New largest prime number found! See all 41,024,320 digits.

[@arthaiser]

i was using that prime as my password, time to change it now, thanks luke

[@GerinoMorn]

meh, we just take 8 first characters anyway... xD

[@Ignotius_Grindelwald]

too late, i already entered it🤣🤣🤣🤣

[@AndreVanKammen]

I was using it for my RSA-136279841 implementation (when an RSA bit number is so high it gives away the key) i gues that's why you shouldn't use mersenne primes for RSA they are way to easy to guess.

[@spingbay7039]

I was using it as one of the keys in RCA-encyption with my mum. I'll have to find a new one :(

[@AntonioBarba_TheKaneB]

ah, only digits! no letters or symbols? such amateur!

[@alalcoolj216]

In base "2^136,279,841 - 1", this number would be written out as "10".

[@ujocdod]

Is X in base X always 10?

[@Rulerofwax24]

@@ujocdod 2 in base 2 is 10, 10 in base 10 is 10

[@ValidatingUsername]

@@ujocdodYes

[@ujocdod]

​​@ValidatingUsername Ok, thought so :)

[@citratune7830]

imagine memorizing that many symbols

[@Voldrix]

The digits are easier to visualize in binary. Just 136,279,841 ones. No zeros.

[@benjaminlynch9958]

What? For real???

[@user-vb8zo6kh4j]

⁠@@benjaminlynch9958yes, the number is 2^136279841 - 1 To look at the number in binary Any number raised to a power in binary is: 2^0 = 1 2^1 = 10 2^2 = 100 2^3 = 1000 2^3 - 1 = 7 Binary: 1000 - 1 = 0111 -> 111 So 2^3 - 1 is 111, 3 ones

[@Qbe_Root]

@@benjaminlynch9958 Yeah, 2^n in binary is 1 followed by n zeroes, so 2^n - 1 is n ones

[@erylkenner8045]

@@benjaminlynch9958 Yes! Any power of 2 minus 1 will be all 1's in binary. Or all F's in hexadecimal.

[@szymonl4363]

@@benjaminlynch9958 Yup, that's how binary works. It's analogous to how you'd write 10¹⁰⁰-1 in decimal, it's obvious that it would just be 100 nines in a row.

[@bengolden870]

This prime was discovered the day after my number theory lecturer told us the previous largest known prime and had to correct himself with this new prime in the next lecture lol

[@Hitarth_Rana]

That's actually great! I mean the fact that your lecturer is that updated with their knowledge!

[@Xanthe_Cat]

Admittedly we’ve only discovered 52 Mersenne primes in the entirety of human history so it’s not like new ones are found every other week.

[@robertunderwood1011]

@@Xanthe_Cat You were right just a few days ago I was thinking Well, it’s been several years now … it’s about time they discovered a new Mersinne prime.

[@PopeLando]

@@bengolden870 I mean after almost 6 years he was onto a good bet!

[@fivenightsofben6096]

That's so exciting!!

[@MartinMllerSkarbiniksPedersen]

If you were to write the latest Mersenne prime in hexadecimal, it would be a 1 followed by 34,069,960 F’s.

[@NonFatMead]

That's a lot of respects paid...

[@gcewing]

We should nickname it the "big effing prime number".

[@PunmasterSTP]

That's an F'ing huge number.

[@NonFatMead]

@@gcewingMersenne Primes are all big F’ing numbers. This one should be known as the Biggest F’ing Prime Number

[@PhoenixClank]

@@NonFatMead … for now.

[@jamgall1010]

Run time of 10:13, 613 seconds. Both 1013 and 613 are prime. Edit: Can we call this 'prime time'?

[@honorarymancunian7433]

That's honestly great

[@porof5ercan]

Dating primes? Meeting at the right time maybe?

[@stevenvanhulle7242]

@@honorarymancunian7433 Not so surprising, though. People tend to underestimate how many primes there are. Between 1 and 100 one in four numbers is prime. Between 1 and 1000 one in six is prime. For instance, near 613, the numbers 607 and 617 are also prime.

[@mjs28s]

@@porof5ercan One must meet in the prime of their life.

[@FocusLRHAP]

@@stevenvanhulle7242 This one is weird: 127 and 113 are the first prime numbers with a difference of 14, from each other. I mean there are no other primes between them.

