# 78557 and Proth Primes - Numberphile

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

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Editing by Pete McPartlan

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- numberphile prime numbers proth prime

Doubtful Guest5 hours agoI'm never going to use this maths.

driven78921 hour agowho care about Proth Primes?!?

mienzillaz2 days agoSo where is that glory for Hungarian..? I don't know his name.. some guy.. pfff

Shiv Service6 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 ☘️

gluino8 days agoJames Grime is my favorite in Numberphile.

tomvondeek15 days 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 achternaam2115 days 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...

Lanetwin15 days ago@numberphile solve the dang cube already😂😂

Dennis E15 days agoDoes Steven Colbert know there are prime numbers named after him?

Kevin Zimmerman18 days agoIs James Grime single?

A Random TASer19 days agoTwo plus two is four minus one that three quick maths

PradeepKumar Rajendran21 day 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!

Sort Tricks25 days ago^{+1}/* Do not display this comment */

Joe QMonth 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 BruceMonth 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 ChakrabartyMonth 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 NicolaeMonth agoCool fact: sqrt(256-31)=15 and sqrt(256)-31=-15

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

Abhishek KumarMonth ago314 people. Why, that's PI!

Oleg ShelemetevMonth agoI am poor.

Plz give me bitcoin

1CXWehPKnWZMHpxcD9YU8RfoTuHAeXr5GC

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

*coughs*

Sorry

Periner FMonth agoЧто за кортонка???? Купи уже себе тетрадь!!

GregoryTheGr8sterMonth agoPrime numbers are so pure.

Rmac524Month ago^{+1}Have people tried to prove that some of the candidates are in fact Sierpinski Numbers?

A R V CMonth 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 RangelMonth agoIt has "truthiness" - I guess James is a fan of Colbert too

Marinela OanaMonth agoWho is watching this yesterday?

JetPackJanMonth agowhat about 19 * 2^0 ?

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

ParadoxMonth agowould $99.00 be called Amazon Prime?

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

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

Vadimeche ErkhovMonth ago^{+1}Союз нерушимый республик свободных

Сплотила навеки великая Русь,

Да здравствует созданный волей народов

Великий, могучий Советский Союз

No NameMonth agothe first pi people

Dr Ivo RobotnikMonth ago82 people with Dyscalculia disliked this video

misterjohn johnMonth ago;~)

hhh hbkMonth ago1=2

2=4

3=16

4=65536

5=?

Hussein BadawiMonth 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

pneumonosaurMonth 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 AtlasonMonth ago2 + 2 = 4

4 - 1 = 3

Quick maths

Artemirr LazarisMonth 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..

zombiebro9Month ago474 is a lychal number

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

Trivendram palMonth 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

DNVICMonth ago0*anything=0

0*2^n+1=1

1 isn't prime

there you go

Emily Nep2 months agolol e

gedstrom2 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.

ahasd2 months agoyou've got funny pronunciation of "Sierpiński"

anyway, nice video :P

jack lloyd2 months agoI had the privilege of seeing James talk about codebreaking at Salford University last Thursday

Corrodias2 months agoBut how was it proven that the one number there never produces a prime?

Olivier L. Applin2 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 F2 months agoSo Mersenne Primes are Proth Primes such that k = 1.

mrdabbleswithpotion2 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.

정제윤2 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 Kersey2 months agois there anything special about 151 136 and 287? (apart from adding the first two :-)

sammbo2502 months agoAre they just running through tons of number using 'computation' or proving it mathematically. I would hope that advanced mathematicians would prove it.

mehdi rejali2 months ago^{+2}does this mean 3 is a proth prime?

1 x 2 + 1

warspyking2 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 Ladell2 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 Holden2 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.

GENIUS2 months agoHere's a fun little exercise:Prove that 78557 will never produce a prime when taken in the form :78557*2^n+1

Hedning13902 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...

rlt1522 months agoTruthiness- I don't think I have ever heard that term on here before :)

msolec20002 months agoIt's always nice seeing Dr. James Prime doing his thing.

Georticon YT2 months agoThere is always a Rubik's cube in the background...

Hands of Science2 months agoI enjoy your enjoyment of math far more than enjoying the math itself.

P Hampton2 months agoSurely it can't be long until there's something called a "Grime Prime".

T Perm2 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)

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

J Bonaroti2 months agoRubik's cube!!! Yas!

NGEternal2 months ago9*17, fyi

Jake Fisher2 months agoIf you write a large number, no one has ever before written, have you invented it, discovered it, or neither?

amandus westin2 months agoCan't they just check the remaining candidates like they did with 78557??

K Johnson2 months agowhy are they writing on paper towels in every video...

Peter Kovacs2 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 Dohnal2 months agoBut how can we know for sure that 78557 will NEVER produce a Prime Number? What if the Prime is just really large?

//Sloth //4k:2 months agowhat's the truthiness out of 10?

Roger Hudson2 months agoIs there something special about videoing brown wrapping paper?

Jiggerjaw2 months agoTruthiness. Nice.

TheIrishMan2 months ago^{+1}I discovered the largest prime...grahams number factorial minus 1.....

JooolseMonth agoFor 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...

TheIrishManMonth agoJooolse

Youll never know!

Jooolse2 months agoThe probability that this number be prime is less than 1/(Graham's number)... so zero in short!

Blur 4102 months agotruthiness, is that a colbert reference?

Abid Abdullah2 months agoThere 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 Mendel2 months agoColbert helps get rid of political candidates, I reckon?

Invincible2 months ago^{+1}First 314 subscribers... 3.14

InuYasha66512 months agoJames Grime is my favorite!

Thomas Latkowski2 months agoI like how truthiness was a Colbert reference at the end

C. Ray2 months agoThis 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 Eats2 months agoI’ve never seen someone so excited about numbers

ronindebeatrice2 months agoWhy is the current smallest k known, whereas the others are still questioned? What's the math which proves k never produces a prime?

Pro_Triforcer2 months agoTruthiness? Is it Parker's truth?

KatanaBart2 months agoWhen it comes to finding the elusive pattern in primes, what progress has been made using alternatives to the base-10 system?

Abdul Kheil2 months agoWhy do we use differentials in multiple integral and not partials?

Pretzel2 months agoGuys 24737 x 2^2857425774215674 + 1 is prime

Steffen Widmaier2 months ago78557=17*4621; 21181=59*359; 24737=29*853; 55459=31*1789

jbkrauss2 months agotwo plus two is four, minus one that's three quick mafths

Patrick Rogan2 months agoAm I the only one who thinks Mr Grime looks like young Sting?

FaRo2 months agoIn 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.

Laatikkomafia2 months agoI have discovered a truly remarkable proof that all of those lead to a prime which this comment box is too small to contain.

Paul Smith2 months agoCancelling bitcoin mining program and firing up smallest-k finding program right now... I'll get back to you.

Sharon Klinkenberg2 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 😀

biokaese2 months agoParker Truth