Why Do We Need a 23 Million Digit Prime Number?

Finding the biggest prime number might not only have applications in computing, it could also win you some serious money. Here’s how.
The ‘Ham Sandwich Theorem’ Will Change How You See the Universe… Seriously - • The ‘Ham Sandwich Theo...
Read More:
How a FedEx employee discovered the world’s largest prime number
www.popsci.com/worlds-largest...
“Pace first became interested in searching for primes back in 2003, when he read an article about the discovery of the 40th known Mersenne prime- a special kind of prime number, and a rare, numerical creature.”
Largest prime number ever found has over 23 million digits
www.newscientist.com/article/...
“The new prime number, known as M77232917, is one million digits larger than the previous record. It is also a particularly rare type of prime called a Mersenne prime, meaning that it is one less than a power of two.”
Welcome to GIMPS, the Great Internet Mersenne Prime Search
www.mersenne.org/
“GIMPS was founded in 1996 by George Woltman. The software ran on Intel i386 systems using hand-tuned assembly code for the critical calculations, resulting in highly optimized Lucas-Lehmer code. It wasn't long before GIMPS had its first discovery in November of that same year, showing the effectiveness of distributed computing in harnessing spare computer cycles in a coordinated effort.”
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[@BobMcCoy]

*Password Requirements in 2020 be like*

[@TommoCarroll]

haha, so true!

[@justsomepandawithinternet]

Lol

[@Master_Therion]

You know what will really transform the world? When we find the Optimus Prime.

[@mipmip4575]

lol

[@PeterNg93]

We did find him. We made a few movies about him saving earth a couple of times.

[@abhi36292]

lol ri8

[@TommoCarroll]

Bit of a side note: I'm not ashamed to admit I'm so excited for the bumblebee movie - getting some real good Iron Giant vibes!

[@ryangraham71]

Easy brother the time isnt right yet

[@SPcamert]

My coworker said "Shouldn't the prize also be a prime number?"

[@nidhigoyal6558]

It's more like a lottery than Bitcoin mining.

[@swaystar1235]

bitcoin mining is a lot like lottery too tho

[@zodiacfml]

Crypto mining is lottery. The computer does the guesses and hope to be right. It is just doesn't appear like with the mining pools.

[@killer30556]

Free lottery tho

[@BothHands1]

killer30556 not free, electric cost of running a powerful GPU on max is not super cheap, plus it shortens the life of your hardware

[@emzy6]

most PoW mining is lottery based

[@tabel4844]

Girlfriend: "What's your screen unlock password?" Me:

[@aitbeq]

The information about the prize for 100M digit prime is a little misleading. It is not that simple. The prize of 150000$ is offered by another organization not GIMPS. If you happen to find that number using GIMPS software, they will award you with 50000$ and submit the number to that organization that originally offered the 1500000$ prize. You may think, well, I will submit directly to original organization and get my 150000$. Not that simple. The rules to get the 150000$ is to publish a paper about finding the number and getting it reviewed and confirmed. GIMPS will take all that work to itself and reward you with 50000$ almost immediately, while the other way may take you years to get your hands on triple the bounty.

[@debaterofeverythingpresent2775]

I think it's fair enough. It's their programme and they will do the working. The real question is whether prize is limited to the U.S.

[@sjakierulez]

50000 dollars, and what do you have to do for it? I thought I as a Dutchman was greedy but damn, youre worse than Uncle Scrooge

[@aitbeq]

beunhaas who the hell is saying this is not fair? All I am saying is that it had additional steps or that GIMPS does not give 150000$ as video might mislead viewer. I would be find with the video if they did not mention 150000$ alongside with 3000$ prize. If it was like “3000$ for any new Mersenne and 50000$ for 100M digit number from GIMPS and 150000$ from original prize” that would be perfect. So, you, a Dutchman or Uncle Scrooge, keep your greed status to yourself.

