน +14

      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
      @SamuelRamirez-js5rb 4 หลายเดือนก่อน

      Do you know what a gimp suit is? If not look it up lol.​@@LeVasTiaN

    • @drunkredninja
      @drunkredninja 4 หลายเดือนก่อน +3

      OG distributed computing projects were the best way to stress test overclocks back in the day. did alot of gimps, fah and seti myself.

  • @olivierbeaudry-ogden938
    @olivierbeaudry-ogden938 19 วันที่ผ่านมา

    it's quite fascinating how this problem in terms of how we view the numbers like in binary or other mod 4s etc is very similar to how we end up in the 3x+1 problem though in both cases it doesn't seem to lead anywhere. Moreover it's even fascinating to see that these numbers are a series of consecutive series of powers of two, while in the 3x+1 problem the last non-even number before getting stuck in the 4,2,1 loop will always be a consecutive series of powers of 4 or a alternating series of powers of 2.

  • @kurthueston1511
    @kurthueston1511 หลายเดือนก่อน +2

    Numbers are the tools used to create the universe. We can use some of those "tools" - (herein simply tools) - to put a man on the moon. They can be used to do many great things. But they are just tools.
    At 27:30 to 28:00 you briefly commented on the purpose and usefulness of perfect numbers, etc.
    Now back to the tool analogy. Understanding how and why tools work the way they do is good and helpful. But let's not forget to appreciate WHAT they do. (I am not implying that you don't.) Understanding how to build a car is necessary, and understanding why a car runs is fascinating, but when I'm looking at a nice new shiny blue Corvette, those are the last things I'm thinking about. And i don't need to understand photosynthesis to enjoy the beauty of a flower.
    Numbers are just the tools.
    The fact that perfect numbers exist means they must have had SOME part in the creation of the universe. (Albeit maybe just a very tiny part.) But perhaps there is no more "usefulness" than that. Perhaps we have discovered a tool that is beyond the abilities of our finite brain to comprehend.
    I'm just saying, "Perhaps."

  • @ZenZooZoo
    @ZenZooZoo 4 หลายเดือนก่อน +5840

    Not me watching thinking I’m gonna try to solve this while eating hot cheetos

    • @zhixinhuang4084
      @zhixinhuang4084 4 หลายเดือนก่อน

      Ghost pepper, Cheeteeeeeeeaeeeaeaeaeaeaeaeaeaeaeaeæéêēêåeeeaeaeaeaeaea

    • @matt88townsend
      @matt88townsend 4 หลายเดือนก่อน +202

      this comment just blew my mind🤯 doing this exact thing while high

    • @jin_cotl
      @jin_cotl 4 หลายเดือนก่อน +105

      Nah it’s alright. Better an attempt at solving it, than not trying at all ❤

    • @CananaMan
      @CananaMan 4 หลายเดือนก่อน +177

      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
      @joshuagoodsell9330 4 หลายเดือนก่อน +24

      That's so inspiring haha thanks​@CananaMan

  • @jasoncheng3303
    @jasoncheng3303 4 หลายเดือนก่อน +668

    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
      @DJFracus 4 หลายเดือนก่อน +52

      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
      @dorianguerrazzi5040 4 หลายเดือนก่อน +6

      Same, I literally shed a tear.

    • @rogerszmodis
      @rogerszmodis 4 หลายเดือนก่อน +19

      I remember when a computer beating a human at chess was newsworthy.

    • @elLooto
      @elLooto 4 หลายเดือนก่อน +3

      Now realize that LLMs dont even come close to representing that increase in the efficiency of labour....

    • @FLPhotoCatcher
      @FLPhotoCatcher 4 หลายเดือนก่อน +4

      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.

  • @MIris44474
    @MIris44474 2 หลายเดือนก่อน

    Its crazy how deep and complex maths is.

    @AADVS-RPY หลายเดือนก่อน

    This video dives deep into one of math's most enduring mysteries - the quest for odd perfect numbers. The clarity and depth here are fantastic! Who else finds these mathematical puzzles endlessly fascinating?

