# 78557 and Proth Primes - Numberphile

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**Published on Nov 13, 2017**- James Grime is back and talking prime numbers.

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Editing by Pete McPartlan

Music by Alan Stewart

Read about Sierpinski Numbers: en.wikipedia.org/wiki/Sierpinski_number

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FGV Cosmic5 days agoIdiots.... K=0....

K*2^n+1 always=1...

1 is not a prime..........

guy from belgium15 days agowhy does this guy look like the Walmart Yoddel kid

Gegi Zambakhidze23 days agoPrime numbers are so weird. It's one of the things that humanity still hasn't found general formula of.

Jesse Bailey27 days agoWhat if my K is equal to 0 ;)

Nice ShadoWmAsTeRMonth agohow did the addition function appear?

Ink SansMonth agoI was think it could be 301 views

nDante LiveMonth agoWhy don't try a proof like the number 78557? Thx

Kshitij AroraMonth agoCan you plss put up a video for integral((√sinx)dx)

Caesar C.Month agoHow many possible combinations of notes are on an 88 keys piano ? As in a chord

Chris The GamerMonth agoSooo... your sexually attracted to numbers?!?

Ricky's BeetsMonth agowait are they called proth primes or colbert primes?

David BrittMonth agoAny chance we can get a James Grime video on Gaussian primes? There has to be something cool to see when you put together primes and the complex plane.

James CooperMonth agoOff topic but could you please explain why, 2,3,7&8 don't exist in perfect squares???. & is there a proof they don't?

mahdi mcheik2 months agobig fan :) can you please explain the FFT reordering trick and how it works

satish kumar Ranjan2 months agoplease make video on approximation techniques for tough number... please

James Bateman2 months agoHey in my math class we got a problem where you had to find the area of a shaded area in a triangle. It is Geometry so it's fairly simple and the area of the Shaded triangle is also a trapezoid if you solve it by finding the area of the whole triangle and subtracting the area of the smaller triangle on top it comes out with a different answer than if you just find the area the trapezoid our teacher can't figure out why and I was wondering if I sent this to you you guys could explain why this was the way it was

Дрозд Анатолий2 months ago111 111 111 kare = 1.2345679 × 10^(16), menm jan li pral gade san yo pa yon kalkilatris?

Anastasios Chronopoulos2 months agoUhh... 0 works as a Sierpiński number

Fusion Tricycle2 months agoTry k=1

The Peanut Butter Crew RBLX2 months agoi wish i learned this in 5th grade

slinkytreekreeper2 months agoWhy is this important to know the largest primes with scores and scores of numbers?

abhay prakash singh2 months agoRequest or suggestion: Hi...please do something on AVERAGE SPEEDS, like where we can replace (two different) speed(s) by average speed etc...like 'Every day a person walks at a constant speed, V1 for 30 minutes. On a particular day, after walking for 10 minutes at V1, he rested for 5 minutes. He finished the remaining distance of his regular walk at a constant speed, V2, in another 30 minutes. On that day, find the ratio of V2 and his average speed (i.e., total distance covered /total time taken including resting time)'.....and guess what, it is 1:1. Plz do something like this please.

Rajiv Pokharel2 months ago"12345679" is quite a special number too.....

Drag0nEYE 15102 months agoIt looks like he's drawing on a trailer house curtain.

Herrgolani2 months agoI have a question concerning their testing method. You can test if one of these numbers is a prime, but not if it isn't. I mean at what power to you say "Ok, this is probably isn't a prime"? Even then, it doesn't prove that they do not have a prime number. Perhaps its just taken to a power higher than what was previously tested. I'd love to hear an answer! :)

Leo1793 months agocould you do the first 78557 people get 78.557% off?

Doubtful Guest3 months agoI'm never going to use this maths.

driven7893 months agowho care about Proth Primes?!?

mienzillaz3 months agoSo where is that glory for Hungarian..? I don't know his name.. some guy.. pfff

gluino3 months agoJames Grime is my favorite in Numberphile.

tomvondeek3 months agoHuh 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 achternaam213 months agobut 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...

Lanetwin3 months ago@numberphile solve the dang cube already😂😂

Dennis E3 months agoDoes Steven Colbert know there are prime numbers named after him?

Kevin Zimmerman3 months agoIs James Grime single?

A Random TASer3 months agoTwo plus two is four minus one that three quick maths

PradeepKumar Rajendran3 months agoI'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!

