What do 5, 13 and 563 have in common?

We're talking Prime Numbers again... Featuring Dr James Grime.
More links & stuff in full description below ↓↓↓
Extra footage: • Wilson's Theorem (extr...
Our Prime Numbers extravaganza: bit.ly/primevids
Brown paper: bit.ly/brownpapers
Liar Numbers: • Liar Numbers - Numberp...
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[@louisgil9630]

Do you guys just have a huge storage filled with brown paper?

[@numberphile]

Louis Gil I have a pretty big box of them!

[@slayersdragon6129]

+Numberphile Oh............., a very traditional thing for you guys.

[@314rft]

+Numberphile This channel is known for the brown paper.

[@jjovereats]

+Numberphile Don't lie to me! It's a roll.

[@GGViraN]

+jjovereats A mile long one!

[@fakjbf]

James, you need to charge your phone

[@lucasissa5536]

why?

[@Eggemeyers]

And turn on show battery percentage. I hate the ambiguity of no percentage, it really should come with the percentage showing out of the box.

[@Whovian1029]

Nice Tree of Gondor

[@jonathanc8845]

right? I couldn't even watch the calculator bits.

[@karmanyaahm]

And Bluetooth is on

[@HowToBasic]

Eggs

[@unslaadkrosis9435]

+HowToBasic NO FOOKING WAY!!

[@danielshao9161]

Howtobasic loves math

[@want-diversecontent3887]

HowToBasic
*cough*
Eggs! Eggs! E double g s eggs.

[@ButtonMasherReal]

e * g^2 * s

[@ChickenBatmanplayz]

this goes to show that even howtobasic can be interested in math if this channel has it.

[@legoboy1707]

"7 factorial...hmm I wonder what that is..." *looks up, as though calculating* "Aha! 5040!"
Me: Wow, I wish I could calculate like that!
Camera moves to the calculator
"No don't show them that!"

[@vicr123]

Calculators are valuable tools :)

[@elaxter]

Mental math is a gimmick.

[@alejandrocampos1682]

Legoboy

[@bowlchamps37]

I guess it was more of a joke. Every math doctor knows at least up to 10!, right. x! is for university students what x² is for school kids.

[@MrGrumbleguts]

I dunno, I would have thought most people know up to 10! but james (indeed all the numberphile people) seems to be very light on for arithmetic.

[@Twewy13]

Dr James Grime should change his name to Dr James Prime.

[@tabularasa0606]

I agree: Dr James "Prime" Grime sounds weird.

[@rubadux]

he is indivisible, though. Ôo

[@johnojohnovono7666]

My dad is a doctor and his name is James Grimes so this name change would keep his name on google

[@alexandertownsend3291]

So you mean Dr James'

[@anmoljawalia5967]

😂

[@WarpRulez]

What's the difference between a mathematician and a physicist?
A physicist uses a TI scientific calculator. A mathematician uses an iPhone.

[@robin-vt1qj]

at our school we are only allowed to use the TI calculator at maths class.

[@ceselb]

I use a TI emulator on my android. What does that make me?

[@fatmccat1513]

@@ceselb You're a physicist AND a mathematician

[@picks6500]

@@fatmccat1513 he was using an android, not an iPhone tho, so not a mathematician

[@Triantalex]

false.

[@mephostopheles3752]

"Don't show them that!"
They don't want to tell high schoolers that even real mathematicians use calculators. Then they'd have an excuse.

[@Reydriel]

Of course they use calculators. Stuff gets pretty hard to calculate in your head :P

[@mephostopheles3752]

***** Exactly.High school teachers need to stop bullshitting us.

[@BBBuilds12]

Knowing how to basic calculations on paper or in your head is useful, but the majority of the time stick with a calculator. In high school now you use calculators all the time.

[@katzen3314]

Sure, but it's better and faster to be a bit independent from your calculator, which comes with practice.

[@stevenglikin3219]

+SeaBiscuit Hogwarts?... I think you've been watching too much Harry Potter xD I think you meant Harvard

[@floryan1087]

What do 5, 13 and 563 have in common?
They're numbers. Solved

[@mudkip_btw]

Thank you

[@Cardmaster12]

they're all odd

[@JL-zw7hi]

there all prime

[@audiblemagician6751]

They don't have decimals
(well technically there 5.000000000.... 13.00000000000..... 563.00000000....

[@rombow1319]

6?