[@MorgothBauglyr]

a video where you can watch the youtube encoder sweat

[@davidbrooks2375]

Reminds you just how much data is being stored and transmitted for 1 video

[@gorlix]

​@@davidbrooks2375 now remember all these kids wasting traffic for 10 hour versions. this is why we can't have nice things

[@ncot_tech]

You might say it's a prime example of how the number of bits is fixed...

[@renat1786]

@@davidbrooks2375 , well it's ~280 MB for 1080 HD one, kinda comparable with those 41,024,320 digits

[@lucbloom]

It's the math equivalent of confetti

[@LanceThackeray]

Casually doxing hundreds of thousands of phone numbers.

[@abigailcooling6604]

And passwords, bank PINs, vault keys, user IDs and account numbers. Matt should be more careful with what he puts online.

[@michaelbauers8800]

Lol that was funny, thanks for the laugh. Maybe even entire words that were used by shakespear.

[@instazx2]

bee movie script is probably in there somewhere

[@stapleman007]

The list of who wasn't doxed is probably shorter.

[@ericpaul4575]

@@abigailcooling6604 and SSNs

[@tylerlarsen1842]

From hand to institutes with supercomputers to hobbyists with home computers to a hobbyist with a supercomputer

[@kaminakaminakaminakamina]

Next a supercomputer with a home?

[@arondesilva4008]

0:11 yeah I thought it was, glad to know someone was on the same page as me

[@amgwilly565]

i laughed way too hard at this

[@vigilantcosmicpenguin8721]

i mean, if someone showed me that and asked me if it was prime, i'd probably say "sure, why not"

[@KhanStopMe]

Cycling through the digits on screen is SO bad for the compression/bitrate on your face lol

[@standupmaths]

My face!

[@youdontknowme5969]

Beard.

[@JotaSE30]

Looks fine in 4k :)

[@Anklejbiter]

luckily switching to 4k fixes that problem - even if you don't have a 4k screen lol

[@NicoBaumgarten]

I wonder if the compression will "steal" digits or frames or change/alter digits and introduce artifacts, in effect altering the theoretical number of digits displayed.

[@sketchups4672]

I did it. I watched it all the way through! Whenever I blinked I went back several seconds and kept going. I expect several awards going forward

[@kierangrasby5728]

I went back to when the numbers started scrolling, then started watching again but alternating which eye was closed, with a full open between each individual eye closing.

[@sketchups4672]

@@kierangrasby5728 efficient. Clearly you have outdone me!

[@andor_yoko]

​@@kierangrasby5728speedrunner strats. Now get a 120Hz screen and watch it at 2x speed

[@SiberCatLP]

How about the "69 likes" award?

[@TropicalCoder]

I set the playback speed down to the lowest it would go - 0.25, so I would miss a digit. Took quite a while that way, and the guy's voice was very deep.

[@alexbanks9510]

Fully appreciating how precise the timing of the start/stop was

[@rudivonstaden]

We already knew that Matt is good at waffling, but to be able to waffle for exactly 6:50 and hit all the key points in that time is next level.

[@lindhe]

2:30 I don't think it's such a big deal to have seen every single digit of the biggest known prime number, there's only ten of them.

[@colinkirkpatrick5618]

Reading a library isn’t impressive either, we learned everything on the wall in primary school

[@malignusvonbottershnike563]

I'm taking a number theory course at uni this year, and on Saturday 12th our professor brought up the largest known Mersenne prime during discussion in a lecture, only to rock up on Tuesday 15th and tell us they'd found this new one! So that's quite fun

[@stevevernon1978]

are you at the same uni as @bengolden870 ? he said almost exactly the same thing!

[@bigpopakap]

I kept thinking: he must have a timer behind the camera, right? And yay, it was revealed! It's still so impressive how you can talk in one take, manage the timing, and envision how the visuals will be displayed, quickly enough to do it on the beach on vacation. Maths KZbin legend 🙇‍♂️

[@fantasia55]

He could manipulate the speed slightly. Easy Peasy

[@strengthman600]

⁠@@fantasia55assuming he was telling the truth about 1 bunch of digits per frame, it’s not the type of thing that can be sped up without losing information

[@bigpopakap]

@@strengthman600 someone should go in frame by frame to verify if there are, in fact 10,000 digits in each frame and if they are, in fact, the correct digits. I would volunteer, but I am scheduled to cease existing sometime in the next 1000 years, so I'm not sure I'll have the time, sadly.