  • @jmwmusic5665
    @jmwmusic5665 4 หลายเดือนก่อน +274

    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
      @Fire_Axus 4 หลายเดือนก่อน +4

      your feelings are irrational

    • @mcpr5971
      @mcpr5971 4 หลายเดือนก่อน +4

      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
      @CCCompiler 4 หลายเดือนก่อน +6

      ​@@Fire_Axus your comment is perfectly odd

    • @FuncleChuck
      @FuncleChuck 4 หลายเดือนก่อน

      Where’s the proof

  • @gamefrom31
    @gamefrom31 2 หลายเดือนก่อน

    just found this channel. make math more interesting than I learn in schools

  • @TheRealPinkWish
    @TheRealPinkWish 7 วันที่ผ่านมา

    15:45 my brain exploded! good job!

  • @wfaction
    @wfaction 4 หลายเดือนก่อน +674

    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
      @zeevtarantov 4 หลายเดือนก่อน +80

      It is used for stress testing overclocks because it is sensitive to mistakes in the calculation caused by overclocking too much.

    • @isthismyfinalform169
      @isthismyfinalform169 4 หลายเดือนก่อน +16

      Damn thats interesting

    • @fulgerion
      @fulgerion 4 หลายเดือนก่อน +6

      It says this during the test.

    • @ViliamF.
      @ViliamF. 4 หลายเดือนก่อน +22

      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
      @tauzN 4 หลายเดือนก่อน +7

      @@fulgerion you probably also read EULA’s 💀

  • @lifeisfakenews
    @lifeisfakenews 4 หลายเดือนก่อน +538

    17:37 ish
    "he gave a talk" "without saying a word" thats a new level of genius

    • @LuisSierra42
      @LuisSierra42 4 หลายเดือนก่อน +3

      Based genius

    • @maddawgzzzz
      @maddawgzzzz 4 หลายเดือนก่อน +1

      Based AF braa

    • @djangosouthwest6043
      @djangosouthwest6043 4 หลายเดือนก่อน +5

      Actions speak louder than words

    • @edwinkjobi
      @edwinkjobi 4 หลายเดือนก่อน +1

      Nelson Cole is the main Character!

    • @CrimsonA1
      @CrimsonA1 4 หลายเดือนก่อน +2

      *Drops chalk and walks off stage

  • @oranlooney9736
    @oranlooney9736 หลายเดือนก่อน +3


  • @GaryBickford
    @GaryBickford หลายเดือนก่อน

    Now I'm curious about what patterns might be found in the digits of those big Mersenne primes.

  • @Kari-Bond
    @Kari-Bond 4 หลายเดือนก่อน +514

    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
      @tristanmoller9498 4 หลายเดือนก่อน +35

      Why is the only irrelevant question in math.

    • @4ELt774
      @4ELt774 4 หลายเดือนก่อน +4


    • @ItsJustKaya
      @ItsJustKaya 4 หลายเดือนก่อน +4

      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
      @GodplayGamerZulul 4 หลายเดือนก่อน +8

      @@ItsJustKaya Why are you writing like this?

    • @petergibson2318
      @petergibson2318 4 หลายเดือนก่อน +4

      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.

  • @The90DegreeOfficial
    @The90DegreeOfficial 3 หลายเดือนก่อน +291

    > starts watching video
    > gets engrossed
    > gets the motivation to find the odd perfect number
    > forgets what a perfect number is
    > refuses to elaborate
    > leaves

  • @Trockenfurz
    @Trockenfurz หลายเดือนก่อน

    i'm not a mathematician, but i've sensed a correlation between the amounts of added up squared numbers inbetween the previous perfect numbers, relatively early in the vid. going by that, it might actually be pretty easy to find new numbers, even nowadays. the billionth long thing too.

    @BLESSINGSMBEWE-md5lm 2 หลายเดือนก่อน +2

    Plz create more content of math history 😊

  • @wenaolong
    @wenaolong 4 หลายเดือนก่อน +313

    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
      @nachoijp 4 หลายเดือนก่อน +12

      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
      @RUHappyATM 4 หลายเดือนก่อน +3

      I sometimes wonder what else could be invented or discovered if the productivity is redirected to some other endeavours.

    • @marinmarinhola
      @marinmarinhola 4 หลายเดือนก่อน +5

      Exactly, this whole quest spawned Prime95, which has helped me overclock PCs for years now.

