The Man Who Found the World's Biggest Prime - Numberphile

[@numberphile]

Durant Interview: kzbin.info/www/bejne/l3urgXd9n55mY9k Woltman Interview: kzbin.info/www/bejne/b36vY6Rmpppmn9E Full playlist of Mersenne Prime videos: kzbin.info/aero/PLt5AfwLFPxWKsTwVXpLscZdfiiqAkkGCA For people who are inquiring, Luke wears some mechanical support on his nose to help with his breathing.

[@OutbackCatgirl]

it's got like, 200 views and i have no clue how youtube reccomended it to me but i figured letting you know about it might be potentially important, even if it turns out to be a bust

[@adipy8912]

James Grime never ages

[@absolutjackal]

@@adipy8912 he’s like the Paul Rudd of maths

[@ChuffingNorah]

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!

[@amguadix]

Paul is always in his prime.

[@Fleshcut]

But he melts in the sun.

[@guillaumelagueyte1019]

That's because he's high on enthusiasm.

[@661cyclist]

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!

[@numberphile]

The next one is yours!

[@jasertio]

@@guptayush179 wtf

[@stephenbeck7222]

lol how long does it take your computer to check one possible prime? Insane that Luke basically single-handedly 10x’d the rate of testing.

[@661cyclist]

@@stephenbeck7222 I did one in the 130's and it took about 6-7 weeks. And that was running almost 24/7. I don't think it bumped up my electricity bill all that much, but it sure made the room warm ... and that was in mid-summer!

[@pajeetsingh]

@@guptayush179 What on earth!

[@JMUDoc]

Matt Parker: goes on holiday. * new prime discovered. Matt Parker: oh, for god's sake - Lucy, get the camera...

[@Stephen_Lafferty]

MP released his video on the new Prime from holiday yesterday! 21/10/24.

[@AnotherPointOfView944]

@@Stephen_Lafferty TBH it was a bit dull.

[@JacobsKrąnųg]

ok dude, but where is Matt Parker in this video? this comment doesnt make any sense here

[@k0pstl939]

He's often on numberphile, especially with regards to prime numbers​@@JacobsKrąnųg

[@mostlyokay]

@@JacobsKrąnųg I see you haven't watched the video to the end...

[@Alonbs9]

My new password

[@isavenewspapers8890]

A special kind of password where you can openly share it without fear, assuming it has to be typed by hand.

[@jordandimitrov5583]

Mine too!

[@yanntal954]

111111...111 in base 2 😂

[@hewhomustnotbenamed5912]

Then change one randomly selected digit, just to throw malicious people off.

[@heiheihehehhe1]

passwords missing a capital letter

[@jwolfe01234]

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.

[@numberphile]

Good for you.

[@KNemo1999]

Luke, use the brute force!

[@rajneeshmishra6969]

😂😂😂😂

[@3Max]

Also, today's characters are George and Luke (presumably Lucas). coincidence??

[@okohsamuel314]

No it wasn't ... but instead he used Brute Patience.

[@jamppa-87-1]

😂😂

[@RickLindstrom]

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.

[@dihydrogen]

or it could have made an uncanny valley picture of a dog with one and a half heads

[@nanamacapagal8342]

🙃

[@JacobsKrąnųg]

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.

[@teelo12000]

Or it could have been used to brute-force the hash of a fictional currency ponzi scheme

[@Kükenshredder]

@@RickLindstrom They could have run doom!

[@cmcgl]

Bro had that $NVDA money

[@shiccup]

Before they were the most valuable company

[@3zObafouzr]

them stock options be hitting rn

[@ferretyluv]

Definitely. He got those stock options so he was able to dedicate all his energy to this.

[@travisrose2277]

Could've been crypto mining but he had other ideas.

[@dfmayes]

They should give him a lifetime supply of Breathe Right strips for this.

[@rif6876]

He had a beautiful dream. he was reading all the millions of digits from high to low. He woke up screaming - the last number was 2.

[@absolutjackal]

Umm….I have questions but not about primes.

[@ronald3836]

I hope you aren't being nosey.

[@anticarnick]

weird because on google image search he looks normal otherwise... Did he know he looked like that?

[@GilesBathgate]

@@anticarnick who k'nose.

[@andrybak]

Best guess: camouflage/protection against AI scraping/training.

[@jetlaw_1]

He looks like Hannibal Lecter in the thumbnail!

