How they found the World's Biggest Prime Number - Numberphile

Featuring Matt Parker...
More links & stuff in full description below ↓↓↓
See part one at: • New World's Biggest Pr...
Part three on Numberphile2: • More details about the...
Matt's interview with Curtis Cooper: • New World-Record Large...
The previous record: • New Largest Known Prim...
Mersenne Numbers and Mersenne Primes: • 31 and Mersenne Primes...
More on Mersenne Primes: • Perfect Numbers and Me...
GIMPS: www.mersenne.org
Prime Playlist: bit.ly/primevids
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[@vinnyoh4274]

Matt: ... I know 5 is a prime number. Brady: What?? Matt: Probably..... What a classic Parker Square moment.

[@arielzaitcev1716]

1:59

[@themobiusfunction]

Stop making Parker squares a thing! -Matt Parker

[@sebastianorellana3912]

@computer hi matt

[@createyourownfuture5410]

What's a Parker square?

[@sebastianorellana3912]

@@createyourownfuture5410 "parker square" refers to an infamous mistake by mathematician Matt Parker

[@NomTom]

instead of searching for the biggest prime number, I went searching for the smallest. After two years of calculating, my computer finally found it: 2

[@randomcat5262]

try hunting for more even primes

[@gatlinggun511]

Isn’t one also a prime or is it not considered a prime because it’s also a square

[@christinebeatrixconsul2031]

@@gatlinggun511 1 is not a prime due to the fact that it only has 1 factor. a prime number has 2 factors, 1 and itself

[@camo5553]

@@gatlinggun511 1 isn't considered prime because it would break the fundamental theorem of arithmetic, as they would then have infinite prime factorizations due to being able to have an arbitrary number of ones in the factorization, so we decided to just not include it as prime (among other reasons, but this is a big reason why)

[@dopesponge8430]

It’s infinity right?

[@donbasuradenuevo]

Finding the 2^127-1 Lucas number... by hand. Imagine messing up just one freaking number.

[@ramuk1127]

eZ

[@conomotoapologize1125]

+donbasuradenuevo Use binomial expansion.

[@monicarosas264]

3,848,889,888 3,848,889,890 3,848,888,897 whoops gotta start over

[@ahsannadeem346]

I predict you just tested 2^7-1 already.. Didn't u??

[@MikeRosoftJH]

@@monicarosas264 The mathematician William Shanks took 15 years to calculate 707 decimal digits of pi, but he made a mistake at the 528th position.

[@egormatuk3786]

03:43 they grow up so fast ;-;

[@fakefirstnamefakelastname8305]

E

[@markiyanhapyak349]

They do.

[@vikram03]

He'll grow.

[@MrWabadabadoe]

2 forests where destroyed to make that book

[@thelatestartosrs]

+mrkarlhey not really unless you're really into that stuff and can compare it to other values for random activities

[@edinburghcopyshop1705]

+Wabadabadoe It's only a ream and a half per copy

[@mahinalam]

+mrkarlhey It wasn't found with extremely advanced computers rather 800ish very average computers months.

[@mahinalam]

+mrkarlhey It wasn't found with extremely advanced computers rather 800ish very average computers months.

[@mahinalam]

+mrkarlhey It wasn't found with extremely advanced computers rather 800ish very average computers months.

[@harrytsang1501]

this number is fabulous in binary

[@kemkyrk8029]

+Harry Tsang Like all Mersenne numbers

[@REMagic42]

+Harry Tsang Yeah, I am so smart that I learned it by heart!

[@parakmi1]