LiveToon's Gujarati4 months ago^{+1}/* Do not display this comment */

Joe Q4 months 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 Bruce4 months agoCan 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 Chakrabarty4 months agoGreat 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 Nicolae4 months agoCool fact: sqrt(256-31)=15 and sqrt(256)-31=-15

Tinta Dunia Maya4 months agopleaseee. use whiteboard instead of papers. :'(

Abhishek Kumar4 months ago314 people. Why, that's PI!

Oleg Shelemetev4 months agoI am poor.

Plz give me bitcoin

1CXWehPKnWZMHpxcD9YU8RfoTuHAeXr5GC

Jack Rycroft4 months ago0:13 WHAT IF I SAY IM NOT LIKE THE OTHERS

*coughs*

Sorry

Periner F4 months agoЧто за кортонка???? Купи уже себе тетрадь!!

GregoryTheGr8ster4 months agoPrime numbers are so pure.

Rmac5244 months ago^{+1}Have people tried to prove that some of the candidates are in fact Sierpinski Numbers?

A R V C4 months 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 Rangel4 months agoIt has "truthiness" - I guess James is a fan of Colbert too

Marinela Oana4 months agoWho is watching this yesterday?

JetPackJan4 months agowhat about 19 * 2^0 ?

Agustin Caputo4 months agoplease watch this videos at 0.5 x speed, is hilarious

Paradox4 months agowould $99.00 be called Amazon Prime?

Leo Liu4 months agohow do they eliminate a number if they have to check all the values of N till infinity?

Joseph Sabo4 months agoMaths is everywhere you go. Snow widows homes plants eta.

Vadimeche Erkhov4 months ago^{+1}Союз нерушимый республик свободных

Сплотила навеки великая Русь,

Да здравствует созданный волей народов

Великий, могучий Советский Союз

No Name4 months agothe first pi people

Dr Ivo Robotnik4 months ago82 people with Dyscalculia disliked this video

misterjohn john5 months ago;~)

hhh hbk5 months ago1=2

2=4

3=16

4=65536

5=?

Hussein Badawi5 months agoHi 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.

Hussein

pneumonosaur5 months agoPlease 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 Atlason5 months ago2 + 2 = 4

4 - 1 = 3

Quick maths

Artemirr Lazaris5 months agoWhy 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..

zombiebro95 months ago474 is a lychal number

Chris Pi5 months agoNo one reacts about the Rubik's cube stuck in the armrest ?

Trivendram pal5 months agosir 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

DNVIC5 months ago0*anything=0

0*2^n+1=1

1 isn't prime

there you go

Emily Nep5 months agolol e

gedstrom5 months agoIs 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.

ahasd5 months agoyou've got funny pronunciation of "Sierpiński"

anyway, nice video :P

jack lloyd5 months agoI had the privilege of seeing James talk about codebreaking at Salford University last Thursday

Corrodias5 months agoBut how was it proven that the one number there never produces a prime?

Olivier L. Applin5 months agoI 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 F5 months agoSo Mersenne Primes are Proth Primes such that k = 1.

mrdabbleswithpotion5 months agoDumbass. 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.

정제윤5 months agoIsn'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 Kersey5 months agois there anything special about 151 136 and 287? (apart from adding the first two :-)

sammbo2505 months agoAre they just running through tons of number using 'computation' or proving it mathematically. I would hope that advanced mathematicians would prove it.

de way5 months ago^{+2}does this mean 3 is a proth prime?

1 x 2 + 1

warspyking5 months agoA 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 Ladell5 months agoHow 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 Holden5 months agoFor 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.

GENIUS5 months agoHere's a fun little exercise:Prove that 78557 will never produce a prime when taken in the form :78557*2^n+1

Hedning13905 months agoWhy 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...

rlt1525 months agoTruthiness- I don't think I have ever heard that term on here before :)

msolec20005 months agoIt's always nice seeing Dr. James Prime doing his thing.

Georticon YT5 months agoThere is always a Rubik's cube in the background...

Hands of Science5 months agoI enjoy your enjoyment of math far more than enjoying the math itself.

P Hampton5 months agoSurely it can't be long until there's something called a "Grime Prime".

T Perm5 months ago^{+2}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)

Adrian Jonathan4 months ago^{+1}T Perm you think you're smarter than him huh

J Bonaroti5 months agoRubik's cube!!! Yas!

NGEternal5 months ago9*17, fyi

Jake Fisher5 months agoIf you write a large number, no one has ever before written, have you invented it, discovered it, or neither?

amandus westin5 months agoCan't they just check the remaining candidates like they did with 78557??

K Johnson5 months agowhy are they writing on paper towels in every video...

Peter Kovacs5 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 Dohnal5 months agoBut how can we know for sure that 78557 will NEVER produce a Prime Number? What if the Prime is just really large?