[@ayyythatguy]

Prime Time with Dr. Grime, how sublime!

[@venkz7788]

and just in time!, and i couldn't resist my urge to chime in rhyme, hope that isn't a crime

[@AquilaSornoAranion]

Dr. Grime

[@ayyythatguy]

@@AquilaSornoAranion My bad, oops

[@HopUpOutDaBed]

for someone who spent $2million on this project he seems completely unimpressed and more excited about his computer or something.

[@herkatron]

It’s probably because he’s more of a COMPUTER scientist than mathematician. It appears he was a former SWE at NVIDIA. I would certainly expect him to have a big background in computer engineering and programming. As he said, the project gets the headlines, but for him the most impressive work was putting together the GPU cloud architecture.

[@eggman969]

Or his breathing strip

[@andreweinhorn]

That prime number, if typed out, would fill 41 full volume encyclopedias. Mind blown.

[@Weeble68]

Was wondering why they didn't pop it on the screen

[@andreweinhorn]

😂😂

[@hareecionelson5875]

will Japan print this one as a book? would have to be a set of books, even with their tiny font size

[@brian_jackson]

What is the highest prime number known, for which we are certain there is no smaller prime number undiscovered?

[@numberphile]

That’s a cool question.

[@gibletgravy]

I did a brute force check and got up to 11. I have strong reason to suspect that we have discovered all primes less than 11

[@hb1338]

I found a suggestion that the value is around 4 × 10^18. This arises from people working to test the various Goldbach conjectures. Once integer numbers get beyond that sort of value, they start to lose meaning because it take so long and so much space to write them down !

[@entp_adventures]

​@@gibletgravy not sure, there's just too many numbers under 11 to be sure

[@LittleCloveredElf]

We got a new Mersenne prime before GTA 6

[@prochinczyk2]

Also before The Elder Scrolls VI

[@cuberomer]

Also before Silksong

[@DmitryArciszewski1]

@@prochinczyk2 Also before the Half Life 3

[@smbernard]

Doors of stone

[@turolretar]

Before ww3

[@paul8731]

Shouid hsve checked his spam folder for those other 2 smaller primes

[@javen9693]

*flipping through mail* "Scam... Scam... Bills... Scam... World's largest prime... Bills..."

[@Matthew-bu7fg]

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

[@RWBHere]

"It's fun!" Wow! I wish I had a spare 2 million US dollars to spend on fun. 🤔

[@ianstopher9111]

I assumed he sold some Nvidia shares to finance it.

[@ferretyluv]

He has Nvidia stock options. At least he spent it on something contributing to science instead of buying a super car.

[@notashark8069]

@@ferretyluv Why is buying a sport car not a valuable option if that is what he chooses to spend his money on?

[@ferretyluv]

@@notashark8069 He could do that, but he chose to contribute to society instead with his money, which is better.

[@notashark8069]

​@@ferretyluv It's completely arbitrary. While contributing to society may benefit the majority, buying a sports car could be a more fulfilling choice for him personally. Labeling this as selfish overlooks his individual desires and aspirations.

[@Luper1billion]

Im getting the sense that the supercomputer is the real achievement

[@ZER0--]

The certainly are contributing to climate change with the huge amounts of energy they use.

[@TuckerLeeC]

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?”

[@JorgetePanete]

I'm*

[@ytmadpoo]

It's the power of distributed computing to tackle complex problems. Nothing new these days, but back when GIMPS started, it was unexplored territory. I don't know for sure that Primenet is the longest running distributed computing project (since 1996'ish) but if not, it's gotta be close.

[@kamilgorski137]

@@ytmadpoo even seti@home/boinc was later, seems primenet was first

As a Software Engineer I'm interested in the tech side of this, how can a GPU test huge numbers, I would love an explanation on that, maybe something for Computerphile.

[@hoebare]

I'm speculating here, but I bet it's an approach similar to Matt Parker's method of calculating digits of Pi with 200-ish humans. They find ways to break the problem up into relatively small portions (128 bits maybe?), operate on those, then re-combine them. The tricks are in how the operation and recombination steps manage the boundaries between chunks. For example, to attempt to divide 127 by 3, you could break 127 into binary 11, 11, 11, and 1 and then divide each of those by binary 11. The first three nibbles turn into 01 and the last one isn't 11, so three doesn't divide 127. Of course, this trivial example also shows that any Mersenne prime 2^n - 1 must have an odd n or else the number would be divisible by three. I hope this is enough to demonstrate my guess? Fascinating stuff!