    • @GaussianEntity
      @GaussianEntity หลายเดือนก่อน

      The methodology is a crucial component in math, sometimes even more than the answer itself.

  • @Wunba
    @Wunba 4 หลายเดือนก่อน +5702

    They lowkey tricked me with the outro at 16:25 I was so disappointed for a second 😂

    • @The7Shadows.
      @The7Shadows. 4 หลายเดือนก่อน +136

      I was so relieved it was finnally over. BUT IT WASNT

    • @PriggarGaming
      @PriggarGaming 4 หลายเดือนก่อน +86

      What da faq you doing here ?

    • @ruskcoder
      @ruskcoder 4 หลายเดือนก่อน +91

      Fr Minecraft TH-camr on math 😮

    • @parthhooda3713
      @parthhooda3713 4 หลายเดือนก่อน +112

      ​​@@ruskcoderso what?
      Everyone enjoys Veritasium whether they like maths or not

    • @aamirkhan_
      @aamirkhan_ 4 หลายเดือนก่อน +14

      I was looking for this comment..

  • @leniorrb
    @leniorrb 2 หลายเดือนก่อน +1

    Great video! Just need an update in the Portuguese-Audio, it seems that you upload the Pi audio into this video.

  • @johnmartinez71
    @johnmartinez71 หลายเดือนก่อน +19

    Who else is here pretending they understood EVERYTHING in this video (including the math equations)?... 🤣

    • @brabhamfreaman166
      @brabhamfreaman166 หลายเดือนก่อน

      🤷 Less than everyone
      Edit: I think this is my most pointless comment ever 🤷. Mea culpa.

    • @grindingtopdontstop5834
      @grindingtopdontstop5834 หลายเดือนก่อน +1

      I guess me

    • @kennethhammond4028
      @kennethhammond4028 4 วันที่ผ่านมา

      51% per cent understood is a pass. Or just achieved. 😅

  • @joshuazelinsky5213
    @joshuazelinsky5213 4 หลายเดือนก่อน +762

    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
      @jamesknapp64 4 หลายเดือนก่อน +33

      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
      @Featherless1 4 หลายเดือนก่อน +41


    • @asheep7797
      @asheep7797 4 หลายเดือนก่อน +3

      Do you know any papers that rely on the existence of odd perfect numbers?

    • @daniels8625
      @daniels8625 4 หลายเดือนก่อน +26

      ​@@Featherless1keep going...

    • @justusimperator537
      @justusimperator537 4 หลายเดือนก่อน +11


  • @sil1235
    @sil1235 4 หลายเดือนก่อน +351

    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
      @mehrabnikoofaraz233 4 หลายเดือนก่อน +4

      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
      @sil1235 4 หลายเดือนก่อน +1

      @@mehrabnikoofaraz233Thanks for correction, I've changed it to different example to avoid confusion.

    • @TruthNerds
      @TruthNerds 4 หลายเดือนก่อน +4

      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
      @HeadOnAStick 4 หลายเดือนก่อน +3

      @@TruthNerdsClear and informative. Thank you.

    • @ragnkja
      @ragnkja 4 หลายเดือนก่อน +2

      It’s because it’s both: it’s fast-growing but _also_ easy relatively to check.

  • @BigFatBugRat
    @BigFatBugRat 2 หลายเดือนก่อน

    Great discusion. I love it. Tnx. 👍

  • @CaptainSpock1701
    @CaptainSpock1701 หลายเดือนก่อน +1

    Love the bit at 22:00 where the positive Mersenne primes are explained as infinitely many and as rare in the next sentence!
    Shows how difficult is to wrap your head around the size of very large numbers and even more around the concept of infinity!

  • @MarkArandjus
    @MarkArandjus 4 หลายเดือนก่อน +233

    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
      @periodictable118 4 หลายเดือนก่อน +27

      Imagine he just wrote some random ass numbers and it didn't even multiply to the original

    • @cloudyblueskye
      @cloudyblueskye 4 หลายเดือนก่อน


  • @saswatachakraborty4937
    @saswatachakraborty4937 4 หลายเดือนก่อน +704

    This channel is one of the greatest argument in favour of TH-cam as a wonderful medium of learning.

