78557 and Proth Primes - Numberphile

  • Published on Nov 13, 2017
  • James Grime is back and talking prime numbers.
    Check out Brilliant.org by using the link: brilliant.org/numberphile (20% off premium subscription)
    More on prime numbers: bit.ly/primevids
    James Grime: singingbanana.com
    Editing by Pete McPartlan
    Music by Alan Stewart
    Read about Sierpinski Numbers: en.wikipedia.org/wiki/Sierpinski_number
    PrimeGrid: www.primegrid.com
    Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile
    We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
    Website: www.numberphile.com/
    Numberphile on Facebook: www.facebook.com/numberphile
    Numberphile tweets: twitter.com/numberphile
    Subscribe: bit.ly/Numberphile_Sub
    Videos by Brady Haran
    Patreon: www.patreon.com/numberphile
    Brady's videos subreddit: www.reddit.com/r/BradyHaran/
    Brady's latest videos across all channels: www.bradyharanblog.com/
    Sign up for (occasional) emails: eepurl.com/YdjL9
  • Science & TechnologyScience & Technology

Comments • 637

  • Doubtful Guest
    Doubtful Guest 5 hours ago

    I'm never going to use this maths.

  • driven789
    driven789 21 hour ago

    who care about Proth Primes?!?

  • mienzillaz
    mienzillaz 2 days ago

    So where is that glory for Hungarian..? I don't know his name.. some guy.. pfff

  • Shiv Service
    Shiv Service 6 days ago

    ✨God is visible in the beauty of this whole creation.
    Why is that so! If you draw a line passing from all points of Pythagoras triplets (I really mean EVERY possible Pythagoras triplet) on number lines ( in 2 dimensions), you get an infinite lines passing through a single point. (Btw this implies infinity, something growing from a point, to infinity) and many other wonders of pi and root of 2 ☘️

  • gluino
    gluino 8 days ago

    James Grime is my favorite in Numberphile.

  • tomvondeek
    tomvondeek 15 days ago

    Huh i haven't seen a video about Pi for a long time... here is a question i asked myself, but i'm not mathematician enough to answer it myself:
    if you add / substract / add / substract etc. all digits of pi... what whill happen?
    e.g. 3.14159265359... = 3-1+4-1+5-9+2-6+5-3+5-9... right now its -5. But in theory... would it be possible to go up to infinty? or to negative infinity? after all, would it converge to 0, because after all, digits are kind of equally distributet? is there any way to get any sort of answer? may some fellow mathematician try to answer? ^^

  • voornaam achternaam21
    voornaam achternaam21 15 days ago

    but what if one of these five IS the smallest one?, if we only stripe them away, and there is one, we will never find it...

  • Lanetwin
    Lanetwin 15 days ago

    @numberphile solve the dang cube already😂😂

  • Dennis E
    Dennis E 15 days ago

    Does Steven Colbert know there are prime numbers named after him?

  • Kevin Zimmerman
    Kevin Zimmerman 18 days ago

    Is James Grime single?

  • A Random TASer
    A Random TASer 19 days ago

    Two plus two is four minus one that three quick maths

  • PradeepKumar Rajendran

    I'll grateful if any of the regular subscribers could answer my irrelevant question. I am looking for a video that I watched more than a year ago or so, with Dr. James Grime talking about possible outcomes/predicting outcomes. I vaguely remember that he also simulated all the possible outcomes that was making a pattern and he ends up with a philosophical view "...if freewill exist?". I'm not sure those outcomes were inside the mandelbrot set.
    Strikes bell to anyone? I'm desperately looking for that video. Thank you!

  • Sort Tricks
    Sort Tricks 25 days ago +1

    /* Do not display this comment */

  • Joe Q
    Joe Q Month ago

    "We don't know it's true. It just feels true - in our guts; it has truthiness." Yes. It smells like truth. No need for further research. Truthiness is truth everyone.

  • Susan Amber Bruce
    Susan Amber Bruce Month ago

    Can a number be expressed as being pregnant?
    e. g. 1 + 1 = 2, how can 1 be expressed as being added to before it's value changes?

  • Promit Chakrabarty
    Promit Chakrabarty Month ago

    Great video as always. BTW, I can't figure out this problem. Finally posting this on a mathematically inclined group as no one on the Internet seems to be willing to answer this. Actually I'm appearing for an important test and it would be very helpful for me to know some facts. Based on current performance analysis on mock tests, my guesses are likely to be correct 50 percent of the times(ie, 50 percent chance of getting an Mcq correct or 50 percent accuracy) in a 4 option multiple choice question exam (mcq type exam) of total 300 questions, with 4 marks awarded for a correct answer and 1 mark deducted for every wrong answer. This 50 percent accuracy is for the 1st 250 questions I attempt which I tend to get right in the above mentioned percentage. For the next 50 however, upon guessing I would be right no more than a random chance of 25 percent. Then what is the optimum number of questions I should attempt to get the maximum marks, while getting the minimum negative marks? And what would that value be for a range of 40 to 60 percent accuracy for the first 250 questions ? I apologise if my question seems too complicated, as I myself am flummoxed by it. Would it be best to answer all, as the marking scheme seems to favour guessing? Thanks in advance for indulging in the cerebral effort.