[@mattseery7943]

Protect this man at all costs. His joy is absolutely infectious. What a wonderful teacher.

[@shekillaboom4729]

now that i know this i am unstoppable.

[@MMmk1]

xD

[@bmxscape]

just like when i memorized 33 digits of pi my life has never been the same, i am far beyond this generation
3.14159265358979323846264338327950

[@ScilexGuitar]

***** I memorized some of the digits too :) 3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000568127145263560827 785771342757789609173637178721468440901224953430146549585371050792279689258923 542019956112129021960864034418159813629774771309960518707211349999998372978049 951059731732816096318595024459455346908302642522308253344685035261931188171010 003137838752886587533208381420617177669147303598253490428755468731159562863882 353787593751957781857780532171226806613001927876611195909216420198938095257201 065485863278865936153381827968230301952035301852968995773622599413891249721775 283479131515574857242454150695950829533116861727855889075098381754637464939319 255060400927701671139009848824012858361603563707660104710181942955596198946767 837449448255379774726847104047534646208046684259069491293313677028989152104752 162056966024058038150193511253382430035587640247496473263914199272604269922796 782354781636009341721641219924586315030286182974555706749838505494588586926995 690927210797509302955321165344987202755960236480665499119881834797753566369807 426542527862551818417574672890977772793800081647060016145249192173217214772350 141441973568548161361157352552133475741849468438523323907394143334547762416862 518983569485562099219222184272550254256887671790494601653466804988627232791786 085784383827967976681454100953883786360950680064225125205117392984896084128488 626945604241965285022210661186306744278622039194945047123713786960956364371917 287467764657573962413890865832645995813390478027590099465764078951269468398352 595709825822620522489407726719478268482601476990902640136394437455305068203496 252451749399651431429809190659250937221696461515709858387410597885959772975498 930161753928468138268683868942774155991855925245953959431049972524680845987273 644695848653836736222626099124608051243884390451244136549762780797715691435997 700129616089441694868555848406353422072225828488648158456028506016842739452267 467678895252138522549954666727823986456596116354886230577456498035593634568174 324112515076069479451096596094025228879710893145669136867228748940560101503308 617928680920874760917824938589009714909675985261365549781893129784821682998948 722658804857564014270477555132379641451523746234364542858444795265867821051141 354735739523113427166102135969536231442952484937187110145765403590279934403742 007310578539062198387447808478489683321445713868751943506430218453191048481005 370614680674919278191197939952061419663428754440643745123718192179998391015919 561814675142691239748940907186494231961567945208095146550225231603881930142093 762137855956638937787083039069792077346722182562599661501421503068038447734549 202605414665925201497442850732518666002132434088190710486331734649651453905796 268561005508106658796998163574736384052571459102897064140110971206280439039759 515677157700420337869936007230558763176359421873125147120532928191826186125867 321579198414848829164470609575270695722091756711672291098169091528017350671274 858322287183520935396572512108357915136988209144421006751033467110314126711136 990865851639831501970165151168517143765761835155650884909989859982387345528331 635507647918535893226185489632132933089857064204675259070915481416549859461637 180270981994309924488957571282890592323326097299712084433573265489382391193259 746366730583604142813883032038249037589852437441702913276561809377344403070746 921120191302033038019762110110044929321516084244485963766983895228684783123552 658213144957685726243344189303968642624341077322697802807318915441101044682325 271620105265227211166039666557309254711055785376346682065310989652691862056476 931257058635662018558100729360659876486117910453348850346113657686753249441668 039626579787718556084552965412665408530614344431858676975145661406800700237877 659134401712749470420562230538994561314071127000407854733269939081454664645880 797270826683063432858785698305235808933065757406795457163775254202114955761581 400250126228594130216471550979259230990796547376125517656751357517829666454779 174501129961489030463994713296210734043751895735961458901938971311179042978285 647503203198691514028708085990480109412147221317947647772622414254854540332157 185306142288137585043063321751829798662237172159160771669254748738986654949450 114654062843366393790039769265672146385306736096571209180763832716641627488880 078692560290228472104031721186082041900042296617119637792133757511495950156604 9631862947265473642523081770367515906735023507283540

[@michaelwright9432]

ScilexGuitar You're no where near my level.