+TheJman0205 00110000 00110001 00110001 00110000 00110001 00110001 00110001 00110001 00100000 00110000 00110001 00110001 00110000 00110001 00110001 00110001 00110000 00100000 00110000 00110001 00110001 00110000 00110000 00110001 00110000 00110001 00100000 00110000 00110000 00110001 00110000 00110000 00110000 00110000 00110000 00100000 00110000 00110001 00110001 00110001 00110000 00110001 00110000 00110000 00100000 00110000 00110001 00110001 00110000 00110001 00110000 00110000 00110000 00100000 00110000 00110001 00110001 00110000 00110000 00110000 00110000 00110001 00100000 00110000 00110001 00110001 00110001 00110000 00110001 00110000 00110000 00100000 00110000 00110000 00110001 00110000 00110000 00110000 00110000 00110000 00100000 00110000 00110001 00110001 00110001 00110000 00110001 00110001 00110001 00100000 00110000 00110001 00110001 00110000 00110001 00110001 00110001 00110001 00100000 00110000 00110001 00110001 00110001 00110000 00110000 00110001 00110000 00100000 00110000 00110001 00110001 00110000 00110001 00110000 00110001 00110001 00100000 00110000 00110001 00110001 00110001 00110000 00110000 00110001 00110001 00100000 00110000 00110000 00110001 00110000 00110000 00110000 00110000 00110000 00100000 00110000 00110001 00110001 00110000 00110000 00110000 00110001 00110000 00100000 00110000 00110001 00110001 00110000 00110001 00110001 00110001 00110001 00100000 00110000 00110001 00110001 00110001 00110000 00110001 00110000 00110000 00100000 00110000 00110001 00110001 00110000 00110001 00110000 00110000 00110000 00100000 00110000 00110000 00110001 00110000 00110000 00110000 00110000 00110000 00100000 00110000 00110001 00110001 00110001 00110000 00110001 00110001 00110001 00100000 00110000 00110001 00110001 00110000 00110000 00110000 00110000 00110001 00100000 00110000 00110001 00110001 00110001 00110001 00110000 00110000 00110001 00100000 00110000 00110001 00110001 00110001 00110000 00110000 00110001 00110001 00100000 00110000 00110000 00110001 00110000 00110000 00110000 00110000 00110000 00100000 00110000 00110001 00110001 00110001 00110000 00110001 00110001 00110001 00100000 00110000 00110001 00110001 00110000 00110001 00110000 00110000 00110001 00100000 00110000 00110001 00110001 00110001 00110000 00110001 00110000 00110000 00100000 00110000 00110001 00110001 00110000 00110001 00110000 00110000 00110000 00100000 00110000 00110000 00110001 00110000 00110000 00110000 00110000 00110000 00100000 00110000 00110001 00110001 00110000 00110000 00110000 00110001 00110001 00100000 00110000 00110001 00110001 00110000 00110001 00110001 00110001 00110001 00100000 00110000 00110001 00110001 00110001 00110000 00110000 00110000 00110000 00100000 00110000 00110001 00110001 00110001 00110001 00110000 00110000 00110001 00100000 00110000 00110000 00110001 00110000 00110000 00110000 00110000 00110000 00100000 00110000 00110001 00110001 00110000 00110000 00110000 00110000 00110001 00100000 00110000 00110001 00110001 00110000 00110001 00110001 00110001 00110000 00100000 00110000 00110001 00110001 00110000 00110000 00110001 00110000 00110000 00100000 00110000 00110000 00110001 00110000 00110000 00110000 00110000 00110000 00100000 00110000 00110001 00110001 00110001 00110000 00110000 00110000 00110000 00100000 00110000 00110001 00110001 00110000 00110000 00110000 00110000 00110001 00100000 00110000 00110001 00110001 00110001 00110000 00110000 00110001 00110001 00100000 00110000 00110001 00110001 00110001 00110000 00110001 00110000 00110000 00100000 00110000 00110001 00110001 00110000 00110000 00110001 00110000 00110001

[@AbandonedVoid]

01001101 01000100 01000101 01110111 01001101 01010100 01000001 01111000 01001101 01010100 01000101 01100111 01001101 01000100 01000101 01110111 01001101 01000100 01000101 01111000 01001101 01010100 01000101 01100111 01001101 01000100 01000101 01110111 01001101 01000100 01000101 01111000 01001101 01010100 01000101 01100111 01001101 01000100 01000001 01111000 01001101 01000100 01000001 01110111 01001101 01000100 01000101 01100111 01001101 01000100 01000001 01111000 01001101 01000100 01000001 01110111 01001101 01000100 01000001 01100111 01001101 01000100 01000101 01110111 01001101 01000100 01000001 01110111 01001101 01010100 01000001 01100111 01001101 01000100 01000101 01111000 01001101 01000100 01000101 01110111 01001101 01000100 01000101 01100111 01001101 01000100 01000101 01111000 01001101 01000100 01000101 01111000 01001101 01010100 01000001 01100111 01001101 01000100 01000101 01111000 01001101 01000100 01000001 01110111 01001101 01000100 01000101 01100111 01001101 01000100 01000101 01111000 01001101 01010100 01000001 01110111 01001101 01010100 01000001 01100111 01001101 01000100 01000101 01111000 01001101 01010100 01000101 01110111 01001101 01000100 01000101 01100111 01001101 01000100 01000001 01111000 01001101 01000100 01000001 01110111 01001101 01000100 01000001 01100111 01001101 01000100 01000101 01111000 01001101 01010100 01000001 01111000 01001101 01000100 01000001 01100111 01001101 01000100 01000101 01111000 01001101 01000100 01000101 01110111 01001101 01000100 01000001 01100111 01001101 01000100 01000101 01111000 01001101 01010100 01000001 01110111 01001101 01010100 01000001 01100111 01001101 01000100 01000101 01111000 01001101 01000100 01000001 01111000 01001101 01000100 01000101 01100111 01001101 01000100 01000101 01111000 01001101 01000100 01000001 01110111 01001101 01000100 01000101 01100111 01001101 01000100 01000101 01111000 01001101 01000100 01000001 01111000 01001101 01000100 01000001 01100111 01001101 01000100 01000001 01111000 01001101 01000100 01000001 01110111 01001101 01000100 01000101 01100111 01001101 01000100 01000001 01111000 01001101 01000100 01000001 01110111 01001101 01000100 01000001 01100111 01001101 01000100 01000001 01111000 01001101 01010100 01000101 01110111 01001101 01010100 01000001 01100111 01001101 01000100 01000101 01110111 01001101 01000100 01000001 01111000 01001101 01000100 01000001 01100111