[@nicolascampailla]

I imagine that it's for the same reason that GPUs are used for crypto mining, not sure on the specifics though

[@Alex1611AD]

They have CUDA-optimized binaries that run in parallel on multiple GPUs. So really fast stuff.

[@raresaturn]

"Under two million"... I thought he was going to say a couple of thousands dollars😲😲

[@sshrpe]

Just had my mind blown by the realisation that a Mersenne Prime (2^n -1) would be represented in binary by a string of n 1’s

[@Filipnalepa]

That nicely shows why n has to be prime in order to 2^n-1 be prime. For pendants, it's necessary, but not sufficient.

[@Xanthe_Cat]

Mersenne primes 2^p-1 are always the maximal numbers with a prime number p of p binary digits. :)

[@fixminer9797]

It is a fun fact, but also sort of trivial. Positions in binary numbers represent powers of two (instead of the powers of ten in the decimal system). 1=1 2=10 4= 100, etc. So a power of two is always a one followed by all zeros. That minus one is naturally all ones. In other words, if Mersenne primes were of the form (10^n)-1 they would always be a string of nines in decimal.

[@jakeb3849]

@@Filipnalepawould you kindly explain a little more?

[@calmelbourne]

@@jakeb3849 Multiplying by a power of 2 will add zeroes to the end of a number, just like multiplying by a power of 10 in base 10. So for example, 1 111 111 111 (10 1s) can be expressed as 11111 (5 1s) multiplied by (10000 + 1), which will add five zeroes and then replace them with a copy of the original, resulting in 10 1s. A similar thing can be done with other factors, eg 111 111 111 = 111 * (1 000 000 + 1 000 + 1).

[@adamcionoob3912]

I've been waiting for this vid since yesterday.

[@bmenrigh]

I’m always excited anytime GIMPS finds another!

[@louis-philip]

"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.

[@turolretar]

Except that space exploration was in part political

[@100percentSNAFU]

Also with space exploration you can build space stations for research, and eventually build bases on the moon to have a low gravity launch site to reach other destinations where colonies could be built, mining for rare materials could be done, etc. Or you can get geek clout for discovering a big number that has no practical use. 🤔

[@KrudlerTheHorse]

He used off-the-shelf cloud services. He just had fun playing around and innovated nothing. Complete waste of $2M

[@aL3891_]

putting those nvidia stocks to good use :)

[@shiccup]

Keep in mind he was spending the money for the last 2 years Nvidia only blew up in the last year

[@RALL123456]

I respect he gives credit to work that others did

[@Blaqjaqshellaq]

Notice that if n is an even number 2*m, then 2^n - 1=(2^m+1)(2^m-1), so the only resulting Mersenne prime is 2^2 - 1=3, since one of its two factors is 1. All others come from n being odd.

[@lexyeevee]

i think, offhand, that for composite n, a^n - b^n can always be factored in a similar way, hence why n has to be prime

[@kayblis]

I see the problem almost as a benchmark for humanity's computing capability at any given point in time. You could classify a whole generation of humanity by the largest Mersenne prime they discovered up to that point in history.

[@jamestappin4741]

A somewhat tangential question, but possibly worth a video sometime: to what value of N do we know all of the primes ≤ N?

[@VincentToups]

@@joseflat For any N there is a finite number of primes less than N.

[@perrydimes6915]

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.

[@GreatOutdoors1]

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.

[@jamestappin4741]

@@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.

[@worldbfr3e263]

Read more better buddy

[@Sp4mMe]

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".

[@yogisaputro3410]

Please make the computerphile video about generating number that big

[@GARDENER43]

136 279 841 is easy to remember, break them into three digits : 136 is the first 3 triangular numbers, 279 is 2+7 = 9 , and 841 is a square 29^ 2

[@acelm8437]

Also it's almost pandigital (only missing 5)

[@ZieselRocks]

​Also missing a zero...

[@xyz.ijk.]

Also that 136,279,841 is, itself, a prime number.

[@RCPlanes59]

Luke is the guy from Willy Wonka who bought all the chocolate bars trying to win a golden ticket

[@topsecret1837]

Smooth Priminal

[@InigoQuilez]

That's about 1 dollar per 20 digits or $0.05/digit. I'd be curious to track the evolution of this index over time.