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3995678979817278609204622868397357798151118681526598846069497589654813146511503926263777495137615572481951161198772503445647107385134359273555387124623755981938132142384415819290700463897716838872079163617414324970791096581627464297170728717251427458983568970955346268201690853561089448984071005819203021769451207717745887955195104733841847399807963067678858451675757299043069715426423834980098708699336709121083944535062459224323123482785496603746571880148929379451478705406079245759006012196221239287200172155886663457349714095337211516559857579417244198890261670161016115578343150254603287811984240274846085107224066767787608552476177738330895026100643883505502054563243461678594519417956698749685152448838475136181806671083161655642093692705206118985172926171417144346555087063060635510129494003097591677991584260491971209543227026784326542965724032720887143219996453132025871096771651285496699625526986073117637182074988273997706019913620930832307368382064557325637659829125781314922242204279712...

[@ScilexGuitar]

Rusty Shacklford Wow, man. That is awesome!

[@deliveryguy1981]

2:41 I wouldn't be leaving my phone out on with a low battery.

[@deliveryguy1981]

.

[@numberphile]

Brown paper from this video available --- see ebay link in description if you're interested.

[@nerdbot4446]

Dr. James Prime is back! Awesome!!

[@PrimusProductions]

That makes him sound like a Transformers character.

[@petrowolke]

5...13...563...>20.000.000.000
Well, that escalated quickly!

[@DuringDark]

Tree(1),tree(2),tree(3)

[@jankisi]

Missed three zeros (0:34)

[@lonestarr1490]

@@jankisi That doesn't make it wrong, though, because of the ">".

[@VarmDild]

At 2:38 he could just say that 5041 is odd, and odd numbers are never divisible by 8.

[@Harmoniou-s]

it only worked with primes

[@Riganotza]

Never hurts to check. Don't want to be surprised

[@Methodenlehre]

5 is an even more special prime number since it is the only Wilson prime where the division leads back to the prime itself, as in:
((a - 1)! + 1) / a = a is only true for a = 5

[@mamcstaffviewsteeve5581]

hey hey hey, thats my new number type im stealing

[@DanDart]

It's also true for some non-integers such as -3.02002626182918... and 1.37439467883103...

[@DanDart]

obviously you'd have to use the gamma function instead of plain factorials but yeah

[@AlfaEcho]

Well, that's what we call a Mainzer Prime now

[@lesleyvids2610]

4:00 he should charge his phone...

[@ChaimS]

or turn off Bluetooth- it's draining it!

[@BRE3ZYE]

Do you think there are numbers that pass this test 3 times?

[@libinwang2267]

+3ZYBRE percchance

[@psionic0]

+Ryan Vickers Yes, and they don't :-)

[@Eggemeyers]

That's what I was wondering! Considering there are at least like 20 billion Wilson primes, I would imagine yes.

[@Bluedragon2513]

Easy, take a number, cube it, subtract one.
Now find a number to match up to that with factorials.

[@fancyprogrammer2040]

+Anthony Nguyen Now find a **prime** number to match up to that with factorials

[@adityaphanindra]

I felt so bad that your phone was almost completely discharged.

[@Ninterd2]

It works for 1, which isn't a prime! (1-1)! + 1 = 1+1 = 2
Divisible by 1. But maybe that doesn't count.

[@kurichannn]

1 is neither prime nor composite

[@MegaScytheman]

but wait that would be 0 factorial plus 1

[@jazzabighits4473]

@@romyrconcepcion5458 Why isn't 0! = 0?

[@evetheeevee2977]

Ask the calculator

[@JohnDixon]

@@jazzabighits4473 You can think of it like this; any number n! equals (n+1)!/(n+1)
So 0! = 1!/1 = 1

[@ZyphLegend]

Let's see, what is 7! Hmm... 5040
*Zooms to calculator app*
No! Don't show them that!

[@Cloiss_]

Zyph_Legend Me: *has 7 factorial memorized*

[@katzen3314]

+EpikCloiss37 Sounds like a useful life skill. :) JK, I'm just as bad.

[@Teth47]

I love how enthusiastic Dr. Grime is, and how much his title makes him sound like a supervillain in a Mr. Clean comic. I've learned more about math through him than my entire educational career...

[@kiro9291]

"...5040."
[camera points to phone with camera app]
"don't show em that!"

[@AlRoderick]

It's been a while since we've seen Dr. Grime, welcome back, sir.

[@jaredbrooks7764]

I love how excited the people from numberphile are about math and stuff.

[@ianw8479]

Shouldn't James know 7! is 5040? It's a highly composite number, as taught by the man himself

[@Pepper-cd9yr]

Am I the only one who thinks the redheaded mathemetition (sorry, don't know his name) is absolutely adorable?