[@sjakierulez]

Aitbek I know I was high, but I completly misread your comment, I'm Dutch

[@kujmous]

In binary, 2^n - 1 is written with 1 written n times. If n were not prime (if it were 12 perhaps), then the number is divisible by any 2^m - 1 where m divides n (2, 3, 4, and 6). This is why Mersenne primes require prime exponents.

[@Theo0x89]

(2^(mq) − 1) / (2^m − 1) = 2^(m(q−1)) + 2^(m(q−2)) + ... + 2^m + 1 en.wikipedia.org/wiki/Geometric_series#Formula

[@benitollan]

I totally just understood that. I promise.

[@sjakierulez]

Yes

[@hardiksharma5441]

Friend: Give me your password (While holding a gun on my head) Me,an intellectual: .....................

[@TommoCarroll]

Did you just give us your password? Cheers Hardik!

[@w01dnick]

Friend with a gun at your head?.. You have really bad friends.

[@RizzoDaManiac]

You should go to meme prison for this horrible misuse of the “me, an intellectual” meme

[@Nightmare.853]

I watched the whole video and understand nothing haha I'm so smart

[@gheedm.9678]

I love your channel! Keep it up!

[@TommoCarroll]

As Mallory said: *"Because it's there"*

[@avochanneladrianvalolonan3258]

Prime numbers remind me of the sci-fi horror movie "Cube". Underrated gem

[@Scarletraven87]

To get the grasp of 23 million digits, I had to think that we never hear of numbers past the 9 digits.

[@pierreabbat6157]

They're also used for (non-cryptographic) pseudo-random numbers. The Mersenne Twister is a generator that consists of an LFSR whose period is a Mersenne prime.

[@Mothalas]

The number 23 was always my favorite number. I never knew why. I always wondered why it was important. I would say 23. When asked why I would say I don’t know. As time went on I likes how 23 was lebron James number when I was into basketball. When I was into space and science I liked it cause the earth was on a 23 degree angle so perfectly that we have seasons and the earth has the ability to sustain life. As time went on I saw it more and more. Videos I watched where 23 mins long. My dad won 10k dollars from the loto from playing the number 23. It just creeps it’s way into my life. It’s so strange. Btw I am not born on the 23. But my dad mum am all 3 grandparents are. April 23 August 23 November 23 December 23 My dad won the loto on the 23 of November. It is so strange. And now a 23 million didgit prime number W H A T

[@mikew6933]

Heh you would like Joel Schumacher's film from 2007! ;)

[@TheTechAdmin]

1:03 because you still have your silhouette here, I thought someone was standing behind me and almost broke my neck with how fast I whipped my head around.

[@l0g1cseer47]

Nice one!

[@tatjanagobold2810]

I thought this was going to involve the Riemann Hypothesis which was claimed to be proved only this week😂

[@azizuladnan2957]

Oh my, I haven't heard the term "Prime Number" since like... a year ago XD

[@RevJynxed]

It's not like they're hidden, they're just too damn big to prove.

[@rray2526]

Obviously just to claim more money from that one website I forgot the name of

[@andrewkelley7062]

Has anyone tried 3 along it's line minus 2 and plus 2 then factoring out all it's repetitiveness.

[@riku9745]

Solves Riemann Hypothesis. Discovers 200 new prime numbers, collect prize money for primes, then reveal you have solved the Hypothesis for another million.

[@ankitk5530]

You want the largest prime number ?Hold my bear, let me grab a calculator.

[@BeauDadda]

Is the gentleman (rainman was inspired by) still alive and do you know where he is physically or ghostly??

[@ONDANOTA]

This is like the X.-factor. you take a gigantic number of useful people/computers and make a lottery in which only one wins and all the others contribute to the project without seeing a penny

[@TheJoeSwanon]

Yeah my brain clicked off within 30 minutes of this video

[@user-zm5wr2zw2t]

We don't, it just exists because its want to

[@MrMeeseeksthe1st]

Well shit, this guy is only half an hour away from me lol.

[@nonothebot]

Is there a GIMPS module for BOINC ?