[@PathOfDamn]

+Abandoned Void 01000010 01101001 01101110 01100001 01110010 01111001 00101100 00100000 01110100 01101000 01100101 01101110 00100000 01000010 01100001 01110011 01100101 00110110 00110100 00101100 00100000 01110100 01101000 01100101 01101110 00100000 01100010 01101001 01101110 01100001 01110010 01111001 00100000 01100001 01100111 01100001 01101001 01101110 00101100 00100000 01100101 01101000 00111111 00001101 00001010 00001101 00001010 01010000 01101111 01101001 01101110 01110100 01101100 01100101 01110011 01110011 00101110 00101110 00101110 00100000 01000010 01110101 01110100 00100000 01101001 01110100 00100111 01110011 00100000 01100110 01110101 01101110 00101100 00100000 01001001 00100000 01100111 01110101 01100101 01110011 01110011 00101110

[@Azide_zx]

fun fact, Prime95, which is the prime finder tool made by GIMPS, is also used as a stress test for CPUs for overclocking

[@Pedro14ceara]

Can confirm, I saw a technician test my PC with it.

[@knighty0220]

If you'd figure out a pattern, would you get more money for publishing a prime every month or for publishing the pattern?

[@flibujo]

Like pharmaceutical companies. They make less from curing disease than by treating it.

[@lucasng4712]

Are you the guy who believes the thing that they're withholding cancer cures too?

[@hyprolxag]

Lucas Ng yes and no. "Yes" is Companies wont produce any product they think unprofitable. if they could, the process would be secret and the ingredients be partly secret too, so we dont know if there was any better way possible. "No" is hardly found a company invest in such researches, investing in cancer research is super risky, so public laboratories run by the goverment will do this job, and yes, they will publish everything.

[@ervinm.5065]

publish a prime every month. there will be many more pages each time so it will cost more and more. do not publish the pattern if you're able to find a prime each month or anyone will do it

[@workhardism]

A company that had the cure for cancer would make an untold fortune from it and would never withhold it. It wouldn't be relevant to them that other companies would no longer profit from treating the disease. Government agencies are run by people who have a vested interest in keeping their funding going on and on forever. There is much mere accountability in private concerns because you only get paid for what you actually accomplish an what you can market. Public (government) concerns exist to milk more and more research money, which would end as soon as they were to find a cure.

[@GamesFromSpace]

My brain just threw an exception.

[@TanmayPatil37]

I hope you caught it

[@tubular618]

You have an exceptional mind.

[@gooz1691]

Don't see how it could've thrown an exception, integer overflow maybe

[@danjbundrick]

Oh is that what that sound was?

[@blue9139]

All even numbers can't be primes expect 2

[@TofranBohk]

I found one! 11 is a prime number!

[@black_platypus]

+t0f0b0 and in binary too^^ ...and quaternary ...and senary Cool, works in 4 distinct bases :D ...But it's not a Mersenne prime >:(

[@jordanlynch571]

+Benjamin Philipp Wouldn't it be prime in an infinite number of distinct bases as 11 would simply whatever base you choose plus 1?

[@black_platypus]

Jordan Lynch Of course... :D Somehow I was focused on decimal so much that I thought "well, the 'value' of 11 won't change in higher bases" as if it was a distinct digit, making higher bases irrelevant. That's what I meant by "distinct bases": "Eleven is still going to be eleven in bases higher than 10 and will always be a prime" - neglecting the fact that eleven would look like "Ɛ" for example.

[@tubular618]

I can count to potato!

[@nickjimenez9983]

11 has four factors: 1, 2, 5.5, 11 Trololoollooll jk jk jk jk J U S T K I D D I N G J US T A B R A N K. P R O

[@thelasttimeitookashowerwas7069]

this is beyond my imagination how they come up with say something like lucas series and check if a number is prime or not from that series... props to the legends like these..

[@Fish-ec8nq]

4:05 He fast forwarded those numbers because he started by saying “2 billion”, not “2 quintillion. Ripparoni

[@dvndavid]

Fish Nugget it’s ~ 2 billion billions. Maybe thats why

[@blue9139]

David - Yea prop lol. But saying a quintillion is better

[@anandsuralkar8376]

@@blue9139 lol

[@12tone]

Any chance we'll get an explanation of why that method works?

