The Man Who Found the World's Biggest Prime - Numberphile
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- Опубліковано 21 жов 2024
- There's a new "world's biggest prime" and we speak to the man who found it, Luke Durant... More links & stuff in full description below ↓↓↓
Also in this video are George Woltman (from GIMPS) and James Grime.
Full Durant interview: • The World's Biggest Pr...
Full Woltman interview: • GIMPS's George Woltman...
Press release on the prime discovery: www.mersenne.o...
The Great Internet Mersenne Prime Search: www.mersenne.org
See our full playlist of Mersenne Prime videos: • Mersenne Primes on Num...
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Durant Interview: ua-cam.com/video/aJHPDGj93-w/v-deo.html
Woltman Interview: ua-cam.com/video/9ML2q0q53io/v-deo.html
Full playlist of Mersenne Prime videos: ua-cam.com/play/PLt5AfwLFPxWKsTwVXpLscZdfiiqAkkGCA.html
It could have been me! One of the exponents I tested on GIMPS, using my home computer, was only about 500,000 away from the bullseye.
Ah well - congrats to Luke and all the GIMPS team. Well deserved glory!
The next one is yours!
Some deserve glory, others glory hole!
Matt Parker: goes on holiday.
* new prime discovered.
Matt Parker: oh, for god's sake - Lucy, get the camera...
MP released his video on the new Prime from holiday yesterday! 21/10/24.
@@Stephen_Lafferty TBH it was a bit dull.
ok dude, but where is Matt Parker in this video? this comment doesnt make any sense here
He's often on numberphile, especially with regards to prime numbers@@JacobsKrąnųg
What a tragic waste of resources! Those computers could have been used to figure out the best left right shooting survival game ad to serve us before this video.
or it could have made an uncanny valley picture of a dog with one and a half heads
🙃
yeah, many people here support "green" bs, but no one is against things like that - discovering primes that huge is basically pointless and it produces so much CO2.
James Grime never ages
@@adipy8912 he’s like the Paul Rudd of maths
In a dark & dank attic there is a wicked portrait of him with all the vile sins of the world etched on his corrupt physiognomy: such as 2+2 = 5; pi is the solution to a polynomial equation; I've just proved the Riemann Hypothesis, etc, etc, etc!
Paul is always in his prime.
But he melts in the sun.
That's because he's high on enthusiasm.
Bro had that $NVDA money
Before they were the most valuable company
My new password
A special kind of password where you can openly share it without fear, assuming it has to be typed by hand.
Mine too!
111111...111 in base 2 😂
Then change one randomly selected digit, just to throw malicious people off.
passwords missing a capital letter
Prime Time with Mr. Grime, how sublime!
and just in time!, and i couldn't resist my urge to chime in rhyme, hope that isn't a crime
Luke, use the brute force!
"It's fun!"
Wow! I wish I had a spare 2 million US dollars to spend on fun. 🤔
Great stuff. Puts faces to all the names I've been seeing.
I contributed to GIMPS in the early days, but even back then it took a long time to test primality. The numbers were smaller, but the computing power was lower and the software was less efficient. I shifted to another project and found a prime with over 100,000 digits. That's nothing today, but back then it was somewhere in the Top 100 largest primes known at that point. I've drifted away from those projects, but I still have that 100,000+ digit prime with my name on it.
Good for you.
Umm….I have questions but not about primes.
I hope you aren't being nosey.
weird because on google image search he looks normal otherwise... Did he know he looked like that?
@@anticarnick who k'nose.
I've been waiting for this vid since yesterday.
We got a new Mersenne prime before GTA 6
Also before The Elder Scrolls VI
Also before Silksong
@@prochinczyk2 Also before the Half Life 3
Doors of stone
A somewhat tangential question, but possibly worth a video sometime: to what value of N do we know all of the primes ≤ N?
there’s infinitely many primes, so there’s no such N
@@joseflat For any N there is a finite number of primes less than N.
That is a great question. If you look up tables of the pi function (prime counting function) you can find various webpages with tables but they don't seem to get very far and past that there are large gaps.
I think we have found all of the primes up to around 10^20. For numbers larger than that we have only discovered primes of special forms.
@@GreatOutdoors1 Thanks, that was what I was looking for. So to about the level of the 2nd highest-known at the end of the 19th century. (2^127 - 1) got in too early by the progression.
2 million $?! damn. ok. ok.
dr disrespect did nothing wrong
@@cz19856 Pedo
@@cz19856neither did Uncle A
Smooth Priminal
Im getting the sense that the supercomputer is the real achievement
The certainly are contributing to climate change with the huge amounts of energy they use.