[@bueb8674]

Sadly no, it's its own specialized program (Prime95). There are some other projects that search for different kinds of primes on BOINC though right?

[@beenaalavudheen4343]

0:24 he obviously hasnt seen cowbelly say gucci gang a million times

[@josephruiz8495]

He trying to push grimps on us but dosent use it himself

[@nakiaudaku8691]

Even it's name is long...

[@lifethrownoutofthewindow]

When you run out of passwords

[@spontaneouscombustion5014]

I don't know why but the name pentatrixillion makes me think of a googolplexian to the 534 nonillionth power.

[@TheBaltorusite]

What the hell, theres no upload notif yesterday and you uploaded today? Wow, even Infographics Show uploads like daily with bunch of videos

[@hasanmertsk]

Bruh chill

[@im_aleey]

What's the link for that software again?

[@GreatOutdoors1]

It's in the description.

[@MustyMouse]

When RSA gets broken by quantum computing, just adding larger primes isn't going to help in any way... So realistically, these primes will never be useful, according to Seeker at least.

[@silverzero9524]

True. But we can still search for bigger primes for fun

[@spontaneouscombustion5014]

This is me thinking of big numbers.

[@ryanschroering3606]

Couldn't you do M(M7723917)?

[@takyikobbie3679]

Wooow I always thought maths like this were useless u just proved me wrong

[@padalex18]

Is that money before or after tax

[@zodiacfml]

3:33 download the software? some use the software to find weaknesses or break a computer. Aside from wear, you'll be paying a bit more for electricity

[@bueb8674]

Usually to test stability (look for errors) when overclocking. If you're a computer enthusiast and know what you're doing, you're probably ok (read: proper cooling). If you've never opened a computer to blow the dust out and use the stock heatsink, don't run it.

[@francisdo6990]

wait, that's the guy from nvidia

[@jesusroks545]

I understand so so so little of this video. Sounded like a different language

[@geewhizzzz9387]

Seeker: prime numbers...blah, blah, blah.... Viewers: started computing if its true...lel Good luck guys! XD

[@kazutohonouin6217]

I didnt get it, can someone explain to me what is this prime and why it is cost that much... Yup the video said it use for encryption.. But how?

[@fossforever512]

Kazuto Hououin a prime number is a number you can’t divide by any other number but itself and one and end up with a whole number. For example 7 is a prime number 7/1=7 7/7=1 But there are no other number you can divide 7 by and get a number that doesn’t have a fraction in it. The reason it’s useful in encrypting is that two prime numbers multiplied by each other equal a number that is only divisible by itself, 1 and the two primes that it’s the product of. For example 3*7=21 21/21=1 21/7=3 21/3=7 21/1=21 But if you try and divide 21 by any other number it will end up with a fractional part. Meaning that if you use a key for encryption that is the products of two primes then to ever unencrypt that key You need the two prime numbers. And the reason that is so good is because there are so many prime numbers it’s practically impossible to just guess the right two!

[@kazutohonouin6217]

@@fossforever512 ooohh i see now i get it. I have some more question. Why someone or other ask and buy for it? I mean if they just build a lots of computer then they can search for it for themselve? Edit: btw the video said only 50 mersenne primes found? What was that, is it the same with prime number? and why it so hard to find it? Is the latest computation machine can't find it in just a little amount of time?

[@GreatOutdoors1]

@@kazutohonouin6217 These really large primes are for research purposes only. They are way bigger than the ones used for encryption. They offer large prizes in discovering the really large primes to help drum up interest.

[@kazutohonouin6217]

ehhh.. i thought it was something too important or some secret. Anyway, big thanks for answering

[@fossforever512]

Kazuto Hououin as someone else said they’re offering awards simply to get people more interested! The mersenne numbers are just a type of prime numbers So there are a huge number of primes but only a small number of those are mersenne primes Mersenne primes are defined as being a prime number who equals (2 to some power) - 1 So for example 7 is a Mersenne prime because it’s a prime number and it’s equal to (2^3) -1 But 53 is not a Mersenne prime Because while it IS a prime the closest power you can raise 2 to to equal 53 is 6 but (2^6) - 1 = 63 not 53 Making 53 a prime But not a Mersenne prime

[@neutrino3869]

I am Optimus Prime. Calling all autobots.