[@DanDart]

+Pepper3961 He's Dr James Grime. Now you can stalk him :3

[@bunbacheso]

I agree.

[@potatoheadpokemario1931]

+Dan Dart HAHAHA

[@XenophonSoulis]

@@DanDart aka James Prime.

[@billlson]

Hey, those are my primes

[@philipwilson46]

Mine too!

[@mithunvasudevan7796]

Lol

[@VulcanOnWheels]

2:33 Obviously not, because it's an odd number.

[@katzen3314]

+Bert Visscher I'm sure he knew that...

[@BlazeCyndaquil]

Wait a second... He divided 5041 by 8 to see if it is divisible...
Isn't it pretty obvious, seeing as 5041 is odd, and 8 is even? No need for a calculator.

[@Halosty45]

True, but since he was on camera, he likely wasn't thinking about it.

[@jonathanfowler2932]

Absolutely great. Glad to see DR Grime back for more prime stuff. Love it.

[@RobFlaxMusic]

I was today years old when I learned the iPhone calculator had a factorial button (and lots more operators). Had never bothered to turn it sideways. Thanks!

[@thechickennuggetoffate9139]

Question, James: Does 1 count as a prime when using this theorem? Because (1-1)! + 1 ÷ 1 = 0! + 1 ÷ 1 = 2 ÷ 1 = 2, which is an integer and would pass the test.

[@The123Christian]

Are there primes where you can do this three times?

[@Kibadda123]

Wanna find out?

[@chmis3]

Well, you can easily check that neither of known Wilson primes do that so we have to wait for somebody to discover a new one and check it. Still, because there are probably infinitely many Wilson primes, there should be infinitely many that can do that n times.

[@k-town5535]

13 can.

[@k-town5535]

whoops. I read it as two times....

[@sSunbeamM]

Yes. It's Grahams Number + 1

[@yanava]

James is my favourite numberphiler. He presents the content with such joy and enthusiasm. It inspires me to know more about math. Great to see him back!

[@KunamaElgar]

I love how excited he is about proving this kind of thing. Wonderful to see generally unsung professionals getting an audience on this channel.

[@HowardHughes33]

I know the answer! The number 5 is the number 5 and the number 5 is the first number in 563. The last number in 13 is the number 3 and the last number in 563 is also 3. The first number in 13 is 1 and the middle number in 563 is 6. Obviously, the number 1 is the drunk or cursive version of the number 6. Problem solved!

[@jacobwaddell7455]

Lance Watson 5+1==6

[@HowardHughes33]

Yes! 5+1=6!

[@zeser5230]

illuminati confirmed

[@zeser5230]

illuminati confirmed

[@VechtMalthos]

Ack. That low battery!

[@TrevorNestorsLab]

I really appreciate the way that math is presented in an exciting and interesting way that everybody can understand on this channel. I am a UC Berkeley alumni and think that we need more professors that make subject matter interesting like you (or you guys)

[@FeetLikeFrodo]

Thanks for explaning even the easy things, I learn so much from these videos!

[@scottgauer7299]

Did a PhD mathematician just use a calculator to add one?

[@squeakybunny2776]

He also used a calculator to divide 721 by 7 i mean is it gonna get any easier

[@Eggemeyers]

Yep, 3 key strokes instead of 10

[@user-vo8ss2bm3p]

...and to check if 5041 is diviible by 8.)

[@Alfetto8]

Mathematics is not about counting, that's accounting.

[@drmontorsi7498]

Alfetto8
As a person that is currently undergoing maths exams in his college career, I second that.
As a person that has a diploma in accounting in high school, I feel offended.

[@martijnkemperman7689]

Dr James Grime, more like Dr. James Prime

[@PinkChucky15]

Awesome video! So glad to see Dr. Grime back :-)

[@rubiskelter]

I really like this guy. Hope to see him in all the future numberphiles

[@ThaNinjazTube]

Am I the only one that subbed to this channel for the mindfucks?

[@hakoeski]

The last Grahams number video blewmy mind!

[@bartholomeusbelisari1865]

Somehow I doubt that.
I know I did.
And, I also know that I am not the only one that clicked this video link for the seductive image they used for the thumbnail.