  • Donțu Daniel Nicolae

    Cool fact: sqrt(256-31)=15 and sqrt(256)-31=-15

  • Tinta Dunia Maya
    Tinta Dunia Maya Month ago

    pleaseee. use whiteboard instead of papers. :'(

  • Abhishek Kumar
    Abhishek Kumar Month ago

    314 people. Why, that's PI!

  • Oleg Shelemetev
    Oleg Shelemetev Month ago

    I am poor.
    Plz give me bitcoin

  • Jack Rycroft
    Jack Rycroft Month ago


  • Periner F
    Periner F Month ago

    Что за кортонка???? Купи уже себе тетрадь!!

  • GregoryTheGr8ster
    GregoryTheGr8ster Month ago

    Prime numbers are so pure.

  • Rmac524
    Rmac524 Month ago +1

    Have people tried to prove that some of the candidates are in fact Sierpinski Numbers?

  • A R V C
    A R V C Month ago +1

    I have a challenge for you:
    I call it the Kalen challenge (don’t ask about the name).
    You have to find a number that is divisible by a formula formed by numbers from 0 to 100 or just the number (include the zero!).
    For example:
    9900 divided by 100= 99
    9900 divided by 99=100
    9900 divided by 3x3||3=100
    For the ecuations, you can use: addition, subtraction, multiplication, division, brackets, powers (they have to be of the same number), roots (the same number, so I don’t see much utility), concatenation, factorials (the ! thing) and points of the same number (12.12).
    You’re also not allowed to do formulas that always give the same result, like (n+n) divided n, which always equal 2, and you’re not allowed to use the number 0 as the answer to the challenge, since that number can be divided by every other number.
    A tip is for the last two digits to be 00, which immediately makes it divisible by 100, 10, 5, 4 and 2.
    Have fun!

  • Iván Rangel
    Iván Rangel Month ago

    It has "truthiness" - I guess James is a fan of Colbert too

  • Marinela Oana
    Marinela Oana Month ago

    Who is watching this yesterday?

  • JetPackJan
    JetPackJan Month ago

    what about 19 * 2^0 ?

  • Agustin Caputo
    Agustin Caputo Month ago

    please watch this videos at 0.5 x speed, is hilarious

  • Paradox
    Paradox Month ago

    would $99.00 be called Amazon Prime?

  • Leo Liu
    Leo Liu Month ago

    how do they eliminate a number if they have to check all the values of N till infinity?

  • Joseph Sabo
    Joseph Sabo Month ago

    Maths is everywhere you go. Snow widows homes plants eta.

  • Vadimeche Erkhov
    Vadimeche Erkhov Month ago +1

    Союз нерушимый республик свободных
    Сплотила навеки великая Русь,
    Да здравствует созданный волей народов
    Великий, могучий Советский Союз

  • No Name
    No Name Month ago

    the first pi people

  • Dr Ivo Robotnik
    Dr Ivo Robotnik Month ago

    82 people with Dyscalculia disliked this video

  • misterjohn john
    misterjohn john Month ago


  • hhh hbk
    hhh hbk Month ago


  • Hussein Badawi
    Hussein Badawi Month ago

    Hi Brady,
    I really appreciate your ongoing hard work and wish you all the best.I have one question which I kindly request you to pass it to Dr. Grime which is: “what is the limit of x^2+x as x goes to infinity”?
    Many thanks in advance.

  • pneumonosaur
    pneumonosaur Month ago

    Please sirs and madams, I would like to know more about the number 72. Of all of the numbers should not this one top the charts as being oddly important!!

  • Frídi Atlason
    Frídi Atlason Month ago

    2 + 2 = 4
    4 - 1 = 3
    Quick maths

  • Artemirr Lazaris
    Artemirr Lazaris Month ago

    Why not the significance of primes in music intervals, and how changing the hertz in its relation within primes can find other iterations of harmony, of course not every marriage is complete, within this thought, there would be stepping stones between, but basing the freq. in bases of differing primes rather than just the fifths, allows for a broader depth of musical scoring. Which would be .. something interesting... but I suppose in some regard that is done, by other means, but not to scale... Hmmm Thoughts..