Same. The take away here could be “primes are neat” or “if we can calculate a distinct number 20 million digits long by stringing together super computer what else can we do?”
The way he casually says less than 2 million really shows that he just threw money at the problem like it doesn't matter to him.
Shouid hsve checked his spam folder for those other 2 smaller primes
*flipping through mail*
"Scam... Scam... Bills... Scam... World's largest prime... Bills..."
One day in the future someone is probably going to need a perfect number for a specific physics discovery and we'll be ready
Those numbers are so long they are meaningless in physics.
I was playing around with shift symmetrical tensor fields, just toy model stuff. When your tensor transforms as T->T+M(x) where x is your coordinates.
Turns out that the only way for this to be generally covariant (i.e. work with gravity), M(x) must be a magic square (or the higher dimensional equivalent.
The dude must have a prim(e)al instinct for this. Please make him Primeminister.
Thank goodness you got in with the terrible jokes before I did! :o)
@@andrewharrison1194 To my defense: I was a little bit primed on this one!
As long as he’s not a suprimacist.
I have been using the GIMPS program for several years at home and my PC struggles along for a couple of weeks to verify a value for the exponent, n in the Mersenne Prime relationship (p^n-1).
The software runs in the background and pushes the CPU usage on the PC to 95%.
Boo. 🙂
"ya know" - Luke
Off topic: Still unbelievable that the sum of the reciprocals of all prime numbers (Sum of 1/primes) diverges to infinity.
The sum of the reciprocals of the Mersenne primes is certainly finite though :)
@@ronald3836 lol
@@ronald3836Oh yeah? Prove it.
@@HellHeaterthe sum 1/2^n converges absolutely (just a geometric series), so 1/(2^n-1) converges absolutely (ratio test) so every subseries must converges. In particular the subseries of reciprocals of Mersenne primes converges.
Compared to the billions that big companies spent on large language models, 2mil doesn't sound too bad for finding the largest prime
Well, except it's completely useless
Except those companies are developing products and essentially investing into future profits.
But yeah. Big numbers are cool too.
Not? It is shocking to me! Beyond imagination.
@@Tatman2TheResQmore like stealing from artist, musicians and everyone else for future profits.
@@lem0nhead84 As opposed to Large Language Models, which are helping future doctors cheat so they can spend more time drunk. Great job guys.
I’m always excited anytime GIMPS finds another!
Congratulations Luke! Great job.
Please make the computerphile video about generating number that big
I like that the youtube algo breaks up giving me "game industry rage" to give me actual interesting things like this
Paying $2 million to get your name on the history books of maths seems like a fair deal to me.
not many people read history books about primes. The ones who read, tend to ignore names.
@jasertio you're not a financial planner are you😅
@@DekarNL What do you mean?
there has been such a long gap since the last new longest prime that kids today heard about a new prime and asked whether it came in lemon and lime flavour
For a while, I had GIMPS program run on my dorm computer during my college days.
This guy is 100% the guy I would paint if you ask me to draw a guy who finds a Prime number 😅
What is the best way to check if a candidate number is a prime number?
there's a function that evaluate to 1 only on prime numbers and doesn't take an insane computational power
"World's biggest"? So there's a different biggest prime number on Mars?
it's the biggest currently known by humankind
Can't we just double it and add one for another prime?
The exponent needs to be a prime. In this case, 136279841 is prime; 136279842 won't be.
On top of that, it doesn't work for all prime exponents: 2^7 - 1 is prime, but 2^11 - 1 is not.
There will be a book on this prime number
The number is a book
2 million wtf
putting those nvidia stocks to good use :)
Keep in mind he was spending the money for the last 2 years Nvidia only blew up in the last year
Well done to Adam Ant 🎶Stand and Deliver 🎶
LOVEBITES - Stand And Deliver (Shoot 'Em Down)
And yes, I know the old Adam & the Ants song... was even in England and that time!
First Largest Prime Number in 6 years!
6:25 "We had missed a couple of primes, because they had sat in the database"
....
"What's the point of this?" #1 Fun. #2 Pushing the boundaries of how we resolve difficult problems. We could ask the same thing about space exploration, and then look at all the actual practical innovations that came out of it.
Do the primes *need* to be found in sequential order ? Or can you randomly guess at numbers and check if they are Prime.
Amazing work! Now find a factor for 2^1277-1.
I feel like google could throw their weight behind this and get like 5 new ones by tomorrow.