[@wassimwazzi539]

(2-1)! +1 = 2. 2 is divisible by 2

[@zakaryahgerman9485]

wassimo wazzio 2 is prime

[@yashchauhan8044]

Yes 1.1

[@deld9968]

NICE TO SEE YOU BACK MAN!

[@doltifantara]

If I remember correctly John Wilson (1741 - 1793) was a contemporary with Gauss.
He was a student of Edward Waring associated with Waring's problem.
I think Wilson's theorem is amazing I sort of wish there was another way to understand why, if people want to know more about those numbers, the UTM prime pages would have more information.

[@JLDoctorWho]

"All primes and only primes pass this test."
Counterexample: 1.
(1-1)!+1 = 2
2 is divisible by 1.
1 is not prime. =>

[@gamerdio2503]

1 is also not composite (lenny)

[@Forssa1]

4:05 Oh look, an iphone with low battery, how surprising.

[@renatoherren4217]

This fellow reminds me of my favorite maths teacher. He looks like he did back then and he also shows the passion for maths my teacher had. 😎😎😎😎

[@xanokothe]

Has beeing a while James, nice to see you again!

[@dogquick6535]

What about 1, it passes the test for a prime number, and since it passes the test it must be a prime number, and it then passes the test for a Wilson prime, wouldn't 1 be a Wilson prime?

[@dansattary4005]

1 isn't prime

[@MorRobots]

Factorial must seriously limit our ability to bruit force this test. Question is, what about one that divideds 3 times or is their a fundamental element to division of numbers that prevents this?

[@marttiranta469]

NEW VIDEO NEW VIDEO OMG! I'VE BEEN WAITING FOR SO LONG!!! And with Dr Grime as well!

[@webmediafactors4]

im going to try and find a way to use this in a program. it would be cool geekiness to have some kind of conditional system revolving around testing between primes, composites, and wilson primes as the 3 object types

[@kamshik]

That guy could have at least chosen a number that's not even, for this thing always gives odd results ..... (except for 1 and 0 I suppose. Also 1 is not prime but this thing makes it out to be)

[@BrittBerg]

Wait....
(P-1)! + 1
If you fill in 1 for P you get:
(1-1)! +1 = 2
2 is divisible by 1, so 1 must be prime right? ;)
ps. I know that 1 is actually not prime :)

[@arnavnarula1534]

No. What we are saying is if the number is prime, it will follow this argument (in the video). We are not saying that if the number follows this argument, then it is prime. This is similar to saying all squares are rectangles, but we can't say that all rectangles are squares.

[@nekoblitz]

Arnav Narula You copy-pasted that. Wow. But he clearly states that ONLY prime numbers pass it, and that it is a 100% test.

[@want-diversecontent3887]

Flash Even though he did, look through the channel and he says 1 is not prime.

[@19Jackattack95]

So glad to see James back

[@onealrocky70]

I really enjoy this guy, expresses a true passion for math.

[@goldenera7090]

why didn't you say - (P-1)! + 1 is divisible by P-square??
divisible by P twice means the same thing - in it??

[@kxmode]

Because 1 always divides to be 1 would this value be considered a Wilson prime? I realize people don't consider 1 to be a prime number, but it doesn't mean that 1 cannot be a Wilson Prime. It passes all the tests. :)
Yes I know 1 doesn't really go anywhere, but it is still a value. A value of won! :D

[@MartKencuda]

You answered your own question. 1 cannot be a Wilson Prime because 1 isn't prime in the first place.

[@SabertoothSeal]

Well, let's see.
(1-1)!+1
=0!+1
=1+1
=2
Two is divisible by one! Therefore, one is an "infinite" Wilson prime. Right?
Actually, no. Despite Wilson's Theorem, one is not a prime. One is the positive real unit -- and units, by definition, cannot be primes as all primes are greater than their corresponding unit.

[@Halosty45]

The actual theorem does give an exception for +-1 in the claims to being prime numbers. However, that's a really good thought.

[@kxmode]

Fredrick Everson You hear that science?! Primes are greater than their corresponding unit!

[@kimf.wendel9113]

And that answered something completely different for me, called Optimus Prime..! Thx!

[@cellogirl0096]

Yay, welcome back, Dr. Grime!

[@Bombshocked]

Dr James Prime.

[@brandonwalsh7681]

then technically 1 is a prime and a Wilson prime as (1-1)!+1=0!+1=2 and 2 is divisible by 1 and infinite number of times. so correct me if i am wrong then is this test not the most perfect because as you said in another video 1 is not a prime.