    • @colepeterson5392
      @colepeterson5392 4 หลายเดือนก่อน +24

      channels like these are why I love TH-cam in general

    • @MikkoRantalainen
      @MikkoRantalainen 4 หลายเดือนก่อน +24

      I agree, Veritasium, Vsauce, SmarterEveryDay and Sabine Hossenfelder are prime examples of channels that make TH-cam worth using even if you wouldn't like all the ads and random stuff.

    • @farmertree8
      @farmertree8 4 หลายเดือนก่อน +21

      @@MikkoRantalainen "prime" examples

    • @james6401
      @james6401 4 หลายเดือนก่อน +4


    • @talosgak1236
      @talosgak1236 4 หลายเดือนก่อน +5

      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

  • @BallofJustice
    @BallofJustice หลายเดือนก่อน +4

    If I was a teacher I'd play your videos in class

  • @martafixarcoolt5993
    @martafixarcoolt5993 4 หลายเดือนก่อน +1046

    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
      @ThisHandleIsAlreadyTaken839 4 หลายเดือนก่อน +55

      I love when people spell immediately correctly

    • @rishabhchauhan8948
      @rishabhchauhan8948 4 หลายเดือนก่อน +1


    • @hanu6158
      @hanu6158 4 หลายเดือนก่อน +22

      @@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
      @gavinathling 4 หลายเดือนก่อน

      @@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
      @RH-ro3sg 4 หลายเดือนก่อน +22

      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?)

  • @Ferrohh
    @Ferrohh 4 หลายเดือนก่อน +1000

    Math is a hell of a drug

    • @oliverthomas3134
      @oliverthomas3134 3 หลายเดือนก่อน +8

      It will mad u

    • @WaddieJoe
      @WaddieJoe 3 หลายเดือนก่อน +6

      68th like

    • @RAGHAV4882
      @RAGHAV4882 3 หลายเดือนก่อน +16

      @@WaddieJoe you mean (n-1)?

    • @LucasLiang-fi9cf
      @LucasLiang-fi9cf 3 หลายเดือนก่อน

      @@oliverthomas3134you sound like your on drugs

    • @lucienli4553
      @lucienli4553 3 หลายเดือนก่อน +6


  • @LuciousX
    @LuciousX 2 หลายเดือนก่อน +1

    Amazing information

  • @aescritadouniverso
    @aescritadouniverso 14 วันที่ผ่านมา

    Show... wonderful. Tks a lot

  • @periodictable118
    @periodictable118 4 หลายเดือนก่อน +777

    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
      @PTfan54 4 หลายเดือนก่อน +76

      A book containing the largest known prime and a text file containing the largest known prime are actually equally useless.

    • @falconerd343
      @falconerd343 4 หลายเดือนก่อน +44

      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
      @BishopStars 4 หลายเดือนก่อน +8

      ​@@falconerd343Benford's Law. One Time Pad.

    • @jamesmnguyen
      @jamesmnguyen 4 หลายเดือนก่อน +4

      Imagine how much energy and computation went into making that book.

    • @kingkarlito
      @kingkarlito 4 หลายเดือนก่อน +3

      actually there were just not many copies actually printed. he completely made up the part about it being a top seller on amazon.

  • @arbalist5
    @arbalist5 4 หลายเดือนก่อน +193

    11:10 Euler named the function after himself

    • @barneyronnie
      @barneyronnie 4 หลายเดือนก่อน +10

      The Euler Totient Function...😮

    • @lgachaboyyt
      @lgachaboyyt 4 หลายเดือนก่อน +26

      look up how many things are named after Euler

    • @romyojitpaul2200
      @romyojitpaul2200 4 หลายเดือนก่อน +29

      Sigma Eular 😅

    • @theunknowman12
      @theunknowman12 4 หลายเดือนก่อน +8

      Well if you discover new function i think you earned the right to named it after yourself

    • @abdurrezzakefe5308
      @abdurrezzakefe5308 4 หลายเดือนก่อน +17

      he meant sigma guys, chill :)

  • @reid3031
    @reid3031 2 หลายเดือนก่อน

    Imagine showing this video to Euclid, imagine him trying to process the absolute gravity of what he started

  • @nitinprasad7163
    @nitinprasad7163 16 วันที่ผ่านมา

    Thank you Versatium for inspiring millions of us!