[@mtarek2005]

​@@fantasia55a lot easier to pre-calculate the time and adjust the script accordingly (if scripted, which it probably is)

[@mtarek2005]

​@@strengthman600probably adjusting his own speed slightly (most often by shortening gaps or more rarely lengthening them)

[@alexander0the0gray]

Luke Durant now suddenly has a meeting scheduled tomorrow to explain the electricity usage for the last 12 months in the data centers he manages 😂

[@zrodger2296]

Yeah, my question: who paid for all the computing time?

[@DukeBG]

Luke Durant is (was?) the principal engineer of CUDA Software, NVIDIA.

[@ytmadpoo]

Luke used publicly available cloud GPU time, spot pricing. Pretty impressive really. Sometimes the spot prices are very affordable and he took great advantage of that. Along with scripting to coordinate work distribution, starting new instances when the prices were "just right", and so on. GIMPS is very happy to have his contributions. His efforts progressed the search for the next prime YEARS ahead of where we would have been otherwise.

[@gavin5410]

​@@ytmadpooThat's incredible, thank you for sharing.

[@BetaDude40]

I'm glad people are thinking more about the cost of computation. Green Computing definitely needs to be a topic covered more frequently in computer education

[@noreply5576]

If you pause a video in KZbin on desktop, you can then use the '.' and ',' keys (period and comma) to advance one frame forwards or backwards in the video. That way you won't miss any of the digits!

[@JohannaMueller57]

oh damn, didn't know this works on youtube too. thanks

[@Ztingjammer]

Didn't know that, so thank you! Will need to make use of that for this video tomorrow! 😎

[@hinz1]

I rather watch it in binary or hex ;-)

[@bertblankenstein3738]

I'll bring an extra keyboard.

[@Bluhbear]

Can't wait to spend the next few months reading every single digit.

[@Osmium78]

Thanks for taking time during your vacation to inform us!

[@alexbradmckay]

Beautiful!! Thanks for taking time away from your vacation to inform us of this important discovery!

[@quantum1861]

Hi Matt! I’m doing my undergraduate senior thesis on Mersenne numbers and related topics, mainly because I’ve been a fan of math KZbin for many years so obviously this is huge news to me. I’ll have to go and update my presentation I’m giving in about an hour!

[@DKdrop]

It’s been an hour, so I assume you’re either giving it or just finished. How’d the presentation go?

[@hubblebubble1550]

how'd it go?

[@bananogamer6972]

We are all curious

[@grantbaugh2773]

Also wanting to hear the update, I can only imagine the stress of updating with such big news so last minute.

[@quantum1861]

Would love to say there was much fanfare but I guess not everyone is as excited by prime numbers as we are lol. Advisor agreed that it’s always cool to see new developments in your field of research.

[@winklethrall2636]

Rats, I blinked and missed some of the digits.

[@Cossieuk]

You just need to watch it a few times and hope you blinks happen at different times

[@lazykbys]

I'm pretty sure I saw the silhouette of a weeping angel in those digits.

[@Schikane07]

You can just pause the video when you need to blink 😂

[@amirkal4487]

i read this comment and missed some digits

[@maynardtrendle820]

​@@lazykbysEvery time a Mersenne prime is found, an Angel is made to clean out the Elysian Stables. There are many hyperhorses, and very much hyperhorse poop. This is the reason for their tears...😢

[@aenetanthony]

1:11 “KZbin Compression Hates This One Trick!”

[@jh-ec7si]

Increase your resolution if it happens to bother you. KZbin automatically lowers resolution (on mobile at least) to compensate for high bitrate images which makes it worse but you can up the resolution and it's usually much better. Learnt that from watching the slomo bros channel.

[@hectorurdiales4570]

8:05 I was kinda hoping the last digit was a 2

[@eboone]

yeah. maybe next time

[@danielyuan9862]

Parker prime

[@diobrando2820]

2 raised to the power of any positive, whole number is an even number and all even numbers end in an even digit (0, 2, 4, 6, or 8). Subtracting 1 from an even number will always give a number that ends in 1, 3, 5, 7, or 9 (an odd number). So, it would have been impossible for this number to end in two. Also, we know that because the number is prime, it cannot end with the digit 2, because prime numbers can not be even (except the for the number 2 itself). If a number is even, it is divisible by 2 and therefore not prime.