[@iAkrobat_]

if only prime numbers work with this AND 1 is not a prime, why is
(1-1)! + 1
0! + 1
1+1
2
divisible by 1?
MWAHAHA :D

[@epiSkoglund]

+Jeens Ko, 1 is not a prime number by definition even though it has the properties for it. Any integer should be able to divide into an unique prime factorization. If 1 was a prime number "21" could be 7*3 OR 7*3*1*1*1*1... eg. not unique. That´s why. They have a video about it.

[@MMrandomdude12]

+Jeens Ko Damn, I thought someone else would have already noticed this.

[@chaimlukasmaier335]

+Wolfgang Ambrus i just watched the video and noticed this :)

[@katzen3314]

0! isn't 1 is it??? It still works either way.

[@elmiraguth]

+Katzen4u It is. Although the ordinary definition fails for zero, the common consensus is that 0! is counted as 1

[@xct321]

I love this guy! Dr Grime is the man!

[@Manakaiser]

amazing as all vids you upload, keep it up

[@randomasdf97]

IMHO the numberphile crew were foolish to come up with such a title.
"What do 5, 13 and 563 have in common?" doesn't fit, why not something like e.g. "5,13, 563 and Wilson Primes". If a person wants to find out something about the Wilson primes on youtube, how's he gonna find this video huh?

[@numberphile]

randomasdf97 might change the title later when the video moves from "new, fun and curious" to "old archive resource"... Wilson Primes are in the description and meta data though!
Yours in Foolishness
Numberphile Crew

[@6446henry]

Umm it actually can't be called 5, 13, 563 and Wilson Primes. Because those are the only ones found.

[@MordecaiV]

Numberphile I don't see wilson primes in the description?

[@randomasdf97]

***** me neither.. and I also typed in the search 'wilson primes numberphile' & this video appeared on the 3rd page only :/

[@jacksainthill8974]

Not only that, the question as it was put is banal - for example, the three numbers have an infinite list of trivial commonalities such as 'none is equal to 78' and so on.

[@mahmoudelsharawy5405]

Butm if you use Wilson's Theorem, can I prove that 1 is prime?

[@rahulbansode1537]

Mahmoud Elsharawy u can divide anything by 1

[@mahmoudelsharawy5405]

Ya, that is my point.

[@arnavnarula1534]

No. What we are saying is if the number is prime, it will follow this argument (in the video). We are not saying that if the number follows this argument, then it is prime. This is similar to saying all squares are rectangles, but we can't say that all rectangles are squares.

[@mahmoudelsharawy5405]

But at 0:36 he says, "And it ONLY works for Primes"

[@ailderwitha5591]

1 = (1-1) = 0! = 1 + 1 = 2/1 = 2/1 = 2/1 = 2/1 = continuous.

[@DanTheMan5420]

Neat video! I'm now inspired to find a new Wilson Prime!

[@ramiel555]

I was going to ask about numbers that can do it 3 times in a row, but then I remembered that there were only the 3 Wilson primes discovered, and I imagine that, if any of them could, it would have been mentioned (or, rather, if 563 could, since we saw the other 2 in real time)

[@MozartJunior22]

We have a foolproof test for primes? Why are we not funding this?

[@aliciabutteriss6274]

The Wilson Theorem? My guess is because factorials get *really* unwieldy as n grows larger (like, ridiculously so). For the massive primes that we're looking for now (millions of digits long - the current largest prime has over 17 million digits), it's functionally impossible to run the test. At any rate, there are other tests, and they're considerably quicker to run (and 'easier' computationally) - Wikipedia has more information on this topic: en.wikipedia.org/wiki/Primality_test

[@MozartJunior22]

Is this like Mill's Constant?

[@aliciabutteriss6274]

I honestly don't know. Edit: Just watched the additional video, I don't even know if my original comment is remotely accurate (well, the first part at least).Double edit: Actually, I *think* I'm about right on the issue with using Wilson's, but I'm not sure.

[@MozartJunior22]

Alicia Butteriss Look up the Numberphile video about Mill's constant

[@goatlink]

he said it in the video, its because using the test on large primes includes getting the factorial of p-1 which would be so stupidly big that it couldn't be done with modern computers.

[@bengtbengt3850]

There is actually a number that is not Prime that works on this test. Its 1.

[@CDLatin]

1 never counts for these things haha

[@katzen3314]

And you have to do 0! which apparently = 1 but it doesn't sound right to me.

