# 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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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

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bscutajarMonth agoJames Grime is the guy who got me into math with his singing banana videos. My favourite was the shortest road network thing with the soap experiment about local and global minimums. That or the Benford's law thing.

Interesting NumbersMonth ago73 is my favorite number

Katpasniss2 months ago🤔

0*2^n+1 will also never it a prime number, since 1 isn't a prime number, so 0 is the smallest

Cheeseburger Monkey3 months ago19 x 2^1 + 1 = ~50% of 19 x 2^2 + 1

Vaughn Tiffany3 months agoah, yes, the most important thing. truthiness.

Venkatesh babu3 months agoThere are two fields electric and magnetic which spin orthogonally with lines of masses created out of this fields. Some primes create matter and others anti matter. Usually smaller and smaller primes interaction are dark matter. Interaction between smaller and larger primes are just ripples and energy transfer and expansion and spins. The interaction between larger primes are matter sun and stars and galaxies. Larger twin primes are always stars. Interaction of larger distant primes are always atoms and elements and chemical reactions. Galaxies are extremely large twin primes.

MalcolmCooks5 months agoI program my home computer, beam myself into the future

Hamster 54545 months agoJames is the best guy on numberphile

Or matt

Mykala Hawkins6 months agoYou have a new sub.

Lau Bjerno6 months ago"Truthiness"?? Never heard that word before. It sounds like someone trying to sell a lie.

Lego Mini Movies RJG6 months agoYou came to my school today yay!

Lux Ferre6 months agoJames Prime is back!

Strathaird6 months agoWow... Unbeleivable!

FGV Cosmic6 months agoIdiots.... K=0....

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

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

Arian.behbahani7 months agowhy does this guy look like the Walmart Yoddel kid

Gegi Zambakhidze7 months agoPrime numbers are so weird. It's one of the things that humanity still hasn't found general formula of.

Jesse Bailey7 months agoWhat if my K is equal to 0 ;)

flomeister ShadoWmAsTeR8 months agohow did the addition function appear?

Miss Boo Boo8 months agoI was think it could be 301 views

nDante Live8 months agoWhy don't try a proof like the number 78557? Thx

Kshitij Arora8 months agoCan you plss put up a video for integral((√sinx)dx)

Caesar C.8 months agoHow many possible combinations of notes are on an 88 keys piano ? As in a chord

Christian McKee8 months agoSooo... your sexually attracted to numbers?!?

Sausprem8 months agowait are they called proth primes or colbert primes?

David Britt8 months 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 Cooper8 months 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 mcheik9 months agobig fan :) can you please explain the FFT reordering trick and how it works

satish kumar Ranjan9 months agoplease make video on approximation techniques for tough number... please

James Bateman9 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

Pro100 Drozd9 months ago111 111 111 kare = 1.2345679 × 10^(16), menm jan li pral gade san yo pa yon kalkilatris?

Anastasios Chronopoulos9 months agoUhh... 0 works as a Sierpiński number

Fusion Tricycle9 months agoTry k=1

digital princesses9 months agoi wish i learned this in 5th grade

slinkytreekreeper9 months agoWhy is this important to know the largest primes with scores and scores of numbers?

abhay prakash singh9 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 Pokharel9 months ago"12345679" is quite a special number too.....

Drag0nEYE 15109 months agoIt looks like he's drawing on a trailer house curtain.

Herrgolani9 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! :)

Leo1799 months agocould you do the first 78557 people get 78.557% off?

Doubtful Guest10 months agoI'm never going to use this maths.

driven78910 months agowho care about Proth Primes?!?

mienzillaz10 months agoSo where is that glory for Hungarian..? I don't know his name.. some guy.. pfff

gluino10 months agoJames Grime is my favorite in Numberphile.

tomvondeek10 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? ^^

Bram Klinkhamer10 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...

Lanetwin10 months ago@numberphile solve the dang cube already😂😂

I dont do birthdays10 months agoDoes Steven Colbert know there are prime numbers named after him?

Kevin Zimmerman10 months agoIs James Grime single?

A Random TASer10 months agoTwo plus two is four minus one that three quick maths

PradeepKumar Rajendran10 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!

Gujarati Shayari10 months ago^{+1}/* Do not display this comment */

Joe Q11 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 Bruce11 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 Chakrabarty11 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 Nicolae11 months agoCool fact: sqrt(256-31)=15 and sqrt(256)-31=-15

Tinta Dunia Maya11 months agopleaseee. use whiteboard instead of papers. :'(

Abhishek Kumar11 months ago314 people. Why, that's PI!

Oleg Shelemetev11 months agoI am poor.

Plz give me bitcoin

1CXWehPKnWZMHpxcD9YU8RfoTuHAeXr5GC

Jack Rycroft11 months ago0:13 WHAT IF I SAY IM NOT LIKE THE OTHERS

*coughs*

Sorry

Periner F11 months agoЧто за кортонка???? Купи уже себе тетрадь!!

GregoryTheGr8ster11 months agoPrime numbers are so pure.

Rmac52411 months ago^{+1}Have people tried to prove that some of the candidates are in fact Sierpinski Numbers?

A R V C11 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 Rangel11 months agoIt has "truthiness" - I guess James is a fan of Colbert too

Marinela Oana11 months agoWho is watching this yesterday?

JetPackJan11 months agowhat about 19 * 2^0 ?

Agustin Caputo11 months agoplease watch this videos at 0.5 x speed, is hilarious

Paradox11 months agowould $99.00 be called Amazon Prime?

Leo Liu11 months agohow do they eliminate a number if they have to check all the values of N till infinity?

Joseph Sabo11 months agoMaths is everywhere you go. Snow widows homes plants eta.

Плесень и Липовый Мёд11 months ago^{+1}Союз нерушимый республик свободных

Сплотила навеки великая Русь,

Да здравствует созданный волей народов

Великий, могучий Советский Союз

Sideways Rain11 months agothe first pi people

Linus Hyper11 months ago82 people with Dyscalculia disliked this video

misterjohn john11 months ago;~)

hhh hbk11 months ago1=2

2=4

3=16

4=65536

5=?

Hussein Badawi11 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

pneumonosaur11 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 Atlason11 months ago2 + 2 = 4

4 - 1 = 3

Quick maths

Artemirr Lazaris11 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..

zombiebro911 months ago474 is a lychal number

Chris Pi11 months agoNo one reacts about the Rubik's cube stuck in the armrest ?

Trivendram pal11 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

DNVIC11 months ago0*anything=0

0*2^n+1=1

1 isn't prime

there you go

Emily NepYear agolol e

gedstromYear 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.

ahasdYear agoyou've got funny pronunciation of "Sierpiński"

anyway, nice video :P

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

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

Olivier L. ApplinYear 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 FYear agoSo Mersenne Primes are Proth Primes such that k = 1.

mrdabbleswithpotionYear 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.

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

sammbo250Year agoAre they just running through tons of number using 'computation' or proving it mathematically. I would hope that advanced mathematicians would prove it.

Why So Tense?Year ago^{+2}does this mean 3 is a proth prime?

1 x 2 + 1

Mulijadi Tee6 months agoLost Realms no

warspykingYear 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 LadellYear 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 HoldenYear 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.

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

Hedning1390Year 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...