[@shashishekharsingh4652]

So not a prime..

[@taterpun6211]

Can somebody check if the digits add up to a multiple of 9?

[@gekfurian]

The compression algorithm must love this video

[@amits4744]

The worst thing is that there are infinitely many primes bigger than this number

[@jeremykraenzlein5975]

I was thinking of asking a snarky question of "Now is this the last one?". Obviously it isn't. As you noted, there will always be infinitely more prime numbers left for us to discover.

[@TymexComputing]

Its more important that it is a Mersenne prime, so it leads to a Perfect number , and there is no proof that there are infinitely many perfect numbers ;)

[@amits4744]

@@TymexComputing if there are infinitely many Mersenne primes, then there are infinitely many perfect numbers too

[@crasystar-c8x]

​@@amits4744 Dont think we know if there are infinite many Mersenne primes though... Believe mathmaticians think there is, but there is no proof.

[@oliviapg]

@@amits4744 But there is no proof of there being infinitely many Mersenne primes. The Lenstra-Pomerance-Wagstaff conjecture posits that there are, but it's not proven.

[@Richard0915]

Luke really put finding the next prime number over mining bitcoin with all those GPUs, i respect that

[@owen_brady]

mining bitcoin, or placing your name worldwide forever in the history books.... I'd do the same if I was smart enough.

[@quillaja]

The cost of the GPU time probably is more than the bitcoin he'd be able to mine.

[@markshiman5690]

People who are already rich do not need to mine btc

[@DeJay7]

You respect what? It is objectively and undeniably the better choice.

[@amigalemming]

Why not establish a blockchain where the challenges to solve are not hash functions, but prime numbers?

[@voodootrois]

If this number was read aloud at 4 digits per second, it would take about 17 weeks.

[@hens0w]

There's a corresponding perfect number right, any idea how long that would take? (wikipeda says it has 82,048,640 digits)

[@randomcoder5]

@@hens0w It would take exactly twice as long so 34 weeks

[@randomcoder5]

@@deathschi_ ????? It’s an 82 million digit number, so it’s twice as long, therefore it will take twice as long to read. How long it takes to read depends on how long the number is, not the value of the number itself.

[@real_momoxi]

​no its not@@randomcoder5

[@deathschi_]

@@randomcoder5 good point

[@maximehaldane]

Loving this prime content. Always of a high quality. Have a nice holiday, I was very excited to bump into Matt by chance at the TMBG concert and have since put the picture I took with him on my ClassPad such that it will comfort me during my upcoming Yr 12 Exams. Hope he enjoy his time back over here in the land of Aus

[@rwjoyner]

Hurrah, Mr. Parker -- thanks for this! A genuine reason to celebrate!

[@samreid6010]

Actually I’m pretty sure that’s divisible by 17

[@davidli719]

You can disprove your own statement with the information taught in this video! Fermat's little theorem states that a^(p-1)≡1 (mod p), which means that 2^16≡1 (mod 17). It follows that 2^136,279,841=2 * 2^(16*8,517,490)=2 * (2^16)^8,517,490≡2 * 1^8,517,490≡2 (mod 17) So our prime, 2^136,279,841-1≡2-1≡1 (mod 17). The remainder is nonzero, so the number is not divisible by 17. And this is why we love Fermat's little theorem.

[@davidli719]

Ok this is nicer than my proof but here's a question: is 2 a primitive root for infinitely many primes?

[@mikeallison5549]

@@thisnamewastakentoo_ 💯 but not e…… obviously

[@samreid6010]

@@davidli719 I know, I was making a joke

[@Elesario]

@@samreid6010 Be aware that all jokes on this channel have to be mathematically accurate, or within a Parker approximation of accurate.

[@Jack93885]

I like the idea of using this number in this way to make static noise.

[@scottgriz]

Except it isn't random noise. It's predictable.

[@Jack93885]

@@scottgriz It needn't be random - its just visual noise. I like it specifically because it's not random, because it is specific and particular.