[@shrewd407]

Do I need powerful computer to find prime number or I could just use my laptop?

[@bueb8674]

The more powerful the better. My i7-7700HQ laptop takes about 15 days to test 1 number. There's another test they do: double-checking old numbers that were first done about 5 years ago, at the time they were at the 'front of the line' of numbers being tested, but now they're relatively easy to check quickly. It still helps the project, but there's practically no chance of winning prize money(unless by some freak event the first test was corrupt and you find one that was actually missed) So if you have a slow computer and want to just help out, double checks are good. If you really want to try for the prize, as slow as it may be, that's up to you lol

[@Juniperus_Godegara]

It will help to get out the Cube.

[@shashank8725]

Half the times I don't understand these videos, for dis one i cudnt get my eyes of Einstein's face.

[@yoleaf7313]

um by now its 24-25 million digits.

[@tramsgar]

A: "To win a price"?

[@ericmcgarrh7551]

Once the quantum computers are running, you won’t need our help.

[@darkspace5762]

I thought there was no algorithm to prove a number was prime after X huge number of digits. You could only say probably it was prime?

[@CrashM85]

Mersenne primes found using the Lucas-Lehmer primality test are an exception and a guaranteed to be prime.

[@darkspace5762]

@@CrashM85 That's good bro.

[@spaghetti7782]

Nice shirt

[@thatoneguy_0218]

Is there not a more efficient way to do this?

[@Cat-ct9hn]

ThatOneGuy _02 We don‘t really know.

[@TheVineOfChristLives]

For all of Nerdy eternity!!!!!

[@phoule76]

I only count using numbers that have their own nicknames: Uno, Deuce, Dozen, Baker's Dozen, Fitty, Gross, M77232917... (I skipped a few)

[@tabishkhan6292]

Don't you think, this software could be only out for public just to crack prime number, so then can break already encrypted data. Cheers

[@user-vm9sz6l02q]

Quantum computing

[@Daniyalshahid1]

I want that shirt so bad!!!

[@jaymethodus3421]

Is it called GIMPS software because it slows down your computer

[@bueb8674]

The program (Prime95) is meant to run at the lowest priority it can on your computer, meaning if your computer needs to do anything else it stops Prime95. So unless you're really doing something else that needs a good portion of cpu, like gaming, it shouldn't slow it that much. Though for fun if you want it to really freeze, you can set the program's priority to 10, then your computer will prioritize it over pretty much everything and become non-responsive.

[@snitox]

It's fucking 5 am

[@khgrewjgh4074]

Maybe its a copy-paste numbers

[@kiranunity]

Its just number. We cannot use it or read it or write it . So what's the point of getting such huge number? I think you should talk technology behind it

[@filipsperl]

Just like many others on this channel, this video was clickbait. I have gained zero knowledge. The question was "why do we look for primes?" and the only thing that you said was "if you find it, you get money". That's obviously just a motivation to get more people to join the search and doesn't tell at all, what the point of it is. And by the way, the chance of finding the prime is really really small, it's basically like a small lottery which you pay for with your prossesing power.

[@drewviz5102]

Tony Stark: Hey Strange, what are you doing? Dr. Strange: I was looking at all possible futures of the fight. Tony Stark: How many did you find? Dr. Strange: 2^84********** Tony Stark: How many did we win? Dr. Strange: 1 Tony Stark: So basically we have 2^84**********-1 possibilities of losing.

[@wa54]

Who already knew about this from an episode of QI

[@albertosalcedo4522]

Where's my prime95 squad at

[@malkilia]

Bitwalking shit brought me here

[@xav9159]

Woah 26dec is my birthday

[@Discusser]

Why the hell not?