I think the benefit is experimenting with computation algorithms and processes.
I want to see the picture in James's attic.
Prime95 still sits on all of my PCs. I use it only to punish and torture my CPU - when I need to see how hot my CPU could get with the cooling I have. Too bad we can't work any real assignments in the time used when "torture testing" with Prime95.
In my mind he did nothing impressive whatsoever. He didn't come up with a new technique to search for them, he didn't design the hardware that performed the search (apart from his prior work for Nvidia, which I won't disparage, but which wasn't done specifically for this project and may or may not have helped at all), he engaged in essentially no intellectual labor aside from navigating some red tape... he just paid an amount of money that would be life-changing for the rest of us. That's not a feat of mathematical understanding to brag about, that's being lucky enough to be rich.
Exactly. It's kinda fun and a lot more defensible when it's some random person running it on their home computer but this just feels... kinda awful. He basically just bought a Mersenne Prime for ~2m dollars. Saudi oil baron behavior.
Some other people have the capability to do what he did but they don't that's simply what he did
“Navigating some red tape” is putting it mildly. He created a one-man company to skirt licensing regulations, and even proudly admits it! This isn’t a mathematical achievement, it’s throwing money at a useless problem for bragging rights.
Very interesting.
A bit of a Lukewarm reaction he got
Curtis Cooper finally had his streak ended.
Jonathan Pace had done that in 2017 with 2^77232917-1.
Luke is the guy from Willy Wonka who bought all the chocolate bars trying to win a golden ticket
That's gonna be 136279841 digits of 1 in binary
I sense a new T-shirt being released soon!
I think about "the longest prime number" idea far more often than I should.
That dude can smell out a prime
For now!
The 52nd perfect number = (2^136279841 -1) * 2^136279840
Have they also calculated the largest known perfect number that goes with this prime?
Yes
(2^136279841 - 1) . 2^136279840;
in binary, 136279841 ones followed by 136279840 zeroes.
Just a reminder people modulus is scalar coefficient and log base equivalence is powers
The fascinating part to me is “leaving the code running”
The only thing I am familiar with is my phone which automatically stops any attempt at a “code” after so long.
Lots of code runs continuously. For example, the youtube servers, where you are watching this video being streamed from, runs continuously. The OS on your phone runs cintinuously. In fact, most code runs until explicitly stopped - eg. if you have a console and ever played a game, it will run until you explicitly close the program.
It's not a big leap to envision a custom bit of code that hunts for a certain number and then have it run until it either finds it or is explicitly stopped. Then you just never shut down your computer and let it calculate...
Your phone is constantly running code unendingly, checking for signals, checking its battery charge, etc. Machines just run code until they are manually turned off.
numberphile would go straight to the source
And yet there are infinitely more primes thereafter...
Wow $2 million is wild, I wonder how he funds it? Surely NVIDIA wouldn’t pay enough for that even considering stock appreciation?
They do pay that much. 2M is probably just the RSU hiring bonus after the stock exploded.
Bro just cashed his options
The biggest cost is the planet. These pointless pursuits is helping climate change.
@@ZER0-- i mean a single human polutes quite a bit in 80 years, just bring your rationale to its logical conclusion and... do it.
Oh, If you're the right person they do!
Similar to the development in crypto mining, kinda. Go from "some personal computers do it with free computing time" to "specialist super computers solely designed to do it".
Is it possible we missed one prime or did we check each powers of 2 ?
New worlds largest prime dropped ‼️🔝🔛
I always felt like primes are being overrated - now I know!
Luke definitely looks likes a guy who would find the biggest prime number 😂 ... he used a super computer and a lot of weed 😂
I want to see his working on paper
If I ever win the lottery I'd spend it all on finding large primes.
That and a bunch of cocaine and hookers
How long did it take?
now try 2^(2^136,279,841-1) -1
That was my first idea. It might be the next biggest.
That would be an incomprehensible leap in magnitude. I wonder how long it would take to run the check.
@@PrometheusZandskiThe nth Mersenne prime typically follows roughly 2^(2^n), well under that actually, so that number certainly wouldn’t be the next one.
@@robertgamer3112 there's no software currently that could event try that check.
For context: the idea to use the mersenne primes themselves as the exponents is not new. Let's have a notation of Mp = 2^p-1. So the first mersenne primes are M2, M3, M5, M7, M13, M17, M19, M31, M61, M89, M107 and M127.
MM2 = M3, MM3 = M7, MM5 = M31 and MM7 = M127 are obviously prime.