[@GreatOutdoors1]

A few times a year I check in to see if a new prime was found at GIMPS. A few times in the past I did my own searches for much smaller unknown primes and found 3 different ones that were temporarily on the top 5000 primes list.

[@EarendilStar]

Soooo glad the last few digits didn’t end in “2”.

[@TheQxY]

This must be the most energy spent on finding a single number ever.

[@alexandreflores6678]

Wake up babe, new prime number just dropped!

[@SoI-]

69th like

[@DoxxTheMathGeek]

That is how I would wake up any potential partner. X3

[@williamdixon4936]

I love how it visibly affects the video quality when you start streaming the digits due to the video compression being negatively impacted by the randomness that is all those digits rapidly changing.

[@catcoder7812]

First human to see all of the digits! (Probably- randomly happened to go to KZbin the moment the video dropped and have been pausing each time I need to blink)

[@jakistam1000]

Now, do you remember them? :D

[@stevenreynolds3793]

Hope you enjoyed your vacation. Listened to this video on while in Dominican Republic. Always enjoy your math videos... please keep them coming.

[@jurzal4890]

Happy for Luke! The sheer, raw compute power that Luke brought on the table for the project is hard to describe, but beautiful to see while it happened during the last year. Congratulations, well deserved!

[@trentgraham465]

KZbin's compression is STRUGGLING with the number display!

[@Otmjv]

Honestly that is the perfect location to talk about this in

[@Saultyevil]

The compression algorithm really struggles when the number starts scrolling by

[@Tatman2TheResQ]

Bitrate is king.

[@StarlitWitchy]

Oh!!!!! We THOUGHT it looked like Esperance!!! It's such a beautiful place!!! Enjoy your stay here in Australia hehehe~

[@zoomlines]

Yes! No mistaking it! Beautiful white beaches and rocky islands!

[@ericeaton3551]

Thanks Lucy and Steve!

[@jontisaurusrex9851]

THATS PRETTY BIG

[@slipperynickels]

THAT'S A LOTTA NUTS

[@CKyIe]

for you.

[@ad-mc]

I tried putting it into my calculator to try dividing it by 3, but it was too big.

[@maynardtrendle820]

It's average.

[@WaffleAbuser]

@@CKyIeWas creating a heuristic for finding prime numbers part of your plan?

[@chrisoneal2718]

Congrats! This is huge news! We now also have a new perfect number as a result of this!

[@WindowsXP_YT]

Edit: First ever Mersenne prime exponent with 9 digits Current goals for PrimeGrid-related programs: Find the first ever Wall-Sun-Sun prime, third Wieferich prime, third Wolstenholme prime, fourth Wilson prime, and the sixth Fermat prime Other current goals: Find the first ever composite Fortunate number Current goal for 196: Be the first ever Lychrel number in base 10

[@GavrielFleischer]

I'd be happy if someone found the 1st Fleischer prime!

[@insouciantFox]

Is there anyone searching for an even perfect number?

[@robertpearce8394]

​@insouciantFox 6,28,496,8128 ... I think you mean odd. The consensus is that there are none, but this had not been proved. This annoys as Pure Mathemations like things to be pure.

[@WindowsXP_YT]

@@robertpearce8394 I don't think there will be any odd perfect numbers. The first to prove that there is at least one of quasiperfect, odd perfect, or odd weird number will win a million dollars, which is a prize. To access to them, you must be a mathematician

[@robertunderwood1011]

@@insouciantFox I think not . but if you find an odd one do let us know

[@tag180rotax]

The YT compression algo went nutty when you started showing the numbers

[@antonnym214]

Congrats to the GIMPS team! I was a member of the team for five years back in the mid 2000s, and I'm exceedingly proud of the entire team. Of course, congrats to George Woltman and Mihai Preda who wrote the GIMPS software for graphics cards, also kudos and congratulations to the official winner, Mr. Luke Durant, Aaron Blosser, and everyone who contributed computer time, as you all share in this world record. All good wishes, my friends!

[@jackdog06]

Tip: put the playback speed at 0.25 so you have 4 times as long to read each set of 4000 digits. Hope this helps!