  • zombiebro9
    zombiebro9 Month ago

    474 is a lychal number

  • Chris Pi
    Chris Pi Month ago

    No one reacts about the Rubik's cube stuck in the armrest ?

  • Trivendram pal
    Trivendram pal Month ago

    sir I have a question and please answer it ,,sir as we seen that (1+2+3+4........)=-1/12 gives a negative number then does it will also true for if we add negative numbers and will get apositive number as (-1-2-3-4-5-6........)=1/12 by using the math as. ...-(1+2+3....)=1/12... sir by these results what we can conclude ,,,,our mathematical calculation is wrong ,,,or maths is giving a wrong answer ,,,,,but math cannot give a wrong answer if we have performed it as we do usual then what is the reason behind this we are getting such a absurd result ,,,, doex these results are challinging us that we are wrong

    DNVIC Month ago

    1 isn't prime
    there you go

  • Emily Nep
    Emily Nep 2 months ago

    lol e

  • gedstrom
    gedstrom 2 months ago

    Is there a special shortcut test for Proth primes? I know that the reason that most of the largest primes are Mersenne primes is because there is a special test for them.

  • ahasd
    ahasd 2 months ago

    you've got funny pronunciation of "Sierpiński"
    anyway, nice video :P

  • jack lloyd
    jack lloyd 2 months ago

    I had the privilege of seeing James talk about codebreaking at Salford University last Thursday

  • Corrodias
    Corrodias 2 months ago

    But how was it proven that the one number there never produces a prime?

  • Olivier L. Applin
    Olivier L. Applin 2 months ago

    I just learned about the Catalan number in discrete math class and this thing is AMAZING ! It describes so many different problems. I know it is not related to primes, but I'd love to watch Dr Grimes or Matt Parker (or anyone else as a matter of fact) explaining it!

  • Myles F
    Myles F 2 months ago

    So Mersenne Primes are Proth Primes such that k = 1.

  • mrdabbleswithpotion
    mrdabbleswithpotion 2 months ago

    Dumbass. Stick with following the math problems with those "fun math books" meant to entertain the public of the wonders of math. OK, you can also find those things easily on the internet now.

  • 정제윤
    정제윤 2 months ago

    Isn't every prime a Proth prime(except 2 if you don't want 0 on the exponent)? Cause every prime is odd and odd numbers are 2n+1. In the case of 2, 1×2^0+1=2

  • Kelvin Kersey
    Kelvin Kersey 2 months ago

    is there anything special about 151 136 and 287? (apart from adding the first two :-)

  • sammbo250
    sammbo250 2 months ago

    Are they just running through tons of number using 'computation' or proving it mathematically. I would hope that advanced mathematicians would prove it.

  • mehdi rejali
    mehdi rejali 2 months ago +2

    does this mean 3 is a proth prime?
    1 x 2 + 1

  • warspyking
    warspyking 2 months ago

    A video on the proof of why (the number we currently believe is the smallest that never produce a prime) we know will never produce a prime would be nice.

  • Jack Ladell
    Jack Ladell 2 months ago

    How do you know that 78557 is? If you know that one is by proof cant you apply that method to the other 5? Wouldnt that be faster. Or im i missing something?

  • Jonathan Holden
    Jonathan Holden 2 months ago

    For a quick check, the digits of 153 can be added (1+5+3=9) and the result is divisible by 3, meaning that 153 itself is divisible by 3.

    GENIUS 2 months ago

    Here's a fun little exercise:Prove that 78557 will never produce a prime when taken in the form :78557*2^n+1

  • Hedning1390
    Hedning1390 2 months ago

    Why did 78557 have a proof, but the others have to be done by counterexample?
    Edit: ok, they didn't prove it. I should probably watch the whole video first...

  • rlt152
    rlt152 2 months ago

    Truthiness- I don't think I have ever heard that term on here before :)

  • msolec2000
    msolec2000 2 months ago

    It's always nice seeing Dr. James Prime doing his thing.

  • Georticon YT
    Georticon YT 2 months ago

    There is always a Rubik's cube in the background...

  • Hands of Science
    Hands of Science 2 months ago

    I enjoy your enjoyment of math far more than enjoying the math itself.

  • P Hampton
    P Hampton 2 months ago

    Surely it can't be long until there's something called a "Grime Prime".

  • T Perm
    T Perm 2 months ago +1

    1:56 That's not that hard to check, it's divisible by 3 (if the sum of its digits is divisible by 3 then the number is)

  • J Bonaroti
    J Bonaroti 2 months ago

    Rubik's cube!!! Yas!

  • NGEternal
    NGEternal 2 months ago

    9*17, fyi

  • Jake Fisher
    Jake Fisher 2 months ago

    If you write a large number, no one has ever before written, have you invented it, discovered it, or neither?