  • @Soken50
    @Soken50 4 หลายเดือนก่อน +465

    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
      @marcosmith6613 4 หลายเดือนก่อน +3

      Thanks for sharing this 😊

    • @glennllewellyn7369
      @glennllewellyn7369 4 หลายเดือนก่อน +13

      Toilet flow direction is important.

    • @Whiterioot
      @Whiterioot 4 หลายเดือนก่อน +2

      You sound really smart. Sincerely.

    • @Soken50
      @Soken50 4 หลายเดือนก่อน +2

      @@Whiterioot Thanks, I try my best.

    • @g..h..o..s..t
      @g..h..o..s..t 4 หลายเดือนก่อน

      @@Soken50 congratulations on trying your best to sound really smart, which is what you just agreed with @Whiterioot about. 👍

  • @Tamonduando
    @Tamonduando 4 หลายเดือนก่อน +278

    10:45 I feel that calling Euler a "prodigy" is a bit of an understatement.

    • @jamesknapp64
      @jamesknapp64 4 หลายเดือนก่อน +26

      Yeah Magnus Carlson was just good at Chess at 20 pales to the understatement that 20 year old Euler was just a prodigy

    • @folkrav
      @folkrav 4 หลายเดือนก่อน +7

      @cf-yg4bd I was about to throw one back at you then realized I legitimately can’t think of one either. Well said.

    • @PlayerSlotAvailable
      @PlayerSlotAvailable 4 หลายเดือนก่อน

      What is special about them? It is my first time seeing their name.

    • @timothyobaob3624
      @timothyobaob3624 4 หลายเดือนก่อน +6

      @@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).

    • @azice6034
      @azice6034 4 หลายเดือนก่อน +10

      @@PlayerSlotAvailableHe is the greatest mathematician to ever live. It’s hard to even compare him with other people in other fields. Like I can’t think of anyone having as big of an impact in their field as euler did with mathematics.

  • @jordanremington
    @jordanremington 2 หลายเดือนก่อน

    I am way too stupid to fully understand these videos but I always learn something and appreciate you and your team for making thse videos.

  • @DH-rj2kv
    @DH-rj2kv หลายเดือนก่อน +1

    Euler: "[Something] is a most difficult question."
    *Boss music starts*

  • @happmacdonald
    @happmacdonald 4 หลายเดือนก่อน +248

    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
      @harshrajveermaran5792 4 หลายเดือนก่อน +1

      Hey after 8128 is the next perfect number 41,328?

    • @Grizzly01-vr4pn
      @Grizzly01-vr4pn 4 หลายเดือนก่อน

      @@harshrajveermaran5792 No. The next perfect number is with p = 13, so 2¹²(2¹³ - 1) = 33550336

    • @minerscale
      @minerscale 4 หลายเดือนก่อน +5

      @@harshrajveermaran5792no it's 33,550,336.

    • @KiLLJoYYouTube
      @KiLLJoYYouTube 4 หลายเดือนก่อน

      Veritasium already did a video on Collatz 🫡

    • @Felipe-sw8wp
      @Felipe-sw8wp 4 หลายเดือนก่อน +3

      What if there is only one odd perfect number, and it's the only number at which Collatz Conjecture fails? 😳

  • @Rabcup
    @Rabcup 4 หลายเดือนก่อน +831

    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
      @TheSuperiorQuickscoper 4 หลายเดือนก่อน +9

      When did he move from LA?