[@LOCKEYJ]

It’s in the video

[@eboone]

Interesting seeing you here 4 years later

[@_wetmath_]

@@eboone why is this video suddenly recommended

[@jakemcmillian]

@@_wetmath_ might be my fault... I was binge watching numberphile a couple weeks ago, found this one and made a few comments on it. From what I could tell, the last reply was a year before my comments. Just a guess though.

[@SlashCrash_Studios]

Wait *what?!* What's my favorite music theorist doing here?! Ps. I'm on the spectrum too

[@ElMoShApPiNeSs]

Wrong. The Lucas numbers go 4, 5, 6, 1, 2, 3.

[@blinky_52]

+Thingsandstuff Now it's 4, 5, 6, 1, 2, 3, 7 xD

[@thelatestartosrs]

+Thingsandstuff thanks

[@DrEvil-uw1ju]

+Thingsandstuff No they go: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498, 3010349, 4870847, 7881196, 12752043, 20633239, 33385282

[@EmptyBodies]

Was there a joke here I missed?

[@ElMoShApPiNeSs]

+E.B. White George Lucas

[@clowen00]

This cant be true! The Google Calculator says this number is Infinity!

[@belleren9375]

Then it's wrong

+Clowen00 TIL Infinity fits in three volumes.

[@ramuk1127]

+Belleren savage

[@adriantaylor753]

That's only because the number is too big for the calculator to calculate

[@clowen00]

Epic Wolf Oh really? That sounds actually plausible, didn't thought about that! ;-)

[@SaraSchenstrom]

The fact that people are so nerdy they do this, and then print it out like it was a book, it makes me ridiculously happy. And btw, thank you guys for making videos! I haven't done very advanced math, but through your videos I have been able to at least kind of grasp the idea of some of these amazing things!

[@TehDragonGuy]

You should mass produce those books. I would legitimately buy them.

[@DjGreydanus]

+TehDragonGuy Why?

[@Justaguy19381]

+David Greydanus because

[@allyourcode]

+TehDragonGuy What are you going to do when the next largest prime is discovered?

[@TehDragonGuy]

+allyourcode Chop down even more trees.

[@allyourcode]

I want to know how many tons of coal need to be burned for GIMPS to find the next largest prime.

[@DavidRussell323]

I betcha 2^(2^74207281 - 1)-1 would work

[@alandouglas2789]

Why?

[@vivafeverfifa2524]

+Alan Douglas do you have an idea of how big that number is? It's like trillions of digits long (maybe even bigger).

[@vivafeverfifa2524]

+Alan Douglas do you have an idea of how big that number is? It's like trillions of digits long (maybe even bigger).

[@trevorWilkinson]

+DavidRussell323 was just thinking that, I wonder if the chances of a 2^Mersenne Prime - 1 are more likely the answer is a prime.

[@zacchon]

+VivaFeverFifa 2^74207281-1 contains 22,338,618 digits. 2^10^22,338,618 would be something like 10^22,338,617 digits long.

[@neurospizz75]

if I'm at a restaurant and order a cut of meat, can I use this formula to see if the ribs are prime?

[@blockededited8280]

Gopher it.

[@promerops]

Or at the bank, to ascertain the ruling prime rate?

[@bananya6020]

If they don't give you a prime number of ribs, send it back

[@anandsuralkar8376]

@@bananya6020 lol

[@fandomewhisper]

Side splitting humor 😐

[@MoosesValley]

Excellent video. So engaging, so informing, so entertaining ! The faces Matt pulls are so funny. In fact, I would put them in the "Flippin' hilarious !" category. And him printing the out the largest prime on 745 pages of paper (double sided) is just such a Matt thing to do. And it is not a waste of paper, he will take these volumes to talks, lectures, meetings, and people will look at them and wonder ... On a quiet Sunday afternoon, he will probably put his favorite math's journal aside and flick through these volumes and smile. (Don't worry, I would as well).

[@drink__more__water]

I love watching these videos... Even at school the people which are concentrated in maths tend to not actually care about, or get excited by math. It just makes me happy to see someone else smile because of a property of a sequence of numbers...

[@zioscozio]

Could somebody write this prime in base 26 and print it using English alphabet? Would it reveal interesting words? What would be the longest?

[@keroia]

+scozio Gotta make it base 36. Thou has forgotten the numbers.

[@carlosvargas2907]

+Keroia Just encoding

[@Trooperos90]

+scozio it says 'illuminati'

[@ilexdiapason]

scozio it would say "youhaveallbeenfooledforsolongtherealenemyisthemartians7902g4h8kkkkkk1" somewhere in there

[@doszlopleonard6031]

scozio base 26?!?!?

