# 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

Music by Alan Stewart

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**Runtime**: 8:40- numberphile prime numbers proth prime

mehdi rejali36 minutes ago^{+1}does this mean 3 is a proth prime?

1 x 2 + 1

warspyking3 hours 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 Ladell4 hours 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 hours 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.

GENIUS6 hours agoHere's a fun little exercise:Prove that 78557 will never produce a prime when taken in the form :78557*2^n+1

Hedning13908 hours 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...

rlt15215 hours agoTruthiness- I don't think I have ever heard that term on here before :)

msolec200018 hours agoIt's always nice seeing Dr. James Prime doing his thing.

Georticon YT19 hours agoThere is always a Rubik's cube in the background...

Hands of Science20 hours agoI enjoy your enjoyment of math far more than enjoying the math itself.

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

T PermDay 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 BonarotiDay agoRubik's cube!!! Yas!

NGEternalDay ago9*17, fyi

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

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

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

Peter KovacsDay 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 DohnalDay 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:Day agowhat's the truthiness out of 10?

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

Jiggerjaw2 days agoTruthiness. Nice.

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

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

Blur 4102 days agotruthiness, is that a colbert reference?

Abid Abdullah2 days 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 days agoColbert helps get rid of political candidates, I reckon?

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

InuYasha66512 days agoJames Grime is my favorite!

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

C. Ray2 days 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 days agoI’ve never seen someone so excited about numbers

ronindebeatrice2 days 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 days agoTruthiness? Is it Parker's truth?

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

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

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

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

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

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

FaRo2 days 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 days 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 days agoCancelling bitcoin mining program and firing up smallest-k finding program right now... I'll get back to you.

Sharon Klinkenberg3 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 😀

biokaese3 days agoParker Truth

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.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.

Human3 days agoI have no interest in math whatsoever but I watched your videos cuz they are so interesting.

Ashwin murali3 days agoThis guy looks like Thom Yorke from Radiohead

Gergő Turán3 days ago*Just a hungarian guy's patriotic comment flying through the screen*

Rosie Fay3 days ago0:22 2016. So why wait a year to make the video?

Vesania_63 days agoyou are so cute and an excellent teacher 💋

Alexey Akimov3 days agoWhy 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 Master3 days agoI used to be in my prime when I was on prime time television talking about prime numbers.

hewhoamareismyself3 days agoI 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)

LaGuerre193 days agoGrimes on primes

11Anti113 days agoI 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?

Tom93583 days agoWhy not just prime95 or the corresponding GPU program?

11Anti113 days agoI mean sub-project, sorry if that wasn't clear.

Vivek Ranjan3 days agoHow do we verify million digit as prime?

Tom93583 days agoVivek 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.

LightGuy1013 days ago^{+2}All these Primes and I'm still not Optimus... I know...

Wood Croft3 days agoC🤨L B E R T

Ray Dillon3 days agoWow, your excitement drew me in.

Djorgal3 days ago4:04 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 Blur3 days agowhat is the deal though? why does this matter?

Hey Guys, This Is My New Name3 days ago^{+1}is mayonnaise a prime number?

Matthew Fuerst3 days agoDo 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.

Echo5Delta3 days agoIf 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-Bro3 days agoWas, was that a parker proof?

Muhammad Arifur Rahman3 days agoIts so good to see Numberphile is #27 on Trending. 😁

orthoplex643 days agoI clicked this video because James Grime is worth my time

Tom Heyman3 days agoI wish I knew what any of this meant

Cowslayer78903 days ago^{+1}So if we eliminate another candidate we can get an even bigger prime?

Brandon Lane3 days agoI already have GIMPS, time to add another program for these types of primes

Jacob Miller3 days agoPrimes suck🤘

rtpoe3 days agoAs I'm watching, it's #27 on Trending. Has a Numberphile video ever gotten higher?

James A Clouder3 days agoTruthiness, truly the most scientific term ever uttered.

Jeremy Gant3 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?

Thoughts?

Jeremy Gant2 days ago^{+1}A number that has more factors than all the numbers before it, i.e. 12, 5040, etc

Tom93583 days agoJeremy Gant how do you define antiprime?

Joe Previdi3 days agoThe truthiness plug was A grade!

Lucas Westfal3 days agoWhen the results are no longer reliable?

phuaxy3 days agoI always wonder if the mathematicians know all these numbers off the top of their heads

Czeckie3 days agoare there any (inconclusive, heuristic) reasons why these five shouldnt be Sierpinski numbers?

Woodenwakka3 days agoHow 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 Tulsa3 days agoSolve that damn cube already! Ha

dartagnanx13 days ago^{+1}Why does 78557 seem truthy. Please do a video on that! Great video as usual!

Random Kanji3 days ago"𝑇𝑟𝑢𝑡𝘩𝑖𝑛𝑒𝑠𝑠"

CrypticRaps3 days agoWhat 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!

GIANNIS LYMPEROPOYLOS3 days agoGOOD..JAMES IS MY FAVORITE ON NUMBERPHILE...!!

Alois Mahdal3 days agoClassic Numberphile video. I've been missing these!

Harinandan Nair3 days agoOne thing... What course should we take in order to study the stuff u guys talk abt on this channel?

anony mous3 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 mous3 days ago^{+3}It was the name of the project, yes.

wolfedog993 days ago^{+3}Is "Seventeen Or Bust" the name of the project?

The placement in the comment feels syntactically odd.

Nicholas Hartle3 days ago2 x 2^3 + 1 = 17. Could have just used that as your example.

Simon L3 days agoYou guys really improved your paper!

Simon L3 days ago^{+1}Add a public comment...

Lapis Houndoom3 days agoThe hello internet poster in the back is the 10... ^ ... Prime! thing

kungfuasgaeilge3 days agoThat's Numberwang!

Nadeem Hussein3 days agoCan someone show me the link to john's proof?

Deboogs3 days agoClassic Numberphile material.

Joel Grayson3 days ago^{+1}More James Grime! THANK YOUUUUUU

IAm NAU3 days agoIve 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.

rubikschu3 days agoSolve your cube, it's making me uncomfortable.

Arokace3 days agoReally 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 Ten3 days agoDid you upgrade your paper? Looks like it has some fancy ridges

JEFFF !!!!!3 days agoObserve: K = 0

K * 2^n + 1 = 1

You're welcome