    • @Lapse-a-lot
      @Lapse-a-lot 4 หลายเดือนก่อน +26

      Can confirm. It's midday here in 🌏

    • @jin_cotl
      @jin_cotl 4 หลายเดือนก่อน +4

      Fr I’m about to sleep soon

    • @augisterman3685
      @augisterman3685 4 หลายเดือนก่อน +3

      It's evening for me

      @THICCTHICCTHICC 4 หลายเดือนก่อน +23

      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

  • @fredflintstoner596
    @fredflintstoner596 2 วันที่ผ่านมา

    Mrs Richards: "I paid for a room with a view !"
    Basil: (pointing to the lovely view) "That is Torquay, Madam ."
    Mrs Richards: "It's not good enough!"
    Basil: "May I ask what you were expecting to see out of a Torquay hotel bedroom window ? Sydney Opera House, perhaps? the Hanging Gardens of Babylon? Herds of wildebeest sweeping majestically across the plains?..."
    Mrs Richards: "Don't be silly! I expect to be able to see the sea!"
    Basil: "You can see the sea, it's over there between the land and the sky."
    Mrs Richards: "I'm not satisfied. But I shall stay. But I expect a reduction."
    Basil: "Why?! Because Krakatoa's not erupting at the moment ?"

  • @mithicash1444
    @mithicash1444 หลายเดือนก่อน

    A lot of highlights from this video can be used to showcase just how powerful modern computing is and most of us don't even think about it.

  • @tokenr7414
    @tokenr7414 4 หลายเดือนก่อน +289

    As the co-discoverer of the first GIMPS prime (the 35th), I wasn't even aware of this unsolved problem...!
    -Joel Armengaud

    • @kitfifty
      @kitfifty 4 หลายเดือนก่อน +1

      whgats a GIMPS prime

    • @PaulDeanBumgarner
      @PaulDeanBumgarner 4 หลายเดือนก่อน

      What a waste of time. Look…
      There isn’t an odd one.
      This is now officially solved.

    • @DasAntiNaziBroetchen
      @DasAntiNaziBroetchen 4 หลายเดือนก่อน +17

      @@PaulDeanBumgarner Is the joke that you pretend to be a boomer? Cuz "Bumgarner" surely can't be a real name.

    • @TheCommentor-
      @TheCommentor- 4 หลายเดือนก่อน

      Bro is real

    • @N4SCARfaN
      @N4SCARfaN 4 หลายเดือนก่อน +6

      ​@@DasAntiNaziBroetchenI've seen both Bumgardner and Baumgartner, I'm sure Bumgarner exists somewhere

  • @GroovingPict
    @GroovingPict หลายเดือนก่อน

    When even Euler goes "this is a most difficult problem" I think everyone else can basically just pack it in and not even bother trying

  • @maiabeth6436
    @maiabeth6436 2 หลายเดือนก่อน

    i hate my math class and im almost failing it at school but for some reason I've watched the whole video and a bunch of other ones on numerical problems and I'm genuinely interested in them. lol

  • @Oriol-oo7jl
    @Oriol-oo7jl 4 หลายเดือนก่อน +116

    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

  • @user-pw6sy2sq7y
    @user-pw6sy2sq7y 4 หลายเดือนก่อน +95

    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
      @tensor131 4 หลายเดือนก่อน +3

      a very important observation - good

    • @JBG-AjaxzeMedia
      @JBG-AjaxzeMedia 4 หลายเดือนก่อน

      love me some gimps

    • @zarki-games
      @zarki-games 4 หลายเดือนก่อน

      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
      @warrior4christ777 4 หลายเดือนก่อน

      Ooo ah....your so smart.but are you wise?

    • @WarthogDoctor
      @WarthogDoctor 4 หลายเดือนก่อน


  • @titoub2008
    @titoub2008 2 หลายเดือนก่อน +1

    @2:11 I saw the pattern... start with 6 then 28

  • @fredericbachelier1620
    @fredericbachelier1620 2 หลายเดือนก่อน +5

    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 TH-camr! Congrats!!

  • @NoraOlson-ct7nr
    @NoraOlson-ct7nr 4 หลายเดือนก่อน +180

    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
      @annoy4nce648 4 หลายเดือนก่อน +9

      bro, that's literally part of the foundation of all of science and mathematics.

    • @glacialis3329
      @glacialis3329 4 หลายเดือนก่อน +10

      @@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
      @PotionsMaster666 4 หลายเดือนก่อน

      🫂 we brothers should make our own country

    • @DasAntiNaziBroetchen
      @DasAntiNaziBroetchen 4 หลายเดือนก่อน +2

      These comments are extremely weird.