[@jonathanray4598]

You should plot "THE CROSS" ...vertically 1,2,3...then horizontally 1,2 3...and then use prime numbers like 677 is the 123rd prime number. Then add 123+677=800 then 123+677=800 ....now that's 1600 total plus 11 ( two straight lines that make up the Cross) Now 1600+11=1611. In 1611A.D. The Holy Bible was finished!!!

[@hashimwahbi]

I couldn't carry on watching after GIMPS

[@redfalconsmdx]

Well... I wonder if GPU accleration works...

[@CrashM85]

No it's Integer math rather than floating point math. CPUs are best with Integers and GPUs are better with floating point numbers.

[@bueb8674]

www.mersenne.org/various/math.php#lucas-lehmer

[@moimeme7839]

I prefer a 23 millions bank account

[@spontaneouscombustion5014]

Could decimals be prime numbers? Could fractions be prime numbers? Could a prime number have 1 googolplex digits?

[@sylviaelse5086]

No, no, and probably.

[@stevenvanhulle7242]

Sylvia - I'd say most likely to that last one.

[@PvblivsAelivs]

@@stevenvanhulle7242 The last one is guaranteed. For any number n, there exists a prime p, such that n < p < 2 * n. (In practice, primes are far more frequent.)

[@stevenvanhulle7242]

@@PvblivsAelivs Agreed. I remembered Bertrand's conjecture, but I forgot Chebychev proved it.

[@shawnli9775]

Excuse me, GERMANTOWN? Why is that a town name?

[@oujisanhikari18]

Hi.. i am anhedonic. Can you talk about anhedonia?

[@max__pain]

They could, but would you enjoy it?

[@fossforever512]

I have that shirt!

[@michaelszamocki5587]

So if I take 2 to the M77232917 power like the entire 23 million digit long number and subtract 1, is that a bigger prime number? Since the exponent is prime? Or am I thick.

[@ajgm3974]

I bet i can find you a trillion digit prime... And u pay me billions

[@PeterNg93]

Because we like numbers.

[@TommoCarroll]

Nailed it!

[@KarrasBastomi]

Please don't download GIMPS if you didn't know what it is. Lucas-Lehmer formula is very CPU intensive, it will shorten lifespan of your device!

[@bueb8674]

Debatable, with actual proper cooling it's not that bad. Most laptops and graphics cards don't even have their fans turn on until 50-60 degrees. Mine is just over 60, fans hardly audible, with gimps (Prime95) running. But say, if you get a new computer, and don't have anything better to do with the old one, then why not run it?

[@KarrasBastomi]

@@bueb8674 yeah... But continous load will degrade other components, power delivery is the most common victim. And remember, not all average joe know how to check their PC's health.

[@jameslane2615]

Short answer... no.

[@raz0229]

GIMP??? *_I Already Have That!_* Isn't That The Photoshop Software?

[@kevinfidler6287]

Thought it was a character from the movie Pulp Fiction...

[@ShalK423]

I have that shirt :)

[@rhysabel2276]

There are only approximately 3.0x10^80 particles in the observable universe. This number has no real world practicality at all

[@NicholasHickam]

Not yet possibly.

[@TheRealMisterBam]

maybe virtual practicality.

[@aaryanbg]

i understood the whole video but i sorta started to lost interest at 0:00

[@the1game50]

I don't think it's interesting to find large number numbers..what matter is how !

[@Phil-D83]

Because science

[@chiefanon789]

Just put 1 a bunch of times duh

[@AsphaltAntelope]

Or download World Community Grid and help cure cancer, AIDs, malaria etc for no reward instead of chasing a prime number for cash.

[@01codblackops]

a bigger one is just found m82589933

[@LanDiEvil]

This guy is a software pirate

[@harshyadav9220]

Great 😀😀

[@lastshadowartist]

ai is not out of reach

[@Karan856r]

That's why i hate maths

[@1HololensfansOfNaruto]

What's the probability of you winning the $150000 ? You will know when you win;")