[@neyoshu]

Imagine you and your husband - after much hard work for the last few months - take a flight down to Australia for a few weeks with some close family/friends to have a small break away from work and life in general. You have a wonderful time exploring the local area, the beaches are beautiful, and you greatly enjoy going around this new area with your loved ones. Then - randomly one day - while sitting around doing nothing of note back at your hotel room, you see your husband check his phone; his eyes light up as he starts speed-reading a news article. He silently and immediately gets up, sits down at his laptop, and rapidly searches for information on various mathematics-related news sites, before opening a Word document and frantically typing away at what you can only assume is a... script? But you're on holiday, away from all your responsibilities of work. "Honey, are you okay? What's going on?" He stops typing and slowly cranks his head around, only stopping once his eyes are perfectly aimed at yours. His expressionless face staring deep into your soul, his jaw loosens, and he says: "They found it." (This is my personal headcanon for the origins of this video, I'm totally sure it's 100% accurate description of how it went down lmao)

[@TymexComputing]

Where did you leave children for all that time?

[@Chris-hf2sl]

How to get divorced in one easy lesson.

[@cab63868386]

I think they’re camping on the beach down there not in a hotel room⛺️🏖️

[@ethancollinsworth3927]

I just bought the 39th mersenne prime book can’t wait for the 40th

[@NoUploadsOnThisChannel]

Yoooo Matt I ordered your books and I love them. Thank you!!!

[@kernicterus1233]

Sorry for the delayed reply, it was difficult to concentrate on the actual numbers whilst you were talking, so I had to replay that whole section, but I blinked too many times, so I kept pausing it before blinking. This all took a while and I couldn't be sure I'd seen them all so I repeated that entire section, at 0.25 speed, and muted (to eliminate aural distraction), and with a pillow case covering your portion of the screen (to eliminate visual distraction). I've done as asked, I've seen every digit, and you know what ... I found my date of birth in there - 071171 (November not July) - and this is the 7048th prime. I'm taking a quick break to take some paracetamol and to write this before I start looking for 898409 - the 71171th prime - I'm certain it will be there somewhere. Enjoy your hols, Nottingham is currently quite cold.

[@ggb3147]

KZbin's compression algorithm is like: "what the heck?!"

[@csours]

Bitrate: And I took that personally

[@Neodynium.the_permanent_magnet]

"ends in 551", would have been fun if the end is "552"

[@VicJang]

Great video. Thanks for your coverage during a vacation.

[@grantfraser5430]

Thanks Matt for taking time out from your vacation for that report. A new largest known prime number is always a noteworthy event.

[@toothlessblue]

I love that it was discovered by an engineer annoyed by the misuse of GPUs for AI

[@volundrfrey896]

So he misused GPU's because he was annoyed with people misusing GPU's? The only valid use of a GPU is to play MY LITTLE PONY: A Maretime Bay Adventure

[@ZealanTanner]

I sometimes have a recurring nightmare where there’s something so uncontrollably and overwhelmingly big and it’s too much to handle, this video gives the same vibes. Even a single frame in this video is more than I can imagine. Like my heart rate is up just from watching this

[@railroadisolationist5452]

Geometric nightmares

[@ZealanTanner]

@@railroadisolationist5452 yeah I’ve heard them being called that although I’d describe it more as a mountain or planet rather than a shape

[@fabianziel873]

There‘s an error in 3:07 . The leading 4 should be a 7…

[@Johnz28]

🤓

[@AnubhabKamar]

Yes.. and the last digit should be 9 😂😂

[@kylebowles9820]

Matt you're on the forefront of maths communication; you're a legend! Enjoy your vacation

[@joshyoung1440]

This video is an interesting lesson on the properties of visual snow, randomness, and KZbin compression algorithms.

[@Big-The-Dave]

A number so large it ruins your bitrate. It's like watching someone play Vampire Survivors, but you're fighting a prime number instead of vampires.

[@ChipsandPeas]

But is it numberwang?

[@jnsng]

we got a new largest prime before gta 6

[@ianstopher9111]

And Winds of Winter.

[@GabrielGamerFreitas]

what a time to be alive! and people still think there’s nothing else to be discovered…

[@piraterubberduck6056]

Great content, thank you for interrupting your holiday for this. I hope you enjoy your well deserved beer and days at the beach.

[@badgerfool1980]

Bad news I'm afraid, you have a typo at the 5:36 mark, there's a 7 where there should be a 3.