[@thaer12345]

I love how the interviewer kept trying to prod for some sense of excitement and fun from the researcher to be met only with banal responses about computer monitoring

[@trueriver1950]

My very first you tube was when you featured Matt Parker talking about the PrimeGrid (PG) project, saying he prefers to support the underdog (or words to that effect). That video attached me first to this channel then to other Y-T channels in turn. At the time I was already part of PG so obvs agreed 😅 and it was the interest that that Matt Parker video has generated that motivated me at least to try Y-T. I've not been part of a prime search project for several years but I still agree with Matt: if I was going to invest money in looking for primes I would rejoin PG, not GIMPS. That was a project where with a medium range graphics card I could find a prime week into in the top 5k. Though they don't try to compete for Mersenne primes, so PG will never hold the top spot. "My" prime took about three years from finding to drop out of the top 5k primes, so I got my share of the limelight ... I also liked the fact that even second hand computers bought for £10 could take part (though those were slower running, so more costly per prime to run than the main box with the graphics card. I heated my bedroom for two winters with those computers, and being on electric heating anyway it hardly cost me any extra after I deducted the saving in heating...

[@chsbkr]

How does one get 2 million to spend on finding a prime number

[@fixminer9797]

By working at Nvidia for ten years, more than a third of their employees are multi-millionaires. The Nvidia stock price has exploded in recent years.

[@100percentSNAFU]

​@@fixminer9797Guess I picked the wrong company to work for considering my Citibank stock reverse split 10x and was worth less than a dollar a share when I parted ways with that company (after being valued at over $50/share when the employee stock program bought into it) 😂

[@JustPlainRob]

Is bro wearing anti-facial-rec anti-ai-training makeup? That's next level. This guy computer sciences.

[@barsaf9989]

Nooo.. is that really what it is? That's crazy. Lol

[@screenoholic]

Seems like something similar to Breathe Right Strips.

[@ArawnOfAnnwn]

@@barsaf9989 No. It's a medical support to help with his breathing.

[@darthrainbows]

2:17, it seems odd to me that the very small primes (Mersenne primes 3 and 4: 31 and 127) were not known from the discovery of primes. Testing small numbers is trivially easy, even if your only tool is basic arithmetic. The brute-force algorithm for testing primality is O(n^1/2). Testing n < 1000 could probably be done by hand in a day? Give them a time penalty for not being able to use modern notation (which is more efficient), and call it a month at the absolute most. All it would have taken is someone wanting to know the answer.

[@hb1338]

Think of all the things we know that they didn't - I bet they chose to look at some of those before they looked at frivolous stuff like primes.

[@mikescully6546]

@2:34 why is there a number listed in 2009 in between 2 numbers found in 2008? Did they accidentally skip over a prime?

[@chicken_punk_pie]

Yeah they were found out of order

[@john_hunter_]

wait, he spent over a million of his own money to find the number?

[@PerMortensen]

Yep, that's what I gathered. Probably made it pretty big with Nvidia stock options.

[@bhatkrishnakishor]

For a while, I had GIMPS program run on my dorm computer during my college days.

[@enderslice8378]

One day in the future someone is probably going to need a perfect number for a specific physics discovery and we'll be ready

[@humanbass]

Those numbers are so long they are meaningless in physics.

[@gavinriley5232]

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.

[@stephenbeck7222]

That’s pretty much how most math and physics goes. Physicists need some math and they either come up with it themselves or they open up a never-read book and find the math they need.

[@stevefrandsen7897]

Excellent. The size of these numbers are boggling!

[@amits4744]

I am working on discovering something interesting in mathematics and I am about 50% done. Hoping I am featured on this channel in coming months when it's done

[@OsuAndChess]

What's the context of your work?

[@amits4744]

@@OsuAndChess it's about something which links prime numbers and Collatz-like problems. I am not making any attempt at solving Collatz conjecture, but I am working on finding a link between Collatz-like problems and prime numbers and I have found something and need to test and verify it more, especially with larger inputs

[@jellezwaag]

This guy is 100% the guy I would paint if you ask me to draw a guy who finds a Prime number 😅

[@jeremygreer4039]

I asked for a drawing, not a painting!