What really impresses me is the fact that he decided to print it.

[@zeddash.6695]

Here is a joke. The number 5 was a champion at boxing. He lost when he turned into a 6. The reason he started losing was because he wasn't in his prime.

[@proto9053]

But he was back at it again when he turned 7.

[@darraghmckane4016]

Zed dash. silly joke when he. was. 6 he was perfect.

[@nickjimenez9983]

Jayden Tan It wasn’t a 5-year old 5

[@NickMC512]

Zed dash. This entire thread delivers.

[@digitalfootballer9032]

Why is 6 afraid of 7? Because 7 8 9.

[@Cruuzie]

Matt is so brilliant, gotta love his enthusiasm

[@banemiladinov8202]

He's so brilliant 18 + 29 is fiftyyyyishhh.... ahh 47 !😂😂

[@dancrane3807]

1:35, gives away the answer, THEN says "spoiler". That's not the way a spoiler alert works dang you!

[@tennisdude52278]

Can we have another calculator unboxing?

[@kushal7371]

Great work and this is one of the best channels on youtube...

[@pomegranatechannel]

I love this topic. Please make more videos about prime numbers.

[@fhmxlx9246]

not exactly my field, but maths is always mindblowing and interesting, thanks for the great video Numberphile.

[@jennifersiagian]

I want to say THANK You for everything you give us freeley

[@ProfessorEisenoxid]

This channel is one of the best on KZbin!

[@Prinsten4girl]

I would love to have those three copybooks. Seeing the number actually printed is amazing.

[@samharper5881]

lol "the world's". Because it's prime here but on Mars it's actually divisible by 17 and on Neptune it's an even number.

[@thelatestartosrs]

+Sam Harper ?

[@YourMJK]

+Albert Chan You are so clueless about how jokes work

[@Xnoob545]

I dont unsfdder4y3wfhwhy5

[@DreckbobBratpfanne]

XD

[@protonruffy12]

Maybe "the world's" because an alien species couldve found a bigger one already.

[@ApplicationBot]

they found a new one yesterday

[@rishimilward-bose3544]

10:45 0.5 X speed, the way he says computers kills me

[@marinap5345]

10:46

[@kathorsees]

this is hilarious, he sounds absolutely drunk XDDD

[@gallium-gonzollium]

“for a dAay wE g- gAt sAmthing tOo dOo with oUr côMpüÜtèrs”

[@OddtwangofDork]

Don't know if the third video will cover this, but - Matt mentions here that we only need look for Mersenne primes (2^p)-1 where p is prime, and we're working our way up through prime values of p to check things. However, we know that Mersenne primes (and the other categories we're hunting for) are only a subset of all primes, so don't we eventually reach a point where we're not certain that the next exponent to check is indeed the next prime? For example, if you started only knowing that 2 is prime and that Mersenne primes exist, you'd immediately find that 3, 7 and 127 are prime, but you've already missed 5 and 11 because they're not Mersenne primes, which in turn means you didn't find 31 which is a Mersenne prime. I mean, we presumably know the primality of all numbers up to a point a lot greater than 74million, so I may be worrying about a far-future problem here!

[@KaizokuNiichan]

+Oddtwang of Dork Testing the primality of smaller numbers will take a few seconds at most (probably not even a tenth of a second for a number of the order of a few billion.)

[@Swiftclaw123]

Ok but why does this Lucas number prime test work?

[@sefirotsama]

The real question remains unanswered

[@050138]

The proof is beyond the scope of this video

[@srirachadonut8011]

Just math. You could ask that question about the simplest algebra and end up in a massive loophole of confusing proofs

[@martrayleigh7988]

The one that can answer that is 3blue1brown..

[@jacobshirley3457]

@@050138 The proof is left as an exercise to the viewer.

[@AllHailZeppelin]

“One of my favorite Mersenne Primes” is such a Matt Parker thing to say!

[@juanjosecelada]

Amazing !!!! This can definitely be parallelized.

[@pllplnt]

Can you guys make a video about the other competing software? Like the types of primes it finds and how it does it? Sounds interesting!

[@johnny5021]

I was doing some math and found that (2n)+(n^2)-1 created primes very well if n is even. Example: (2 x 99922222222220)+(99922222222220^2)-1 is prime. I also saw that up to 200 being n (leaving out odd numbers) it spit out a prime 42% of the time.

[@fcvgarcia]

Awesome!!! Thanks for the magic!

[@Dawwwg]

I did PrimeGrid (and other DC projects) for a long time as well; love how distributed computing can help solve unimaginably large problems :)

[@99bits46]

Poor computers

[@nbp2015]

Actual title: "The Biggest Number Anyone's Bothered Proving is Prime"

[@Shyguy5104]

that's a lot of numbers!

