78557 and Proth Primes - Numberphile

  • Published on Nov 13, 2017
  • James Grime is back and talking prime numbers.
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  • Science & TechnologyScience & Technology
  • Runtime: 8:40
  • numberphile  prime numbers  proth prime  

Comments: 667

  • mehdi rejali
    mehdi rejali 36 minutes ago +1

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

  • warspyking
    warspyking 3 hours 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 4 hours 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 5 hours 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 6 hours 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 8 hours 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 15 hours ago

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

  • msolec2000
    msolec2000 18 hours ago

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

  • Georticon YT
    Georticon YT 19 hours ago

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

  • Hands of Science
    Hands of Science 20 hours ago

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

  • P Hampton
    P Hampton Day ago

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

  • T Perm
    T Perm Day 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 Day ago

    Rubik's cube!!! Yas!

  • NGEternal
    NGEternal Day ago

    9*17, fyi

  • Jake Fisher
    Jake Fisher Day 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 Day ago

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

  • K Johnson
    K Johnson Day ago

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

  • Peter Kovacs
    Peter Kovacs Day 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 Day 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: Day ago

    what's the truthiness out of 10?

  • Roger Hudson
    Roger Hudson 2 days ago

    Is there something special about videoing brown wrapping paper?

  • Jiggerjaw
    Jiggerjaw 2 days ago

    Truthiness. Nice.

  • TheIrishMan
    TheIrishMan 2 days ago +1

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

    • Jooolse
      Jooolse Day ago

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

  • Blur 410
    Blur 410 2 days ago

    truthiness, is that a colbert reference?

  • Abid Abdullah
    Abid Abdullah 2 days 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 days ago

    Colbert helps get rid of political candidates, I reckon?

  • Invincible
    Invincible 2 days ago +1

    First 314 subscribers... 3.14

  • InuYasha6651
    InuYasha6651 2 days ago

    James Grime is my favorite!

  • Thomas Latkowski
    Thomas Latkowski 2 days ago

    I like how truthiness was a Colbert reference at the end

  • C. Ray
    C. Ray 2 days 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 days ago

    I’ve never seen someone so excited about numbers

  • ronindebeatrice
    ronindebeatrice 2 days 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 days ago

    Truthiness? Is it Parker's truth?

  • KatanaBart
    KatanaBart 2 days 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 days ago

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

  • Pretzel
    Pretzel 2 days ago

    Guys 24737 x 2^2857425774215674 + 1 is prime

  • Steffen Widmaier
    Steffen Widmaier 2 days ago

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

  • jbkrauss
    jbkrauss 2 days ago

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

  • Patrick Rogan
    Patrick Rogan 2 days ago

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

  • FaRo
    FaRo 2 days 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 days 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 days ago

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

  • Sharon Klinkenberg
    Sharon Klinkenberg 3 days ago +1

    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 3 days ago

    Parker Truth

  • Sean L.
    Sean L. 3 days ago +1

    Lol when I tried to sign up for the website it asked me for my birthdate. But the year I was born in wasn't on there.

    • Sean L.
      Sean L. 3 days ago +1

      Now I don't like the website because I would have to pay monthly to actually use it. Another thing that would have been perfect it it didn't cost money.

  • Human
    Human 3 days ago

    I have no interest in math whatsoever but I watched your videos cuz they are so interesting.

  • Ashwin murali
    Ashwin murali 3 days ago

    This guy looks like Thom Yorke from Radiohead

  • Gergő Turán
    Gergő Turán 3 days ago

    *Just a hungarian guy's patriotic comment flying through the screen*

  • Rosie Fay
    Rosie Fay 3 days ago

    0:22 2016. So why wait a year to make the video?

  • Vesania_6
    Vesania_6 3 days ago

    you are so cute and an excellent teacher 💋

  • Alexey Akimov
    Alexey Akimov 3 days ago

    Why is it so important to know smallest Sierpinski number? Are there some known applications of it or the search is driven by pure mathematical curiosity?