[@jellezwaag]

@@jeremygreer4039 paint me like one of your french girls :D

[@Relkond]

Mersenne primes have a curious relationship with binary - they're a string of all 1s in base 2, and you need too find the right mixes of 1s and 0s to factor different sets of 1s. Or put another way, you want two sets of 1s and 0s that when multiplied, make an unbroken string of 1s, which is a prime number of digits long. (If the number of digits is not prime, the math is trivial - base 2, 111111 factors include 111 and 11)

[@hb1338]

Erm, no. Prime numbers don't have any factors other than themselves and 1.

[@ErikLeppen]

That last bit is actually a really nice way to intuitively explain why the exponent has to be prime.

[@Relkond]

@@ErikLeppen I suppose for others, spelling it out formally, 2^(N*P)-1 will always have 2^(N)-1 and 2^(P)-1 as factors. It's been a few years since I looked at them in any detail. I believe there were further constraints on the factors - if memory serves, every factor whose last two base 2 digits are 11 needs to be paired with a factor that ends 01. That may sound trivial, but considered in combination with the above, for every factor of n, 2^n-1 will have at least twice as many factors. I'd tried looking for other rules to maybe help create a further sieve for Mersenne primes, above and beyond 'must be a prime number of digits', but I do believe the actual math required is beyond my own meager skills.

[@CheshireTomcat68]

I want to see the picture in James's attic.

[@jimmyzhao2673]

Do the primes *need* to be found in sequential order ? Or can you randomly guess at numbers and check if they are Prime.

[@d4slaimless]

No need for any order. There's many unknown prime numbers lower than this. It's just a little bit easier with Mersenne primes.

[@PerMortensen]

No need necessarily to go in sequential order, however the larger the number is the more computation you need to do to check, so it makes practical sense to start low and work your way high.

[@kuisma8]

How much electricity in average is needed to find a new number in this list?

[@ricksaccountant]

I just found a 2 possible new prime number after watching this video…thank you for the inspiration!!

[@xenmaifirebringer552]

I don't know why it takes so much time to find these huge primes. Considering their size, it's not like they can accidently slip behind the sofa or be left misplaced in a drawer...

[@andr101]

Lol nice one

[@Kaelygon]

Compared to the billions that big companies spent on large language models, 2mil doesn't sound too bad for finding the largest prime

[@lem0nhead84]

Well, except it's completely useless

[@Tatman2TheResQ]

Except those companies are developing products and essentially investing into future profits. But yeah. Big numbers are cool too.

[@yeneandthesouldoctors2353]

Not? It is shocking to me! Beyond imagination.

[@cliptomaniac2562]

@@Tatman2TheResQmore like stealing from artist, musicians and everyone else for future profits.

[@themathhatter5290]

​@@lem0nhead84 As opposed to Large Language Models, which are helping future doctors cheat so they can spend more time drunk. Great job guys.

[@SeanStephensen]

We probably have no idea, but I'm curious if there are a finite number of values for n that produce Mersenne Primes, which are prime themselves?

[@colonelgraff9198]

Waiting for an Optimus Prime

[@3dplanet100]

2:14 so it took over 200 years to discover another prime number just two digits long??

[@cylurian]

Back in the day when we had access to computers to run all day, back in the late 90's it was fun to find these numbers. I remember they would take weeks to figure out if they were prime.

[@NtudaI]

"ya know" - Luke

[@DanielPereiraValadés]

He said it like 2^136,279,841 − 1 times 🤣

[@pj20050]

2 million wtf

[@PretzelBS]

If we ever encounter an alien civilization you best believe we’re gonna see which one has the bigger prime number

[@johnchessant3012]

lol for 2 million dollars he could really act more excited about it...

[@Tiqerboy]

I remember the last time one of these enormous numbers was found, they printed an entire volume of the number (in base 10 of course) and it was the size of phone book. I guess they are going to have to print another edition of this book, destined to be a best seller (among math people of course) and I wonder how think that book will have to be!

[@hb1338]

They could have reduced the size a bit by presenting the number in hex.

[@Tiqerboy]

@@hb1338 Yup, it would be all Fs except for the first digit which has to be some other number other than 'F'. Challenge: What is that first digit? I know what it has to be, let's see if other readers can figure it out.

[@Kükenshredder]

The dude must have a prim(e)al instinct for this. Please make him Primeminister.

[@andrewharrison1194]

Thank goodness you got in with the terrible jokes before I did! :o)

[@Kükenshredder]

@@andrewharrison1194 To my defense: I was a little bit primed on this one!

[@ericmckenny6748]

As long as he’s not a suprimacist.

[@PetraKann]

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%.