[@trueriver1950]

The biggest number SO FAR that anyone's bothered proving is prime. As shown by the fact that this number is nowadays nowhere near the biggest any more

[@Cannongabang]

this is probably the best video

[@osamaghaedy1869]

Best video I’ve ever seen in youtube

[@christianpoland8573]

Joined the GIMPS project today, 1.7% done on two exponents!!! I'm feeling lucky :o

[@Moleda1986]

My math expertise is limited to high school algebra. I was always pretty bad at math. And yet I find your videos so interesting! I could watch them for hours!

[@blockbrain2713]

Sup matt today u gave a talk at Denbigh High I really enjoyed it thanks 😄😄😄😄😄😄

[@Handwriting_R]

Love your channel 😍 go on

[@24canidkasi]

Reading that 2^74207281 book would be much more entertaning than reading Twilight.

[@24canidkasi]

-1 (_ _)

[@dolphinsupreme1697]

I mean that's a really low bar to set though.

[@Sengial]

Holy shit that's fucking big

[@quarkyquasar893]

+ytYAEeLxmEYb As compared to infinite...

[@draevonmay7704]

+Red Sniper Well, infinitesimals are actual things, used in calculus, and that is definitely not one, but yes compared to infinity it is a small number.

[@quarkyquasar893]

Draevon May Well thanks for info but i already know that... :P

[@draevonmay7704]

+Red Sniper Assumed you did. I'm used dealing with highschoolers. Not the brightest bunch of people 😆

[@quarkyquasar893]

Draevon May XD

[@aaaaaaaaaaaa9023]

AAH! 1:35 you said spoilers AFTER you said it!! I was looking forward to watching the prime numbers!

[@supercute590]

I love his enthusiasm for prime numbers

[@sahildalvi6892]

a very interesting video...something i didn't know...but something i always wondered how they did it... i have 2 questions 1. what is the mathematical proof that lucas-lehmer sequence filters out prime numbers 2. what is the use of finding bigger and bigger prime numbers? thankyou :-)

[@aleb8243]

Ryan Lochte explaining prime numbers Now I've seen everything

[@rsingh2083]

Smart combover ;-) & great video

[@DaveScottAggie]

This is pretty incredible that there are ways to check a number for primality, or prove it is composite, without finding any factors.

[@neelmodi5791]

Next largest prime: 2^74207281+1. The proof is left as an exercise to the reader.

[@theleftuprightatsoldierfield]

Neel Modi I know for a fact 2^74207281+1 is not prime. It is divisible by 3

[@void9720]

If 2^74207281-1 is prime, and 2^74207281 is an even number with no factor of 2 - then 2^74207281 must divide by 3.

[@santhosh_se5476]

@@theleftuprightatsoldierfield Ohh man u spoiled his attempt for a joke😂😂😂🤣🤣🤣 Anyway that was perfect ....

[@sgssergio]

Jajja, two year ago discovered other Mersenne prime with more than 24 millons of digit. The gigant Merssenes primes numbers discovered in the last 20 years was a distributed work of millons of personal and server comouter around the world using the Primes95 application conected in the GIMP project.

[@jblistener7491]

So basically he wants us all to use G.I.M.P.S. so that he can find the really big numbers using PrimeGrid. Well, I won't fall for that trap! :) On an unrelated note, was anybody else watching him wave the marker around, and waiting for the moment when he accidentally marked up his new prime number books and lost it on camera?

[@BrenTen628]

The "WHAAAT!" from behind the camera at 2:00 is perfect.

[@JMUDoc]

That number has got a carbon footprint thanks to Matt.

[@cmopmoemo]

Could you explain a proof of the test you used?

[@prae197]

Brady's reaction at 2:01 though

[@eddyhans5365]

Nice explanation.

[@MilesEques]

not sure what you'll make of this, but this video inspired me to install Folding@Home

[@rikschaaf]

What is the biggest prime for which we know all the previous primes?

[@janeemmanuel8885]

Rik Schaaf 356787 42157899865323466755443278887765556789000009887665433457788839387474738289254333564215789986532346675544323585858696969699988665323567898531245685652413131453645

[@sergejkeser7270]

@@janeemmanuel8885 I mean, if you are gona smack your head on the keyboard in order to guess an answer to his question, at least make sure it does not end with digit 5 lol

[@zach7009]

Sergej - That's hilarious! I love it.

[@deepghosh7626]

@@sergejkeser7270 😂😂

[@Azide_zx]

@@sergejkeser7270 dont forget about the random space 7 digits through

[@ylette]

Wonder what the biggest prime is where all the numbers below it have been checked.

[@GreatOutdoors1]

they've checked up to around 10^18. I think they've gone a bit further but haven't gotten to 10^19 yet.

[@jordanlynch571]

+Cruzer Since doing so is easiest based on a sieve, once you know the list up to that point, the next is easy to find. Too hard to define a specific point for that reason, and thus little reason to even search.