[@L1K34PR0]

4 you mean

[@tpritha03]

Bruh there are 25 frames per second

[@diamonddave2622]

Squint at the scrolling digits 'Magic Eye' style and you will see something amazing

[@PopeLando]

5¾ years! 50 million powers of 2 with no Mersenne primes!

[@kallekivimaki7825]

The bitrate makes this look cool when the number is scrolling.

[@zadaszenie]

5:13 whoop whoop stop right there ! There’s a typo, 3rd line from the top, there is a 5 in stead of 7

[@8bit_pineapple]

All of the digits in binary are: 1

[@MathewWalls]

Or 0.

[@MonsieurBiga]

@@MathewWalls No, it's 1 less than a power of 2, so it's all ones.

[@cbuchner1]

Should have printed the binary number instead 😂 a lot easier for the compression algorithm…

[@Dimitri_gdr]

The hexadecimal would be even better

[@cbuchner1]

@@Dimitri_gdr ffffff …… 🤡

[@Epic_Ducks1]

That’s quite big.

[@boazgoldstein5419]

The running numbers are crushing the compression

[@treyquattro]

can we just take a moment to congratulate Matt on that excellent timing announcing the end of the sequence. I was trying not to blink and I don't think I missed any video cuts. Kudos.

[@MattGodbolt]

As a Patron I'm delighted to contribute to your wife and brother's meal and drinks :-) I hope you all had a lovely evening and can now go back to enjoying your break!

[@ggb3147]

Sorry to be that guy but i spotted a misprint at 6:06. There should be 6 instead of 9 in row 16. You're welcome!

[@Speedrunner.007]

there's no way that actually happened, matt should have double checked the number before uploading!

[@djadj_]

it's a parker prime

[@Xanthe_Cat]

It wouldn’t be so bad if it was only a single case of "sorry to be that guy" but there’s easily a dozen of you in these comments who've *all* tried the same unfunny joke…

[@Ursi_]

@@Xanthe_Cat dang let people have some fun!

[@logicalfundy]

Even with powerful computers, it's crazy we can verify something this large is prime. That's a very, very large number.

[@ianstopher9111]

Is the last digit 0,2,4,6 or 8? Nope, ok onto the next check.

[@logicalfundy]

@@ianstopher9111 Congratulations! You've narrowed the search from 2^136,279,841-1 numbers to test to 2^136,279,840-1 numbers to test! Needless to say, it's a bit more complicated than that, heh. Raising 2 to such an incredibly high power is mind bogglingly large.

[@edonveil9887]

As close to aleph-null as the former record prime.

[@coxsj]

Thanks for scrolling through the new prime in the side bar, I have it memorized now. ;-)

[@johnjones8580]

Imagine printing this prime number out, only to discover it's the first of a set of twin primes.

[@whoeveriam0iam14222]

what's the largest prime number where we know all the prime numbers up to it? doubling your number every time before checking it misses a lot in between

[@Einyen]

What do you mean by "know"? Primes have been calculated up to at least 2^64 = 1.8 * 10^20 but storing all those would take exabytes and more of storage, and there is no real point to store them. Those we need to use again are almost always faster to calculate again than retrieving from storage. If you mean how high do we know the exact number of primes below that limit, then it is: 10^29, there are 1,520,698,109,714,272,166,094,258,063 primes below 10^29. So this is tiny compared to the new prime, only 30 digits compared to 41,024,320 digits.

[@alexpotts6520]

​@@Einyen I'd never have thought that storage space rather than processing speed would become the limiting factor in enumerating the primes, but yeah, actually that makes perfect sense.

[@Oh_Nanners]

@@alexpotts6520 can't compress a prime number, yeah

[@Einyen]

@@alexpotts6520 Yeah, exactly. From the prime number theorem there are roughly n / ln n primes below n. So for example near 10^20: ln (10^20) ~ 46, so roughly every 46th number at that size is prime on average, and there are A LOT of numbers around that size, so even 1/46th of them is still A LOT of primes, far too many to store on any storage media we possess.