  • Heavyboxes DIY Master

    I used to be in my prime when I was on prime time television talking about prime numbers.

  • hewhoamareismyself
    hewhoamareismyself 3 days ago

    I have been running this since the beginning of the year, highly encourage others to do the same (especially if they’re at uni and don’t pay for their own electricity)

  • LaGuerre19
    LaGuerre19 3 days ago

    Grimes on primes

  • 11Anti11
    11Anti11 3 days ago

    I really wish I had a maths teacher like this in school. Also, thanks for the link to primegrid, I have a lot of spare cpu/gpu cycles at home, which would you recommend downloading?

    • Tom9358
      Tom9358 3 days ago

      Why not just prime95 or the corresponding GPU program?

    • 11Anti11
      11Anti11 3 days ago

      I mean sub-project, sorry if that wasn't clear.

  • Vivek Ranjan
    Vivek Ranjan 3 days ago

    How do we verify million digit as prime?

    • Tom9358
      Tom9358 3 days ago

      Vivek Ranjan the technique to check if something is prime doesn't depend on how large the number is, so you can just let a computer do it.

  • LightGuy101
    LightGuy101 3 days ago +2

    All these Primes and I'm still not Optimus... I know...

  • Wood Croft
    Wood Croft 3 days ago

    C🤨L B E R T

  • Ray Dillon
    Ray Dillon 3 days ago

    Wow, your excitement drew me in.

  • Djorgal
    Djorgal 3 days ago

    4:04 You can do that only if there 78557 is indeed the smallest. Because if there is a smaller one, you can't check that it's never ending by trying. The algorithm doesn't stop.

  • Motion Blur
    Motion Blur 3 days ago

    what is the deal though? why does this matter?

  • Hey Guys, This Is My New Name

    is mayonnaise a prime number?

  • Matthew Fuerst
    Matthew Fuerst 3 days ago

    Do a video on penrose tiling and the “Socolar-Taylor tile” please. I️ saw something about I️t online and I️ want to know more about I️t.

  • Echo5Delta
    Echo5Delta 3 days ago

    If Selfridge proved that all values of 78,557 * 2^n +1 will have one of seven prime factors, I wonder if that quality--guaranteed multiple of one of only a few different prime numbers--is a tell-tale sign of a k-value that yields no primes.
    Is the computer program that's checking the remaining k-values also keeping track of the smallest set of numbers that includes at least one factor of each power of 2 that's been analyzed so far for each of the k-values? Hypothetically, if such a set has >20 members for four out of the remaining five k-values but only 5 members for the other k-value, I wonder if that could help refine our search.

  • Da-Slow- Mo-Bro
    Da-Slow- Mo-Bro 3 days ago

    Was, was that a parker proof?

  • Muhammad Arifur Rahman

    Its so good to see Numberphile is #27 on Trending. 😁

  • orthoplex64
    orthoplex64 3 days ago

    I clicked this video because James Grime is worth my time

  • Tom Heyman
    Tom Heyman 3 days ago

    I wish I knew what any of this meant

  • Cowslayer7890
    Cowslayer7890 3 days ago +1

    So if we eliminate another candidate we can get an even bigger prime?

  • Brandon Lane
    Brandon Lane 3 days ago

    I already have GIMPS, time to add another program for these types of primes

  • Jacob Miller
    Jacob Miller 3 days ago

    Primes suck🤘

  • rtpoe
    rtpoe 3 days ago

    As I'm watching, it's #27 on Trending. Has a Numberphile video ever gotten higher?

  • James A Clouder
    James A Clouder 3 days ago

    Truthiness, truly the most scientific term ever uttered.

  • Jeremy Gant
    Jeremy Gant 3 days ago +1

    Yay! Grime is back! Thanks for sharing this video! I have a little question for everyone.
    Imagine if an "antiprime" is n.
    What's the largest n+1 or n-1 that is prime?