[@jimmyzhao2673]

Boo. 🙂

[@justarandomdood]

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

[@AA-100]

Dont think there is a "next likely candidate".

[@TheMarbleousMarbler]

If I were to ask these people one question, it'd probably be: If we were to prove that there are infinitely many Mersenne primes, would the GIMPS still be running after that?

[@GreatOutdoors1]

I would say yes, since they aren't trying to prove that conjecture, they are just trying to find large primes.

[@luudest]

What is the best way to check if a candidate number is a prime number?

[@ninck8992]

there's a function that evaluate to 1 only on prime numbers and doesn't take an insane computational power

[@oatmilk9545]

obviously by trying to divide it by all natural numbers smaller than itself without getting an integer

[@ytmadpoo]

In the case of potential Mersenne primes, there's a Lucas-Lehmer test that works great because of the way they're constructed, you're not just doing sieving work which would definitely not scale at numbers this large. There's also a prime probability test, which is what Luke used to initially discover the prime (and then an LL test confirmed it). The PRP test takes about as long but thanks to some clever math, there is some error checking built into it and a proof of work output, whereas an LL test has to be independently double-checked to confirm the initial result.

[@gregorymorse8423]

​@oatmilk9545 wrong. Up to the square root is sufficient. Rookie mistake.

[@G5rry]

@@gregorymorse8423 Only need to check the *primes* up to the square root :P

[@PeterVC]

I've been on and off into gimps using George Woltman's Prime95 program for 20 years or so. It's just fun :)

[@robertmiller1299]

Is there an unknown between this one just discovered and the previous biggest prime discovered

[@hammerth1421]

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.

[@dante7228]

I wonder if one day we will figure out the true importance of those primes in a now unforseen and unknown context. Maybe one day those numbers will hold the key for a thoroughly understanding of the universe... Time will show

[@SirKibble15]

Is there any theories on the number of mersenne primes to non mersenne primes? Are there more mersenne primes or since there are infinitely many primes, there’s the same amount of mersenne and non mersenne primes

[@Xanthe_Cat]

Mersenne primes are much rarer than non-Mersenne primes.

[@JanJanssens-s1j]

What's the biggest non Mersenne prime(who's not 2^n -1)?

[@mcheddadi]

2 million $?! damn. ok. ok.

[@cz19856]

dr disrespect did nothing wrong

[@n0mad385]

@@cz19856 Pedo

[@AmmoGus1]

​@@cz19856neither did Uncle A

[@dfmayes]

I wonder if that includes the cost of electricity to run the computers.

[@feraudyh]

Amazon funded this?

[@ghffrsfygdhfjkjiysdz]

Is 2^TREE(GRAHAM NUMBER) -1 a prime?

[@SJrad]

babe wake up, new prime dropped

[@sybo64]

I sense a new T-shirt being released soon!

[@NomadOfOmelas]

Can we determine the likelihood that there is an undiscovered prime number less than the current largest known prime number?

[@dariusoberholster4246]

What is the formula for the number sequence (1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...) In this case, All Primes?

[@Xnoob545]

Willans' Formula

[@hb1338]

1 is not a prime.

[@hb1338]

@@Xnoob545 One of many, it is horribly compute-intensive.

[@VladimirOve]

There are asterisks for n = 49,50,51, and 52. Can someone please explain what they mean?

[@Xanthe_Cat]

They are provisionally given those numbers because the verification effort is incomplete above the forty-eighth Mersenne prime. If there was a false negative amongst the Mersenne numbers that have only received a first test so far, that could mean the 52nd MP is actually the 53rd. Having said that, it’s thought the chances of there being a false negative in the previous unverified results is not great, but it is also definitely non-zero, as not all of those tests had the more robust error checking mechanisms available now.

[@BGPaul]

Does this mean that between the last prime found in 2018 and this new number there aren’t any Mersenne primes in between the two? I assume they checked of course but are all odd numbers looked at?

[@GreatOutdoors1]

All of the candidate primes haven't been tested yet, but they are currently working on it, including the man this video is about.

[@ferretyluv]

No interview with Terry Tao? He does primes.

[@Djorgal]

Do we know whether we might have missed any? Can there be another n, smaller than 136,279,841 that we don't know about that would make 2^n-1 prime or did we check them all up to that point?

[@Regnum0nline]

Should be have checked all.