[@gordontaylor2815]

+xunile1 But remember they (Gimps) are only checking one type of prime - there may be other types which haven't been checked up to that range yet.

[@GreatOutdoors1]

+Gordon Taylor the numbers that GIMPS is searching for are way larger than 10^18, all primes up to 10^18 have been found.

[@spinn4ntier487]

Cruzer i can check the largest ones conceivable factors 2=no 3=no 6972=no We know it is a prime, so we know all of its potential factors aren't it's factors

[@mistycremo9301]

You should do Pascal's triangle and then highlight the multiples of any whole number. Four is my personal favorite, but I only tested 1-5 and with limit space.

[@MM-qd4lh]

This all hurts my head, but I can't look away. It's as cool as trying to follow the logic of the Mandelbrot sets. Like chasing fireflies as a child, sheer joy!

[@hymnodyhands]

Always nice to meet a fellow traveler, chasing fireflies through the fields of math!

[@avsn]

Where can i get a copy and how much?

[@BandidoDescalzo]

+A V Sandi Nack $2^74,207,281 -1 USD

[@avsn]

+josiah O'Neill smart aleck :)

[@avsn]

+YipYapYoup I thought your dollars were bimetal. :)

[@thesimen13]

+A V Sandi Nack commenting for captain

[@oldcowbb]

+A V Sandi Nack mathsgear, maybe

[@SCMabridged]

I'm so conflicted: on one hand, this is so mathematically beautiful; on the other, it's witchcraft!!

[@npip99]

9:00 Note that subtracting off as an algorithm wouldn't qualify as "Not that bad", as it would be very bad. But you can binary search the largest multiple of the modulus that's less than the target number, and then subtract that from the target number.

[@sagartirthasengupta852]

This is the craziest thing I've ever seen!

[@seanm7445]

Any chance of a video on Germain primes?

[@matthewnotreal1118]

yes

[@666Tomato666]

+Sean M would be fun just to hear them struggle with pronunciation

[@WindowsXP_YT]

The primes of the form (3^p)-4: 5, 23, 239, etc.

[@trueriver1950]

The interesting thing about 239 is that it's the only prime number divisible by 239. So what, you say? Well then, why does everyone keep taking me that 2 is the only prime number: all they mean is that it's the only prime number divisions by 2. But you can say an exactly similar thing about EVERY prime. So what?

[@WindowsXP_YT]

@@trueriver1950 There are some other primes of the form x^y-z

[@easysolutions3312]

Just read the first volume, it was heartbreaking😢😢😢 best book.

[@u2lover10]

excelente video!!!!

[@loudandlearnt1758]

Great video! Prime numbers are so fascinating, I actually made a video proof about how there was no largest. We'll be looking for the next biggest one forever :D

[@justagerman140]

I love how the books are printed on brown paper

[@inujosha]

Another great video. Only thing is the audio levels are a little low

[@potassiumpermangante]

I am a Maths lover.Please keep doing many more Interesting videos.

[@omfgmouse]

12:12 Creeper says hi!

[@j.s.b.6299]

I must ask, what is the application of such a large prime? Could it become useful for encryption/decryption on quantum computers?

[@Rudxain]

On quantum, probably not. But for classical, yes, because RSA

[@thejackluo]

Hi Numberphile, I really liked your channel. I just have a question. We haven't proven if prime is infinitely yet. Because this sequence continues, so, that means Either the primes are infinity or the sequence maybe possible the primes won't be primes in the big numbers as the sequence continue, I am just wandering which of the two answers should be correct, can you give me an answer? Thank you.

[@juanjoglvz7]

wow this comes amazingly handy to program anything related to mathemathics.

[@SandraMarkusTrachsel]

Dear Mr. Parker, please allow me to ask you, what is the biggest prime number up to which all previous prime numbers have been found. I assume that the hunt for big primes is leaving huge gaps of undiscovered primes. Thank you very much and best regards, Markus

[@trueriver1950]

Correct: We know all the previous primes of various types. For example, whatever the current biggest Mersenne prime is at any time, we likely know all the smaller ones in that series of primes. Ditto for any other family of primes (Sophie Germain, etc...) What we don't necessarily know is all the primes in between those in the various series of easy-ish primes. We know approximately how many there are in any gap, but without testing exhaustively we never can be sure if we have them all. So your question amounts to asking how far has anyone got doing an exhaustive search for primes starting from 2. Apols if you already figured that out

[@aednil]

how long until this number is used in encryption?

[@TheBalfrog]

+aednil Considering banks use 2048 bit numbers now and modern computing would take thousands of years to break the discrete logarithm problems, it could be a while!