MM13 = M8191 is composite (338193759479 and a 45-digit factors are known, the rest is C2410, using C to signify a composite and then the number of decimal digits)
MM17 = M131071 is composite (known factors 231733529, 64296354767, the rest is C39438)
MM19 = M524287 is composite (known factors 62914441 and five others, biggest being 40 digits, the rest is C157677)
MM31 = M2147483647 is composite (4 known factors, largest 24 digits, cofactor is 646 million decimal digits... I believe it was proven composite by a PRP check, but this is already the territory where the PRP test takes days to run).
MM61 = M2305843009213693951 is too large for any currently known primality test. No known factors.
And people are asking about MM136279841...
$2 million dorras to find a number 🤯
...and he just shared it with everybody
he just let the computer run longer than anyone else
He was using 10 times more compute power than all of the other people running the software combined over the course of the last year.
Prime to what? 1 and it self. If i had a cone. One end would be pointy. What would be 1 and what would be its self. 1 would be the constant. So, the sides( pi, and, or vector). Those types of primes being used will not work in geometry. Not even in divisions or multiplications. Those are factors. Factors are the constants. Area is the it self.
the title....
How long did it take to validate? By the sound of it it was actually rather expensive.
Hang on, so for all we know, 2 to the power of n (where n is world's largest prime) - 1 could also be prime. But that number would be so ridiculously large (trillions upon trillions of digits) we wouldn't know what to do with it. Still, quite fascinating though.
so now I'm curious, if I downloaded the software to help find the next Mersenne Prime, would it be useful to start today? Or should I give it a few years for us to find the next likely candidate first and then my PC could be used to check it lol
so what does a mersenne prime transform into.. a school bus?
There are asterisks for n = 49,50,51, and 52. Can someone please explain what they mean?
I'm sorry, but $2m for bragging rights? Hmpf
good to know that the new prime was found by gimps ( ͡° ͜ʖ ͡°)
That's as closest as it gets to my bank balance 😊
where did he get 2 million dollas???
Used to work at Nvidia.
Every Nvidia employee had stock options that spiked insanely
Put $50 into Nvidia back in 2001 😉
Options, not even regular stock
Honestly, I want to get more involved in this. But I need to build a proper Linux system first to throw a GPU in to even remotely keep up with modern efforts. I’ll get there eventually though!
Hmm, sounds like a prime compression algo could use these long string carriers for token-swap compressions. ::take full Mersenne prime string and reduce to a Mersenne short form (2n-1) without the 2 & "-1"::
Fantástica noticia!!! 💪💪💪
Saludos!
Ya gotta spend money to -make money- find large primes.
How long does it take for someone to validate the primality by themselves for such large primes?
I think Matt Parker said that it was "found" on Monday, check completed on Tuesday and confirmed on Friday.
I wanna go back to the blue room :/
🎉 Yay ! 🎉
Is there an unknown between this one just discovered and the previous biggest prime discovered
Many. The Mersenne prime search isn't about finding all primes, it's a shortcut to finding very big primes while missing out on lots of primes in between.
BRAVO !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
2:30 Seeing as the index numbers of the known Mersenne primes above the 48th (2^57885161-1) aren't known for certain, how about GIMPS fills in the gaps in its search beyond that one?
They are, that is part of the project.
Did you check 2p+1? It used to work 50%of 100% of the time when I was taking abstract math in college 😂
In my experience, 6p±1 is more reliable.
But we have no efficient primality test for 2p+1 where p is a Mersenne prime. We have an efficient test for the Mersenne primes themselves, which is why we look at those.
why all the love for 2^n -1? is there any particular reason we're not looking at 2^n +1?
2^4 -1 is 15, not prime. but 2^4 +1 is 17, that IS prime.
why are we only looking in one direction from the powers of 2?
2^n+1 can only be prime if n is a power of two, or zero. They are known as Fermat primes and they are searched for, but there are only six known, all small.
2^n -1 is popular because there are efficient tests for primality of numbers of this form (Lucas-Lehmer test). 2^n +1 can only be prime if n=0 or n=2^m. These are the Fermat Numbers. They are prime for m=0,1,2,3,4. These are the only known Fermat primes.
2^n - 1 is prime => n is prime
the primes of the form 2^n - 1 are Mersenne's prime
2^n + 1 is prime => n is a power of 2
the primes of the form 2^n + 1 (2^2^p +1) are the Fermat's primes
Big deal.
What's the largest Mersenne prime found using a domino computer.