[@benjaminlynch9958]

@@Einyenstorage media is not that expensive for storing raw numerical values like this. 2^64 ≈ 18.4 quintillion (18.4 x10^18) and if stored in binary representation, you could fit 128 such prime numbers in just a single kilobyte. For those wanting every possible Prime below a certain threshold, particularly those that are not Mersenne primes and are computationally expensive to find and prove, storing them makes a lot of sense.

[@berendharmsen]

Question: does the fact that we now have this biggest prime, and previously we had a - smaller, obviously - biggest prime, also mean that we know there are no more primes in between these numbers? Or does the methodology mean you are forced to skip all kinds of (non-Mersenne?) primes in between?

[@Paul71H]

I think it's likely that many non-Mersenne primes were skipped in between.

[@gdclemo]

I think there is always a prime between N and 2N (except for very small N) but I don't remember who proved that.

[@robertunderwood1011]

The Mersenes are primes in base two.-1 And in that base, they can be represented by a series of ones . In base 10 we found a few such numbers 11, 1111111111111111111, 11111111111111111111111 and a small handful of others repunit primes in base 10 There are a list of generalized rep unit primes in various basis. I’m interested in generalized rep unit primes in prime bases ( other than the Mersenes) Question : If you know the rep United primes and say base seven and also know the rep unit primes in base 11 can you use this information to predict the rep units primes in base 77?

[@berendharmsen]

@@robertunderwood1011 That's way above my prime-knowledge paygrade 🙂

[@OBGynKenobi]

Now, How long of a continuous PI sequence can you find inside that?

[@huellenoperator]

The decimal expansion contains 3141592, but not 31415926

[@janTasita]

Well, the whole thing is a sequence of the digits of pi, just not starting at the beginning.

[@TymexComputing]

There exists a base where all of the numbers are pi.

[@OBGynKenobi]

@@TymexComputing now this I like!

[@ianstopher9111]

Almost certainly that sequence of digits appears somewhere in the decimal expansion of pi. Moreover, the binary expansion of pi should have a sequence of at least 136,279,841 1s, but good luck finding the first occurrence.

[@nurmr]

Enjoy your dinners. Glad I could contribute!

[@vickymcdaid5664]

My family have spent the last 30 mins looking for their birthdays … endless family fun.. thanks Matt

[@Zilli_341]

The YT compression algorithm is having a stroke

[@theaussiewaffle4276]

So they found the new Optimus Prime

[@carultch]

Optimus Prime is Optimus's derivative Or Optimus Double Prime's antiderivative.

[@user-iu1xg6jv6e]

You have a wrong digit in the number, Digit #21,755,124 It should be 9 and not 1

[@NotBroihon]

Yeah, that bothered me too. The video editor really screwed this up when typing in the numbers smh my head 🙄

[@kempshott]

So it's even bigger!

[@danieltojzan6869]

The error was ~8*10^2.1*10^7

[@legygax]

I think you’re wrong. This change would make the whole thing divisible by 827364738.

[@bbgun061]

what timestamp and frame is that?

[@svovy5358]

I can't wait for the subsequent breakthroughs in engineering and technology that this incredibly useful development will contribute to our civilization that really desperately needs a boost in productivity right now

[@emceeboogieboots1608]

I saw from the thumbnail that you were at Twilight Beach in Esperance there. Nice to see the sun out!

[@zoomlines]

Beautiful beach!

[@petergerdes1094]

The next video should calculate how many times the average human needs to watch this video to see every digit. It would be a great way to boost views as well as being amusing.

[@CalebAnderson-gn3ne]

yes

[@walker1054]

If you're trying to find the largest prime number would it not be easier to count backwards from the end instead of keep counting upwards to find more?

[@pleasedontwatchthese9593]

forget logan paul, this is a real prime

[@iceymonster4675]

Been a big fan of distributed computing since late 1999 with SETI@home 'classic' through the BOINC years until its close down in 2020, and have donated many a CPU cycle to GIMPS (though didn't participate as competitively as I did in S@H) over the years in the 00's and 2010's, great to see it still going strong and finding new primes :)

[@LeoDaBest_180_Returns]

I don't want to sound strange, but for me, I understand this as: INDETERMINACY Of-All A.I. Measurement ---> To measure the POWER, true potential, of the Artificial Intelligence.

[@robeik]

Fishing in Esperance, WA?

[@robeik]

ah, watch to the end of the video - anyway, Google image search works.