[@levolta]

+James Purcell I'm not 100% certain of how encryption works, but iirc, this number is even useless for encryption, because it is so well known. It doesn't sound completely right, but I heard it from various sources.

[@TheBalfrog]

levolta The most basic variation is RSA, so in RSA I'd tell you (n,e) = (65,7), e is your encryption component, and n is the product of 2 primes p and q. Obvious with a number this small you can see, p = 13 q = 5. Now if you want to find the decryption component, you do e * d = 1 mod (p-1)(q-1) , so 7 * d = 1mod 48. Again as it's a simple example you can spot if d = 7, then 7*7 = 49mod 48 = 1mod 48. So if I give you a message say M = 3. 3^e mod n = C your ciphertext. So 3^7 = 2187 = (33*65) + 42 mod 65 = 42mod 65. So after encryption of a message M = 3, we get a ciphertext C = 42. If you want to decrypt this, you can do C^d mod n, so 42^7 mod 65 = 3mod 65. So a message raised to the power of the encryption component becomes ciphertext. a ciphertext raised to the power of the decryption component is your original message. If your primes become huge (Banks use 1024 bit primes), these numbers are crazy big, and it is computationally infeasible to find the primes P and Q if given the product N. If they can't find P and Q they can't find the decryption component and you're messages and bank details ect are safe. Because this prime is so large it isn't really an issue, and won't be for a large amount of time. Banks at the moment use two 1024 bit prime numbers, to make a 2048 bit product N, this takes current generation computers millions of years of constant computation to brute force. I doubt banks will ever use a prime this large in security based systems such as RSA.

[@catStone92]

+James Purcell what levolta meant is that if you did decide to use this specific prime, people would already know one of the components, so you already have the job done for you, you successfully decrypted an RSA key the strength of RSA comes from not being able to find the components in useful time, but if you know one of them, the job is already one, it's a linear operation to find out the other one and you can guess the private key.

[@TheBalfrog]

Pedro Gusmão While that is true, banks don't tell you what either of the primes are, if they started using a 44million bit prime people would get suspicious sure, but as more primes are discovered and none mersenne primes are discovered through things like prime grid theoretically a well known prime could be used, but it would be dangerous as you've said

[@sgssergio]

Two year ago discovered other Mersenne prime with more than 24 millons of digit. The gigant Merssenes primes numbers discovered in the last 20 years was a distributed work of millons of personal and server comouter around the world using the Primes95 application conected in the GIMP project.

[@Fritzyboo]

I thought he actually divided it by three.... By hand. I mean of all people, Matt would. But then I remembered it's prime.

[@spencerlemens9321]

So now since the exponent has to be prime some quick use this prime as the exponent and find a ridiculously large one!

[@RanEncounter]

The computing power needed to check that would be astronomical.

[@thelatestartosrs]

+SPENCER LEMENS 2^(2^74207281 -1) -1 ftw

[@frustbox]

+SPENCER LEMENS Sadly, the exponent being prime is only a necessary but not sufficient. Therefor the converse is not true. Example: M11. It's a Mersenne number with a prime exponent: 2^11 - 1 = 2047 but the result is not prime since 2047 = 23 * 89. It's still a good idea to use this prime as exponent and eventually it will be checked at some point ... it may even be prime, who knows -- but it's not guaranteed to be a prime.

[@MeLoonn]

So, is 2 ^"THAT monster prime" -1 also a prime ? XD

[@yamizetsubou8414]

+Plasma Phi My calculator says "ERROR" so it might be

[@unvergebeneid]

+Plasma Phi Can I get back to you on that? ;)

[@a2aaron]

Maybe. 2^n - 1 is prime if n is prime, but if n is prime, 2^n - 1 may be composite

[@robbieelvin4951]

+Plasma Phi It would need to be checked.

[@funnyids3D]

+Plasma Phi I was wondering the exact same

[@luccarawlyk3423]

I wonder if we're getting a Collatz Conjecture (3x+1) video sometime soon ^^

[@MathBuz]

Please provide a reference for your statement “2^127 - 1 is the biggest prime founded by hand” I am working as maths teacher.. And I really appreciate your efforts..

[@brianmckay1256]

Hi Matt Musical Prime if you list from 1 to 24 in colums in ms excel, then cary on counting from 25 on the next row down althe way to 48, then continue this patten in rows and columns, all the primes line up, and make interesting patterns. Then is you make every 5 rows a music staff then you can play the prime numbers on a piano keyboard. you can chose how long or short the note is and the tempo of course, It makes your brain hurt but an interesting tune!!!!!!! have fun regards Brian the novis (just out to have fun)

[@akramfaiza3017]

They just found a new one (2^77232917)-1

[@mr.questionmark5038]

:P

[@goldenera7090]

fantastic way to explain primality - thanks for simplifying

[@enzopalmer4745]

Its so great that they have 3.33 million subscribers