[@marivcenteno9444]

​@@Regnum0nlinenot all candidates between M57,885,161 and M136,279,841 have been eliminated

[@killymxi]

Mentioned in the video: he was focusing on larger n until he found one. Now he redirected the computing power to check skipped ns still waiting for validation.

[@AlexdaCunha]

The smallest primer is much more difficult to find. Specially if you drop it in the middle of the other primes

[@charlieangkor8649]

If there can be a concept of "highest known integer fulfilling condition X", in the case of this video X="is a prime", then when we put X="isn't a prime", there is also the highest known integer which is not a prime. What is that number currently?

[@VincentAubry-hr1ez]

We know an infinite family of non-primes : 2*n where n is any number, so there isn't a biggest composite that we know (just like there isn't a biggest number that we know). We don't know of an infinite family of primes, so there is a biggest prime that we know !

[@sevenvinton6831]

6 * n - 1 or 6*n +1… are all of the “non-primes” in this sequence factors of primes?

[@bigutubefan2738]

Congratulations Luke! Great job.

[@dypteseu]

quite cheap per digit actually...

[@rebuznardo]

Is it gonna be a new edition for the longest prime number book?

[@arnelilleseter4755]

"In my head gimps was always the little men and little women running..." I thought he was going a totally different direction with that sentence.

[@zxzxzzxx7396]

I was so fascinated with this discovery that I took a while to realise it is not Rian Johnson in this video

[@xyz.ijk.]

It's WILD that the power 136,279,841 is, itself, a prime number.

[@tomkilleen3887]

Congratulations Sir!

[@bxdanny]

The GIMPS - not to be confused with the GIMP, the GNU Image Manipulation Program. Funny how two such totally different projects have such similar names.

[@KevinToddMusic]

Could 2 to the power of one of these mersenne primes minus 1 be a prime? Like is that number even computable or is it just too big to check?

[@GreatOutdoors1]

It could be but it is way too large to check.

[@KevinToddMusic]

@@GreatOutdoors1 cool! I wonder what the limit is? Like given the current computing power available, how large of a number could you possibly prove to be prime?

[@Xanthe_Cat]

At the moment you could run exponents up to about 8 gigabits (2^33), but it would be a multi-year effort to test just one exponent at that size. (Luke Durant’s exponent is a little over 2^27.) The largest testable Double Mersenne (MM31) is already known to have four factors, the earliest discovered back in the 1980s. All the larger Double Mersennes have no known factors (and it’s extremely hard to find factors), the next possible Double Mersenne is MM(61) but this is quite untestable for the foreseeable future as the exponent 2^61-1 is way bigger than 2^33. The best that could be done is a negative confirmation that it is not prime, by finding a factor.

[@KevinToddMusic]

@@Xanthe_Catthanks for clarifying! So cool!

[@KevinToddMusic]

@@Xanthe_Cat

[@andrewdunbar828]

more than a mere content creator, you're a context creator

[@robertferraro236]

Can someone answer this question. If one can prove mathematically that there are infinite primes, does it make these quests for the largest primes redundant, or is there still joy in finding the specific number?

[@RunstarHomer]

We've known since ancient times that there are infinitely many primes. There's actually quite a simple proof found by Euclid. So I suppose the answer to your question is there is still joy in it. Personally I just think it's interesting that we're even capable of dealing with numbers that are so big, and learning anything about them.

[@JohnSmith-nx7zj]

@@RunstarHomerworth adding that we don’t know if there’s infinitely many Mersenne primes. Although there’s a conjecture that there is and how many we should find below a certain number. I guess these results might help shed more like on that?

[@luudest]

Off topic: Still unbelievable that the sum of the reciprocals of all prime numbers (Sum of 1/primes) diverges to infinity.

[@ronald3836]

The sum of the reciprocals of the Mersenne primes is certainly finite though :)

[@luudest]

@@ronald3836 lol

[@HellHeater]

​@@ronald3836Oh yeah? Prove it.

[@arnouth5260]

@@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.

[@zanti4132]

​@@HellHeaterIt's easily proven. Let set A = (1/3, 1/7, 1/15, ..., 1/(2ⁿ⁺¹ - 1), ...), set B = (1/2, 1/4, 1/8, ..., 1/2ⁿ, ...). 1/3 < 1/2, 1/7 < 1/4, 1/15 < 1/8, etc. All the Mersenne primes are in set A, each member in set A is less than its corresponding member in set B, and the sum of all members in set B is finite. atiagpts.