  • amandus westin
    amandus westin 2 months ago

    Can't they just check the remaining candidates like they did with 78557??

  • K Johnson
    K Johnson 2 months ago

    why are they writing on paper towels in every video...

  • Peter Kovacs
    Peter Kovacs 2 months ago +1

    James has twice said: "If we can eliminate these candidates, we will have proved that 78557 is the smallest Sierpinski prime number". The use of future perfect in this conditional sentence has been on my mind for quite some time now, as I don't understand why he didn't use future simple "will prove" instead. I don't feel any past reference from a future point in this sentence, or from the given context. I am not a native speaker, but I am trying to master English, so if anyone can explain the usage of future perfect in this particular sentence, I will be very grateful.

  • Paul Dohnal
    Paul Dohnal 2 months ago

    But how can we know for sure that 78557 will NEVER produce a Prime Number? What if the Prime is just really large?

  • //Sloth //4k:
    //Sloth //4k: 2 months ago

    what's the truthiness out of 10?

  • Roger Hudson
    Roger Hudson 2 months ago

    Is there something special about videoing brown wrapping paper?

  • Jiggerjaw
    Jiggerjaw 2 months ago

    Truthiness. Nice.

  • TheIrishMan
    TheIrishMan 2 months ago +1

    I discovered the largest prime...grahams number factorial minus 1.....

    • Jooolse
      Jooolse Month ago

      For sure, I know about the probability... and I can live with a 1/(Graham's number) uncertainty!
      By the way, after Graham's number factorial + 2, there won't be any prime for a long time...

    • TheIrishMan
      TheIrishMan Month ago

      Youll never know!

    • Jooolse
      Jooolse 2 months ago

      The probability that this number be prime is less than 1/(Graham's number)... so zero in short!

  • Blur 410
    Blur 410 2 months ago

    truthiness, is that a colbert reference?

  • Abid Abdullah
    Abid Abdullah 2 months ago

    There is a bigger prime number than the first one(lets call the first one x) in this list and it is 2^x -1. Thank me later.

  • Maxon Mendel
    Maxon Mendel 2 months ago

    Colbert helps get rid of political candidates, I reckon?

  • Invincible
    Invincible 2 months ago +1

    First 314 subscribers... 3.14

  • InuYasha6651
    InuYasha6651 2 months ago

    James Grime is my favorite!

  • Thomas Latkowski
    Thomas Latkowski 2 months ago

    I like how truthiness was a Colbert reference at the end

  • C. Ray
    C. Ray 2 months ago

    This video was published on the day I actually went to a live taping of the Late Show and I actually got to talk to Colbert and ask him a question during Q&A time! How great is this! Colbert, a new Numberphile, and PrimeTime with Grime all in one! 🤗

  • Odis Eats
    Odis Eats 2 months ago

    I’ve never seen someone so excited about numbers

  • ronindebeatrice
    ronindebeatrice 2 months ago

    Why is the current smallest k known, whereas the others are still questioned? What's the math which proves k never produces a prime?

  • Pro_Triforcer
    Pro_Triforcer 2 months ago

    Truthiness? Is it Parker's truth?

  • KatanaBart
    KatanaBart 2 months ago

    When it comes to finding the elusive pattern in primes, what progress has been made using alternatives to the base-10 system?

  • Abdul Kheil
    Abdul Kheil 2 months ago

    Why do we use differentials in multiple integral and not partials?

  • Pretzel
    Pretzel 2 months ago

    Guys 24737 x 2^2857425774215674 + 1 is prime

  • Steffen Widmaier
    Steffen Widmaier 2 months ago

    78557=17*4621; 21181=59*359; 24737=29*853; 55459=31*1789

  • jbkrauss
    jbkrauss 2 months ago

    two plus two is four, minus one that's three quick mafths

  • Patrick Rogan
    Patrick Rogan 2 months ago

    Am I the only one who thinks Mr Grime looks like young Sting?

  • FaRo
    FaRo 2 months ago

    In my program 47 was the lowest number that doesn't produce a prime this way. It might be a "double" overflow, but I take this as proof.

  • Laatikkomafia
    Laatikkomafia 2 months ago

    I have discovered a truly remarkable proof that all of those lead to a prime which this comment box is too small to contain.

  • Paul Smith
    Paul Smith 2 months ago

    Cancelling bitcoin mining program and firing up smallest-k finding program right now... I'll get back to you.

  • Sharon Klinkenberg
    Sharon Klinkenberg 2 months ago +2

    Why wait for someone to solve this on a home computer and not just run it on a cluster and get it over with 😀

  • biokaese
    biokaese 2 months ago

    Parker Truth