    • @rabbr2sdsd799
      @rabbr2sdsd799 4 หลายเดือนก่อน +2

      @@DasAntiNaziBroetchenyou aint lie my boy 😂😂😂

  • @Xelianow
    @Xelianow 4 หลายเดือนก่อน +338

    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
      @November8888 4 หลายเดือนก่อน +1

      its the journey as they say

    • @rishikeshwagh
      @rishikeshwagh 4 หลายเดือนก่อน +12

      'The real treasure is the friends you made along the way'

    • @Ne_Ne_Vova_UA
      @Ne_Ne_Vova_UA 4 หลายเดือนก่อน +1

      Well, i don't think knowing if there is an odd perfect number would help anywhere

    • @Ne_Ne_Vova_UA
      @Ne_Ne_Vova_UA 4 หลายเดือนก่อน +1

      ​@@rishikeshwaghyes, especially the friends from 2000 years ago who wrote about perfect numbers

    • @stxnw
      @stxnw 4 หลายเดือนก่อน

      mathematicians should be banned from using computers

  • @AJ-er9my
    @AJ-er9my 19 วันที่ผ่านมา

    omg Pace Nielsen is a professor at my school! He's brilliant

  • @ellisonchan6204
    @ellisonchan6204 10 วันที่ผ่านมา

    My conjecture is due to the algorithm being related to powers of 2, you can find the perfect numbers more efficiently using a binary search tree, maybe using A*.

  • @grehuy
    @grehuy 4 หลายเดือนก่อน +126

    26:37 : Fantastic how you "caught" his argument from flying! 😂

    • @FeeblePenguin
      @FeeblePenguin 4 หลายเดือนก่อน +3

      It seems likely to be that the heuristic is actually JUST for odd perfect #'s, and the mathematician was briefly confused/incorrect.

    • @Tanystropheus10
      @Tanystropheus10 4 หลายเดือนก่อน +1


    • @joshuazelinsky5213
      @joshuazelinsky5213 4 หลายเดือนก่อน +11

      @@FeeblePenguin Not quite. Veratasium is correct here. The basic form of the heuristic does imply there are only finitely many even perfect numbers. There are some variants that partially avoid this but only partially. One way of thinking about it is that the power of 2 themselves are the culprit and allow a pattern to occur that would otherwise be extremely unlikely. But they allow things to line up just right to avoid the heuristic's probabilistic estimates.

    • @JoelLinus
      @JoelLinus 4 หลายเดือนก่อน

      Although it would raise the question if infinity exists in the first place.@@joshuazelinsky5213

    • @satriorukito
      @satriorukito 3 หลายเดือนก่อน


  • @patrickguth3796
    @patrickguth3796 4 หลายเดือนก่อน +173

    I love your channel so much, because the problems presented are discussed on a very nice level. Not layman's style, not lecture style, right in the middle. Awesome.

    • @Fire_Axus
      @Fire_Axus 4 หลายเดือนก่อน

      your feelings are irrational

    • @Ryan-lk4pu
      @Ryan-lk4pu 4 หลายเดือนก่อน +2

      Your "right in the middle" maybe. For an amoeba like me, he lost me after like 3 mins 🤣🤣
      I'll just be over here licking the window 😂

    • @austinhernandez2716
      @austinhernandez2716 4 หลายเดือนก่อน

      Math was my best subject in school, I made an A in calculus. But it's hard for me to follow sometimes

    • @mcpr5971
      @mcpr5971 4 หลายเดือนก่อน

      agree 100%. I tried reading about number theory when I was in college 20 years ago, before youtube, and I could only make it a couple pages into the first chapter before these textbooks seemingly go off into outer-space. Derek has done a great job of digesting and explaining. Just what I needed.

  • @user-gi4uo7td7x
    @user-gi4uo7td7x 2 หลายเดือนก่อน

    "He made a new weapon. the sigma function" - famous last words

  • @robincharles7057
    @robincharles7057 4 หลายเดือนก่อน +291

    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
      @slooptrooperunlimitedofthe1772 4 หลายเดือนก่อน +13

      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
      @Ceelvain 4 หลายเดือนก่อน +3

      The story is likely romanticised.