    • Jeremy Gant
      Jeremy Gant 2 days ago +1

      A number that has more factors than all the numbers before it, i.e. 12, 5040, etc

    • Tom9358
      Tom9358 3 days ago

      Jeremy Gant how do you define antiprime?

  • Joe Previdi
    Joe Previdi 3 days ago

    The truthiness plug was A grade!

  • Lucas Westfal
    Lucas Westfal 3 days ago

    When the results are no longer reliable?

  • phuaxy
    phuaxy 3 days ago

    I always wonder if the mathematicians know all these numbers off the top of their heads

  • Czeckie
    Czeckie 3 days ago

    are there any (inconclusive, heuristic) reasons why these five shouldnt be Sierpinski numbers?

  • Woodenwakka
    Woodenwakka 3 days ago

    How weird it must be to just have these random numbers stuck in your head and knowing exactly how important each one is.

  • Robert D In Tulsa
    Robert D In Tulsa 3 days ago

    Solve that damn cube already! Ha

  • dartagnanx1
    dartagnanx1 3 days ago +1

    Why does 78557 seem truthy. Please do a video on that! Great video as usual!

  • Random Kanji
    Random Kanji 3 days ago


  • CrypticRaps
    CrypticRaps 3 days ago

    What is the significance of the number 26, you ask? If you divide it by 2, you get 13 - that’s a lucky number. If you times that by 2, you get 26... 26... The number of subscribers I have. It’s not enough!



  • Alois Mahdal
    Alois Mahdal 3 days ago

    Classic Numberphile video. I've been missing these!

  • Harinandan Nair
    Harinandan Nair 3 days ago

    One thing... What course should we take in order to study the stuff u guys talk abt on this channel?

  • anony mous
    anony mous 3 days ago +4

    Astonishing that during the entire video, the name of the project that got us down to those 6 values, Seventeen Or Bust, was not uttered. A lot of us put in a lot of computing time to crack it that far! I think the name at least deserved a mention.

    • anony mous
      anony mous 3 days ago +3

      It was the name of the project, yes.

    • wolfedog99
      wolfedog99 3 days ago +3

      Is "Seventeen Or Bust" the name of the project?
      The placement in the comment feels syntactically odd.

  • Nicholas Hartle
    Nicholas Hartle 3 days ago

    2 x 2^3 + 1 = 17. Could have just used that as your example.

  • Simon L
    Simon L 3 days ago

    You guys really improved your paper!

  • Simon L
    Simon L 3 days ago +1

    Add a public comment...

  • Lapis Houndoom
    Lapis Houndoom 3 days ago

    The hello internet poster in the back is the 10... ^ ... Prime! thing

  • kungfuasgaeilge
    kungfuasgaeilge 3 days ago

    That's Numberwang!

  • Nadeem Hussein
    Nadeem Hussein 3 days ago

    Can someone show me the link to john's proof?

  • Deboogs
    Deboogs 3 days ago

    Classic Numberphile material.

  • Joel Grayson
    Joel Grayson 3 days ago +1

    More James Grime!        THANK YOUUUUUU

  • IAm NAU
    IAm NAU 3 days ago

    Ive been using primegrid through bionc for a while now, bionc is easy to download and you can help the cause for not just the search for primes, but for nearly anything science related.

  • rubikschu
    rubikschu 3 days ago

    Solve your cube, it's making me uncomfortable.

  • Arokace
    Arokace 3 days ago

    Really wish you went over why that 78000 number will never create a prime using that function. Because I am guessing that there is a concrete answer other than we've checked 100 of 1000s of iterations...since that isn't a proof technically by brute forcing...

  • Bladewing Ten
    Bladewing Ten 3 days ago

    Did you upgrade your paper? Looks like it has some fancy ridges

  • JEFFF !!!!!
    JEFFF !!!!! 3 days ago

    Observe: K = 0
    K * 2^n + 1 = 1
    You're welcome