[@bengtbengt3850]

+Katzen4u meh anything to the power of 0 is also one. Does that sound right? Of course it does, Because its an empty product which is equal to one.
0! Is kind of an empty product too Because you dont really have any factors there either do you?

[@katzen3314]

Jeasker S I see. There seem to be quite a few patterns like this that suggest that 0! is equal to 1.

[@maxenis1577]

Exactly. It's similar to x^0 equals one: unintuitive but mathematically solid.

[@krappa]

3 AM
Scrolls through youtube feed one last time before going to bed
Sees James Grine's face on a video.
My sleep can wait 6 minutes

[@MrLmmckenzie]

Finally, Dr. Grime is back!

[@6446henry]

1 passes the test. The only non prime that passes the test..
(1-1)! =0+1 = 1... Well 1 isn't Composite.. Wait. 1 passes infinite times!!

[@esuelle]

0! = 1 actually, but it would still be 2/1 which would pass infinitely aswell. I guess it's because 1 is special?

[@6446henry]

Esuerre oops I actually did the math wrong by accident.
(1-1)! = 1 + 1 = 2

[@yousorooo]

1 is not a prime though

[@6446henry]

Derek Leung I said that..

[@Halosty45]

If you look up the actual theorem, there's an exception for +-1 written in.

[@thetruth2055]

He spits at 0:50.. lol

[@reverberation_9]

Can you make a video on how the quadratic equation was made? I would love to see it.
Keep up with this excellent work.

[@GirGir183]

0:18 I thought you were writing them on someone's bare back for a second.

[@matsv201]

Well, one then?
(1-1)!+1=1
1/1=1.... 1/1=1... and so on...
But one is no prime, or is it?

[@PassingTimeAlong]

One is not a prime number.

[@MrTridac]

(1-1)!+1 / 1 = 2
But it would still "pass" the test.

[@Dsiefus]

In fact 0! = 1, so 0! + 1 = 2

[@matsv201]

Well, the problem with one is that tho there is some prime test it dont pases, it pases most, almost all... i would say that is almost a matter of opinion. I heard math professors stat both statment...
"because it behaves differently from all the other primes. "
Froudian slipp there my friend ;)

[@ScilexGuitar]

dsiefus How do you get 0!=1? 0x0=0

[@MicahGreaney]

Every time I see Dr. Grime, I watch the video. I watch most of the others as well, but Dr. Grime guarantees I'll watch it.

[@SaidarSaraaah]

Fell asleep and woke up to what I thought was you drawing on my tummy when i saw the beige paper!

[@Generalfeldm4rschall]

Mr. Grime is just an wonderful person

[@Iamstupid51]

James Grime is back! Yay!

[@trustnoone81]

Aw yey!! Welcome back Dr Grime ^.^

[@scratchcriminal]

I love showing off these Formulas and amazing things about maths to my maths teachers!!!!

[@skoockum]

Nice interlude music. Very refreshing.

[@pianomanCP]

Good to see Dr Grime again

[@willk7184]

Nice, I memorized 562! awhile back, and now I finally have a use for it.

[@00Skyfox]

Good to see you on here again, James! Where ya' been?

[@luckylarrylive427]

Hey Brady, I've noticed that we see James Grime less and less on this channel. You've done the Questionairre with him about his life, loves, and laughs and it really is interesting to get to know you guys in a way that only UA-cam can express. I'm currently going for my Bachelor's in 'maths' and was wondering if you could do a piece on some of your guests' paths to how they got to where they are, and what it takes to be a great mathematician.

[@juddyyoutube]

I love this guy so much

[@Jamie-st6of]

I should be doing my algebra homework right now. But this is so much more useful.

[@chhayapatel4098]

Very nice...... excellent ... Thank you .
CONGRATULATIONS

[@kevinj4204]

4:44... I love the English and the grammar they use.

[@whochew5573]

idk why i just like james the best for these videos

[@BernardCastle]

"'There's no great use for it, but why do we have to do everything for application?"
-Dr James Grime, 2014

[@zelda12346]

Proof that it doesn't work for any composite numbers has to do with the statement that if you multiply all the number in a set together and then add one, the result is not divisible by any of the factors. If composite number C is factorized into A*B and D is a multiple of A and B, then D+1 is not divisible by either A or B and thus not divisible by C.
As for why it works for all prime numbers, I have no idea.

[@malik_alharb]

I love Dr. G and his energy