    • @zes3813
      @zes3813 4 หลายเดือนก่อน

      wrg, some tech, math etc s k , write that s k, doesn tmatter, no nerx etc nmw

    • @zenmkultra
      @zenmkultra 4 หลายเดือนก่อน

      heh, nerd

    • @Sepi-chu_loves_moths
      @Sepi-chu_loves_moths 4 หลายเดือนก่อน

      ​@zenmkultra are you... are you new here? This is the Veritasium youtube channel

  • @kshitizmalviya6909
    @kshitizmalviya6909 4 หลายเดือนก่อน +114

    16:17 Peter Barlow's statement awakened the mathematician in me until this transition

  • @MayaWu44
    @MayaWu44 18 วันที่ผ่านมา

    If there's unsolved mystery, that's the only reason needed to try to solve it!

  • @charmilli0n
    @charmilli0n หลายเดือนก่อน +4

    ok i'm a math noob but i love stuff like this. It's gonna take me about 50 rewatches to wrap my mind around a lot of this, but its given me something to ponder in my free time so, thanks!

  • @rockykitsune
    @rockykitsune 4 หลายเดือนก่อน +147

    In my intro to abstract math class in college, we had a final project to write a paper that had basically only two requirements: it was about an approved math-related topic and it had a proof that used concepts we were taught. I did mine on perfect numbers and Mersenne primes and gave a proof of the Euclid-Euler Theorem. It was super fun to learn and write about. It is awesome to see Veritasium cover this topic in the amazing quality he does and recognize the stuff that was talked about. I even concluded the paper like the video - it's nice to study stuff just because it's interesting, even if there's no obvious real world uses.

  • @hippynurd
    @hippynurd 4 หลายเดือนก่อน +55

    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

  • @GREG11-c2v
    @GREG11-c2v 2 หลายเดือนก่อน +28

    11:17 what a sigma

    • @XTLmaker
      @XTLmaker หลายเดือนก่อน +1


  • @davevon1786
    @davevon1786 2 หลายเดือนก่อน

    Great video 😊 made me sleep very quickly 😴

  • @vigilantcosmicpenguin8721
    @vigilantcosmicpenguin8721 4 หลายเดือนก่อน +37

    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
      @Larkian 4 หลายเดือนก่อน +2

      After all this years, I have all of them.

  • @samuraichicken9248
    @samuraichicken9248 4 หลายเดือนก่อน +192

    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

    • @skyfeelan
      @skyfeelan 4 หลายเดือนก่อน +40

      on the contrary, matlab or wolfram alpha might not exist without Euler discoveries

    • @mikeinjapan2004
      @mikeinjapan2004 4 หลายเดือนก่อน +14

      ​@@skyfeelan very true, it's because of these number theory why supercomputer turned out to be super... math is the foundation of everything 🎉

    • @miloradmilutinovic7691
      @miloradmilutinovic7691 4 หลายเดือนก่อน

      US would be bombimg mars by now.

    • @therealax6
      @therealax6 4 หลายเดือนก่อน +2

      @@skyfeelan 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
      @XIIchiron78 4 หลายเดือนก่อน +3

      I wonder if they would be even more shocked at how much we still can't solve...

  • @Subhit_Goswami
    @Subhit_Goswami 2 หลายเดือนก่อน

    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..

  • @claudiocesar206
    @claudiocesar206 24 วันที่ผ่านมา

    Muito bom! Parabéns pelo vídeo.

  • @halgerson
    @halgerson 4 หลายเดือนก่อน +211

    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
      @nikhilsharma32907 4 หลายเดือนก่อน +1

      💯 agree

    • @Redmenace96
      @Redmenace96 4 หลายเดือนก่อน +1

      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!!!!

  • @navidahmed1
    @navidahmed1 4 หลายเดือนก่อน +118

    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
      @jonathanberry1111 4 หลายเดือนก่อน +7

      I think I earned about them from watching Pulp Fiction...

    • @user-Aaron-
      @user-Aaron- 4 หลายเดือนก่อน +1

      Nice 🤜🤛

    • @OnixEdge
      @OnixEdge 4 หลายเดือนก่อน +1


    • @PFBM86
      @PFBM86 4 หลายเดือนก่อน +4

      Thank you for your service

    • @randomblueberry5019
      @randomblueberry5019 4 หลายเดือนก่อน +2

      This sounds like crypto mining lol